{
    "url": "http://arxiv.org/abs/2404.16461v2",
    "title": "Large Language Models Perform on Par with Experts Identifying Mental Health Factors in Adolescent Online Forums",
    "abstract": "Mental health in children and adolescents has been steadily deteriorating\nover the past few years. The recent advent of Large Language Models (LLMs)\noffers much hope for cost and time efficient scaling of monitoring and\nintervention, yet despite specifically prevalent issues such as school bullying\nand eating disorders, previous studies on have not investigated performance in\nthis domain or for open information extraction where the set of answers is not\npredetermined. We create a new dataset of Reddit posts from adolescents aged\n12-19 annotated by expert psychiatrists for the following categories: TRAUMA,\nPRECARITY, CONDITION, SYMPTOMS, SUICIDALITY and TREATMENT and compare expert\nlabels to annotations from two top performing LLMs (GPT3.5 and GPT4). In\naddition, we create two synthetic datasets to assess whether LLMs perform\nbetter when annotating data as they generate it. We find GPT4 to be on par with\nhuman inter-annotator agreement and performance on synthetic data to be\nsubstantially higher, however we find the model still occasionally errs on\nissues of negation and factuality and higher performance on synthetic data is\ndriven by greater complexity of real data rather than inherent advantage.",
    "authors": "Isabelle Lorge, Dan W. Joyce, Andrey Kormilitzin",
    "published": "2024-04-25",
    "updated": "2024-04-26",
    "primary_cat": "cs.CL",
    "cats": [
        "cs.CL"
    ],
    "label": "Original Paper",
    "paper_cat": "LLM Fairness",
    "gt": "The recent development of powerful Large Language Models such as GPT3.5 [2] and GPT4 [3] able to perform tasks in a zero-shot manner (i.e., without having been specifically trained or fine- tuned to do so) by being simply prompted with natural language instructions shows much promise for healthcare applications and the domain of mental health. Indeed, these models display more impressive general natural language processing abilities than their predecessors and excel at tasks such as Question Answering and Named Entity Recognition [4, 5, 6, 7]. Models with the ability to process social media content for indicators of mental health issues have the potential to become invaluable cost-effective tools for applications such as public health monitoring [8] and online moderation or intervention systems [9]. In addition, synthetic data produced by LLMs can be a cost effective and privacy-preserving tool for training task specific models [10]. There have been several studies aimed at assessing the abilities of LLMs to perform a range of tasks related to mental health on datasets derived from social media. Yang et al. [11] conducted a comprehensive assessment of ChatGPT (gpt-3.5-turbo), InstructGPT3 and LlaMA7B and 13B [12] arXiv:2404.16461v2  [cs.CL]  26 Apr 2024 on 11 different datasets and 5 tasks (mental health condition binary/multiclass detection, cause/factor detection, emotion detection and causal emotion entailment, i.e. determining the cause of a described emotion). They find that while the LLMs perform well (0.46-0.86 F1 depending on task), with ChatGPT substantially outperforming both LLaMA 7B and 13B, they still underperform smaller models specifically fine-tuned for each task (e.g., RoBERTa). Xu et al. [13] find similar results for Alpaca [14], FLAN-T5 [15] and LLaMA2 [16], with only fine-tuned LLMs able to perform on par with smaller, task-specific models such as RoBERTa [17, 18]. However, we find that previous studies suffer from the following shortcomings: 1. They focus on adult mental health 2. They focus on tasks with a closed (or finite) set of answers, where the model is asked to perform each task in turn 3. They do not investigate how LLMs perform on synthetic data, i.e., text they are asked to simultaneously generate and label There is growing consensus that we are facing a child mental health crisis [1]. Before the COVID-19 pandemic there was already increasing incidence of mental health conditions in children and young people (CYP), such as depression, anxiety and eating disorders [19] as well as rising rates of self-harm and suicidal ideation [20] and cyberbullying strongly linked to adverse mental health outcomes [21]. The advent of the pandemic accelerated this already precarious situation and created additional challenges [22, 23] such as discontinuity of healthcare service provision in addition to interruption to young people\u2019s usual engagement in education and their social lives. This age range is particularly vulnerable to onset of mental health issues, with half of conditions appearing by early adolescence and 10-20% of children and young people experiencing at least one mental health condition [24]. Females, those with low socioeconomic backgrounds, trauma, abuse or having witnessed violence [25] are at heightened risk. On the other hand, social media now forms an important part of children and adolescents\u2019 daily lives, whose impact on mental health is debated, with potential benefits (stress reduction and support networks [26]) as well as potential risks (sleep disturbance, self esteem issues and cyberbullying [27]). Regardless of their detrimental or protective impact, social media may contribute valuable insights into CYP\u2019s mental health, with opportunities for monitoring and intervention, for example identifying those at risk of depression and mood disorders [28]. Given the mental health of CYP is a particularly pressing public health concern, we wished to investigate how LLMs perform on extracting mental health factors when faced with social media content generated by young people aged 12-19. Indeed, several issues related to mental health either exclusively apply to children and adolescents (such as school bullying and ongoing family abuse) or are particularly prevalent in this age range (such as eating disorders [29] and self-harm [30]), making both content type and factors of interest distinct from those found in adult social media posts. In addition, previous studies focused on tasks which had either a binary or closed sets of answers (e.g., choosing between several given conditions or between several given causal factors). In contrast, we wish to examine how LLMs perform on a task of open information extraction, where they are given categories of information and asked to extract any which are found in the text (e.g., asked to detect whether there is any mental health condition indicated in the text). Furthermore, in previous studies the models were tested with each task in turn (e.g., asked to detect depression in one dataset, then detect suicidality in another dataset), whereas we gather and annotate our own dataset in order to be able to ask the LLMs to extract all categories simultaneously (e.g, extract all conditions and symptoms in a given sentence). Finally, to our knowledge there has been no investigation on how LLM performance compares when asked to annotate text as they generate it, i.e., how their performance on synthetic data compares with their performance on real data. There is growing interest in synthetic data for healthcare [31]. Given the potential for training models and running simulations and digital twin experiments with the benefit of reduced issues of data scarcity and privacy, we believe that our work will contribute to better understanding of limitations and benefits of using synthetic data for real-world tasks. 2",
    "main_content": "In summary, we aim to: 1. Generate and annotate with high-quality expert annotations a novel dataset of social media posts which allows extraction of a wide range of mental health factors simultaneously. 2. Investigate performance of two top-performing LLMs (GPT3.5 and GPT4) on extracting mental health factors in adolescent social media posts to verify whether they can be on par with expert annotators. 3. Investigate how these LLMs perform on synthetic data, i.e., when asked to annotate text as they generate it, with the aim of assessing utility of these data in training task specific models 3 Method 3.1 Reddit dataset We use Python\u2019s PRAW library to collect post from the Reddit website (www.reddit.com) over the last year, including posts from specific forum subthemes (\u2018subreddits\u2019) dedicated to mental health topics: r/anxiety, r/depression, r/mentalhealth, r/bipolarreddit, r/bipolar, r/BPD, r/schizophrenia, r/PTSD, r/autism, r/trau-matoolbox, r/socialanxiety, r/dbtselfhelp, r/offmychest and r/mmfb. The distribution of subreddits in the dataset can be found in Figure 1. As in previous works [32], we use heuristics to obtain posts from our target age range (e.g, posts containing expression such as I am 16/just turned 16/etc.) We gather 1000 posts written by 950 unique users. To optimise the annotation process, we select the most relevant sentences to be annotated by embedding a set of mental health keywords with Python\u2019s sentence-transformers library [33] calculating the cosine similarity with post sentences, choosing a threshold of 0.2 cosine similarity after trial and error. We keep the post index for each sentence to provide context. The resulting dataset contains 6500 sentences. 3.2 Ethical considerations In conducting this research, we recognised the importance of respecting the autonomy and privacy of the Reddit users whose posts were included in our dataset. While Reddit data is publicly available and was obtained from open online forums, we acknowledge that users may not have anticipated their contributions being used for research purposes and will therefore make the data available only on demand. The verbatim example sentences given in later sections have been modified to prevent full-text searching strategies to infer the post author\u2019s immediate identity on reddit. To protect the confidentiality of participants, we did not provide usernames or other identifying information to our annotators. Annotators were psychiatrists who were warned that the content of the posts was highly sensitive with potentially triggering topics such as self-harm and child abuse. Reddit\u2019s data sharing and research policy allows academic researchers to access certain Reddit data for the purposes of research, subject to the platform\u2019s terms and conditions. They require researchers to obtain approval through their data access request process before using the API. The policy outlines requirements around protecting user privacy, obtaining consent, and properly attributing the data source in any published work. They reserve the right to deny data access requests or revoke access if the research is deemed to violate Reddit\u2019s policies. Researchers must also agree to Reddit\u2019s standard data use agreement when accessing the data. Our research aims to contribute to the understanding of mental health discourse from adolescents on social media platforms. We believe the potential benefits of this work, in terms of insights that could improve mental health support and resources, outweigh the minimal risks to participants. However, we remain aware of the ethical complexities involved in using public social media data, and encourage further discussion and guidance in this emerging area of study. 3 3.3 Synthetic dataset In addition to the real dataset, we generate two synthetic datasets of 500 sentences each by prompting GPT3.5 (gpt-3.5-turbo-0125) and GPT4 (gpt-4-0125-preview) to create and label Reddit-like posts of 5 sentences (temperature 0, all other parameters set to default). The instructions given were made as similar as possible to those given to annotators, and the model was expliclity told to only label factors which applied to the author of the post (e.g., not to label My friend has depression with CONDITION). The prompt used can be found in Appendix A. Figure 1: Distribution of subreddits 3.4 Annotation schema Given our goal is to obtain a wide range of relevant annotations for each sentence in order to test the LLMs\u2019 ability to generalise and perform open information extraction, and the previously mentioned important factors related to trauma [34] and precarity [35], we create the following six categories in consultation with a clinical psychiatrist: \u2022 TRAUMA (sexual abuse, physical abuse, emotional abuse, school bullying, death, accident, etc.) \u2022 PRECARITY (socioeconomic, parental conflict, parental illness, etc.) \u2022 SYMPTOM (self-harm, low self-esteem, anhedonia, panic attack, flashback, psychosis, insomnia, etc.) 4 \u2022 CONDITION (eating disorder, depression, bipolar, bpd, anxiety, ptsd, adhd, substance abuse/addiction, etc.) \u2022 SUICIDALITY (no subcategories) \u2022 TREATMENT (no subcategories) Nineteen expert annotators were contacted and asked to annotate 500 sentences each for a fixed compensation of \u00a3120 (\u2248\u00a360/hour). These were UK-trained psychiatrists, all of whom had obtained Membership of the Royal College of Psychiatrists by post-graduate experience and formal examinations. Thirteen annotators annotated the Reddit dataset, two annotators annotated the synthetic datasets and four annotators re-annotated samples from the Reddit and synthetic datasets for inter-annotator agreement computation (100 sentences from each dataset, 1500 sentences in total). Annotators were given the above subcategory examples but allowed to use new subcategories when appropriate (no closed set of answers). They were given the post indices to provide context (i.e., so as to be aware which sentences belonged to the same post). They were asked to annotate only school bullying as bullying, and other instances (e.g., sibling harassment) as emotional abuse. Anxiety was to be annotated as a symptom rather than condition unless specifically described as a disorder. Experts performed the annotation by filling in the relevant columns in an Excel sheet with each sentence as a row. Importantly, given the known limitations of language models with negation [36], we wished to annotate both POSITIVE and NEGATIVE evidence in order to test LLMs\u2019 ability to handle both polarities (e.g., I am not feeling suicidal as negative suicidality or We don\u2019t have any money issues as negative socioeconomic precarity). For this purpose, annotators were asked to use the prefixes P and N (e.g., P(adhd) in the CONDITION column or N(socioeconomic) in the PRECARITY column). 3.5 Data processing and dataset statistics In order to compare expert annotations with LLM annotations despite the wide variety of subcategories and terms used by annotators we create dictionaries mapping each term found in the dataset to a standard equivalent (e.g., p(emotional) to p(emotional abuse), p(physical violence) to p(physical abuse), p(gun violence) and p(school shooting) to p(violence), p(rape) to p(sexual abuse), p(financial burden) and p(poor) to p(socioeconomic precarity), p(divorce) to p(family conflict), p(self hatred) to p(low self esteem), etc.). Parental substance abuse is considered family illness and any underspecified subcategories are marked as \u2018unspecified\u2019 (e.g., p(trauma unspecified)). The distribution of subcategories for each category can be found in figures 2, 3, 4 and 5 in Appendix B. The most frequent subcategory in TRAUMA is emotional abuse, which occurs twice as often as physical abuse and death in the dataset. The most frequent form of PRECARITY is family conflict, then family illness (including parental substance abuse) and socioeconomic precarity. The most frequent CONDITIONS are depressive disorders, followed by substance abuse/addiction and ADHD. The most frequent SYMPTOMS are anxiety, low self-esteem, self-harm and low mood. Interestingly, the distribution of subcategories differs quite substantially in the synthetic datasets (distributions for the GPT3.5 and GPT4 generated datasets can be found in Appendix B). Overall, the number of subcategories is reduced, indicating less diversity (however, these are smaller datasets). The top trauma subcategories are sexual abuse for GPT3.5 and school bullying for GPT4, both of which were much less prevalent in real data. The second most prevalent condition for both GPT3.5 and GPT4 is eating disorders, whereas these ranked in 8th place in real data. Finally, unlike in real data, flashbacks and panic attacks are the 3d and 4th most frequent symptoms for both GPT3.5 and GPT4-generated data, whereas self-harm ranks much lower than in real data. Given many of these subcategories were given as examples in the annotator guidelines and LLM prompt, it is likely that the LLMs used them in a more homogenous manner for generation than the distribution which would be found in real data. However, the distribution is not entirely homogenous, which suggests the LLMs did leverage some of the biases learned from their training data. 4 Results Once both human and LLM annotations are standardised, we conduct analyses to assess performance. We provide precision, recall and F1 at the category level and accuracy at the subcategory level 5 collapsed across subcategories (given their high number). We compute category performance in two ways: Positive or Negative, where a point is awarded if the category contains an annotation in both human and LLM annotations, regardless of polarity (i.e., the annotator considered there was relevant information concerning the category TRAUMA) and Positive Only metrics, where negative annotations are counted as no annotations. The difference between the two metrics can be seen clearly in Table 1 (GPT3.5 results), where precision increases but recall diminishes for Positive Only. The increase in precision is due to the fact that GPT3.5 outputs a substantial number of negative annotations in cases where human annotators did not consider it relevant to mention the category. The reduction in recall, on the other hand, results from the fact that LLMs often confuse positive and negative annotations and will occasionally output a negative annotation for a positive one. For real data (Tables 1 and 2), GPT3.5\u2019s performance at the category level is average, with better performance in the Positive Only metrics (0.57). GPT4 performs better, especially in Positive Only metrics (0.63) and subcategory accuracy (0.48 vs. 0.39). In general, recall is higher than precision, indicating LLMs may be overpredicting labels. The performance for synthetic data (Tables 3 and 4) is substantially better, with no gap between the Positive or Negative and Positive Only metrics, suggesting less irrelevant negative annotations. Here again, GPT4 outperforms GPT3.5, both at the category level (0.75 vs 0.70 and 0.73 vs 0.68) and more particularly at the subcategory level, where GPT4 reaches an impressive accuracy of 0.72 (vs 0.42). The gap between recall and precision is reduced for GPT4, whereas GPT3.5 displays higher precision than recall here. In order to assess the upper bound of human performance, we calculate inter-annotator agreement for both real and synthetic datasets using Cohen\u2019s Kappa. Values can be found in Table 5. Interestingly, while performance at the category level in real data is lower (GPT3.5) or similar (GPT4) compared to humans, GPT4 displays a substantially higher accuracy at the subcategory level (0.47 vs 0.35). For synthetic data, GPT3.5 still underperforms human agreement on all three metrics, while GPT4 is on par with humans for the Positive Only and subcategory metrics and only underperforms in the Positive and Negative metric. Category Positive or Negative Positive Only Subcategory Precision Recall F1-Score Precision Recall F1-Score Accuracy TRAUMA 0.38 0.78 0.51 0.56 0.65 0.60 0.39 PRECARITY 0.26 0.43 0.33 0.45 0.31 0.37 0.22 CONDITION 0.33 0.85 0.48 0.54 0.72 0.62 0.55 SYMPTOMS 0.39 0.62 0.48 0.46 0.58 0.52 0.31 SUICIDALITY 0.44 0.79 0.56 0.80 0.68 0.73 / TREATMENT 0.48 0.72 0.58 0.72 0.58 0.64 / ALL 0.37 0.70 0.49 0.55 0.60 0.57 0.39 Table 1: GPT3.5 (real data). Positive or Negative: counting annotation in category regardless of polarity (category level); Positive Only: counting negative annotations as NaN (category level); Subcategory: accuracy at the subcategory level 5 Error analysis We examine some of the sentences annotated by the LLMs in order to perform error analysis and extract the following findings (as mentioned previously some words have been paraphrased to preclude full-text search allowing user identification): \u2022 Both GPT3.5 and GPT4 produce infelicitous negations, i.e., negative annotations which would seem irrelevant to humans, e.g., (I have amazing people around me =>negative parental death or The internet is my one only coping mechanism =>trauma unspecified) \u2022 Despite being specifically prompted to only annotate factors related to the writer/speaker, LLMs (including GPT4) do not always comply, e.g., She comes from what is, honestly, a horrific family situation =>emotional abuse) 6 Category Positive or Negative Positive Only Subcategory Precision Recall F1-Score Precision Recall F1-Score Accuracy TRAUMA 0.44 0.89 0.59 0.57 0.84 0.68 0.57 PRECARITY 0.31 0.52 0.39 0.50 0.46 0.48 0.36 CONDITION 0.46 0.81 0.59 0.61 0.77 0.68 0.57 SYMPTOMS 0.35 0.78 0.49 0.45 0.73 0.56 0.41 SUICIDALITY 0.36 0.93 0.51 0.70 0.87 0.77 / TREATMENT 0.39 0.87 0.54 0.64 0.81 0.71 / ALL 0.39 0.80 0.52 0.55 0.75 0.63 0.48 Table 2: GPT4 (real data). Positive or Negative: counting annotation in category regardless of polarity (category level); Positive Only: counting negative annotations as NaN (category level); Subcategory: accuracy at the subcategory level Category Positive or Negative Positive Only Subcategory Precision Recall F1-Score Precision Recall F1-Score Accuracy TRAUMA 0.90 0.49 0.64 0.90 0.49 0.64 0.38 PRECARITY 0.84 0.69 0.76 0.86 0.69 0.76 0.54 CONDITION 0.44 0.67 0.53 0.47 0.67 0.55 0.59 SYMPTOMS 0.85 0.59 0.70 0.84 0.59 0.69 0.36 SUICIDALITY 0.75 1.00 0.85 0.77 0.90 0.83 / TREATMENT 0.68 0.84 0.75 0.76 0.57 0.65 / ALL 0.74 0.65 0.70 0.77 0.61 0.68 0.42 Table 3: GPT3.5 (synthetic data). Positive or Negative: counting annotation in category regardless of polarity (category level); Positive Only: counting negative annotations as NaN (category level); Subcategory: accuracy at the subcategory level Category Positive or Negative Positive Only Subcategory Precision Recall F1-Score Precision Recall F1-Score Accuracy TRAUMA 0.84 0.95 0.89 0.86 0.92 0.89 0.82 PRECARITY 0.85 0.84 0.85 0.91 0.82 0.86 0.80 CONDITION 0.61 0.67 0.64 0.60 0.67 0.63 0.67 SYMPTOMS 0.49 0.78 0.60 0.53 0.80 0.64 0.69 SUICIDALITY 0.81 0.94 0.87 0.78 0.82 0.80 / TREATMENT 0.85 0.89 0.87 0.87 0.78 0.82 / ALL 0.69 0.83 0.75 0.69 0.79 0.73 0.72 Table 4: GPT4 (synthetic data). Positive or Negative: counting annotation in category regardless of polarity (category level); Positive Only: counting negative annotations as NaN (category level); Subcategory: accuracy at the subcategory level \u2022 Even GPT4 makes errors regarding negation (e.g., I\u2019ve read about people with autism getting temper tantrums/meltdowns, however, that has never really been a problem for me=>negative autism or i had in my head that something inside was very wrong, but i never felt completely depressed all the time so i never took bipolar seriously =>negative bipolar disorder) \u2022 Despite being prompted to annotate suicidality in a separate category, LLMs often annotate it in the SYMPTOM rather than SUICIDALITY category \u2022 GPT3.5 especially often outputs irrelevant/spurious/incorrect labels (e.g., \u2018unemployed\u2019 as condition, \u2018ambition\u2019 as symptom, labelling physical conditions instead of mental conditions only, etc.) 7 Positive and Negative Positive Only Subcategory Annotator vs. Annotator (real data) 0.60 0.59 0.35 GPT3 vs. Annotator (real data) 0.39 0.52 0.37 GPT4 vs. Annotator (real data) 0.43 0.58 0.47 Annotator vs. Annotator (synthetic data) 0.77 0.71 0.68 GPT3 vs. Annotator (synthetic data) 0.64 0.63 0.40 GPT4 vs. Annotator (synthetic data) 0.70 0.69 0.71 Table 5: Inter-annotator agreement (Cohen\u2019s Kappa) \u2022 Even GPT4 makes errors regarding factuality (e.g., It was around my second year in junior high school when my father tried to take his life =>positive death) However, in many cases the assessment is not entirely fair, as the LLMs (particularly GPT4) often catch annotations which human annotators missed, or the difference in subcategories is subjective and open to debate (e.g., school bullying vs emotional abuse, emotional abuse vs abuse unspecified, etc.). Thus it is possible that LLMs, or most likely GPT4, in fact outperformed experts on this task. 6 Discussion The results obtained from our comparison of LLM annotations with human annotations on both real and synthetic data allow us to make a few conclusions and recommendations. Overall, both LLMs perform well. Inter-annotator agreement and performance indicate that GPT4 performs on par with human annotators. In fact, error analysis and manual examination of annotations suggest the LLMs potentially outperform human annotators in terms of recall (sensitivity), catching annotations which have been missed. However, while recall might be improved in LLMs versus human annotators, precision may suffer in unexpected ways, for example through errors in the use of negation and factuality, even in the case of GPT4. LLMs display a particular tendency to overpredict labels and produce negative annotations in infelicitous contexts, i.e., when humans would deem them irrelevant, creating an amount of noise. However, these negative annotations are not technically incorrect. While accuracy errors could be found in the LLM output, the experts\u2019 outputs were not entirely free of them, and previous work by [37] suggests LLMs may both be more complete AND more accurate than medical experts. There may still be a difference in the type of accuracy errors produced by LLMs, which will have to be investigated in future research. In terms of accuracy at the subcategory level, we were surprised to find GPT4 outperformed human agreement by a large margin in real data (0.47 vs 0.35). We hypothesise this is due to the fact that human annotators display higher subjectivity in their style of annotation at the subcategory level (given the lack of predetermined subcategories) and diverge more between them. LLMs are likely to be more \u2018standard\u2019 and generic and thus potentially more in agreement with any given human annotator. More specifically, LLMs tend to be consistent from one annotation to the other with higher recall whereas human annotators showed less consistency. Therefore, if a sentence mentions physical, sexual and emotional abuse, annotators might only mention two out of three but when mentioning all three an LLM is more likely to be in agreement than another annotator, i.e., the LLM will catch more of the perfectly recalled annotations than the second annotator. The better performance demonstrated on synthetic data doesn\u2019t seem due to LLMs performing better on data they are generating, but rather to the synthetic data being less complex and diverse and thus easier to annotate for both LLMs and humans, as evidenced by GPT4 reaching similar inter-annotator agreement scores to humans (with agreement both in humans and LLM/human 10% higher for synthetic data). This better performance could still warrant using synthetic data for e.g., training machine learning models (given more reliable labels) but only in cases where the potential loss in diversity is compensated by the increase in label reliability. This will likely depend on the specific application. 8 7 Conclusion We presented the results of a study examining human and Large Language Models (GPT3.5 and GPT4) performance in extracting mental health factors from adolescent social media data. We performed analyses both on real and synthetic data and found GPT4 performance to be on par with human inter-annotator agreement for both datasets, with substantially better performance on the synthetic dataset. However, we find GPT4 still performing non-human errors in negation and factuality, and synthetic data to be much less diverse and differently distributed than real data. The potential for future applications in healthcare will have to be determined by weighing these factors against the substantial reductions in time and cost achieved through the use of LLMs. Acknowledgment I.L., D.W.J., and A.K. are partially supported by the National Institute for Health and Care Research (NIHR) AI Award grant (AI_AWARD02183) which explicitly examines the use of AI technology in mental health care provision. A.K. declare a research grant from GlaxoSmithKline (unrelated to this work). This research project is supported by the NIHR Oxford Health Biomedical Research Centre (grant NIHR203316). The views expressed are those of the authors and not necessarily those of the UK National Health Service, the NIHR or the UK Department of Health and Social Care.",
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            [
                "Isabelle Lorge",
                "Andrey Kormilitzin"
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                "Isabelle Lorge",
                "Janet B. Pierrehumbert"
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            [
                "Andrey Kormilitzin",
                "Qiang Liu"
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            "Isabelle Lorge": [
                {
                    "url": "http://arxiv.org/abs/2404.16461v2",
                    "title": "Large Language Models Perform on Par with Experts Identifying Mental Health Factors in Adolescent Online Forums",
                    "abstract": "Mental health in children and adolescents has been steadily deteriorating\nover the past few years. The recent advent of Large Language Models (LLMs)\noffers much hope for cost and time efficient scaling of monitoring and\nintervention, yet despite specifically prevalent issues such as school bullying\nand eating disorders, previous studies on have not investigated performance in\nthis domain or for open information extraction where the set of answers is not\npredetermined. We create a new dataset of Reddit posts from adolescents aged\n12-19 annotated by expert psychiatrists for the following categories: TRAUMA,\nPRECARITY, CONDITION, SYMPTOMS, SUICIDALITY and TREATMENT and compare expert\nlabels to annotations from two top performing LLMs (GPT3.5 and GPT4). In\naddition, we create two synthetic datasets to assess whether LLMs perform\nbetter when annotating data as they generate it. We find GPT4 to be on par with\nhuman inter-annotator agreement and performance on synthetic data to be\nsubstantially higher, however we find the model still occasionally errs on\nissues of negation and factuality and higher performance on synthetic data is\ndriven by greater complexity of real data rather than inherent advantage.",
                    "authors": "Isabelle Lorge, Dan W. Joyce, Andrey Kormilitzin",
                    "published": "2024-04-25",
                    "updated": "2024-04-26",
                    "primary_cat": "cs.CL",
                    "cats": [
                        "cs.CL"
                    ],
                    "main_content": "In summary, we aim to: 1. Generate and annotate with high-quality expert annotations a novel dataset of social media posts which allows extraction of a wide range of mental health factors simultaneously. 2. Investigate performance of two top-performing LLMs (GPT3.5 and GPT4) on extracting mental health factors in adolescent social media posts to verify whether they can be on par with expert annotators. 3. Investigate how these LLMs perform on synthetic data, i.e., when asked to annotate text as they generate it, with the aim of assessing utility of these data in training task specific models 3 Method 3.1 Reddit dataset We use Python\u2019s PRAW library to collect post from the Reddit website (www.reddit.com) over the last year, including posts from specific forum subthemes (\u2018subreddits\u2019) dedicated to mental health topics: r/anxiety, r/depression, r/mentalhealth, r/bipolarreddit, r/bipolar, r/BPD, r/schizophrenia, r/PTSD, r/autism, r/trau-matoolbox, r/socialanxiety, r/dbtselfhelp, r/offmychest and r/mmfb. The distribution of subreddits in the dataset can be found in Figure 1. As in previous works [32], we use heuristics to obtain posts from our target age range (e.g, posts containing expression such as I am 16/just turned 16/etc.) We gather 1000 posts written by 950 unique users. To optimise the annotation process, we select the most relevant sentences to be annotated by embedding a set of mental health keywords with Python\u2019s sentence-transformers library [33] calculating the cosine similarity with post sentences, choosing a threshold of 0.2 cosine similarity after trial and error. We keep the post index for each sentence to provide context. The resulting dataset contains 6500 sentences. 3.2 Ethical considerations In conducting this research, we recognised the importance of respecting the autonomy and privacy of the Reddit users whose posts were included in our dataset. While Reddit data is publicly available and was obtained from open online forums, we acknowledge that users may not have anticipated their contributions being used for research purposes and will therefore make the data available only on demand. The verbatim example sentences given in later sections have been modified to prevent full-text searching strategies to infer the post author\u2019s immediate identity on reddit. To protect the confidentiality of participants, we did not provide usernames or other identifying information to our annotators. Annotators were psychiatrists who were warned that the content of the posts was highly sensitive with potentially triggering topics such as self-harm and child abuse. Reddit\u2019s data sharing and research policy allows academic researchers to access certain Reddit data for the purposes of research, subject to the platform\u2019s terms and conditions. They require researchers to obtain approval through their data access request process before using the API. The policy outlines requirements around protecting user privacy, obtaining consent, and properly attributing the data source in any published work. They reserve the right to deny data access requests or revoke access if the research is deemed to violate Reddit\u2019s policies. Researchers must also agree to Reddit\u2019s standard data use agreement when accessing the data. Our research aims to contribute to the understanding of mental health discourse from adolescents on social media platforms. We believe the potential benefits of this work, in terms of insights that could improve mental health support and resources, outweigh the minimal risks to participants. However, we remain aware of the ethical complexities involved in using public social media data, and encourage further discussion and guidance in this emerging area of study. 3 3.3 Synthetic dataset In addition to the real dataset, we generate two synthetic datasets of 500 sentences each by prompting GPT3.5 (gpt-3.5-turbo-0125) and GPT4 (gpt-4-0125-preview) to create and label Reddit-like posts of 5 sentences (temperature 0, all other parameters set to default). The instructions given were made as similar as possible to those given to annotators, and the model was expliclity told to only label factors which applied to the author of the post (e.g., not to label My friend has depression with CONDITION). The prompt used can be found in Appendix A. Figure 1: Distribution of subreddits 3.4 Annotation schema Given our goal is to obtain a wide range of relevant annotations for each sentence in order to test the LLMs\u2019 ability to generalise and perform open information extraction, and the previously mentioned important factors related to trauma [34] and precarity [35], we create the following six categories in consultation with a clinical psychiatrist: \u2022 TRAUMA (sexual abuse, physical abuse, emotional abuse, school bullying, death, accident, etc.) \u2022 PRECARITY (socioeconomic, parental conflict, parental illness, etc.) \u2022 SYMPTOM (self-harm, low self-esteem, anhedonia, panic attack, flashback, psychosis, insomnia, etc.) 4 \u2022 CONDITION (eating disorder, depression, bipolar, bpd, anxiety, ptsd, adhd, substance abuse/addiction, etc.) \u2022 SUICIDALITY (no subcategories) \u2022 TREATMENT (no subcategories) Nineteen expert annotators were contacted and asked to annotate 500 sentences each for a fixed compensation of \u00a3120 (\u2248\u00a360/hour). These were UK-trained psychiatrists, all of whom had obtained Membership of the Royal College of Psychiatrists by post-graduate experience and formal examinations. Thirteen annotators annotated the Reddit dataset, two annotators annotated the synthetic datasets and four annotators re-annotated samples from the Reddit and synthetic datasets for inter-annotator agreement computation (100 sentences from each dataset, 1500 sentences in total). Annotators were given the above subcategory examples but allowed to use new subcategories when appropriate (no closed set of answers). They were given the post indices to provide context (i.e., so as to be aware which sentences belonged to the same post). They were asked to annotate only school bullying as bullying, and other instances (e.g., sibling harassment) as emotional abuse. Anxiety was to be annotated as a symptom rather than condition unless specifically described as a disorder. Experts performed the annotation by filling in the relevant columns in an Excel sheet with each sentence as a row. Importantly, given the known limitations of language models with negation [36], we wished to annotate both POSITIVE and NEGATIVE evidence in order to test LLMs\u2019 ability to handle both polarities (e.g., I am not feeling suicidal as negative suicidality or We don\u2019t have any money issues as negative socioeconomic precarity). For this purpose, annotators were asked to use the prefixes P and N (e.g., P(adhd) in the CONDITION column or N(socioeconomic) in the PRECARITY column). 3.5 Data processing and dataset statistics In order to compare expert annotations with LLM annotations despite the wide variety of subcategories and terms used by annotators we create dictionaries mapping each term found in the dataset to a standard equivalent (e.g., p(emotional) to p(emotional abuse), p(physical violence) to p(physical abuse), p(gun violence) and p(school shooting) to p(violence), p(rape) to p(sexual abuse), p(financial burden) and p(poor) to p(socioeconomic precarity), p(divorce) to p(family conflict), p(self hatred) to p(low self esteem), etc.). Parental substance abuse is considered family illness and any underspecified subcategories are marked as \u2018unspecified\u2019 (e.g., p(trauma unspecified)). The distribution of subcategories for each category can be found in figures 2, 3, 4 and 5 in Appendix B. The most frequent subcategory in TRAUMA is emotional abuse, which occurs twice as often as physical abuse and death in the dataset. The most frequent form of PRECARITY is family conflict, then family illness (including parental substance abuse) and socioeconomic precarity. The most frequent CONDITIONS are depressive disorders, followed by substance abuse/addiction and ADHD. The most frequent SYMPTOMS are anxiety, low self-esteem, self-harm and low mood. Interestingly, the distribution of subcategories differs quite substantially in the synthetic datasets (distributions for the GPT3.5 and GPT4 generated datasets can be found in Appendix B). Overall, the number of subcategories is reduced, indicating less diversity (however, these are smaller datasets). The top trauma subcategories are sexual abuse for GPT3.5 and school bullying for GPT4, both of which were much less prevalent in real data. The second most prevalent condition for both GPT3.5 and GPT4 is eating disorders, whereas these ranked in 8th place in real data. Finally, unlike in real data, flashbacks and panic attacks are the 3d and 4th most frequent symptoms for both GPT3.5 and GPT4-generated data, whereas self-harm ranks much lower than in real data. Given many of these subcategories were given as examples in the annotator guidelines and LLM prompt, it is likely that the LLMs used them in a more homogenous manner for generation than the distribution which would be found in real data. However, the distribution is not entirely homogenous, which suggests the LLMs did leverage some of the biases learned from their training data. 4 Results Once both human and LLM annotations are standardised, we conduct analyses to assess performance. We provide precision, recall and F1 at the category level and accuracy at the subcategory level 5 collapsed across subcategories (given their high number). We compute category performance in two ways: Positive or Negative, where a point is awarded if the category contains an annotation in both human and LLM annotations, regardless of polarity (i.e., the annotator considered there was relevant information concerning the category TRAUMA) and Positive Only metrics, where negative annotations are counted as no annotations. The difference between the two metrics can be seen clearly in Table 1 (GPT3.5 results), where precision increases but recall diminishes for Positive Only. The increase in precision is due to the fact that GPT3.5 outputs a substantial number of negative annotations in cases where human annotators did not consider it relevant to mention the category. The reduction in recall, on the other hand, results from the fact that LLMs often confuse positive and negative annotations and will occasionally output a negative annotation for a positive one. For real data (Tables 1 and 2), GPT3.5\u2019s performance at the category level is average, with better performance in the Positive Only metrics (0.57). GPT4 performs better, especially in Positive Only metrics (0.63) and subcategory accuracy (0.48 vs. 0.39). In general, recall is higher than precision, indicating LLMs may be overpredicting labels. The performance for synthetic data (Tables 3 and 4) is substantially better, with no gap between the Positive or Negative and Positive Only metrics, suggesting less irrelevant negative annotations. Here again, GPT4 outperforms GPT3.5, both at the category level (0.75 vs 0.70 and 0.73 vs 0.68) and more particularly at the subcategory level, where GPT4 reaches an impressive accuracy of 0.72 (vs 0.42). The gap between recall and precision is reduced for GPT4, whereas GPT3.5 displays higher precision than recall here. In order to assess the upper bound of human performance, we calculate inter-annotator agreement for both real and synthetic datasets using Cohen\u2019s Kappa. Values can be found in Table 5. Interestingly, while performance at the category level in real data is lower (GPT3.5) or similar (GPT4) compared to humans, GPT4 displays a substantially higher accuracy at the subcategory level (0.47 vs 0.35). For synthetic data, GPT3.5 still underperforms human agreement on all three metrics, while GPT4 is on par with humans for the Positive Only and subcategory metrics and only underperforms in the Positive and Negative metric. Category Positive or Negative Positive Only Subcategory Precision Recall F1-Score Precision Recall F1-Score Accuracy TRAUMA 0.38 0.78 0.51 0.56 0.65 0.60 0.39 PRECARITY 0.26 0.43 0.33 0.45 0.31 0.37 0.22 CONDITION 0.33 0.85 0.48 0.54 0.72 0.62 0.55 SYMPTOMS 0.39 0.62 0.48 0.46 0.58 0.52 0.31 SUICIDALITY 0.44 0.79 0.56 0.80 0.68 0.73 / TREATMENT 0.48 0.72 0.58 0.72 0.58 0.64 / ALL 0.37 0.70 0.49 0.55 0.60 0.57 0.39 Table 1: GPT3.5 (real data). Positive or Negative: counting annotation in category regardless of polarity (category level); Positive Only: counting negative annotations as NaN (category level); Subcategory: accuracy at the subcategory level 5 Error analysis We examine some of the sentences annotated by the LLMs in order to perform error analysis and extract the following findings (as mentioned previously some words have been paraphrased to preclude full-text search allowing user identification): \u2022 Both GPT3.5 and GPT4 produce infelicitous negations, i.e., negative annotations which would seem irrelevant to humans, e.g., (I have amazing people around me =>negative parental death or The internet is my one only coping mechanism =>trauma unspecified) \u2022 Despite being specifically prompted to only annotate factors related to the writer/speaker, LLMs (including GPT4) do not always comply, e.g., She comes from what is, honestly, a horrific family situation =>emotional abuse) 6 Category Positive or Negative Positive Only Subcategory Precision Recall F1-Score Precision Recall F1-Score Accuracy TRAUMA 0.44 0.89 0.59 0.57 0.84 0.68 0.57 PRECARITY 0.31 0.52 0.39 0.50 0.46 0.48 0.36 CONDITION 0.46 0.81 0.59 0.61 0.77 0.68 0.57 SYMPTOMS 0.35 0.78 0.49 0.45 0.73 0.56 0.41 SUICIDALITY 0.36 0.93 0.51 0.70 0.87 0.77 / TREATMENT 0.39 0.87 0.54 0.64 0.81 0.71 / ALL 0.39 0.80 0.52 0.55 0.75 0.63 0.48 Table 2: GPT4 (real data). Positive or Negative: counting annotation in category regardless of polarity (category level); Positive Only: counting negative annotations as NaN (category level); Subcategory: accuracy at the subcategory level Category Positive or Negative Positive Only Subcategory Precision Recall F1-Score Precision Recall F1-Score Accuracy TRAUMA 0.90 0.49 0.64 0.90 0.49 0.64 0.38 PRECARITY 0.84 0.69 0.76 0.86 0.69 0.76 0.54 CONDITION 0.44 0.67 0.53 0.47 0.67 0.55 0.59 SYMPTOMS 0.85 0.59 0.70 0.84 0.59 0.69 0.36 SUICIDALITY 0.75 1.00 0.85 0.77 0.90 0.83 / TREATMENT 0.68 0.84 0.75 0.76 0.57 0.65 / ALL 0.74 0.65 0.70 0.77 0.61 0.68 0.42 Table 3: GPT3.5 (synthetic data). Positive or Negative: counting annotation in category regardless of polarity (category level); Positive Only: counting negative annotations as NaN (category level); Subcategory: accuracy at the subcategory level Category Positive or Negative Positive Only Subcategory Precision Recall F1-Score Precision Recall F1-Score Accuracy TRAUMA 0.84 0.95 0.89 0.86 0.92 0.89 0.82 PRECARITY 0.85 0.84 0.85 0.91 0.82 0.86 0.80 CONDITION 0.61 0.67 0.64 0.60 0.67 0.63 0.67 SYMPTOMS 0.49 0.78 0.60 0.53 0.80 0.64 0.69 SUICIDALITY 0.81 0.94 0.87 0.78 0.82 0.80 / TREATMENT 0.85 0.89 0.87 0.87 0.78 0.82 / ALL 0.69 0.83 0.75 0.69 0.79 0.73 0.72 Table 4: GPT4 (synthetic data). Positive or Negative: counting annotation in category regardless of polarity (category level); Positive Only: counting negative annotations as NaN (category level); Subcategory: accuracy at the subcategory level \u2022 Even GPT4 makes errors regarding negation (e.g., I\u2019ve read about people with autism getting temper tantrums/meltdowns, however, that has never really been a problem for me=>negative autism or i had in my head that something inside was very wrong, but i never felt completely depressed all the time so i never took bipolar seriously =>negative bipolar disorder) \u2022 Despite being prompted to annotate suicidality in a separate category, LLMs often annotate it in the SYMPTOM rather than SUICIDALITY category \u2022 GPT3.5 especially often outputs irrelevant/spurious/incorrect labels (e.g., \u2018unemployed\u2019 as condition, \u2018ambition\u2019 as symptom, labelling physical conditions instead of mental conditions only, etc.) 7 Positive and Negative Positive Only Subcategory Annotator vs. Annotator (real data) 0.60 0.59 0.35 GPT3 vs. Annotator (real data) 0.39 0.52 0.37 GPT4 vs. Annotator (real data) 0.43 0.58 0.47 Annotator vs. Annotator (synthetic data) 0.77 0.71 0.68 GPT3 vs. Annotator (synthetic data) 0.64 0.63 0.40 GPT4 vs. Annotator (synthetic data) 0.70 0.69 0.71 Table 5: Inter-annotator agreement (Cohen\u2019s Kappa) \u2022 Even GPT4 makes errors regarding factuality (e.g., It was around my second year in junior high school when my father tried to take his life =>positive death) However, in many cases the assessment is not entirely fair, as the LLMs (particularly GPT4) often catch annotations which human annotators missed, or the difference in subcategories is subjective and open to debate (e.g., school bullying vs emotional abuse, emotional abuse vs abuse unspecified, etc.). Thus it is possible that LLMs, or most likely GPT4, in fact outperformed experts on this task. 6 Discussion The results obtained from our comparison of LLM annotations with human annotations on both real and synthetic data allow us to make a few conclusions and recommendations. Overall, both LLMs perform well. Inter-annotator agreement and performance indicate that GPT4 performs on par with human annotators. In fact, error analysis and manual examination of annotations suggest the LLMs potentially outperform human annotators in terms of recall (sensitivity), catching annotations which have been missed. However, while recall might be improved in LLMs versus human annotators, precision may suffer in unexpected ways, for example through errors in the use of negation and factuality, even in the case of GPT4. LLMs display a particular tendency to overpredict labels and produce negative annotations in infelicitous contexts, i.e., when humans would deem them irrelevant, creating an amount of noise. However, these negative annotations are not technically incorrect. While accuracy errors could be found in the LLM output, the experts\u2019 outputs were not entirely free of them, and previous work by [37] suggests LLMs may both be more complete AND more accurate than medical experts. There may still be a difference in the type of accuracy errors produced by LLMs, which will have to be investigated in future research. In terms of accuracy at the subcategory level, we were surprised to find GPT4 outperformed human agreement by a large margin in real data (0.47 vs 0.35). We hypothesise this is due to the fact that human annotators display higher subjectivity in their style of annotation at the subcategory level (given the lack of predetermined subcategories) and diverge more between them. LLMs are likely to be more \u2018standard\u2019 and generic and thus potentially more in agreement with any given human annotator. More specifically, LLMs tend to be consistent from one annotation to the other with higher recall whereas human annotators showed less consistency. Therefore, if a sentence mentions physical, sexual and emotional abuse, annotators might only mention two out of three but when mentioning all three an LLM is more likely to be in agreement than another annotator, i.e., the LLM will catch more of the perfectly recalled annotations than the second annotator. The better performance demonstrated on synthetic data doesn\u2019t seem due to LLMs performing better on data they are generating, but rather to the synthetic data being less complex and diverse and thus easier to annotate for both LLMs and humans, as evidenced by GPT4 reaching similar inter-annotator agreement scores to humans (with agreement both in humans and LLM/human 10% higher for synthetic data). This better performance could still warrant using synthetic data for e.g., training machine learning models (given more reliable labels) but only in cases where the potential loss in diversity is compensated by the increase in label reliability. This will likely depend on the specific application. 8 7 Conclusion We presented the results of a study examining human and Large Language Models (GPT3.5 and GPT4) performance in extracting mental health factors from adolescent social media data. We performed analyses both on real and synthetic data and found GPT4 performance to be on par with human inter-annotator agreement for both datasets, with substantially better performance on the synthetic dataset. However, we find GPT4 still performing non-human errors in negation and factuality, and synthetic data to be much less diverse and differently distributed than real data. The potential for future applications in healthcare will have to be determined by weighing these factors against the substantial reductions in time and cost achieved through the use of LLMs. Acknowledgment I.L., D.W.J., and A.K. are partially supported by the National Institute for Health and Care Research (NIHR) AI Award grant (AI_AWARD02183) which explicitly examines the use of AI technology in mental health care provision. A.K. declare a research grant from GlaxoSmithKline (unrelated to this work). This research project is supported by the NIHR Oxford Health Biomedical Research Centre (grant NIHR203316). The views expressed are those of the authors and not necessarily those of the UK National Health Service, the NIHR or the UK Department of Health and Social Care.",
                    "introduction": "The recent development of powerful Large Language Models such as GPT3.5 [2] and GPT4 [3] able to perform tasks in a zero-shot manner (i.e., without having been specifically trained or fine- tuned to do so) by being simply prompted with natural language instructions shows much promise for healthcare applications and the domain of mental health. Indeed, these models display more impressive general natural language processing abilities than their predecessors and excel at tasks such as Question Answering and Named Entity Recognition [4, 5, 6, 7]. Models with the ability to process social media content for indicators of mental health issues have the potential to become invaluable cost-effective tools for applications such as public health monitoring [8] and online moderation or intervention systems [9]. In addition, synthetic data produced by LLMs can be a cost effective and privacy-preserving tool for training task specific models [10]. There have been several studies aimed at assessing the abilities of LLMs to perform a range of tasks related to mental health on datasets derived from social media. Yang et al. [11] conducted a comprehensive assessment of ChatGPT (gpt-3.5-turbo), InstructGPT3 and LlaMA7B and 13B [12] arXiv:2404.16461v2  [cs.CL]  26 Apr 2024 on 11 different datasets and 5 tasks (mental health condition binary/multiclass detection, cause/factor detection, emotion detection and causal emotion entailment, i.e. determining the cause of a described emotion). They find that while the LLMs perform well (0.46-0.86 F1 depending on task), with ChatGPT substantially outperforming both LLaMA 7B and 13B, they still underperform smaller models specifically fine-tuned for each task (e.g., RoBERTa). Xu et al. [13] find similar results for Alpaca [14], FLAN-T5 [15] and LLaMA2 [16], with only fine-tuned LLMs able to perform on par with smaller, task-specific models such as RoBERTa [17, 18]. However, we find that previous studies suffer from the following shortcomings: 1. They focus on adult mental health 2. They focus on tasks with a closed (or finite) set of answers, where the model is asked to perform each task in turn 3. They do not investigate how LLMs perform on synthetic data, i.e., text they are asked to simultaneously generate and label There is growing consensus that we are facing a child mental health crisis [1]. Before the COVID-19 pandemic there was already increasing incidence of mental health conditions in children and young people (CYP), such as depression, anxiety and eating disorders [19] as well as rising rates of self-harm and suicidal ideation [20] and cyberbullying strongly linked to adverse mental health outcomes [21]. The advent of the pandemic accelerated this already precarious situation and created additional challenges [22, 23] such as discontinuity of healthcare service provision in addition to interruption to young people\u2019s usual engagement in education and their social lives. This age range is particularly vulnerable to onset of mental health issues, with half of conditions appearing by early adolescence and 10-20% of children and young people experiencing at least one mental health condition [24]. Females, those with low socioeconomic backgrounds, trauma, abuse or having witnessed violence [25] are at heightened risk. On the other hand, social media now forms an important part of children and adolescents\u2019 daily lives, whose impact on mental health is debated, with potential benefits (stress reduction and support networks [26]) as well as potential risks (sleep disturbance, self esteem issues and cyberbullying [27]). Regardless of their detrimental or protective impact, social media may contribute valuable insights into CYP\u2019s mental health, with opportunities for monitoring and intervention, for example identifying those at risk of depression and mood disorders [28]. Given the mental health of CYP is a particularly pressing public health concern, we wished to investigate how LLMs perform on extracting mental health factors when faced with social media content generated by young people aged 12-19. Indeed, several issues related to mental health either exclusively apply to children and adolescents (such as school bullying and ongoing family abuse) or are particularly prevalent in this age range (such as eating disorders [29] and self-harm [30]), making both content type and factors of interest distinct from those found in adult social media posts. In addition, previous studies focused on tasks which had either a binary or closed sets of answers (e.g., choosing between several given conditions or between several given causal factors). In contrast, we wish to examine how LLMs perform on a task of open information extraction, where they are given categories of information and asked to extract any which are found in the text (e.g., asked to detect whether there is any mental health condition indicated in the text). Furthermore, in previous studies the models were tested with each task in turn (e.g., asked to detect depression in one dataset, then detect suicidality in another dataset), whereas we gather and annotate our own dataset in order to be able to ask the LLMs to extract all categories simultaneously (e.g, extract all conditions and symptoms in a given sentence). Finally, to our knowledge there has been no investigation on how LLM performance compares when asked to annotate text as they generate it, i.e., how their performance on synthetic data compares with their performance on real data. There is growing interest in synthetic data for healthcare [31]. Given the potential for training models and running simulations and digital twin experiments with the benefit of reduced issues of data scarcity and privacy, we believe that our work will contribute to better understanding of limitations and benefits of using synthetic data for real-world tasks. 2"
                },
                {
                    "url": "http://arxiv.org/abs/2403.15885v2",
                    "title": "STEntConv: Predicting Disagreement with Stance Detection and a Signed Graph Convolutional Network",
                    "abstract": "The rise of social media platforms has led to an increase in polarised online\ndiscussions, especially on political and socio-cultural topics such as\nelections and climate change. We propose a simple and novel unsupervised method\nto predict whether the authors of two posts agree or disagree, leveraging user\nstances about named entities obtained from their posts. We present STEntConv, a\nmodel which builds a graph of users and named entities weighted by stance and\ntrains a Signed Graph Convolutional Network (SGCN) to detect disagreement\nbetween comment and reply posts. We run experiments and ablation studies and\nshow that including this information improves disagreement detection\nperformance on a dataset of Reddit posts for a range of controversial subreddit\ntopics, without the need for platform-specific features or user history.",
                    "authors": "Isabelle Lorge, Li Zhang, Xiaowen Dong, Janet B. Pierrehumbert",
                    "published": "2024-03-23",
                    "updated": "2024-03-26",
                    "primary_cat": "cs.CL",
                    "cats": [
                        "cs.CL"
                    ],
                    "main_content": "2.1. Stance The word stance refers to the intellectual or emotional attitude or position of an author towards a specific concept or entity, such as atheism or the legalisation of abortion (Mohammad et al., 2016). This is different from the concept of sentiment as it is usually defined in sentiment analysis, where it refers to the overall emotion expressed by a piece of text. A given text can then have one sentiment value but express multiple positive and negative stances, the target of which is not necessarily explicitly mentioned in the text. Some concepts lend themselves more easily to the elicitation of stance. For example, consider the following quote from the Wikipedia section on Donald Trump: Donald John Trump (born June 14, 1946) is an American politician, media personality, and businessman who served as the 45th president of the United States from 2017 to 2021. Trump\u2019s political positions have been described as populist, protectionist, isolationist, and nationalist. He won the 2016 presidential election as the Republican nominee against Democratic nominee Hillary Clinton despite losing the popular vote. It would be strange to ask whether the author is in favour or against born, media, businessman, who, is, from, described, presidential or popular. On the other hand, the words in bold type 2 (with the exception of numerals, i.e. dates and ordinals) seem like more appropriate targets for holding an opinion. These words are generally referred to as Named Entities or NEs, a term first coined for the Sixth Message Understanding Conference (MUC-6) (Grishman and Sundheim, 1996). The category aims to encompass expressions which are rigid designators, as defined by Kripke (1980), i.e., which designate the same object in all possible worlds in which that object exists and never designate anything else. In other words, these expressions refer to specific instances in the world, including but not limited to proper names. Common NE categories are: organisations, people, locations (including states), events, products and quantities (including dates, times, percent, money, quantity, ordinals and cardinals). With the exception of the last category, most of these constitute valid targets for extracting author stance because, unlike other terms (e.g., verbs, adverbs, prepositions, some nouns and adjectives) they can be involved in debates and elicit diverging intellectual or emotional viewpoints. Communities tend to be created on the basis of shared traits which are either given (e.g., race, gender, nationality) or acquired (preferences and opinions). Thus, for many contentious issues, agreement and disagreement between individuals are likely to crystallise around attitudes towards a few key entities which define membership identity in a form of \u2018neotribalism\u2019 (Maffesoli, 1995). Stance can be modelled at the post or author level. Here we choose to leverage all posts from a known author to determine their stance toward a specific entity. 2Bold typed words are all word spans identified by Spacy (Honnibal and Montani, 2017) as named entities. 2.2. Signed Graphs Graphs, defined as combinations of nodes and edges, are useful abstractions for a variety of structures and phenomena. They can take several forms: directed (e.g., Twitter following) vs. undirected (e.g., Facebook friends); signed (e.g., likes and dislikes) vs. unsigned (e.g., retweets), homogenous vs. bipartite (with nodes of different types where there is no between-type edges, e.g., employees and companies they worked for). In the current paper, given we model user-entity stances, the graph constructed is a signed bipartite graph. While it is technically directed (the stance is from user towards entity), there are no edges in the opposite direction (i.e., from entity to user), thus we treat the graph as undirected for simplicity. Various methods have been developed for node representation in graphs. When no node features are available, methods relying on connectivity and random walks such as DeepWalk (Perozzi et al., 2014) and node2vec (Grover and Leskovec, 2016) can produce low-dimensional node embeddings using a similar algorithm to skip-gram in Word2vec, i.e., by predicting a node given previously encountered nodes. Graph Neural Networks (GNNs), on the other hand, can leverage both connectivity and node features from a local neighbourhood to produce node representations. Among these, Graph Convolutional Networks (GCNs) were first introduced by Kipf and Welling (2016) and constitute a popular option akin to a generalisation of Convolutional Neural Networks (CNNs), by performing a first-order approximation of a spectral filter on a neighbourhood. GCNs were originally designed to handle unsigned graphs. However, in the case of stance, as well as in many other applications related to social media, we encounter networks which are signed, i.e., which involve positive and negative edges. Processing these types of graphs and producing meaningful node representations is not straightforward, as there is an intrinsic qualitative difference between the two types of edges which cannot be optimally resolved by e.g., treating them alike, ignoring negative edges, or ignoring edges that cancel each other. One solution is to keep positive and negative representations separate from the graph neural network separate and simply concatenate them. Another way suggested by Derr et al. (2018) relies on assumptions from balance theory (Heider, 1946; Cartwright and Harary, 1956), which comes from social psychology and formalises intuitions such as \u2018an enemy of an enemy is a friend\u2019. Thus, for each layer l, the aggregation function would gather on the positive side not only friendly nodes, but friends of friends and enemies of enemies, and similarly on the negative side get information from enemies but also friends of enemies and enemies of friends. The positive and negative convolutions are then concatenated together to produce the final node representations as in the simpler model. In our experiments we test both the simple signed model and the model with additional aggregations based on balance theory. 3. Dataset We use the DEBAGREEMENT dataset for our experiments (Pougu\u00e9-Biyong et al., 2021), a dataset of 42894 Reddit comment-reply pairs from 5 different subreddits (r/Brexit, r/climate, r/BLM, r/Republican and r/democrats) with each pair given one of three labels: agree/neutral/disagree (see dataset statistics in tables 1 and 2). The pairs of posts were labelled by crowdsourcers who received intensive training on the issues discussed in the various subreddits. The disagreement prediction task consists in predicting which of the three labels describes the relation between the comment and reply posts. This is a very difficult task for a number of reasons. First, assessing disagreement around issues such as those discussed in the selected subreddits requires expert knowledge (hence the need for specific training of crowdsourcers). Second, there is a high level of subjectivity involved, which is evidenced by the \u2018clean\u2019 version of the dataset still containing over 60% labels where only 2 out of 3 crowdsourcers agreed. Because of the latter, we choose after examining the data to work with the portion of the dataset that was given the same label by all three crowdsourcers (16723 pairs of posts). Finally, it is worth noting that most previous works focusing on disagreement use Twitter data exclusively (e.g., Darwish et al., 2020; Trabelsi and Zaiane, 2018; Zhou and Elejalde, 2023). Many other platforms like Reddit lack network features such as common hashtags, user following and retweets which are highly useful for detecting endorsement between users. It is then much harder to create user representations indicative of polarisation. This emphasises the crucial need to find alternative features, such as user-entity stances, which can generalise across platforms. While the task has been tackled using user network features (Luo et al., 2023), no previous works have attempted to improve performance without leveraging user interaction features which may not always be available. 4. Framework 4.1. User-Entity Graph Construction Let G = (N, E) be a signed undirected bipartite graph where U \u2208N is the set of user nodes, A \u2208 r/Brexit r/climate r/BlackLivesMatter r/Republican r/democrats start date Jun 2016 Jan 2015 Jan 2020 Jan 2020 Jan 2020 agree 0.29 0.32 0.45 0.34 0.42 neutral 0.29 0.28 0.22 0.25 0.22 disagree 0.42 0.40 0.33 0.41 0.36 Table 1: DEBAGREEMENT statistics per subreddit and period comment-reply count avg length (comment) avg length (reply) r/Brexit 15745 45 40 r/climate 5773 43 41 r/BlackLivesMatter 1929 41 39 r/Republican 9823 38 35 r/Democrats 9624 38 37 Table 2: DEBAGREEMENT post counts and word lengths N is the set of entity nodes and E the set of edges between users and entities, with E+ the set of positive edges and E\u2212the set of negative edges. Since this is a bipartite graph, there are no edges between users or between entities, and the set of positive and negative edges are defined to be mutually exclusive (ie., there is at most one edge, either positive or negative, between a user and an entity) (see figure 2). Figure 2: Example user-entity graph. The network is signed, with each edge representing user stance towards an entity. We build the graph in the following way. First, we extract named entities for each comment and reply post using Spacy (Honnibal and Montani, 2017), discarding entities which pertain to the categories \u2018CARDINAL \u2019, \u2018DATE\u2019, \u2018ORDINAL \u2019, \u2018WORK_OF_ART\u2019, \u2018PERCENT\u2019, \u2018QUANTITY\u2019 and \u2018MONEY\u2019. Since we do not have ground truth for the stance of each author for each extracted entity, we devise an unsupervised method to obtain a proxy of it by leveraging Sentence-BERT (Reimers and Gurevych, 2019). For each entity, we create \u2018pro\u2019 and \u2018con\u2019 sentences using the templates I am for X and I am against X. We then compute the cosine similarity between each SBERT-embedded post sentence and each SBERT-embedded template sentence and subtract the \u2018con\u2019 cosine similarity from the \u2018pro\u2019 cosine similarity 3. Finally, we take the mean of all cosine differences for an entity across all user posts4. The advantage of this method is that it is almost entirely unsupervised and does not require prior domain knowledge or manual selection of relevant topics or entities (only the subreddit titles, see below), these naturally arise among the most frequent entities extracted from the corpus. Therefore, we define our stance measure as: stanceu,e = N X i\u2208P PM s\u2208S cos+ s \u2212cos\u2212 s |S| |P| (1) where stanceu,e is the stance of user u towards entity e, i \u2208P is the ith post contributed by user u, s \u2208S is a sentence in the post, cos+ is the cosine similarity of the post sentence with the \u2018pro\u2019 embedded template sentence and cos\u2212is the cosine similarity of the post sentence with the \u2018con\u2019 embedded template sentence. We notice a negative bias in our extracted cosine similarities whereby the mean \u00b5 of stance values lies around -0.02 and accordingly split edges into positive edges (stanceu,e >= \u00b5) and negative edges (stanceu,e < \u00b5) after verifying that the stances follow a normal distribution and the median is close to the mean. The statistics of the resulting graph can be seen in table 4. When examining the extracted entities, it appears that most entities which occur only a few times in the corpus will be irrelevant to our task. We thus apply a combination of two filters: we 3While this method has to our knowledge not been previously used, we manually examine the results for 100 sentences by calculating the stance for each named entity extracted using the method described and rating it as correct or incorrect and find satisfactory performance (0.68 accuracy). 4In addition, we also mean center all edge weight values by subtracting the mean. american, antifa, aoc, asian, backstop, bernie, biden, black, blm, brexit, brexiteers, brown, christian, cnn, communist, con, confederate, conservative, corbyn, cuomo, dem, democrat, democratic, dems, dnc, fascist, fbi, floyd, george, gop, greta, holocaust, jew, kkk, leave, leftist, liberal, libertarian, maga, marxist, mcconnell, moderate, moron, msm, muslim, nazi, party, patriot, pete, poc, progressive, propaganda, qanon, racist, referendum, remainers, republican, riot, romney, sander, senate, statue, tory, trump, tucker, warren, white Table 3: Extracted target entities |U| |A| |E+| |E\u2212| |D| |D(U)| |D(A)| |CN(U)| |CN(A)| train 7107 67 3997 4615 0.001 1.83 194 0.32 5.67 test 1513 67 863 866 0.002 1.48 37 0.20 0.60 Table 4: User-entity graph statistics for full training and test datasets. |U|: number of users; |A|: number of entities; |E+|: number of positive edges; |E\u2212|: number of negative edges ; |D|: graph density; |D(U)|: average degree (users); |D(A)|: average degree(entities); |CN(U)|: average common neighbors (users); |CN(A)|: average common neighbors (entities) keep entities which are amongst the 5000 most frequent entities and whose embeddings have a cosine similarity above 0.5 to at least one subreddit title embedding (Brexit, climate, BLM, Republican and democrats) (the embeddings used are the initial features for the GCN which are Word2vec embeddings trained on our dataset, see section Training). We obtain both values by conducting a sensitivity correlation analysis on the training set in the following way: we model a negative and positive entity vector for each author respectively as the sum of the negative stance and positive stance entities, concatenate them and measure the Kendall \u03c4 rank correlation between the cosine similarity of the author vectors for a given comments pair and the label (0,1 or 2 as disagreement, neutral and agreement). There is a clear peak in correlation with entities which have over 0.5 cosine similarity with at least one subreddit title and are within the 5000 most frequent entities, thus we select these as our threshold values. We also filter out multiword entities which often show redundancy and misextractions. The final set of 67 target entities can be seen in Table 3, a heatmap of cosine similarities to each subreddit can be found in Appendix A and a visualisation of the user-entity graph can be seen in figure 1. To get a fair assessment of our model and be able to directly compare it with the performance of the GCN model alone, we subset the training dataset to comment-reply pairs which mention at least one of our target entities (for other commentreply pairs the GCN would not have any features). The final dataset is made of 1770 comment-reply pairs. While this constitutes only 10% of the original full agreement dataset, we notice that disagreements which are most closely related to the subreddit\u2019s controversial topic will often contain the target entities 5 . We also believe that given the difficulty of the task (especially on Reddit data where many network features available on Twitter cannot be used), an improvement on a subset of disagreement types is worthwhile and holds promise for applicability. We do provide results for the subset of the dataset where only either comment or reply mentions one of our target entities, which constitutes about 40% of the full agreement dataset or 6174 comment-reply pairs, however we cannot run a comparison with the GCN model alone in this case. 4.2. STEntConv We adopt the Signed Graph Convolutional Network proposed in Derr et al. (2018) and modify it to integrate edge weights for our stance values so that the positive and negative convolutions are as follows: hB(l) i = \u03c3(WB(l)[ X j\u2208N + i hB(l\u22121) j |N + i | wj, X k\u2208N \u2212 i hU(l\u22121) k |N \u2212 i | wk, hB(l\u22121) i ]), (2) 5While our assumption that the model leverages information from entities not present in the text suggests we should be able to use posts which do not mention target entities, we find empirically that this is not the case. However, the better performance over the BERT baseline suggests the model does make use of information not present in the comment-reply pair. We hypothesise that this is because of a correlation between the presence of target entities in specific pairs of posts and the amount of additional information in the entity graph (ie., posts which do not contain target entities tend to come from authors for whom there is little/no entity information). hU(l) i = \u03c3(WU(l)[ X j\u2208N + i hU(l\u22121) j |N + i | wj, X k\u2208N \u2212 i hB(l\u22121) k |N \u2212 i | wk, hU(l\u22121) i ]), (3) where hB(l) i is the weighted aggregation of positive edges for layer l, P j\u2208N + i h B(l\u22121) j |N + i | wj is the weighted sum of \u2018friends of friends\u2019, P k\u2208N \u2212 i h U(l\u22121) k |N \u2212 i | wk is the weighted sum of \u2018enemies of enemies\u2019 and hB(l\u22121) i the previous layer\u2019s positive edges aggregation. Similarly, hU(l) i is the aggregation of negative edges for layer l, P j\u2208N + i h U(l\u22121) j |N + i | wj is the weighted sum of \u2018enemies of friends\u2019, P k\u2208N \u2212 i h B(l\u22121) k |N \u2212 i | wk is the weighted sum of \u2018friends of enemies\u2019 and hU(l\u22121) i the previous layer\u2019s negative edges aggregation. We run experiments both with the additional aggregations from balance theory and without (i.e., only aggregating direct friends for positive edges and direct enemies for negative edges), in which case the respective weighted aggregations are simply: hB(l) i = \u03c3(WB(l)[ X j\u2208N + i h(l\u22121) j |N + i | wj, h(l\u22121) i ]). (4) hU(l) i = \u03c3(WU(l)[ X j\u2208N + i h(l\u22121) j |N \u2212 i | wj, h(l\u22121) i ]), (5) This is also the definition of the aggregations for the first layer l = 1. We build the weighted version of the algorithm by adapting the unweighted Derr et al. (2018) implementation from PyTorch geometric (PyG) (Fey and Lenssen, 2019). The rationale for integrating edge weights to the convolutional layer is that, given our unsupervised method for calculating stance, a high absolute value is more reliable and thus considered more informative. Positive/negative edge and node features should then be weighted accordingly when performing message passing (e.g., a small edge weight is more likely to denote a stance close to neutral). The output of the GCN is concatenated to the output of a BERT layer for comment and reply posts and fed to a one-layer feed-forward network. The final model architecture can be seen in figure 3. 5. Baselines 5.0.1. BERT As a baseline, we fine-tune a BERT (base, uncased) layer as was originally used by Pougu\u00e9Figure 3: Model architecture. Biyong et al. (2021), i.e., we ablate the graph convolutional layer from our model and feed this to the linear layer for classification. 5.0.2. GCN only In addition, we conduct the opposite ablation, i.e., we use only the GCN to assess how the model performs relying only on the positive and negative edges of the stance graph without any access to the text of the posts. 5.0.3. StanceRel Luo et al. (2023) improve on previous results on the DEBAGREEMENT dataset by building a graph autoencoder and training it on a signed undirected user-user interaction graph which creates user representations based on their previous interactions (agreement or disagreement, i.e., positive or negative) and using the decoded user features along with textual features to detect disagreement. While a direct comparison with our approach may not be fully informative (as the two models use different features which may be available in different situations), we train their model on our subset of data and provide results on our test set to give a picture of the differential value of various user features. 5.0.4. FALCON We also test an instruct-trained version of Falcon (Almazrouei et al., 2023), specifically vilsonrodrigues/falcon-7b-instruct-sharded implemented through the transformers library (Wolf et al., 2019). Prompt and hyperparameters used can be found in Appendix B. 6. Training We train 100-dimensional word2vec6 embeddings on the full dataset and use the resulting vectors 6We also experiment with GloVe embeddings but the performance is worse. as initial features for our entities. User features are initialised as 100-dimensional vectors of zeros. We obtain contextual text embeddings for comment and reply posts through the transformers library (Wolf et al., 2019) implementation of a BERT (base, uncased) layer whose output we mean pool, excluding special tokens, and concatenate these together with the output of our weighted Signed Graph Convolutional Network layer before feeding this to a one-layer linear classifier. Since the classes are not entirely balanced, we compute class weights and weigh class loss accordingly during training. We use cross entropy as loss function, a batch size of 16, a hidden size of 300 for the first convolutional layer, a learning rate of 3e-5 and the Adam optimiser with weight decay 1e-5. We split the data into 0.80 train, 0.10 dev and 0.10 test and train for 6 epochs (models with BERT layers) and 11 epochs (GCN only). We experiment with number of convolutional layers (one versus two), type of aggregation (balance theory or only direct friends and enemies), edge weights (binary versus weighted) and sentences used to calculate stance (full post versus only sentences containing target entity). We train the models with three different random seeds and average the results. 7. Results Results can be found in Table 5. The best performing model uses one convolution layer, only direct friends and enemies, weighted edges, and the full text of the post for stance extraction. As can be seen, on the (c&r) subset the addition of the user stance graph information helps improve model performance by 7 points on average compared to the BERT baseline and 6 points over the StanceRel model which previously obtained the best results on this task. While the improvement in performance is weaker for the version of STEntConv trained on the (c|r) dataset (since this dataset includes authors for whom the model has no relevant stance information), the model still achieves a 3 point increase over the BERT baseline. In the non-multiple aggregation model, the boost from the stance graph information is lowest for r/Republican. This is consistent with additional analyses we conduct on the test dataset showing that the r/Republican subreddit has the highest ratio of target entities present in posts versus all entity information available for authors, meaning that there is little extra information from the GCN to be used and most relevant information is already available to the BERT model. Thus, it is likely that the better performance of our model is due to STEnTConv being able to leverage stance information about entities not present in the comment-reply pair being classified. Adding the second aggregation from (Derr et al., 2018) performs better on the r/Brexit and r/Republicans subreddits. This would tend to indicate that the additional aggregations for these subreddits remain relevant to the task whereas they introduce noise for r/climate. This is supported by r/climate subreddit having the lowest cosine similarity on average to the target entities. Falcon performs particularly poorly, in addition to requiring over an hour for inference on the test set (vs. a few seconds for BERT-based models and GCN). StanceRel, while above the BERT baseline, underperforms our model on the test set. Given that the model leverages user history which represents a strong additional signal, we expected it to perform better. The lower performance may be due to sparseness in the user interaction graph or to the model requiring a larger dataset to learn features from interaction history. In addition, the graph StanceRel uses is weighted by frequency which may be prone to biases (e.g., user A from the Green Party agreed with user B from the Green Party many times, but they disagreed on an issue involving a specific entity, e.g. French nuclear company AREVA). Finally, they leverage the assumptions from balance theory which we show may not be useful for this particular task. Unsurprisingly, the neutral class is hardest to classify, with an f1 of 0.4 versus 0.8 for the agree/disagree classes. Examining the data indicates one reason for this might be the heterogenous nature of the class, with some neutral pairs of posts discussing unrelated topics and others agreeing and disagreeing in equal amounts. The confusion matrix between classes can be seen in figure 4. Figure 4: Confusion matrix (STEntConv) r/Brexit r/climate r/Republican r/democrat r/BLM* all (sd) (c|r) BERT .75 .79 .73 .69 .72 .72 (0.03) (c|r) STEntConv .78 .78 .76 .71 .75 .75 (0.02) (c&r) FALCON .40 .25 .45 .38 1.0 .42 (0.28) (c&r) BERT .58 .54 .69 .63 .67 .64 (0.06) (c&r) StanceRel .67 .30 .67 .60 1.0 .65 (0.22) (c&r) STEntConv (GCN) .36 .44 .44 .37 .67 .43 (0.11) (c&r) STEntConv (m.agg) .70 .41 .73 .69 1.0 .70 (0.18) (c&r) STEntConv .62 .64 .70 .74 1.0 .71 (0.14) Table 5: Macro averaged F1 for each model and subreddit. STEntConv = our model enhanced with entity stances; BERT= BERT model (base, uncased); StanceRel = relation graph model from Luo et al. (2023) FALCON: Falcon model (instruct trained, 7B); GCN = STEntConv without BERT component; m.agg: multiple aggregations, i.e. using the \u2018friend of friend\u2019 additional aggregation from Derr et al. (2018). (c&r) = dataset with target entity in comment and reply; (c|r) = dataset with target entity in comment or reply. Best in bold.*The (c&r) test set only contained one comment-reply pair from the r/BLM subreddit. 8. Related Work There have been a number of studies aimed at modelling stance and disagreement. Regarding stance, a supervised task was introduced at SemEval 2016 along with a small dataset of 4870 tweets annotated for stance against five topics (Atheism, Climate Change is a Real Concern, Feminist Movement, Hillary Clinton and Legalization of Abortion) (Mohammad et al., 2016). Winning teams used CNNs and ensemble models. However, the limited data and specificity of both style and topics make it difficult to extend a model trained on this data to detecting stance in other domains. Regarding unsupervised methods for both stance and disagreement, most methods have focused on modelling users through dimensionality reduction and clustering of content (Darwish et al., 2020) or through platform-specific (Trabelsi and Zaiane, 2018; Zhou and Elejalde, 2023) or non platform-specific (Luo et al., 2023) network features from user-user interactions. To the best of our knowledge, no previous method used a userentity graph to model user representations. Importantly, as stated in the introduction, most previous works use Twitter data which contains platform-specific network features. Thus, our work aligns with other efforts to build alternative network features in polarised communities when user endorsement features (e.g., retweets and follows) are not available, as is the case for Reddit data. For example, Hofmann et al. (2022) build a graph of edges between social entities (concepts and subreddits) to identify the level of polarisation for a given concept. In addition, even previous works which do not use platform-specific data still rely on features which may not always be available, such as user interaction history (Luo et al., 2023) and restrict ability to use graph features to known users. By contrast, our method can leverage entity stances at inference time to model novel users which have similar allegiances to users seen in training. To our knowledge, the current paper is the first to use representations from a signed graph between users and entities for the purpose of predicting disagreement. 9. Conclusion We presented a simple, unsupervised and domainagnostic pipeline for creating graph user features to improve disagreement detection between comment-reply pairs of social media posts. We ran several experiments against baselines and performed ablations to examine the contribution of model components and parameters. Our model uses GCN convolutions over a signed bipartite graph of automatically extracted user-entity stances. STEntConv can be leveraged to create comprehensive user representations which take into account stance towards various target entities in order to better predict whether two users are likely to agree or disagree on a range of controversial topics, regardless of availablity of platformspecific network features or user interaction history. As a next step, this method could easily be extended to target entities beyond named entities to include common nouns which are particularly relevant to the controversial topic, especially in cases where the topic is less likely to involve named entities. 10. Limitations Scale. We acknowledge that the improvement we demonstrate over the baseline applies to only a subset of the original dataset. However, given the difficulty of the task and the lack of additional network features for Reddit data we believe this improvement is still worthwhile. Furthermore, our method could potentially be extended to include stance towards relevant common nouns in addition to named entities. Domain. While the dataset we used covers a range of controversial topics from socio-cultural to political issues, it was extracted from 5 specific subreddits and thus it is uncertain to what extent our results would apply to other topics of disagreement and whether the model could be generalised to other domains. However, we note that our pipeline for extracting relevant entities is entirely domainagnostic and thus we believe it could be applied successfully to any forum debating a controversial topic. Acknowledgements The authors would like to acknowledge support from the EPSRC (EP/T023333/1). X.D. acknowledges support from the Oxford-Man Institute of Quantitative Finance. This study was supported by EPSRC Grant EP/W037211/1. 11.",
                    "introduction": "Social media now form an integral part of many people\u2019s lives. While these tools have allowed users unprecedented access to shared content, ideas and views across the world, they have also permitted the fast rise and spread of harmful forms of communication, such as fake news, abuse and communities acting as radicalising echo chambers at unseen scales (Terren and Borge, 2021). It is then of high interest to investigate the polarisation of opinions as a reflection of ever-shifting politi- cal and socio-cultural dynamics which have direct impact on society. For example, detecting disagree- ment between users can help assess the contro- versiality of a topic, give insight into user opinions which would not be obtainable from their post in isolation or provide a way to estimate numbers for sides of a debate. Online communities constitute an ideal terrain for this investigation, as they are likely to foster vari- ous tensions and debates and allow researchers to examine them in real time or longitudinally (Alkhal- ifa and Zubiaga, 2022). Previous work on detect- ing disagreement has focused on supplementing textual information with user network information, either gathered through platform-specific features such as Twitter\u2019s following system, retweets and hashtags (which cannot be generalised across plat- forms) (e.g., Darwish et al., 2020 or through user- user interaction history (which is not necessarily available) (e.g., Luo et al., 2023). Instead, to the best of our knowledge we are the first to represent users through a user-entity signed graph weighted Work completed while Li Zhang was a postdoctoral assistant at the University of Oxford. by stance. In addition to being generalisable to any platform and not requiring user interaction his- tory, our method has the potential to provide more explainable representations for users by explicitly tracing disagreements back to entities they feel positively or negatively about. Furthermore, the graph can easily be adapted to various controver- sial topics by selecting entities relevant to that topic, is able to accommodate different amounts of infor- mation per user, and a user-entity signed network constitutes a natural and explicit representation of polarising allegiances (cf. figure1). Finally, we derive stance towards entities in an unsupervised manner which means there is no need to obtain costly manual labels. We make the choice to use BERT both for unsu- pervised stance detection and for the textual part of the model itself. This choice is partially to be able to directly assess the additional contribution of our signed network to the former best model from Pougu\u00e9-Biyong et al. (2021) for this dataset, but also because we build it with the view of a rela- tively lightweight model with potential for real time applications. In addition, large language models have been shown to underperform smaller state- of-the-art fine-tuned models on specific tasks, for example in the biomedical domain (Ateia and Kr- uschwitz, 2023). However, we do provide results for the performance of an open-source large lan- guage model (Falcon, Almazrouei et al. 2023) on the task as a comparison. Our main contributions are as follows1: 1) We offer a simple, unsupervised method to 1We make all our code and data available at https: //github.com/isabellelorge/contradiction arXiv:2403.15885v2  [cs.CL]  26 Mar 2024 Figure 1: User-entity graph visualised with Gephi (Bastian et al., 2009) (positive edges). We ap- ply a force atlas layout. Pink nodes are entities, blue nodes are users which we can see clustered around the target entities they expressed a positive stance for. extract user stances towards entities by leveraging sentence-BERT. 2) We build a model using a weighted Signed Graph Convolutional Network on a user-entity graph with BERT embeddings to detect disagree- ment, improving on previous state-of-the-art results on a dataset of Reddit posts. 3) We present various model ablation studies and demonstrate the robustness of the proposed framework. We start by outlining current research regarding stance and signed graphs which is relevant to our task. We then move on to describing the dataset used and graph extracted from our data, the archi- tecture and various parameters of our model. We finally present experimental results and discuss their implications."
                },
                {
                    "url": "http://arxiv.org/abs/2402.07645v1",
                    "title": "Detecting the Clinical Features of Difficult-to-Treat Depression using Synthetic Data from Large Language Models",
                    "abstract": "Difficult-to-treat depression (DTD) has been proposed as a broader and more\nclinically comprehensive perspective on a person's depressive disorder where\ndespite treatment, they continue to experience significant burden. We sought to\ndevelop a Large Language Model (LLM)-based tool capable of interrogating\nroutinely-collected, narrative (free-text) electronic health record (EHR) data\nto locate published prognostic factors that capture the clinical syndrome of\nDTD. In this work, we use LLM-generated synthetic data (GPT3.5) and a\nNon-Maximum Suppression (NMS) algorithm to train a BERT-based span extraction\nmodel. The resulting model is then able to extract and label spans related to a\nvariety of relevant positive and negative factors in real clinical data (i.e.\nspans of text that increase or decrease the likelihood of a patient matching\nthe DTD syndrome). We show it is possible to obtain good overall performance\n(0.70 F1 across polarity) on real clinical data on a set of as many as 20\ndifferent factors, and high performance (0.85 F1 with 0.95 precision) on a\nsubset of important DTD factors such as history of abuse, family history of\naffective disorder, illness severity and suicidality by training the model\nexclusively on synthetic data. Our results show promise for future healthcare\napplications especially in applications where traditionally, highly\nconfidential medical data and human-expert annotation would normally be\nrequired.",
                    "authors": "Isabelle Lorge, Dan W. Joyce, Niall Taylor, Alejo Nevado-Holgado, Andrea Cipriani, Andrey Kormilitzin",
                    "published": "2024-02-12",
                    "updated": "2024-02-12",
                    "primary_cat": "cs.CL",
                    "cats": [
                        "cs.CL"
                    ],
                    "main_content": "A number of studies have examined the use of machine learning (ML) techniques to directly identify treatment response (Perlis, 2013; Nie et al., 2018). Several of these re-use the Sequenced Treatment Alternatives to Relieve Depression (STAR*D) cohort dataset (Rush et al., 2006), where four successive treatment steps were administered, patients having the option of exiting the study if they experienced sufficient remission of symptoms after a given step. These ML studies identified predictive features including depression severity, the presence of co-morbid physical illness, psychosis, Post-Traumatic Stress Disorder (PTSD), anxiety disorder alongside minority ethnic heritage, work and poor social adjustment. Other factors identified in later studies include recurrence of depressive episodes, age, response to a first antidepressant, suicidality, educational attainment and occupational status (Kautzky et al., 2017, 2019). Another recent study uses age, gender, race, diagnostic codes (including both ICD-9 and ICD-10), current procedural terminology codes and medications with a tree-based algorithm (Lage et al., 2022). These studies achieved relatively good performance using traditional ML models such as random forests, GBDT (gradient-boosted decision trees) and logistic regression, however they use data from structured data fields in electronic health records (EHRs) and focus on delivering a binary TRD outcome. In addition to the above studies using structured data fields, a few studies have used terms extracted from narrative EHR notes, notably Perlis et al. (2012), who leverage regular expressions to extract terms identified by clinicians as important for prediction and compare the outcome of a model trained with billing data to a logistic regression model trained with concepts extracted from narrative notes, finding that the latter performs substantially better. Similarly, Sheu et al. (2023) use a variety of deep learning models with features from both categorical variables and terms extracted from narrative notes using regular expressions (pattern matching) as well as Longformer vectors of the clinical note history to predict treatment outcome. Thus, previous works leveraged either structured categorical data (e.g., registered comorbidity, sociodemographic factors etc.), overall scores on standardised questionnaires, terms extracted from notes using rule-based techniques such as regular expressions or, in the case of Sheu et al. (2023), a nonexplainable vectorised representation of the full patient history. An alternative is to use Natural Language Processing (NLP) models trained to extract information from the narrative clinical notes (Vaci et al., 2020; Kormilitzin et al., 2021). For example, recent work by Kulkarni et al. (2024) uses a BERT model for extracting suicidality and anhedonia in mental health records using ground-truth manually annotated EHR data. NLP models are both flexible and ecologically valid, and have been increasingly used successfully for various applications in psychiatry (Vaci et al., 2021; Senior et al., 2020) and clinical neuroscience in recent years (Le Glaz et al., 2021; Liu et al., 2022). The models can be trained either to directly predict a phenotype based on treatment outcome using text features as in Sheu et al. (2023) or, as in the current study, to extract relevant features suggestive of a phenotype or syndrome (e.g., in the case of DTD, a history of abuse, self-harm and suicidality) to present to clinicians for decision making. However, there are significant hurdles to obtaining training data, such as data scarcity and the high financial and time cost of manual annotations. 3 Difficult-to-treat depression Difficult-to-treat depression or DTD is a more recent framework than TRD which was developed following a number of issues becoming apparent with using the latter concept. As described in McAllister-Williams et al. (2020): \u2022 The current definition of TRD largely ignores psychotherapy and neurostimulation treatments \u2022 The definition does not allow for differential levels of success in response or remission \u2022 The phrasing could imply treatment failure is a property of the patient, rather than inadequacy of the intervention \u2022 The term implies a medical model which may exclude social and environmental factors previously shown to be significant predictors of treatment response For these reasons, the more inclusive and flexible concept of difficult-to-treat depression was put forward by an international consensus group and a number of factors were identified through literature review and expert consensus, grouped under the categories of PATIENT, ILLNESS and TREATMENT factors (McAllister-Williams et al., 2020). Given the novelty of the framework, there have been few attempts to operationalise it, with the exception of Costa et al. (2022) who partitioned patients from five specialist mental health National Health Service (NHS) Trusts according to a criterion encompassing both recurrence and resistance (at least 4 unsuccessful treatments including two antidepressant medications) and analysed correlations with environmental and clinical factors, confirming previous findings. In the current work, we use the concept of difficult-to-treat depression rather than treatment-resistant depression. 4 Large Language Models and synthetic data for medical and mental health research The recent development of large language models (LLMs) with substantially increased size and capabilities allowed great strides of improvement across domains such as question answering and text summarisation, including in the biomedical domain (Agrawal et al., 2022; Hu et al., 2023; Liu et al., 2023; Tang et al., 2023a; Taylor et al., 2023); becoming potentially able to perform information extraction on large quantities of data. However, privacy considerations prevent directly feeding highly-confidential patient data into LLM APIs such as OpenAI\u2019s chatGPT (Brown et al., 2020). In addition, while LLMs show impressive performance in applications related to text generation, they still fall short of specifically trained SOTA systems on biomedical NLP tasks (Ateia and Kruschwitz, 2023). A recent paper demonstrated that even when fine-tuned on target tasks, a LLaMA model, (Touvron et al., 2023) orders of magnitude bigger (7B vs 100M) and requiring substantially more compute power still underperforms compared to BERT-based discriminative models by up to 10% (Yang et al., 2023). For these reasons, a paradigm is emerging whereby a smaller local domain or task-specific model is fine-tuned on synthetic labelled data generated by an LLM, mitigating concerns of privacy as well as efficiency. This paradigm has been used successfully for diagnosis and mortality prediction by Kweon et al. (2023), who generated synthetic clinical notes using GPT3.5-turbo (Brown et al., 2020) and trained a domain specific LlaMA model, and for Named Entity Recognition and Relation Extraction by Tang et al. (2023b), who used prompts involving named entities and gene/disease relations from PubMed and fine-tuned BERT family models. Another recent work uses LLM-generated synthetic data to augment gold annotated data training a Flan-T5 model to perform multilabelling of sentences for social determinants of health (SDoH) such as housing, employment, transportation, parental status, relationship status and social support (Guevara et al., 2024). However, perhaps due to the small amount of added synthetic data (1800 synthetic sentences added to over 30k gold sentences), the synthetic addition does not lead to substantial or consistent improvement in performance (in fact it sometimes worsens it) and the performance training with synthetic data only is extremely poor (< 0.1 F1). In the domain of psychiatry, another study augmented training data with LLM-generated interviews and used traditional machine learning classifiers for binary classification of Post-Traumatic Disorder (PTSD) with a 10% increase in performance (Wu et al., 2023). The generated synthetic data has the potential to mimic important statistical properties and patterns of real data while avoiding the expensive and effortful process of obtaining large quantities of labelled data. Therefore, we intend to attempt training a DTD feature span extraction model exclusively on synthetic data obtained from LLMs. 5 Aims Previous studies used machine learning techniques to predict treatment response or identify treatmentresistant depression. In contrast, the more comprehensive concept of difficult-to-treat depression allows us to leverage a wider variety of factors \u2013 rather than relying on a strict \u2018two-course\u2019 acutephase response to pharmacological interventions \u2013 that potentially enables early detection and more personalised care that addresses reasons for suboptimal treatment response. Recent research has indeed been focusing on early detection and linking prognostic factors with a continuum of treatment response (Lage et al., 2022; Sheu et al., 2023). Furthermore, previous works mostly focused on sentence classification rather than the more complex process of span extraction. Contrary to multilabelling, span extraction presents clinicians with the specific part of the text which is linked to a particular label, allowing them to focus more efficiently on relevant information. Finally, to our knowledge no previous study successfully trained a model exclusively on synthetic data for the purpose of extracting prognostic factors. Success, even partial, would represent an extremely important step in developing AI applications for healthcare, given the known issues of data scarcity and manual labelling costs. Therefore, the present paper aims to: \u2022 Add to the recent body of works demonstrating the utility of leveraging synthetic data for decision-supporting information extraction in biomedical domains \u2022 Introduce an annotation scheme (abductive annotation) that leverages domain experts on narrative clinical notes to facilitate explicit extraction of PATIENT, ILLNESS and TREATMENT related-factors for DTD \u2022 Build a curated synthetic dataset of annotated narrative clinical notes which can be freely shared with the research community \u2022 Build and train a model which extracts spans of text and labels them with the relevant factor with the goal of downstream clinician decision guidance 1 6 The DTD Phenotype In consultation with a clinician expert, we operationalise the prognostic factors originally reported in McAllister-Williams et al. (2020) into the annotation schema presented in Table 1. There are several reasons for the changes made. First, we aim to develop a schema which could potentially be extended to other conditions or strata of populations (e.g. we created general categories for physical and mental comorbidities). Second, because we leverage the use of a large language model for generating and annotating data, we endeavour to create labels which are semantically transparent enough 1The code and synthetic data are available at https:// github.com/isabellelorge/dtd that they are likely to be understood by the model and yield better annotation accuracy. Finally, When a clinician interprets the data contained in a patient\u2019s EHR (e.g., to establish a diagnosis) they will employ abductive (rather than inductive or deductive) reasoning (Douven, 2021; Rapezzi et al., 2005; Altable, 2012; Reggia et al., 1985) meaning they will seek evidence to support or refute a number of competing hypotheses (e.g., differential diagnoses). Consequently, we wish to be able to extract both positive and negative evidence in favour or against a designation of difficultto-treat depression in order to provide clinicians with a comprehensive picture of the patient\u2019s current presentation, illness and treatment history for downstream decision making. 7 Synthetic dataset In the first instance, we prompt ChatGPT (GPT3.5turbo-0613) through its Python API to generate and annotate a dataset of 1000 clinical notes with labels from our annotation schema (e.g., [PATIENT_FACTOR(POSITIVE):older_age]). We used a temperature of 1.2 and default values for remaining parameters. Experimenting with various prompts, we find that the best prompts balance the need to provide examples to correct recurrent mistakes in model\u2019s behaviour against the tendency for the model to frequently repeat given examples, even with a high temperature parameter to encourage diversity in token generation. We thus add examples as needed to correct various errors (tendency to not label age, to output only positive labels, to group all labels after the sentence rather than after the relevant span, etc.). An example generated annotated note can be found in Appendix A and the final prompt used can be found in Appendix B. We notice from manual inspection of examples that the output is relatively accurate, though the model does output errors, meaning that the labels are noisy and should be considered as a silver rather than gold standard. We use a combination of regular expressions and heuristics to extract labels from each sentence, discarding labels which do not fit our schema (in a small proportion of notes the model hallucinates new factors or uses a different formatting). We first experiment with a syntactic heuristic to extract shorter spans (labelling the closest finite verb phrase with each label) but eventually settle on a simpler heuristic of labelling all text beFactor Orig. New NO_ANNOTATION 10708 35884 family_member_mental_disorder_POS 1188 2337 childhood_abuse_POS 1052 2116 non_adherence_POS 954 1919 side_effects_POS 883 1768 recurrent_episodes_POS 876 1774 multiple_antidepressants_POS 862 1744 multiple_psychotherapies_POS 860 1726 physical_comorbidity_POS 824 1673 long_illness_duration_POS 796 1603 severe_illness_POS 732 1447 anhedonia_POS 731 1449 suicidality_POS 706 1396 antidepressant_dosage_increase_POS 705 1420 multiple_hospitalizations_POS 668 1345 older_age_POS 545 1138 mental_comorbidity_POS 473 941 improvement_POS 403 786 substance_abuse_POS 400 787 illness_early_onset_POS 382 751 substance_abuse_NEG 314 787 multiple_hospitalizations_NEG 247 1375 suicidality_NEG 160 1178 older_age_NEG 140 960 physical_comorbidity_NEG 135 1133 abuse_POS 94 187 improvement_NEG 78 721 mental_comorbidity_NEG 64 680 non_adherence_NEG 60 709 abuse_NEG 53 690 childhood_abuse_NEG 42 805 family_member_mental_disorder_NEG 34 996 side_effects_NEG 29 701 antidepressant_dosage_increase_NEG 18 506 multiple_psychotherapies_NEG 16 746 multiple_antidepressants_NEG 11 587 long_illness_duration_NEG 7 567 severe_illness_NEG 6 488 recurrent_episodes_NEG 6 718 illness_early_onset_NEG 5 382 anhedonia_NEG 4 541 Table 1: Annotation schema labels and span counts for original and new (final) datasets. We shorten the polarity words in the table for space considerations (the labels used in prompts and GPT3.5-turbo outputs use full words, e.g., [PATIENT_FACTOR(POSITIVE):older_age]). fore each label up to sentence boundary (e.g., for \u2019XXXXX [label_X] YYYYY [label_Y]\u2019, we extract XXXXX as span for label X and YYYYY for label Y). This is because early prompt attempts showed that when prompting chatGPT for span boundaries (e.g., \u2019YYYYY{XXX} [label_X]\u2019), the boundaries obtained were very error-prone and unreliable, while a strategy of simply asking the model to insert the label after each relevant span yielded much better results. From the span counts in Table 1, it can be seen that the label distribution is heavily skewed, with a very strong bias in favour of positive factors against negative factors. We believe this would reflect clinicians\u2019 annotations, as positive evidence is much more likely to be expressed and noticed than negative evidence and arguably contributes more heavily to final decision making. However, to reduce data imbalance we prompt the model for another 1000 notes with the same prompt and a third set of 1000 notes with a prompt asking exclusively for negative labels. The final dataset thus contains 3000 notes which yield 75094 sentences. The updated factor counts of the final dataset can be seen in Table 1 and the negative prompt can be found in Appendix C. We explore the word distribution for each factor to try and get a sense of the synthetic dataset\u2019s diversity and/or repetitiveness. To achieve this, we extract words from labelled spans for each label and calculate their TF-IDF score, defined as: tfid f_score = (wl/Wl)/ log(w/wl + 1) (1) Where wl is the frequency of a given word for a given label, Wl is the total number of words for the label and w is the total frequency for the word across labels. A sample of labels and their 10 highest scoring words can be seen in Table 2, along with their prevalence (number of occurrences/number of label spans). Interestingly, while there is a tendency for the model to repeat examples given in the prompt, the extent of this behaviour varies substantially depending on specific examples. Indeed, while our prompt example for family_member_mental_disorder_POSITIVE mentions anxiety, the most frequent disorder which appears for this label is bipolar disorder (48% of spans), whereas an overwhelming 80% of spans labelled with mental_comorbidity_POSITIVE do include the word \u2018anxiety\u2019 without having been prompted with it. Similarly, our prompt example for childhood_abuse_POSITIVE mentions motherly abuse but only 19% of spans with this label contain the word \u2018mother\u2019, superseded by 34% of spans mentioning the word \u2018father\u2019. The physical_comorbidity_POSITIVE factor is more evenly distributed than mental_ comorbidity_POSITIVE, with most frequent conditions split between hypertension, diabetes and fibromyalgia. The model displays strong biases which are not driven by prompt examples, as evidenced by 70% of substance_abuse_POSITIVE spans mentioning the word \u2018alcohol\u2019. We hypothesise that the above biases result from the distribution of the model\u2019s training data. We also note that spans from some labels have a high probability of mentioning all label words explicitly: abuse, both NEGATIVE (91%) and POSITIVE (80%), side_effects, both POSITIVE (88%) and NEGATIVE (84%), improvement, both POSITIVE (84%) and NEGATIVE (73%), substance_abuse_NEGATIVE (84%) and childhood_abuse, both NEGATIVE (76%) and POSITIVE (75%). There is a tendency for the model to mention label words explicitly more often for negative than positive labels, probably due to higher variety for spans providing positive evidence. Only 10% of spans for physical_comorbidity_POSITIVE and mental_comorbidity_POSITIVE mention label words explicitly, suggesting that the model still relies on its training data for phrasing and does not systematically repeat prompt labels. The numbers for all labels can be seen in Figure 3 in Appendix D. Finally, to assess the similarity in word overlap between pairs of spans for a given label we calculate the Jaccard similarity between lemmatized words of each pair of spans within a label. The similarities range from 0.02 for spans with no label to 0.35 for substance_abuse_NEGATIVE. The full numbers for all labels can be seen in Figure 4 in Appendix D. 8 Real-World clinical data To evaluate the performance of the developed model on real clinical data, we utilised a sample of de-identified secondary mental health records from the Oxford Health NHS Foundation Trust, which provides mental healthcare services to approximately 1.2 million individuals across all ages in Oxfordshire and Buckinghamshire in England. Access to the de-identified data was obtained through the Clinical Record Interactive Search (CRIS) system powered by Akrivia Health, which enables searching and extraction of de-identified clinical case notes across 17 National Health Service Mental Health Trusts in England. For this study, we sampled clinical summaries for 100 adult patients over 18 years old, randomly selected from 19,921 patients with confirmed diagnosis of depression (ICD-10 codes F32 and F33) readily available from structured data fields in CRIS. Access to and use of de-identified patient records from the CRIS platform has been granted exemption by the NHS Health Research Authority for research reuse of routinely collected clinical data. Factor Words % family member mental disorder family bipolar history disorder mental mother illness diagnosed reports sister 0.72 0.48 0.87 0.65 0.68 0.44 0.65 0.39 0.41 0.16 childhood abuse childhood abuse emotional neglect father history physical experienced discloses mother 0.83 0.95 0.56 0.30 0.34 0.46 0.35 0.22 0.11 0.19 physical comorbidity hypertension physical diabetes comorbidities pain chronic fibromyalgia medical comorbidity history 0.38 0.62 0.29 0.31 0.19 0.22 0.14 0.25 0.24 0.41 mental comorbidity anxiety generalized disorder comorbid also mental panic diagnosis diagnosed comorbidity 0.80 0.47 0.77 0.28 0.31 0.23 0.08 0.14 0.16 0.15 substance abuse alcohol substance abuse history use mechanism patient specifically cope also 0.70 0.82 0.85 0.53 0.20 0.10 0.34 0.17 0.10 0.23 Table 2: Sample factors with their 10 highest TFIDF scoring words and their % or prevalence (n occurrences/n spans). The project was reviewed and approved by the Oversight Committee of the Oxford Health NHS Foundation Trust and the Research and Development Team. 9 Task We extract character indexes of start, end and corresponding label for labelled spans in each sentence and remove label text from sentence text. There are 41 labels (positive and negative polarity label for each factor and a \u2019NO_ANNOTATION\u2019 label). 10 Models Figure 1: Span-level model architecture. We experiment with a variety of models trading off complexity and granularity. 10.1 Token-level The first model simply leverages a BERT (base, cased) layer for classification at the token level, thus spans are represented as contiguous series of tokens labelled with a specific label. We use one linear layer and no IOB flags (given that each span starts where the previous span ends). The output of the classification layer for each token is fed to a softmax activation layer which outputs probabilities for each label. This is similar to the traditional technique used for Named Entity Recognition (NER). We use a custom Pytorch class and Huggingface\u2019s transformers library (Wolf et al., 2019) implementation for the BERT layer. 10.2 Span-level Given the longer lengths of our spans compared to traditional NER tasks, we also experiment with a model inspired from Question Answering (QA) systems, where the model does not predict a label for each token in the sequence but instead predicts a \u2018start\u2019 and \u2018end\u2019 position. However, traditional Question Answering systems are generally limited to one response span, restricting the scope of the classification task, while in our case there can potentially be any number of spans within a given sequence, each of which could be of any length, expanding the training search space exponentially. To solve this issue, we follow Hu et al. (2019) and take inspiration from computer vision by using a variant of Non-Maximum Suppression (NMS), whereby non-overlapping outputs are selected in decreasing order of confidence. To achieve this, a separate classifier is trained to predict the number (N) of spans within a sequence from the sequence output of a BERT (base, cased) layer, and subsequently the top N non-overlapping start/end pairs with the highest combined probabilities are selected. We find that given start and end of sentences consistently have very high probabilities for our dataset (since spans are full sentences in cases where there is a single factor in the sentence), a greedy approach on combined start/end probabilities as used by Hu et al. (2019) does not work. Instead, we predict the number (N) of spans and separately select the top N starts and N ends with highest probabilities, which we order by token number so that we select non-overlapping start/end combinations in order by taking the closest end for each start (e.g., if 2 predicted spans with top starts [1, 10] and top ends [20, 10], the indexes are ordered so that the first span is not [1, 20] but [1, 10], and the second span is [10, 20]). The model goes through each selected start/end pair and uses a linear layer span classifier to label the relevant tokens from the sequence. For training (given possible inconsistencies between true and predicted number of spans), the output of the span classifier is passed through a softmax layer and all predicted spans are max pooled into a single vector to match the ground truth multilabel one-hot encoded vector for the full sentence (soft selection). At inference time, the indices of the maximum probability for each predicted span are taken as labels (hard selection). We also experiment with a version of the model where factors are merged together across polarities and a separate classifier is trained to predict negative polarity from a concatenation of the BERT sequence output and predicted labels 2. As for the token-level model, we implement a custom class and loss function in Pytorch and leverage Huggingface\u2019s implementation of the BERT layer. The architecture of the 2The results are substantially worse and in the interest of space considerations we do not report them. span-level model can be seen in Figure 1. 10.3 Sentence-level Finally, we also model the task in a simplified way as a multilabel sentence classification task. For this, we again leverage the sequence output of a BERT (base, cased) layer which we feed to a linear classifier layer. The output of the classifier is then passed through a sigmoid activation layer and labels with probabilities above a 0.5 threshold are taken as predictions. In this case the start and end positions of spans for the predicted labels are unknown. Again, we use Huggingface\u2019s BERT layer implementation and a custom Pytorch class for classification with one linear layer. 11 Training We split the synthetic dataset into train, development and test sets with proportions 0.8, 0.1 and 0.1. We use a batch size of 16, learning rate of 3e-05, dropout rate of 0.1 and weight decay of 0.001. We experiment with different forms of class weights to mitigate the imbalance in labels. For the span model, we find the model performs better with a logarithmically scaled class weighted loss, whereas there is no difference for the token level model, and the sentence-level model performs better without class weights. We train until convergence, 4 epochs for span, 5 epochs for the token model and 7 epochs for the sentence-level model. 12 Experiments 12.1 Synthetic data We first test the model on a held-out test set of synthetic data. 12.1.1 Results The results on the synthetic test set for the three models can be seen in table 3 and a log-scaled confusion matrix can be seen in Figure 2 3. Given the imbalance in labels, we present precision, recall and F1 for each class as well as F1 averaged across classes, with macro averaged F1 being the accepted standard metric in similar tasks. The three models 3While we used simplified terms in our labels to ensure the best LLM output after prompting trial and error, the appropriate medical terms should be used in the final output of the model for the following: episodes severity for severe illness, episode remission for improvement, medical comorbidity for physical comorbidity, substance use for substance abuse, adequate dosage for antidepressant dosage increase and adherence medication for non-adherence. perform fairly well. We find our custom span-level model outperforms the simpler, token-level model by a large margin (0.65 vs 0.57). To our surprise, we also find that our span level model slightly outperforms the sentence-level classification model, despite the added difficulty of having to predict the correct start and end of spans in order to be able to accurately predict labels. The models tend to perform substantially better on the positive classes. The sentence and span level models perform similarly across factors, each claiming best performance for an approximately equal number of factors, whereas the token-level model only outperforms other models for the abuse_POSITIVE class. There appears to be little difference between the performance for the different factor domains (PATIENT, ILLNESS and TREATMENT). We notice that the model struggles with the category \u2018older age\u2019, which points to a well-known shortcoming of language models (along with negation) regarding ability to count and evaluate quantities. The confusion matrix in Figure 2 shows how the category gets confused with most other classes (lit up vertical line). The worst performing positive classes is abuse_POSITIVE (most likely due to scarcity of training examples) and worst performing negative class is improvement_NEGATIVE. Examination of synthetic data reveals GPT3.5 particularly struggled with correctly labelling negative examples of improvement, which led to many being in fact positive examples (e.g., There has been improvement in symptoms [ILLNESS_FACTOR:improvement(NEGATIVE)]). This seems in fact to be a side-effect of GPT3.5\u2019s \u2018common sense\u2019, indeed all other negative classes indicate a positive outlook (e.g., no history of abuse or disorder, no substance use, no hospitalisations, etc.), thus when prompted for negative examples the LLM produced sentences coherent with the rest of the note, i.e., sentences mentioning improvement. The secondary lit up diagonal on the left of the confusion matrix confirms that the model struggles with negation, with a tendency to predict the positive counterpart for negative classes and vice versa (right-hand side diagonal). 12.2 Clinical data While performance of the span extraction model is well above chance, it still appears low given that we are testing the model within distribution (i.e., on the same synthetic data it was trained with) with the exFigure 2: Log-scaled confusion matrix (synthetic data). pectation of a drop in performance when taken outof-distribution (i.e., to EHR clinical data). Grounds for this concern are confirmed by a first test on a test set of 482 sentences from the above mentioned electronic health records annotated by a consultant psychiatrist for our target features, which yields quite a low overall performance (0.30 F1). This prompts us to further examine the synthetic training data and to perform in-depth error analysis to understand the reasons underlying the low performance both on the synthetic and on the clinical test sets. The analysis reveals the following issues: \u2022 Many spans are mislabelled across labels \u2022 Many spans tend to be repetitive/reuse the same words for a given label (e.g., \u2018family\u2019 for family disorder, \u2018abuse\u2019 for substance abuse, etc.) \u2022 The style and format of the synthetic notes (articulate, using possessives, articles, pronouns, auxiliary verbs, punctuation and connectors consistently) differs substantially from that of the real clinical data (telegraphic, with frequent ellipsis of articles, pronouns, verbs and connectors, deidentification placeholders, missing spaces and punctuation, inconsistent casing, etc.) which leads to lack of robustness in the model predictions (i.e., predictions changing when a pronoun is changed, period is removed, etc.) \u2022 In up to 30% of cases (from manually examining 100 spans), spans with negative labels are in fact positive spans, which means 1) the model is confused between negative and positive factors and fails to properly learn them and 2) many \u2018errors\u2019 in the synthetic test set are in fact correct predictions with incorrect ground truth labels To address these challenges, we thus perform the following changes: \u2022 We use heuristics to remove the bulk of wrongly labelled spans (by removing most spans for a given label which contain keywords from other labels, leaving a few to avoid overfitting) \u2022 For each label, we upsample the \u2018diverse\u2019 spans (i.e., spans that do not mention label words explicitly, e.g., spans that do include \u2018family\u2019 or \u2018disorder\u2019 for family disorder, or \u2018sustance\u2018 and \u2018abuse\u2019 for substance abuse) \u2022 We add \u2018noise\u2019 to the data by randomly removing possessives, articles, pronouns, auxiliary verbs and punctuation and replacing some pronouns with deidentification placeholder strings (\u201cFFFFF\u201d and \u201cXXXXX\u201d) that are used to pseudonymise our research EHR data \u2022 We switch to BERT-base-uncased to avoid casing issues \u2022 We remove the older age category (which is available as structured data in an EHR) and merge childhood abuse and abuse classes into a single abuse category (due to the scarcity of the latter class) \u2022 We remove the sentences with no labels from the original dataset and specifically prompt GPT3.5-turbo for 3000 clinical sentences which do not mention our target features. This is done both because the original unlabelled sentences had a high amount of noise (the plan would mention prognostic/risk factors or features but was not annotated by the language model) and to ensure more diversity in unlabelled sentences. The resulting dataset contains 55924 sentences. We retrain our model on this new synthetic data and obtain an average F1 of 0.75 on the synthetic test set (keeping in mind that since a percentage of test set examples are wrongly labelled, this does not reflect the real performance of the model). We then re-test the model on the annotated EHR sentences. 12.2.1 Results The results on the clinical data can be seen in Table 4. The overall performance is 0.60 F1, with manual perturbation analysis indicating that the model is much more robust to changes in style or format (e.g., removing pronouns or punctuation). The performance varies widely across classes, with some classes performing very well (0.95 F1 for recurrent episodes POSITIVE) while others show poor performance (0.19 F1 for non-adherence NEGATIVE). Performance for negative classes is again unsurprisingly worse than for positive classes. In general, recall is higher than precision, with a tendency for the model to overpredict factors. This is unsuprising given the high overlap in topic and broad range of our factors. Indeed, negative classes such as negative multiple antidepressants (e.g., She takes antidepressant X), negative anhedonia (e.g., She enjoys hobbies like painting and reading or negative abuse e.g., She likes spending time with her family might be virtually indistinguishable from NO_ANNOTATION spans, and arguably most sentences could be said to contain a span within our target factors if we include negative classes. We come back to this issue in the Discussion. To remedy the model\u2019s oversensitivity, we can increase the confidence threshold for predicting factors, that is only outputting factor predictions above 0.5 probability and no label otherwise. This also has the advantage that it ensures any output predictions are robust (i.e., made with high confidence rather than being \u2018lucky guesses\u2019), which is particularly desirable in medical settings. Finally, it increases recall of the NO_ANNOTATION class to 0.90. When this threshold is increased to 0.5, four high confidence classes emerge (abuse POSITIVE, family member mental disorder POSITIVE, severe illness POSITIVE and suicidality POSITIVE) which can be confidently predicted with 0.85 average F1 and 0.95 precision (see Table 5.) A significant factor contributing to the model\u2019s lower performance is the model confusing positive and negative classes (partially due to noise in the synthetic training data as mentioned previously). This is demonstrated by collapsing predictions across polarities, which increases average F1 to 0.70 (see Table 6). Given the goal of the model is to present clinicians with evidence from extracted spans for their consideration, the nonpolarised model could also have clinical utility. 13 Example extractions Here we show some examples of successful span extractions in synthetic test sentences with (start, end, label) for each extracted span: \u2022 Treatment History: patient already tried multiple antidepressant medications from different classes including SSRIs and SNRIs but did not experience significant improvement. spans: (0, 46, multiple antidepressants POSITIVE); (47, 74, improvement NEGATIVE) \u2022 XXXXX has been inpatient twice for mental health treatment due to severity of illness with recurrent episodes of major depressive disorder occurring approximately every 3-4 months. spans: (0, 81, multiple hospitalizations POSITIVE); (82, 175, recurrent episodes POSITIVE \u2022 FFFFF reports no family history of mental disorders and denies any history of abuse spans: (0, 51, family member mental disorder NEGATIVE); (52, 83, abuse NEGATIVE) \u2022 patient reports no significant physical comorbidities but mentions mild anxiety symptoms spans: (0, 53, physical comorbidity NEGATIVE); (54, 88, mental comorbidity POSITIVE) \u2022 has been on citalopram, fluoxetine and sertraline spans: (0, 57, multiple antidepressants POSITIVE) \u2022 patient recalls being severely bullied at school spans: (0, 48, abuse POSITIVE) \u2022 she battles with heroin addiction spans: (0, 33, substance abuse POSITIVE) \u2022 he denies intent to end his own life spans: (0, 36, suicidality NEGATIVE) \u2022 she did not suffer any neglect as a child spans: (0, 41, abuse NEGATIVE) \u2022 he talked about how his friend was bullied spans: (0, 42, NO ANNOTATION) \u2022 her brother was diagnosed with ptsd spans: (0, 35, family member mental disorder POSITIVE) 14 Discussion In the synthetic test dataset, we find that our custom span-level model which uses a variant of NonMaximum Suppression (NMS) outperforms the simpler token-level model which is standardly used for span extraction. Additionally, we find that the sentence-level model performs slightly under the span-level model overall. We hypothesise that this might be because the model learns to more specifically map labels with the relevant tokens, rather than relying on fuzzier learning over full sentences. Performance on positive classes is significantly higher than for negative classes. This is due to a Sentence-level model Span-level model Token-level model Class Precision Recall F1 Score Precision Recall F1 Score Precision Recall F1 Score older age POSITIVE 0.46 0.57 0.51 0.42 0.83 0.56 0.5 0.57 0.54 family member mental disorder POSITIVE 0.75 0.9 0.82 0.74 0.9 0.81 0.7 0.89 0.78 abuse POSITIVE 0.6 0.25 0.35 0.69 0.38 0.49 0.84 0.4 0.54 childhood abuse POSITIVE 0.77 0.87 0.81 0.73 0.89 0.8 0.78 0.85 0.81 long illness duration POSITIVE 0.72 0.76 0.74 0.79 0.64 0.7 0.7 0.69 0.69 severe illness POSITIVE 0.45 0.33 0.38 0.47 0.39 0.43 0.34 0.22 0.26 suicidality POSITIVE 0.61 0.64 0.63 0.69 0.61 0.65 0.48 0.63 0.55 multiple hospitalizations POSITIVE 0.8 0.84 0.82 0.76 0.88 0.81 0.66 0.75 0.7 recurrent episodes POSITIVE 0.63 0.62 0.63 0.65 0.73 0.69 0.55 0.65 0.59 improvement POSITIVE 0.58 0.64 0.61 0.55 0.57 0.56 0.47 0.58 0.52 physical comorbidity POSITIVE 0.72 0.76 0.74 0.64 0.83 0.73 0.72 0.8 0.76 mental comorbidity POSITIVE 0.81 0.75 0.78 0.78 0.72 0.74 0.81 0.72 0.76 substance abuse POSITIVE 0.74 0.64 0.68 0.71 0.83 0.77 0.67 0.78 0.72 anhedonia POSITIVE 0.58 0.67 0.62 0.62 0.8 0.7 0.59 0.7 0.64 illness early onset POSITIVE 0.65 0.63 0.64 0.67 0.75 0.7 0.61 0.55 0.58 multiple antidepressants POSITIVE 0.82 0.78 0.8 0.79 0.83 0.81 0.7 0.79 0.74 antidepressant dosage increase POSITIVE 0.73 0.86 0.79 0.82 0.78 0.8 0.68 0.65 0.66 multiple psychotherapies POSITIVE 0.64 0.75 0.69 0.73 0.72 0.72 0.66 0.8 0.72 side effects POSITIVE 0.81 0.71 0.76 0.74 0.74 0.74 0.67 0.68 0.68 non adherence POSITIVE 0.75 0.66 0.7 0.76 0.77 0.76 0.68 0.68 0.68 older age NEGATIVE 0.44 0.55 0.49 0.58 0.41 0.48 0.49 0.39 0.43 family member mental disorder NEGATIVE 0.71 0.62 0.66 0.72 0.71 0.72 0.62 0.5 0.55 abuse NEGATIVE 0.54 0.76 0.63 0.6 0.8 0.69 0.55 0.7 0.62 childhood abuse NEGATIVE 0.73 0.74 0.74 0.64 0.69 0.66 0.53 0.49 0.51 long illness duration NEGATIVE 0.49 0.4 0.44 0.58 0.43 0.5 0.42 0.35 0.38 severe illness NEGATIVE 0.37 0.31 0.34 0.62 0.41 0.49 0.31 0.41 0.35 suicidality NEGATIVE 0.68 0.85 0.75 0.61 0.77 0.68 0.64 0.71 0.67 multiple hospitalizations NEGATIVE 0.76 0.83 0.8 0.77 0.79 0.78 0.72 0.68 0.7 recurrent episodes NEGATIVE 0.75 0.48 0.59 0.76 0.49 0.6 0.58 0.39 0.46 improvement NEGATIVE 0.42 0.42 0.42 0.35 0.49 0.4 0.34 0.26 0.29 physical comorbidity NEGATIVE 0.66 0.71 0.68 0.67 0.68 0.68 0.59 0.61 0.6 mental comorbidity NEGATIVE 0.65 0.68 0.67 0.72 0.65 0.68 0.5 0.56 0.53 substance abuse NEGATIVE 0.7 0.91 0.79 0.69 0.89 0.78 0.62 0.75 0.68 anhedonia NEGATIVE 0.55 0.3 0.39 0.61 0.34 0.44 0.56 0.3 0.39 illness early onset NEGATIVE 0.7 0.57 0.63 0.75 0.53 0.62 0.53 0.5 0.51 multiple antidepressants NEGATIVE 0.32 0.2 0.25 0.59 0.37 0.45 0.37 0.3 0.33 antidepressant dosage increase NEGATIVE 0.56 0.57 0.56 0.54 0.59 0.56 0.53 0.41 0.46 multiple psychotherapies NEGATIVE 0.58 0.52 0.55 0.63 0.37 0.47 0.47 0.2 0.28 side effects NEGATIVE 0.58 0.67 0.62 0.58 0.64 0.61 0.56 0.37 0.44 non adherence NEGATIVE 0.39 0.43 0.41 0.37 0.44 0.4 0.33 0.42 0.37 NO ANNOTATION 0.81 0.79 0.8 0.84 0.77 0.8 0.8 0.81 0.81 POSITIVE 0.68 0.68 0.68 0.69 0.73 0.70 0.64 0.67 0.64 NEGATIVE 0.59 0.59 0.58 0.63 0.58 0.59 0.53 0.49 0.50 PATIENT 0.63 0.66 0.63 0.64 0.70 0.65 0.63 0.59 0.59 ILLNESS 0.64 0.63 0.63 0.66 0.64 0.64 0.57 0.59 0.57 TREATMENT 0.62 0.62 0.61 0.65 0.62 0.63 0.58 0.52 0.54 All 0.63 0.63 0.63 0.66 0.65 0.65 0.58 0.57 0.57 Table 3: Precision, recall and macro averaged F1 for each model and factor (synthetic data). best in bold Class Precision Recall F1 Score N NO ANNOTATION 0.59 0.34 0.43 99 anhedonia POSITIVE 0.76 0.59 0.67 27 antidepressant dosage increase POSITIVE 0.31 0.83 0.45 12 abuse POSITIVE 0.94 0.80 0.86 20 family member mental disorder POSITIVE 0.61 0.92 0.73 12 illness early onset POSITIVE 0.50 1.00 0.67 8 improvement POSITIVE 0.68 0.42 0.52 31 long illness duration POSITIVE 1.00 0.80 0.89 5 mental comorbidity POSITIVE 0.43 0.38 0.40 8 physical comorbidity POSITIVE 0.50 0.67 0.57 9 multiple antidepressants POSITIVE 0.75 0.62 0.68 29 multiple psychotherapies POSITIVE 0.38 0.38 0.38 13 non adherence POSITIVE 0.50 0.19 0.27 16 recurrent episodes POSITIVE 1.00 0.90 0.95 10 severe illness POSITIVE 0.55 1.00 0.71 6 side effects POSITIVE 0.79 0.44 0.57 34 substance abuse POSITIVE 0.71 0.62 0.67 13 suicidality POSITIVE 0.80 0.75 0.77 32 antidepressant dosage increase NEGATIVE 0.50 0.56 0.53 16 improvement NEGATIVE 0.60 0.16 0.25 19 multiple antidepressants NEGATIVE 0.20 1.00 0.33 3 multiple psychotherapies NEGATIVE 0.51 0.93 0.66 28 multiple hospitalizations NEGATIVE 0.75 1.00 0.86 3 non adherence NEGATIVE 0.12 0.40 0.19 5 severe illness NEGATIVE 0.64 1.00 0.78 7 side effects NEGATIVE 0.65 0.68 0.67 19 substance abuse NEGATIVE 0.33 0.33 0.33 3 suicidality NEGATIVE 0.78 0.78 0.78 9 POSITIVE 0.66 0.67 0.63 285 NEGATIVE 0.51 0.68 0.54 98 All 0.60 0.66 0.60 482 Table 4: Precision, recall and macro averaged F1 for each factor (clinical data). Classes with n <2 excluded. Class Precision Recall F1 Score abuse POSITIVE 1.00 0.80 0.89 family member mental disorder POSITIVE 0.85 0.92 0.88 severe illness POSITIVE 1.00 0.67 0.80 suicidality POSITIVE 0.96 0.75 0.84 All 0.95 0.78 0.85 Table 5: Precision, recall and macro averaged F1 for each factor (clinical data -high confidence classes with 0.5 confidence threshold). Class Precision Recall F1 Score NO ANNOTATION 0.59 0.34 0.43 anhedonia 0.75 0.86 0.80 antidepressant dosage increase 0.48 0.86 0.62 abuse 0.95 0.90 0.93 family member mental disorder 0.61 0.92 0.73 illness early onset 0.33 1.00 0.50 improvement 0.88 0.42 0.57 long illness duration 0.67 0.57 0.62 mental comorbidity 0.38 0.38 0.38 physical comorbidity 0.50 0.80 0.62 multiple antidepressants 0.79 0.97 0.87 multiple psychotherapies 0.64 1.00 0.78 multiple hospitalisations 0.75 0.75 0.75 non adherence 0.55 0.57 0.56 recurrent episodes 0.92 1.00 0.96 severe illness 0.59 1.00 0.74 side effects 0.87 0.64 0.74 substance abuse 0.88 0.79 0.83 suicidality 0.87 0.83 0.85 All 0.68 0.77 0.70 Table 6: Precision, recall and macro averaged F1 for each factor (clinical data -non-polarised). number of reasons. First, despite our additional prompting for negative factors exclusively, there is still an imbalance with more positive than negative labels. Second, it is a well-known fact that language models struggle with negation (Ettinger, 2020). Finally, negation will often be present in the sentence but not necessarily in each negated span, even if the scope of the negation encompasses the span, e.g., The patient denies suicidality [suicidality NEGATIVE] and substance abuse [substance abuse NEGATIVE], where the text of the second span does not contain an explicit negation. While each span\u2019s tokens contextual embeddings should have some signal which indicates there is a negation somewhere in the sentence, it might not be strong enough compared to classifying a span which contains an explicit negation token. While average F1 on real data is 0.60, our model trained exclusively on synthetic data already has practical clinical use, as it can be used out of the box with a confidence threshold of 0.5 to extract abuse, family disorder, severe illness and suicidality with 0.85 F1 and 0.95 precision, a performance comparable to Kulkarni et al. (2024), who used real data annotated manually in a costly and timeconsuming way to train a model to extract two clinical factors (suicidality and anhedonia). This is despite the high syntactic and semantic variability among spans expressing these factors. For example, our model is able to identify spans mentioning events as varied as emotional neglect, violence or bullying as abuse, and a wide range of combination of family member and various conditions (brother, aunt, schizophrenia, bipolar disorder, etc.) as a family history of mental disorder. Obtaining such high performance with a model trained on synthetic data only shows this is a promising direction of research for cost-efficient AI applications in healthcare. Indeed, the cost of producing the synthetic training data used in this study was under \u00a310, versus the thousands of pounds required for compensating expert annotators. We believe there are several reasons the model fails to achieve higher average performance across all factors. First, many classes are very close to one another, for example long duration and early onset, classes which mention antidepressants, physical comorbidities and side effects, etc. It is no coincidence that the model performs best on classes which are most distinctive (abuse, family disorder, suicidality). Secondly, many classes are highly subjective, e.g., early onset (how early?), long duration (how long?), substance abuse (how much consumption?) and spans are often ambivalent (e.g., \u2018some improvement then worsening\u2019; \u2018some side effects then none\u2019, etc.) Finally, many negative classes are not well defined or consistent, e.g, negative multiple psychotherapies (mentions only one therapy? any span mentioning therapy?), negative multiple antidepressants (any span mentioning a single antidepressant?), negative multiple hospitalisations? (having been hospitalised once? Never?), negative anhedonia (any span mentioning subject performing activities?), negative severe illness (moderate illness? mild symptoms?), etc. In view of these challenges, it is likely that training a model to extract a wide range of factors requires some real annotated clinical data, however impressively high performance can already be achieved on a subset of factors by exclusively training on synthetic data. 15 Future work The paradigm we used could be extended and scaled to other phenotypes with a different set of risk/prognostic factors or clinical features in the future. Future research could also investigate whether using a model which has been domain pretrained on mental health data (such as MentalBERT, (Ji et al., 2021) would improve performance. Works such as (Guevara et al., 2024) suggest that a sequence-to-sequence model such as T5 could achieve even better performance than a BERT-based classifier model. Using GPT4 instead of GPT3.5 could help generate synthetic data with reduced noise and more accurate labelling of negative factors. Finally, an optimal weighting scheme for the extracted factors which would best allow identification of difficult-to-treat depression could be developed in consultation with clinicians. 16 Conclusion The goal of this study was to train a model to extract spans which contain factors associated with the syndrome of difficult-to-treat depression. To achieve this, we generated annotated synthetic clinical notes with both positive and negative factors of interest using a Large Language Model (GPT3.5turbo) and subsequently trained various BERTbased classifier models (sentence, token and span level) to extract factors. We show it is possible to obtain good performance on real clinical data on a set of as many of 20 different factors, and high performance on a subset of clinically-relevant factors by training exclusively on LLM-generated synthetic data. 17 Acknowledgements I.L., A.K. and D.W.J. were supported in part by the NIHR AI Award for Health and Social Care (AI-AWARD02183), A.K. by a research grant from GlaxoSmithKline. The views expressed are those of the authors and not necessarily those of the UK National Health Service, the NIHR or the UK Department of Health. This study was supported by CRIS Powered by Akrivia Health, using data, systems and support from the NIHR Oxford Health Biomedical Research Centre (BRC-1215-20005) Research Informatics Team. We would also like to acknowledge the work and support of the Oxford Research Informatics Team: Tanya Smith, Research Informatics Manager, Adam Pill, Suzanne Fisher, Research Informatics Systems Analysts and Lulu Kane Research Informatics Administrator.",
                    "introduction": "Major depressive disorder (MDD) is highly preva- lent with a heavy economic, social and personal \u2217Department of Psychiatry, University of Oxford, UK \u2020Civic Health Innovation Lab and Institute of Population Health, University of Liverpool, UK \u2021Mersey Care NHS Foundation Trust, UK \u00a7Oxford Health NHS Foundation Trust, Warneford Hos- pital, UK \u00b6Oxford Precision Psychiatry Lab, NIHR Oxford Health Biomedical Research Centre, UK burden of disability worldwide and affecting up to 6-12% of the adult global population, a propor- tion which has been rising in the last few years (Santomauro et al., 2021). The DSM-V (Diagnos- tic and Statistical Manual of Mental Disorders V) operationalises MDD as a continuous period of at least two weeks characterised by a change in mood leading to loss of interest or pleasure in activities, along with other symptoms such as weight loss or gain, sleep or cognitive issues and suicidal thoughts causing substantial distress or impairment to func- tioning (American Psychiatric Association et al., 2013). Depressive disorders are conditions with sub- optimal treatment outcomes, with up to 70% of patients failing to achieve remission after receiv- ing pharmacological treatment (Caldiroli et al., 2021). This led to the development of the con- cept of treatment-resistant depression (TRD) and although definitions vary (Brown et al., 2019) a common point of consensus is the failure to achieve treatment response after sequential, adequate- duration and minimally-effective dosed trials of two antidepressant-class medications. Designating a patient as having TRD focuses on acute-phase symptom improvement in response to pharmaco- logical intervention. Despite these efforts at refining the definition of depression to address treatment responsiveness, the cumulative rate of chronicity and lack of re- sponse or remission amongst MDD patients re- mains high, with around 30% of patients not achiev- ing remission even after four courses of antidepres- sants (Rush et al., 2006). In addition, treatment resistant depression may be associated with higher risks of suicide (Papakostas et al., 2003). This underlines the importance of improving the iden- tification of the relevant features (or signature) of people with depression where treatment has not provided adequate remission. The relatively new concept of difficult-to-treat 1 arXiv:2402.07645v1  [cs.CL]  12 Feb 2024 depression is proposed McAllister-Williams et al. (2020) as a more comprehensive model that empha- sises biomedical, psychological and social factors and interventions that may influence response to treatment beyond the acute symptomatic response to pharmacological interventions in TRD."
                },
                {
                    "url": "http://arxiv.org/abs/2305.16426v2",
                    "title": "Not wacky vs. definitely wacky: A study of scalar adverbs in pretrained language models",
                    "abstract": "Vector space models of word meaning all share the assumption that words\noccurring in similar contexts have similar meanings. In such models, words that\nare similar in their topical associations but differ in their logical force\ntend to emerge as semantically close, creating well-known challenges for NLP\napplications that involve logical reasoning. Modern pretrained language models,\nsuch as BERT, RoBERTa and GPT-3 hold the promise of performing better on\nlogical tasks than classic static word embeddings. However, reports are mixed\nabout their success. In the current paper, we advance this discussion through a\nsystematic study of scalar adverbs, an under-explored class of words with\nstrong logical force. Using three different tasks, involving both naturalistic\nsocial media data and constructed examples, we investigate the extent to which\nBERT, RoBERTa, GPT-2 and GPT-3 exhibit general, human-like, knowledge of these\ncommon words. We ask: 1) Do the models distinguish amongst the three semantic\ncategories of MODALITY, FREQUENCY and DEGREE? 2) Do they have implicit\nrepresentations of full scales from maximally negative to maximally positive?\n3) How do word frequency and contextual factors impact model performance? We\nfind that despite capturing some aspects of logical meaning, the models fall\nfar short of human performance.",
                    "authors": "Isabelle Lorge, Janet Pierrehumbert",
                    "published": "2023-05-25",
                    "updated": "2023-10-22",
                    "primary_cat": "cs.CL",
                    "cats": [
                        "cs.CL"
                    ],
                    "main_content": "We begin by introducing some concepts from linguistic semantics and pragmatics that motivate our study. 2.1 Scales and operators The workhorse of document retrieval is the fact that the topic under discussion hugely influences what entities people refer to. According to semantic theory, individual unique entities are referred by proper nouns; common nouns refer to sets of entities. The bursts in uses of proper and common nouns associated with the current topic provide the basis for the distributional hypothesis about word meanings. In contrast to nouns, many other types of words have more complicated semantic structures. Partee (1992) develops a typology of word types according what implicit variables they contain. In Altmann et al. (2009), this typology is simplified and applied to explain why some types of words are typically much less bursty than nouns. Of particular relevance here is the distinction between entities and operators. Operators are words that have hidden variables in their semantic representations, which are supplied by the context. The many different ways of filling in these hidden variables means that they can be used in many different contexts. As a corollary, Altmann et al. (2009) demonstrate that they are much less bursty than words referring to entities. One much-studied class of operators is gradable adjectives such as hot or tall. These position the expression they modify on a scale. By using them, the speaker indicates that the modified expression has a position on the scale that is more extreme than a given threshold, which is inferred from the context (Lassiter and Goodman, 2013). For example, by hearing someone described as tall, or water described as hot, the listener will apply their knowledge about people\u2019s heights, or water temperatures, to infer that the height or temperature being described is significantly above its typical value. This means that formal semantic representations of tall, hot each contain a hidden variable, representing the threshold whose value is contextually determined. For negative adjectives such as short, cold, the corresponding inference is that the value falls below a critical threshold. The adverbs in our study themselves modify scalar adjectives, introducing a further level of abstraction. Consider the following sentences: 1. The water is VERY hot (DEGREE) 2. The water is OFTEN hot. (FREQUENCY) 3. The water is PROBABLY hot. (MODALITY) Adverbs of DEGREE simply move the degree threshold of the original adjective (Bennett and Goodman, 2018), i.e., very hot water has an inferred range of temperatures higher than hot water. Adverbs of FREQUENCY, on the other hand, do not act on the (continuous) intensity of a single event, but rather describe a point on a scale of discrete occurrences of the relevant property (Doetjes, 2007). Lastly, modal or epistemic adverbs do not modify the adjectival property itself, but instead are an evaluation of the likelihood of the property by the speaker (Lang, 1979). Because they pertain to different scales, these categories can be freely combined without contradiction; e.g a person may be often slightly angry, certainly slightly angry, occasionally very angry, or sometimes definitely angry. Thanks to their hidden, contextually determined variables, operators are freely available in a wide variety of contexts. It follows that the context provides little information about which operator was selected in any instance. While always and never differ greatly in their logical force, they may differ little in their contexts of use. It follows that the particular context may provide little information about which one the speaker actually selected. 2.2 Entailment One of the main tasks used to evaluate natural language inference is an entailment task. We accordingly define an entailment task to probe how well LLMs reason about scalar adverbs. For a typical entailment task, (e.g., MNLI, Williams et al., 2018) crowdworkers are asked to label the relations between two ordered sentences as entailment, neutral or contradiction. Thus the NLP literature considers sentence A to entail sentence B if B can be normally inferred from A. This is a loose definition in relation to the research literature in linguistics, which has since Grice (1975) drawn a critical distinction between entailment (a semantic concept based on the logical meanings of words) and implicature (Huang, 2011). Implicatures are inferences made in the context of the discourse, including relevant real world knowledge, which do not meet the strict criteria for logical entailment. Unlike entailments they are readily cancelled without engendering contradictions. For example, the MNLI dataset characterizes ... people began to form a line ... as \u201centailing\u201d ... people formed a line .... However, initiating an action does not necessarily mean that the action was completed; something might happen to prevent this. Pervasive confusion between entailment and implicature in the NLP literature means that levels of success on entailment tasks may be inflated due by common associations of events, rather than logical reasoning. Here, we confine our attention to entailment in the strict logical sense. A critical observation is that entailment may only be strictly defined over word relationships that involve the same scale. For example, if it is very cold, it is at least somewhat cold but if it is very cold, it is unclear whether it is at least often cold. Previous work indicates that pretrained language models struggle with entailment relations, such as hypernymy and hyponymy (Guerin and Chemla, 2023). 3 Materials Building on the approach of Ribeiro et al. (2020) and R\u00f6ttger et al. (2021), we had the goal of designing a balanced diagnostic dataset for probing how well models capture the meanings of scalar adverbs. Our primary dataset consists of 960 items, which are based on posts from the year 2015 in the Reddit politosphere dataset introduced in Hofmann et al. (2022). This slice represents about 6GB of data from a range of political subreddits (e.g., r/conservative or r/anarchist). It offers naturalness and domain consistency as well as a certain amount of diversity in linguistic usage. To select the posts, we first used SpaCy (Honnibal and Montani, 2017) to extract phrases of the form \u2018ADV ADJ.\u2019 where there is a dependency between the adjective and the adverb. We take only phrases in which this construction occurs in final position, so that the phrases are also guaranteed to be well-formed in isolation. We then include the previous context from the same post, up to a maximum of 40 words, cutting at a sentence boundary. In semantic theory, preceding context is known to be important (Beaver, 2001; Roberts, 1995), but this factor is unfortunately disregarded in most of the related NLP research. Aiming for at least 40 different adjectives to occur with each target adverb, we selected 8 distinct adverbs that expressed the speaker\u2019s judgment on a scale of likelihood (MODALITY), 8 that express a position on a temporal scale (FREQUENCY), and 8 with more general applicability (DEGREE). The adverbs were selected to span the full range of each scale, and hence include adverbs with negative force i.e., hardly and never. To shed light on the contrast between scalar adverbs and outright negation, the word not is reserved as a benchmark and not used as a target. Both the adverbs themselves, and the ADV ADJ bigrams, were selected to span the range of available frequencies to the extent possible, using Google Ngram (Lin et al., 2012) frequencies. The target adverbs are listed in Target Context certainly You are conflating the issue. Slavery was not moral but it was [MASK] legal. frequently Doesn\u2019t really matter what republicans say, democrats are going to call them racist. Because what Republicans say is [MASK] racist. very You need verifiable proof. I mean, it\u2019s not like saying you\u2019re self trained is [MASK] reputable. Table 2: Example target phrases and sentences for MLM task Table 1. According to Paradis (1998), some of our chosen scalar adverbs are \u2018maximizers\u2019 (e.g., completely) which tend to occur with extreme adjectives (e.g., freezing) or limit adjectives (e.g., dead). Others typically combine with stereotypically scalar adjectives (e.g., cold). However, these are tendencies rather than rules (Kamoen et al., 2011). Indeed, phrases such as very dead or completely cold can be perfectly acceptable in some contexts (e.g., I can assure you he was very dead). Therefore, we do not restrict our phrases to traditional scalar adjectives and include any occurrences involving the target adverbs. Example items and targets can be seen in Table 2. The dataset features (word lengths and adjective overlap between adverbs) can be found in Table 11 in the Appendix. These items were used as such in an MLM task. The same target adverbs are also used in the entailment task, but constructing items with templates rather than using the natural contexts. For the adverb ranking task, we combined each target scalar adverb with (the same) 40 common adjectives to try and get an average of generic embeddings: able, bad, big, black, clear, different, early, easy, economic, federal, free, full, good, hard, high, human, important, international, large, late, little, local, low, military, national, new, old, only, political, possible, public, real, recent, right, small, social, special, strong, white, young. We describe the construction of the entailment items below in 4.4. 4 Tasks Similar to Talmor et al. (2020), Liu et al. (2021) and Jiang et al. (2022), our main tasks are zero-shot evaluations without fine-tuning so as to examine the representations learned from pretraining. We first evaluate the extent to which the rankings in Table 1 can be recovered from the embedding space in BERT and RoBERTa. We then look at MLM (as one of the training objectives for the models) and finally entailment (as a canonical logical task). In the Appendix, we also consider a model fine-tuned on a Natural Language Inference dataset (MNLI, Williams et al., 2018). 4.1 Ranking adverbs by scalar position Our first question is whether the rankings of the various scalar adverbs along their relevant scales are observable in the embeddings. Resources that provide scalar rankings for adverbs are scarce, and the few available, such as Taboada et al. (2011), confound scalar position with other factors. Therefore, we defined our own gold standard (cf. Table 1), on the basis of WordNet definitions. We first applied both methods described in Soler and Apidianaki (2020) for assessing the scalar position of scalar adjectives. Their first method (SIM) uses a reference point, specifically the top end of each scale, and computes the cosine similarity for each target from the reference point; the similarity should decrease as we move down the scale. Their second method (DIFF) uses the difference between between the maximum and minimum words on a scale to define an abstract vector of scale position; the cosine similarity of any word to this vector is taken to indicate its scale position. Broadly inspired by Maillard and Clark (2015) and Socher et al. (2012)\u2019s work on semantic composition for nouns, we also devised a third method (AdjDIFF). Reasoning that the effect of the scalar adverb on the contextual embedding of the adjective may correlate with the scalar adverbs\u2019 position on the scale, we obtain embeddings for each adjective with and without the scalar adverb. We subtract the unmodified embedding from the modified embedding of the adjective to obtain an estimate of the vector for the scalar adverb. We then take the cosine similarity of each resulting vector with the same referent vector as in the DIFF method and average them to obtain the final cosine similarity value. rankAdjDiff = cos(\u20d7 vadj(+adv) \u2212\u20d7 vadj, \u20d7 vtop \u2212\u20d7 vend) (1) The results for the AdjDiff method, which was overall the best performing, can be found in Table 3. We report the pairwise accuracy, Spearman \u03c1 and tie corrected Kendall\u2019s \u03c4 for RoBERTa, BERT large and BERT base. (See the Appendix for the results using the Soler and Apidianaki (2020) methods). Overall, the performance is worse than what Soler and Apidianaki (2020) obtained for adjectival half-scales. Adverb ranking may be more difficult than adjective ranking and/or full scales may be difficult to tank than half scales. However the overall accuracy of 0.64 for the BERT-large method indicates that some information about the relations has been captured. It is interesting that BERT-large performs better than RoBERTa, for which the existence of negative values of Spearman \u03c1 and Kendall\u2019s \u03c4 is particularly problematic. We also note that the FREQUENCY category shows the worst performance. 4.2 Masked Language Modelling MLM is one of two training objectives for BERT, and the only objective for RoBERTa. For BERT or RoBERTa to form good representations of the scalar adverbs, the larger context needs to contain information about which ones are most likely in any given instance. According, we directly evaluate the raw Masked Language Modelling outputs for the target phrases we selected. How well does each model predict a scalar adverb in a context when it is masked? Based on the discussion in Section 2, we expect this task to be extremely difficult. For most of our examples, it appears that humans would be unlikely to succeed in predicting the masked word. However, through learned attention weights, BERT and RoBERTa integrate information over a large time window, potentially performing better than expected. Possible sources of information about the scalar adverb include collocations or selectional restrictions involving the following adjective, and rhetorical devices or idiomatic expressions that involve the preceding context. Hence, we systematically explore the success of MLM in predicting a masked adverb. If MLM is successful, that means that the predictive information is present in a way that is not intuitively evident, whereas if MLM fails, that tends to suggest that predictive information is simply lacking in the text stream. In light of the difficulty of the task, we report two measures. One is the Mean Reciprocal Rank (MRR) for the original adverb, which scores high if the adverb that occurred is ranked highly even if it is not the one that actually appeared 1 . MRR is defined as MRR = 1 N N X n=1 1 rankadv (2) Where N is the number of items for the original target adverb and rankadv is the rank of the original target adverb among the model\u2019s predictions. Our other metric is whether the model ranked the original adverb above not. In our materials, replacement with not is always syntactically possible, but would either contradict the previous context, or contradict what the speaker actually said. Thus, not should generally be ranked as less likely than any scalar adverb, with the exception of other negative polarity items such as hardly and never2. We test three models in the BERT family: BERT base, BERT large and RoBERTa large. We also test GPT-2 (Radford et al., 2019), which unlike BERT family models is an autoregressive model and helps us to see whether the right-hand context contains relevant information. We use the pretrained cased BERT large and BERT base from the Huggingface\u2019s transformers library (Wolf et al., 2019), replacing our target scalar adverb with the [MASK] token and obtaining the logits which we convert back into probabilities. We use neutralised versions of the sentences e.g., \u2018is ADV ADJ.\u2019 as a baseline for predictions. This provides the BERT-family models with a syntactic cue plus any selectional biases from the ADJ. 4.3 MLM Results Results can be found in Table 4. All models perform extremely poorly in the neutral context, indicating that adjectives alone are not sufficient to predict adverbs. (The GPT2-neutral condition of course has no success, since GPT2 does not use 1Unlike Truong et al. (2023), we do not use Weighted Hit Rate (WHR) since this requires a fixed set of wrong predictions. 2Since we do not have precise numbers of negation acceptability for our examples (a difficult issue in naturalistic contexts which is beyond the scope of this article, see Limitations), this metric should be regarded as indicative only, in contrast to MRR. Pacc. Spearman \u03c1 Kendall \u03c4 BERT-b 0.60 f: 0.68 m: 0.77 d: 0.32 f: 0.52 m: 0.66 d: 0.23 BERT-l 0.64 f: 0.78 m: 0.88 d: 0.39 f: 0.62 m: 0.77 d: 0.24 ROBERTA 0.53 f: -0.32 m: 0.77 d: 0.64 f: -0.24 m: 0.67 d: 0.52 Table 3: Results of scalar ranking tests BERT-b = BERT base; BERT-l = BERT large; ROBERTA; f = FREQUENCY, m = MODALITY. d = DEGREE). right-hand context). The results for the full context are better. Both BERT large and BERT base get a significant boost from the full context both in upranking the original adverb (MRR doubling for both models) and in ranking the original adverb above negation. RoBERTa performs best overall. The MODALITY category gets the highest boost from context, from 0.02 to 0.57, this may be due in part to the fact that English lacks a negative item in this category. Error analysis shows that BERT still yields negation as the top prediction or among the top predictions even in cases where the context makes it unlikely (eg., not is the top prediction for the first two examples in Table 2). We construct confusion matrices between original target adverb and the top output prediction for each example for each model and context. We select the first of our target adverbs in the top 10 outputs, or the category \u2018other\u2019 when none of the top 10 predictions appears in our list. The heatmaps with context can be seen in Figure 1 (the full set of heatmaps, including outcomes for the neutral context, can be found in Figure 2 in the Appendix). While there is some indication of ability to predict the original adverb from BERT (i.e., the faintly lit up diagonal), it is clear that the decision is strongly driven by prior frequency effects, with not and very topping the predictions for all targets. RoBERTa gets a better performance, as is evidenced by the more strongly lit up diagonal, but frequency effects still dominate (the vertical lines for items such as very). The figure is laid out so that within-category confusions would show up on a block diagonal pattern. No such pattern exists, indicating that scalar adverbs within the same semantic category do not emerge as particularly similar. The fact that the models enjoy some success when provided with the left-hand context of the target indicates that the left-hand context \u2013 unlike the right-hand context \u2013 contains information about which scalar adverb is more likely in which instance. However, because of the naturalistic and varied nature of our examples, it is uncertain to what extent this success derives from distributional patterns versus logical relationships. 4.4 Scalar entailment task The adverb rankings in Table 1 can readily be translated into entailments. Evaluating putative entailments is an established test of logical reasoning: It is always cold entails It is sometimes cold, but the reverse is not true. If the models have reliably learned the logical relations between scalar adverbs during pretraining, they should rank completions which create correct entailments higher than completions which create contradictions. We set up an entailment task as a MLM task in two conditions, which we illustrate now with example items constructed from the ADV ADJ combination often special. For the BELOW condition, we create items where we expect an adverb which is below the premise adverb on the relevant scale, e.g. If it is often special, then it is at least [MASK] special (sometimes, occasionally, etc.). For the ABOVE condition, we expect a completion which is above the premise adverb, e.g., If it is [MASK] special, then it is at least sometimes special (often, usually, etc.). We craft items using eight different templates for each condition (varying order of premise and mask as well as subordinating conjunction). These can be found in the Appendix along with detailed results for each template. We omit the scalar adverbs which are technically negations (hardly, never) and omit bottom scalar adverbs (sometimes, maybe, slightly) for the BELOW condition and top scalar adverbs (always, definitely, completely) for the ABOVE condition, since no correct answer is available for these. In contrast to the natural items for the MLM task, not is always a logically impossible completion for all items in the entailment task. We used 160 adjectives systematically varied in frequency. From our Reddit data, we selected adjectives in the low frequency range (log frequency -18 to -14), medium frequency range (log frequency -14 to -10) and high frequency range (log frequency -10 BERTb(c) BERTb(n) BERTl(c) BERTl(n) RoBl(c) RoBl(n) GPT2(c) GPT2(n) ac. r ac. r ac. r ac. r ac. r ac. r ac. r ac. r FREQ. .22 .11 .02 .04 .36 .15 .06 .05 .52 .21 .06 .04 .08 .04 .00 .01 MOD. .19 .09 .00 .02 .33 .11 .01 .02 .57 .18 .02 .02 .09 .05 .00 .01 DEG. .4 .2 .08 .10 .53 .24 .22 .15 .67 .28 .29 .16 .16 .06 .00 .01 avg. .27 .14 .03 .05 .41 .17 .17 .07 .59 .22 .12 .07 .11 .05 .00 .01 Table 4: Accuracies (ac.), i.e., number of times the original adverb was ranked above not and Mean Reciprocal Rank (r) for each adverb and semantic category. (c) = full context; (n) = neutral context. (a) BERT large with context (b) RoBERTa large with context Figure 1: Heatmap of confusion matrices per scalar adverb for each model with context (items are grouped by semantic category). In the interest of space considerations, we only show results for BERT large and RoBERTa to -6). We use the recent wordfreq Python library for this purpose (Speer, 2022), which is sourced from the Exquisite Corpus project and compiles multilingual data from 8 domains. In addition, we selected 40 pseudo words as adjectives from the highest ranked items in (Needle et al., 2022) under the constraint that they are not compounds of real words, so that the pretrained models\u2019 WordPiece tokenization does not introduce any previous information. We combine these 160 adjectives with our target adverbs for each template and condition to create a dataset of 40960 sentences for which we collect MLM completions from BERT large and RoBERTa. 4.5 Entailment results As in the MLM task, to construct confusion matrices we select the first answer on our adverbs list from the top 10 completions of the model (including negative items: not, hardly and never), and the category \u2018other\u2019 if no completion in the top 10 is found in the relevant category. To calculate accuracies, we exclude trivial answers (e.g., If it is sometimes strong, then it is sometimes strong) as well as \u2018other\u2019 answers which do not pertain to the target semantic category (e.g., mostly when the category is temporal). However, we do report trivial answer percentages separately. A model which randomly picks an adverb in the relevant category produces 0.13 trivial answers. The results when taking into account negative answers are very poor. The models output a high percentage of negations (especially \u2018not\u2019) even though negations constitute logical contradictions for all sentences in the entailment dataset. To get a more nuanced picture of the models\u2019 behaviour and support comparisons with the MLM results, we also build heatmaps without taking negative answers into account, and calculate accuracies without negations. Results (with and without negations) can be found in Table 5. More detailed results by adjective frequency can be found in Table 8 in the Appendix. Both sets of heatmaps (including negative answers) can also be found in Figures 3 and 4 in the Appendix. When choosing the top relevant answer excluding negations the results improve drastically to near ceiling. However, the models most likely benefit from biases in both conditions. In the ABOVE condition, the most frequent items (always, actuBERTl (acc.) BERTl (triv.) RoBERTa (acc.) RoBERTa (triv.) with negation 0.35 0.20 0.42 0.17 without negation 0.88 0.33 0.88 0.25 BELOW 0.53 0.25 0.60 0.21 ABOVE 0.69 0.28 0.71 0.14 Table 5: Results for scalar entailment dataset (BERT large and RobERTa). (without negation) = not taking into account negations as answers, acc. = accuracy, triv. = number of trivial answers (e.g., If it\u2019s sometimes ADJ, it\u2019s sometimes ADJ, which we do not take into account for accuracies), BELOW = expects item below on the relevant scale, ABOVE = expects item above on the relevant scale (best in bold). ally, very) constitute correct answers in a majority of cases. In the BELOW condition all templates have a textual hint (at least/at most) which strongly suggests an item outside the top of the scale (?at least/at most always/completely/definitely). The benefits from the bias towards high frequency topof-scale adverbs in the ABOVE condition are probably stronger than those from the textual hints in the BELOW condition, which may explain why the models perform worse in the BELOW condition. The adjective frequency has little effect on performance, which is in fact slightly better for low frequency adjectives and pseudowords. This provides further evidence that the models are not memorizing ADV-ADJ combinations. This observation is strengthened by adverb frequency effects which prevail across scales (i.e., vertical lines in the heatmaps e.g., \u2018slightly\u2019, \u2018really\u2019) in both BERT large and RoBERTa. The rate of trivial answers in both models also appears to be far above what would be expected from humans (although this remains to be tested by collecting human judgments). To summarize, both BERT large and RoBERTa show very poor ability to distinguish between nonnegative scalar adverbs and negation. The models perform well if we consider first completions excluding negations. However they most likely benefit from frequency biases and it is doubtful whether they learned a separate logical representation of the adverbs\u2019 scalar property. The models also output a high number of trivial, uninformative completions and seem affected by noise associated with frequent adjectives. Finally, differing performance on the ABOVE and BELOW conditions, which are logically equivalent, indicates that neither model has a general grasp of the underlying logic. 5 Conclusion The goal of this paper was to examine how well pretrained language models such as BERT and RoBERTa represent and process full scales of scalar adverbs in the absence of any specific task fine-tuning. We used naturalistic data from Reddit and also constructed sentences in order to explore the language models\u2019 ability to predict different types of scalar adverbs in context, and to distinguish them from negation. The models achieved some success when a left context of up to 40 words was available. However, we note many shortcomings: weak differentiation amongst the semantic classes of adverbs, poor ability to discriminate scalar adverbs from negations even in contexts where a negation would create a contradiction, strong effects of adverb frequencies and lack of generalisation across two logically equivalent entailment constructions. 6 Limitations Scale: While our list of adverbs was carefully curated to include different semantic categories, full scales (including negations) and downsizer adverbs (e.g., slightly) unlike in previous works, they are a restricted sample of only 24 adverbs. While we do believe this is a representative list, it is by no means an exhaustive one and the conclusions drawn in this paper have to be confined to the semantic categories explored. Thus we cannot exclude the possibility that experiments using a larger list of adverbs would produce different results. Acceptability of negation: For some of our natural stimuli, the use of not would be infelicitous or illogical. For others, not would be possible but would express a meaning that contradicts what the speaker chose to express. Without a large-scale exploration of alternative contextualizations of the items, it is difficult to separate these cases. For example, for item 498, a substitution of not would appear to be rather infelicitous; however, by imagining further context we can see that this substitution would not be impossible. 1. Including the bill itself, I think you\u2019ll be looking at around 600 A4 pages of reading. And a lot of it is really dry. 2. Including the bill itself, I think you\u2019ll be looking at around 600 A4 pages of reading. And a lot of it is not dry. 3. Including the bill itself, I think you\u2019ll be looking at around 600 A4 pages of reading. And a lot of it is not dry. Your week might be more thrilling than you expect. Models: While we tried to explore the predictions from different types of pretrained models (i.e., GPT and BERT), we acknowledge that we did not run an extensive study of models from different families. This is in part because these are the most commonly used models in applications, but also because our study is qualitative and we were mostly interested in comparing the models\u2019 outputs with and without context and comparing performance between our semantic categories, rather than between different models. We also wished to focus on open-source models for which we could extract embeddings to explore a potential subspace for scalar properties. Gold standard: There are few resources for providing gold standard labels of position on the scale for scalar adverbs in general, and especially when including different semantic categories and downsisers as well as maximisers. This limited our available choices for scalar adverbs to investigate. We provided the gold standard labels for the list of adverbs, based on information in WordNet and claims in the research literature, excluding adverbs whose semantics appeared unclear. While these rankings are informed by our best knowledge of semantics as experienced linguists, they were provided by a few researchers rather than by gathering judgments from many crowdsourcers as in other studies. 7 Acknowledgements This study was supported by EPSRC Grant EP/W037211/1. We are grateful to Valentin Hofmann, Fangru Lin, and Paul R\u00f6ttger for useful comments on a previous draft.",
                    "introduction": "Large pretrained language models such as BERT (Devlin et al., 2018) all rely on the assumption that the meanings of words are revealed by the company they keep (Harris et al., 1954); Masked Language Modelling (MLM) is a useful training objective be- cause words in the context of the masked word pro- vide cues to its identity. This assumption is highly appropriate for nouns and named entities. Differ- ent topics of discussion involve different entities, and in discussing any given topic, the associated entities will be referred to repeatedly. However, the assumption holds less well for some other classes of words that can be used in discussing virtually any topic. These include quantifiers (e.g. few, many, all), words expressing negation (e.g. not, no, never) and the focus of the present paper, which is scalar adverbs, such as perhaps, certainly, never, often, very, completely. Many scalar adverbs tend to oc- cur in similar contexts but have distinct meanings. As Abrusan et al. (2018) put it, distributional mod- els tend to be \u2018blind\u2019 to logical meanings because the latter are topic independent and thus their mean- ings tend to not be reflected in their distributional contexts. Accurate processing of scalar adverbs is perti- nent to a wide variety of NLP applications, includ- ing sentiment analysis (De Melo and Bansal, 2013; Ruppenhofer et al., 2014), entailment inferences (McNally, 2017), detecting contradictions, and in- direct Question Answering (De Marneffe et al., 2010). BERT family models succeed without fine- tuning on a remarkable variety of tasks, and unsu- pervised embeddings from BERT base have been used fairly successfully to rank gradable adjectives according to their scalar position on half-scales from a neutral to an extreme value (e.g., warm < hot < scalding) (Soler and Apidianaki, 2020). This result suggests that the BERT architecture might also be successful in exploiting diffuse or indirect cues for the selection of scalar adverbs. However, the same models have had little success in repre- senting negation (Ettinger, 2020) or antonymy (Tal- mor et al., 2020). In fact, even large language mod- els (LLMs) still struggle substantially with nega- tion (Truong et al., 2023). Soler and Apidianaki (2020) do not evaluate adjectival antonyms, such as {cold, hot}. However, it is worth noting that scalar adverbs intrinsically include antonym pairs, (e.g.,{never, always}). Furthermore, the word not is syntactically possible wherever a scalar adverb can occur, yet would express a contradictory mean- ing to any positive scalar adverb. These latter observations suggest that scalar ad- arXiv:2305.16426v2  [cs.CL]  22 Oct 2023 Category Adverbs MODALITY (14.8%) {maybe, perhaps, possibly}, arguably, probably, actually, certainly, definitely FREQUENCY (5.3%) never, occasionally, some- times, often, generally, usu- ally, frequently, always DEGREE (46.8%) hardly, slightly, basically, pretty, quite, very, really, com- pletely Table 1: Scalar adverbs in each semantic category ranked by scalar position using semantic theory and WordNet definitions. Bracketed items are tied. Per- centages for each category are the overall percentage of that category in the Reddit slice in relation to the set containing the target adverbs and not. verbs might present important challenges for LLMs, and point to the need for a deep assessment. We look at full scales, and directly compare scalar adverbs to explicit negation. We consider the 24 adverbs in Table 1, selected through the process described in Section 3. These vary widely in fre- quency, with very found 22818 times in the Reddit slice and frequently found only 52 times. At 40986 occurrences, not is more frequent than any scalar adverb (see Appendix for full adverb frequencies). We ask the following questions: 1) Are pre- trained language models able to distinguish be- tween different semantic categories of scalar ad- verbs? 2) Do they have general representations of full scales for adverbs, from maximally negative to maximally positive? 3) Do their representations support success in three tasks: ranking, MLM, and evaluating entailments? 4) In what way do the pat- terns of success and failure relate to word frequency and contextual factors?"
                }
            ],
            "Andrey Kormilitzin": [
                {
                    "url": "http://arxiv.org/abs/2010.08433v2",
                    "title": "An efficient representation of chronological events in medical texts",
                    "abstract": "In this work we addressed the problem of capturing sequential information\ncontained in longitudinal electronic health records (EHRs). Clinical notes,\nwhich is a particular type of EHR data, are a rich source of information and\npractitioners often develop clever solutions how to maximise the sequential\ninformation contained in free-texts. We proposed a systematic methodology for\nlearning from chronological events available in clinical notes. The proposed\nmethodological {\\it path signature} framework creates a non-parametric\nhierarchical representation of sequential events of any type and can be used as\nfeatures for downstream statistical learning tasks. The methodology was\ndeveloped and externally validated using the largest in the UK secondary care\nmental health EHR data on a specific task of predicting survival risk of\npatients diagnosed with Alzheimer's disease. The signature-based model was\ncompared to a common survival random forest model. Our results showed a\n15.4$\\%$ increase of risk prediction AUC at the time point of 20 months after\nthe first admission to a specialist memory clinic and the signature method\noutperformed the baseline mixed-effects model by 13.2 $\\%$.",
                    "authors": "Andrey Kormilitzin, Nemanja Vaci, Qiang Liu, Hao Ni, Goran Nenadic, Alejo Nevado-Holgado",
                    "published": "2020-10-16",
                    "updated": "2020-10-24",
                    "primary_cat": "cs.CL",
                    "cats": [
                        "cs.CL",
                        "cs.IR"
                    ],
                    "main_content": "2.1 Data The data in this study were sourced from the UK-Clinical Record Interactive Search system (UK-CRIS), which provides a research platform (https://crisnetwork.co/) for data mining and analysis using de-identified real-world observational electronic patients records from twelve secondary care UK Mental Health NHS Trusts (Goodday et al., 2020). UK-CRIS provides access to strucarXiv:2010.08433v2  [cs.CL]  24 Oct 2020 tured information, such as ICD-10 coded diagnoses, quality of life scales and demographic information, as well as various unstructured texts, such as clinical summaries, discharge letters and progress notes. The study cohort jointly comprised records from 24,108 patients diagnosed with Alzheimer\u2019s disease and various types of dementia, containing more than 3.7 million individual clinical documents from two centres: Oxford and Southern Health Foundation NHS Trusts. The \ufb01eld of clinical NLP in general, and of mental health and Alzheimer\u2019s research in particular, largely suffers from the dearth of gold-annotated data. The reason is due to the shortage of trained annotators with clinical background who are also authorised to access sensitive patient-level data. Therefore, to develop a robust information extraction (IE) model from an insuf\ufb01cient amount of data, we leveraged the idea of transfer learning using the publicly available MIMIC-III corpus (Johnson et al., 2016) comprising information relating to patients admitted to intensive care units (ICU) with more than 2.1 million clinical notes as well as 505 gold-annotated by clinical experts discharge summaries from the 2018 n2c2 challenge (Henry et al., 2020). We assert that the study was independently approved and granted by the Oxfordshire and Southern Health NHS Foundation Trust Research Ethics Committees. 2.2 Information extraction model The information extraction model was developed to identify diagnosis, medications and cognitive health assessment Mini-Mental State Examination score (MMSE) (Pangman et al., 2000). Additionally, the identi\ufb01ed entities were classi\ufb01ed according to several attributes, such as the \u2019experiencer\u2019 modality (i.e., whether the MMSE was actually referring to a patient or to a family member), temporal information (i.e the date of diagnosis or MMSE score) and negations (i.e. discontinued medications) (Harkema et al., 2009; Gligic et al., 2019). Such drug mentions were discarded in order to extract the most accurate information. Generic and brand drug names were normalised using the British National Formulary, the core pharmaceutical reference book (Committee et al., 2019). The architecture of the named entity recognition model comprised a hybrid approach of an ontologybased fuzzy pattern matching and a bi-directional LSTM neural network architecture with the attention mechanism (Bahdanau et al., 2014) for sequence classi\ufb01cation. The GloVE word embedding (Pennington et al., 2014) were \ufb01ne-tuned on both MIMIC-III and UK-CRIS data (Vaci et al., 2020a; Kormilitzin et al., 2020). The developed IE model was trained only on data from the Oxford Health NHS Trust instance and externally validated on a sample of data from a regionally different Southern Health NHS Foundation Trust. 2.3 The signature of a path Repeated measurements, speech, text, time-series or any other sequential data might be seen as a path-valued random variable. Formally, a path X of \ufb01nite length in d dimensions can be described by the mapping X : [a, b] \u2192Rd, or in terms of co-ordinates X = (X1 t , X2 t , ..., Xd t ), where each coordinate Xi t is real-valued and parametrised by t \u2208[a, b]. The signature representation S of a path X is de\ufb01ned as an in\ufb01nite series: S(X)a,b = (1,S(X)1 a,b, S(X)2 a,b, ..., S(X)d a,b, S(X)1,1 a,b, S(X)1,2 a,b, ...), (1) where each term is a k-fold iterated integral of the path X labelled by multi-index i1, ..., ik: S(X)i1,...,ik a,b = Z a<tk<b ... Z a<t1<t2 dXi1 t1 ...dXik tk . (2) However, in many real-life applications the \ufb01rst k-terms of the truncated signature at level L give a satisfying approximation. Intuitively, it is analogous to statistical moments of a d-dimensional vector-valued random variable, such as mean, variance or higher moments. One can de\ufb01ne statistical moments of a path-valued random variable, which are essentially the signature moments (Chevyrev and Oberhauser, 2018) de\ufb01ned in Eq. (2). The signature S(X) completely characterises a path X up to tree-like equivalence and is invariant to reparameterisation (Hambly and Lyons, 2010). The signature can also be expressed in a more compact form known as log-signature (Liao et al., 2019; Morrill et al., 2020a), which is the formal power series of log S(X), while carrying the same information. Informally, the path signature captures the order of events. For example, consider two sequences X1 = aabba and X2 = baaab consisting of a simple vocabulary with only two letters {a, b}. The sequences might be presented as paths in 2d space as shown in Fig. 1. Each linear segment between Figure 1: Two paths X1 = aabba and X2=baaab. two points (Fig. 1) corresponds to a single letter in the sequence and the arrows denote the temporal direction of the sequence. Despite the same Level 1 2 3 4 S(X1) 3 2 1 -0.5 -1 -1/3 -0.5 0 S(X2) 3 2 0 1.5 0.5 0 0 0 Table 1: The \ufb01rst k = 8 terms of the log signature expansion up to level L = 4. The difference between two sequences X1 and X2 is apparent starting from the second level. number of letters in the sequences {a = 3, b = 2}, the order of letters matters. The signature easily picks the differences and the \ufb01rst four levels of the log-signatures of paths are shown in Table 1. The lower order signature terms S(i) are the increments along the i-th direction (i.e. the distance between the endpoints), for example, S(1) = 3 \u22120 = 3 and S(2) = 2 \u22120 = 2 as can be seen in Figure 1. The second order corresponds to the area enclosed by a path and a chord connecting endpoints (Chevyrev and Kormilitzin, 2016). The usefulness of a path signature as a feature map of sequential data was demonstrated theoretically (Chevyrev and Oberhauser, 2018) as well as in numerous machine learning applications in healthcare (Morrill et al., 2019; Kormilitzin et al., 2016; Arribas et al., 2018; Morrill et al., 2020b; Kormilitzin et al., 2017), \ufb01nance (Arribas, 2018), computer vision (Yang et al., 2017; Xie et al., 2017), topological data analysis (Chevyrev et al., 2018) and deep learning (Kidger et al., 2019). 2.4 Independent and outcome variables The independent variables used in the prognostic model were medications and the MMSE scores collected over time. The dependent outcome variable was right-censored time to death data in months. A synthetic example of the patient\u2019s records (Table 2) and the corresponding algorithmically extracted longitudinal data is presented in Table 3. The outcome variable was encoded as a tuple: (True, 34.17) indicating that a person has died after 34.17 months since the very \ufb01rst visit to a specialist memory clinic. The patient was treated by two different medications with a changing pattern and eventually was tapered off medication due to no further expected improvement. 2.5 Baseline longitudinal data summarisation The signature transformation might be seen as a hierarchical statistical summarisation (\u201cfeature extraction\u201d) of the longitudinal data along the temporal dimension. In order to benchmark the proposed method, we used a time-honoured linear mixedeffects regression as a baseline model for longitudinal summarisation. Speci\ufb01cally, each patient-level longitudinal MMSE scores were modelled using a linear regression and the resulting coef\ufb01cients, such as an intercept and a slope, were used as features representing the progression of the MMSE over time. The median number of medication categories was used as an additional feature, resulting in three features for each patient. 2.6 Survival random forests The common statistical approach to analyse the time-to-event survival data is based on the linear Cox model (Collett, 2015). However, Miao et al. (2015) showed that a survival random forest (SRF) approach (Ishwaran et al., 2008) outperformed linear Cox model, based on the Harrell\u2019s concordance index (C-index) (Harrell et al., 1982), and was understandably capable of identifying non-linear effects of the input variables as opposed to linear Cox model. Therefore, we chose the SRF as the preferred method. The SRF approach was implemented in Python using \u201cscikit-survival\u201d package (P\u00a8 olsterl et al., 2015). The Harell\u2019s C-index (the concordance index) is a goodness of \ufb01t measure for risk scores models. It is a common statistical approach to evaluate risk models in survival analysis, where data may be right-censored and corresponds to rank correlation between predicted risk scores and observed time points, similarly to Kendall\u2019s \u03c4. 3 Results 3.1 Information extraction model We used a hybrid approach to developing an IE model consisting of training a baseline model using MIMIC-III and n2c2 annotated data. Speci\ufb01cally, the named-entity recognition (NER) model Doc date Text 05-Oct-2016 Today I saw a patient diagnosed with Alzheimer\u2019s, who deteriorated: MMSE 23/30 as compared to 25/30 from 1st January. Started on Rivastigmine. 12-Feb-2017 Today MMSE 19, the patient didn\u2019t respond to Rivastigmine and was changed to Donepezil. 03-Feb-2018 Great response to new treatment (MMSE 23/30), continue on Donepezil. 01-Apr-2019 The patient stopped responding to Donepezil and severely deteriorated (MMSE 14/30), stop Donepezil. Table 2: A synthetic example of chronological medical records. Date Medication MMSE 01-Jan-2016 NoMed 25/30 05-Oct-2016 Rivastigmine 22/30 12-Feb-2017 Donepezil 19/30 03-Feb-2018 Donepezil 23/30 01-Apr-2019 Discontinued 14/30 Table 3: Extracted and chronologically structured data from Table 2. comprised a transition-based system based on the chunking model (Lample et al., 2016) where tokens were represented as hashed and embedded representations of the pre\ufb01x, suf\ufb01x, shape and lemmatised features of words, followed by the rulebased matching using the BNF vocabulary. The IE model was implemented using \u201cspaCy\u201d python library1, including negations and temporal information identi\ufb01cation as well as relationships classi\ufb01cation between the word-tokens using linguistic features, such as part-of-speech and dependencies. Finally, the active learning tool \u201cProdigy\u201d2 was used for iterative model improvement (Vaci et al., 2020b). Target domain training, validation and external validation data contained a collection of gold-annotated drug names, diagnosis and cognitive health assessment MMSE scores as shown in Table 4. The IE model achieved a good and conConcept Training Validation External val. Total Drug 216 153 30 399 MMSE 169 87 23 279 Diagnosis 570 352 26 948 Table 4: The number of gold-annotated instances in the training, validation and external validation data sets. sistent performance on both validation and external validation data sets (Table 5). The annotation schema was developed following the recommendations of Pustejovsky and Stubbs (2012). The tokenlevel performance metrics were evaluated using the SemEval schema (Segura Bedmar et al., 2013) and the inter-annotator agreement (IAA) of two clinical 1https://spacy.io 2https://prodi.gy annotators was computed using F1 score. Validation External val. IAA Concept Pr Re F1 Pr Re F1 F1 Diagnosis 89.6 96.3 92.8 84.1 86.3 84.8 95 Drug 98 98 98.1 92.4 68.4 78.3 96 MMSE 92.6 74.7 82.8 85.6 81.2 82.6 100 Table 5: Performance (shown in %) of the information extraction model. IAA inter annotator agreement. n male female survival time died 1962 841 1121 52.2(22.8) censored 1500 529 971 28.4(16.6) Table 6: Summary statistics of the extracted data for survival analysis. Survival time is shown as mean(std) in months. The MMSE scores were not observed for censored people later in time, while date of death was recorded in hospital. 3.2 Prognostic model Four prognostic models were developed and compared to each other. All models estimated the survival probability of a patient diagnosed with Alzheimer\u2019s disease since their \ufb01rst admission to a memory clinic. We compared signature (\u201cSig\u201d, Sec. 2.3) versus non-signature (\u201cNon-sig\u201d, Sec. 2.5) models. We also estimated the added value of the sequential information contained in the treatment course with medications. Speci\ufb01cally, we used two sets of input variables: {time, MMSE} and {time, MMSE, medications}, where time corresponds to the date of MMSE score or prescribed medication as presented in Table 3. For the \u201cSig\u201d model, the input variable were \ufb01rst transformed into signatures, where the categorical medication names were one-hot encoded and augmented with numerical MMSE scores to create a path. For the \u201cNon-sig\u201d model, the longitudinal MMSE scores were summarised by means of linear models adjusting for each patients and the median number of distinct medications were computed. Both models were trained and validated using the same folds of strati\ufb01ed 5-fold cross validation (with \ufb01xed random seed). The quality of predictions was assessed using the Harell\u2019s C-index and the results are summarised in Table 7. The signatures were computed using the \u201cesig\u201d Python library3, however, alternative libraries are also available (Reizenstein and Graham, 2018; Kidger and Lyons, 2020). Features Sig Non-sig {time, MMSE} 0.626(0.009) 0.574(0.022) {time, MMSE, meds} 0.621(0.011) 0.571(0.019) Table 7: Harell\u2019s C-index measure of four models. Values reported as mean(std) over 5-fold cross validation. We also estimated the time-dependent area under the curve of receiver operating characteristics (Lambert and Chevret, 2016). It is a natural extension of a common AUC ROC analysis to possibly censored survival times where the patients\u2019 cognitive health is usually better at the very \ufb01rst visit to a memory clinic, while their condition may deteriorate later. The time-dependent cumulative dynamic AUC ROC of all four models are presented in Fig. 2. The signature features outperformed the non-signature ones at all times and the inclusion of sequential information from switching medications improved AUC ROC at later times. However, both models struggle to reliably predict the future outcomes further than 3 years. This is due to the limitation of predictors and the available number of patients after 3 years rather than the capacity of our model. 10 15 20 25 30 35 40 Months since the first admission to memory clinic 0.600 0.625 0.650 0.675 0.700 0.725 0.750 0.775 Time-dependent AUC Sig no meds Non-sig no meds Sig with med Non-sig with meds Figure 2: Time-dependent AUC of risk prediction over time since the \ufb01rst admission to a memory clinic. 4 Discussion and future direction Unstructured longitudinal electronic health records, such as free-text clinical notes, inherently contain rich information about patients\u2019 health and outcomes over time. The right analytical tools capable 3https://esig.readthedocs.io/ of capturing sequential information can therefore maximise utilisation of longitudinal EHRs and can be valuable for supporting clinical decisions and prognostic models. In this work we implemented a signature-based approach to represent chronological events extracted using natural language processing from clinical notes. Extracted chronological events can be seen as a trajectory (path) embedded in a high-dimensional multi-modal space of events (i.e. different medications, interventions, measures, etc) and the signature uniquely characterises the path in the most succinct way. The signature-based feature extraction approach was compared to handcrafted features, comprising a slope and an intercept of MMSE scores over time and the median number of medications for each patient. The signatures represent a hierarchical collection of features, where the \ufb01rst order is proportional to linear statistical moments (i.e. mean) and is not sensitive to the order of data points, as illustrated in Table 1. We demonstrated that the sequential information about medications has signi\ufb01cantly improved the timedemented AUC as captured by the signatures (Figure 2). In future works we will extend the proposed framework to include the structured information available in EHR (i.e. lab results, coded procedures or clinical encounters) and will develop an interpretability framework to make the signature-based models explainable. Acknowledgments The study was funded by the National Institute for Health Research\u2019s (NIHR) Oxford Health Biomedical Research Centre (BRC-1215-20005). This work was supported by the UK Clinical Records Interactive Search (UK-CRIS) system funded and developed by the NIHR Oxford Health BRC at Oxford Health NHS Foundation Trust and the Department of Psychiatry, University of Oxford. AK, NV, QL, ANH are funded by the MRC Path\ufb01nder Grant (MC-PC-17215). HN was supported by the Alan Turing Institute under the EPSRC grant EP/N510129/1 and under the EPSRC EP/S026347/1. The views expressed are those of the authors and not necessarily those of the UK National Health Service, the NIHR, or the UK Department of Health. We highly appreciate the work and support of the Oxford CRIS Team: Tanya Smith, Lulu Kane, Adam Pill and Suzanne Fisher and Dr Peter Phiri of the Southern Health NHS Foundation Trust CRIS team.",
                    "introduction": "Electronic health records (EHRs) have now become ubiquitous and offer novel opportunities for clinical research by supporting the development of intel- ligent decision support systems and improvement of patients\u2019 care. One of the distinct features of EHR is that the data are being collected over time and might be seen as health data streams, allow- ing research to study longitudinal trends and make inference about the progression of disease, treat- ments and outcomes. However, the proper repre- sentation of sequential medical events still remains 1Equal contribution. a challenge. Moreover, longitudinal clinical notes exhibit a multi-level hierarchical structure, where events are described and embedded in sentences, sentences in paragraphs and eventually resulting in chronologically ordered documents. Recent works have addressed the problem of capturing this information directly from raw texts by intro- ducing novel neural network architectures, such as attention-based recurrent neural networks (Bai et al., 2018) and time-aware Transformers (Zhang et al., 2020). When dealing with chronological clin- ical notes, practitioners make multiple decisions on how to structure and transform these sequential events, which are often simpli\ufb01cations of medical histories. In this work we proposed a different methodology to address the problem of learning from events found in clinical notes, by \ufb01rst extract- ing them using natural language processing and then representing the sequential order by means of the path signatures. The signature (Lyons, 2014) is a non-parametric representation of heterogeneous sequential data, offers a feature extraction method from longitudinal events and can naturally be inte- grated within a general data mining pipeline. To demonstrate the methodology, we used the largest secondary care mental health EHR data in the UK to develop a survival prognostic model for patients diagnosed with Alzheimer\u2019s disease."
                },
                {
                    "url": "http://arxiv.org/abs/2003.01271v2",
                    "title": "Med7: a transferable clinical natural language processing model for electronic health records",
                    "abstract": "The field of clinical natural language processing has been advanced\nsignificantly since the introduction of deep learning models. The\nself-supervised representation learning and the transfer learning paradigm\nbecame the methods of choice in many natural language processing application,\nin particular in the settings with the dearth of high quality manually\nannotated data. Electronic health record systems are ubiquitous and the\nmajority of patients' data are now being collected electronically and in\nparticular in the form of free text. Identification of medical concepts and\ninformation extraction is a challenging task, yet important ingredient for\nparsing unstructured data into structured and tabulated format for downstream\nanalytical tasks. In this work we introduced a named-entity recognition model\nfor clinical natural language processing. The model is trained to recognise\nseven categories: drug names, route, frequency, dosage, strength, form,\nduration. The model was first self-supervisedly pre-trained by predicting the\nnext word, using a collection of 2 million free-text patients' records from\nMIMIC-III corpora and then fine-tuned on the named-entity recognition task. The\nmodel achieved a lenient (strict) micro-averaged F1 score of 0.957 (0.893)\nacross all seven categories. Additionally, we evaluated the transferability of\nthe developed model using the data from the Intensive Care Unit in the US to\nsecondary care mental health records (CRIS) in the UK. A direct application of\nthe trained NER model to CRIS data resulted in reduced performance of F1=0.762,\nhowever after fine-tuning on a small sample from CRIS, the model achieved a\nreasonable performance of F1=0.944. This demonstrated that despite a close\nsimilarity between the data sets and the NER tasks, it is essential to\nfine-tune on the target domain data in order to achieve more accurate results.",
                    "authors": "Andrey Kormilitzin, Nemanja Vaci, Qiang Liu, Alejo Nevado-Holgado",
                    "published": "2020-03-03",
                    "updated": "2020-04-24",
                    "primary_cat": "cs.CL",
                    "cats": [
                        "cs.CL",
                        "cs.IR",
                        "cs.LG"
                    ],
                    "main_content": "The topic of clinical natural language processing and information extraction has been actively researched over the past years, in particular with the introduction and adoption of electronic health records platforms. The methods have evolved from simple logic and rule-based systems to complex deep learning architectures [16, 17]. One of the common approaches to information extraction is by transforming free text data into coded representation via lookup tables, such as universal medical language system (UMLS) [18] or structured clinical vocabulary for use in an electronic health record (SNOMED CT). Some rule-based systems used semantic lexicons to identify concepts in biomedical literature [19] with more complex linguistic features. With the advances in machine learning algorithms, such methods as hidden Markov models and conditional random fields [20] were used to label entities for the NER task. In in last decade, deep learning methods have played an essential role in developing more capable models for natural language processing and in particular, in the biomedical domain. Word embeddings [21, 22] were introduced as numerical representation of textual data and were used as input layers to deep neural networks. For a comprehensive review on word embeddings for clinical applications please refer to [23]. More recently, the unsupervised model pre-training on a large collection of unlabelled data with further fine-tuning on a downstream task, has taken off and demonstrated its high potential [24]. Since the introduction of the Transformer-based deep neural network architectures, such as BERT [3], Roberta [25], XLNet [26] and others, the transfer learning approach of reusing pre-trained models became the method of choice for the majority of NLP tasks. Some notable examples of pre-trained deep learning models for biomedical natural language processing are: BioBERT [27] for text-mining, ClinicalBERT [28, 29] for contextual word representations fine-tuned on the electronic health records and predicting hospital readmission. Another open source Python library \u2019scispaCy\u2019 [30] was recently introduced for biomedical natural language processing. In this work we developed an open source named-entity recognition model dedicated to identification of seven categories related to medications mentioned in free-text electronic patient records. 3. Materials and Methods 3.1. Data The annotated data set was sourced from MIMIC-III (Medical Information Mart for Intensive Care-III) electronic health records data base [9] as part of the Track 2 of The 2018 National NLP Clinical Challenges (n2c2) Shared Task on drug related concepts extraction, including adverse drug events (ADE) and reasons for prescription [31]. The data set comprised a collection of discharge letters from the Intensive Care Unit (ICU) and contained very rich and detailed information about medications used for treatment. The data set was randomly split and provided by the organisers into training and test sets with 303 and 202 documents respectively. The documents were annotated for nine categories: ADE, Dosage, Drug, Duration, Form, Frequency, Reason, Route and Strength. For the purpose of the current work we considered only seven drug-related categories and discarded two categories such as ADE and Reason. We aimed to 3 develop a model for medications and their related information extraction which will be bene\ufb01cial to biomedical community and be robustly used in a variety of downstream nature language processing tasks using free text medical records. The description of the data sets and annotation statistics are summarised in Table 1. Types of annotated entities Train Test Total Dosage 4227 2681 6908 Drug 16257 10575 26832 Duration 592 378 970 Form 6657 4359 11016 Frequency 6281 4012 10293 Route 5460 3513 8973 Strength 6694 4230 10924 Number of documents 303 202 505 Total number of words 957972 627771 1585743 Total number of unique words 27602 21729 35763 Table 1: Distribution of gold-annotated entities and text summary statistics of the training and test data sets. The number of unique tokens is computed by lowercasing words. In addition to MIMIC-III and 2018 n2c2 data sets, we evaluated the developed model on electronic medical records sourced from the Clinical Record Interactive Search (UK-CRIS) platform, which is the largest secondary care mental health database in the United Kingdom. UK-CRIS contains more than 500 million clinical notes from 2.7 million de-identi\ufb01ed patient records from 12 National Health Service (NHS) Network Partners across the UK 2. 3.2. Methods 3.2.1. Text pre-processing In order to compare the performance of the developed medication extraction model using MIMIC-III (n2c2 2018) and UK-CRIS data, basic text cleaning and pre-processing steps were taken to standardise texts. UK-CRIS notes that were uploaded as scanned documents and transformed into electronic texts via optical character recognition (OCR) process, were cleaned from such artefacts as email addresses, non-ASCII characters, website URLs, HTML or XML tags. Additionally, standard escape sequences (\u2019\\t\u2019, \u2019\\n\u2019 and \u2019\\r\u2019) were also removed and the o\ufb00sets of gold-annotated entities were adjusted accordingly. 3.2.2. Self-supervised learning The main obstacle to developing an accurate information extraction model is the dearth of a su\ufb03cient amount of high-quality annotated data to train the model. In contrast to publicly available large manually annotated data sets for computer vision [5, 6] and for various natural language processing downstream tasks [32, 33, 34] manually annotated texts for clinical concepts extraction are quite rare [31]. The shortage of annotated clinical data is mainly due to privacy concerns and potential identi\ufb01cation of personal medical information of patients. Several lines of research have addressed the problem of learning from limited annotated data in the clinical 2https://crisnetwork.co 4 domain [35, 36, 37] and pre-training of the underlying language model and word representations generally leads to better performance with less data [24]. In this work, we used the spaCy\u2019s 3 implementation of a cloze-style word reconstruction, similar to the masked language model objectives introduced in BERT [3], but instead of predicting the exact word identi\ufb01er from the vocabulary, the GloVe [22] word\u2019s vector was predicted using a static embedding table with a cosine loss function. The pre-trained language model was then used to initialise the weights of convolutional neural network layers, rather than starting with random weights. We experimented with various combinations of hyperparameters of the language model, such as the number of rows and width of embedding tables and a depth of convolutional layers. 3.2.3. Named entity recognition model The task of locating concepts of interest in unstructured text and their subsequent classi\ufb01cation into prede\ufb01ned categories, for example: drug names, dosages or frequency of administration is a sub-task of information extraction and called named-entity recognition (NER). There are various implementations of NER systems, ranging from rule-based string matching approaches [10] to complex Transformer models [2] or their hybrid combinations. In this work the namedentity recognition model for extraction of medication information was implemented in Python 3.7 using spaCy open source library for NLP tasks [38]. Although there exists a good number of NLP libraries, such as: NLTK [39], NLP4J [40], Stanford CoreNLP [41], Apache OpenNLP and a very recent open source collection of Transformer-based models from Hugging Face Inc. [42], the spaCy library is optimised for speed on CPUs, has an intuitive API and easily integrates with the active learning-based annotation tool Prodigy [43]. The architecture of SpaCy\u2019s NER model is based on convolutional neural networks with tokens represented as hashed Bloom embeddings [44] of pre\ufb01x, su\ufb03x and lemmatisation of individual words augmented with a transition-based chunking model [45]. We also experimented with various combinations of hyperparameters of the neural network architecture, dropout rates, batch compounding, learning rate and regularisation schemes. We set aside 30 documents (10%) sampled at random from the training data as a validation set. 3.2.4. Model training augmentation with bootstrapped noisy labels Several recent lines of research have demonstrated a clear bene\ufb01t in terms of achieving higher accuracy and better generalisation of neural networks trained with corrupted, noisy and synthetically augmented data [46, 47, 48, 49]. Training with data augmentation also alleviates the problem of learning from a limited amount of manually annotated data. Similar to the idea presented in \u2019Snorkel\u2019 [50], we designed a number of labelling functions (LF) by compiling a list of rules and keyword patterns for all seven named-entity categories. Additionally, we exploited a \u2019sense2vec\u2019 approach [51] which was \ufb01ne-tuned on the entire MIMIC-III corpora to bootstrap keywords and patterns. \u2019Sense2vec\u2019 is a more complex version of the \u2019Word2vec\u2019 method [52] for representation of words as vectors. The major improvement over \u2019word2vec\u2019 is that \u2019sense2vec\u2019 also learns from linguistic annotations of words for sense disambiguation in their embeddings. The resulting labelling functions were used to created a \u2019silver\u2019 training set consisting of annotated data by string pattern matching. The NER model was then trained by using a combination of gold and silver annotated examples in each batch. In order to prevent data leakage and 3https://spacy.io 5 Con\ufb01guration Width Depth Time Size (default) 96 4 73 3.8 128 8 90 18.3 256 8 118 47.6 256 16 164 66.1 Number of documents 2,083,054 Number of words 3,129,334,419 Table 2: Model pre-training characteristics for various combinations of convolutional layers dimensions. Time and the resulting model size are reported in minutes and megabytes (MB) respectively. 0 50 100 150 200 250 300 Epoch 17.25 17.50 17.75 18.00 18.25 18.50 Loss Configuration (96, 4) (128, 8) (256, 8) (256, 16) Figure 1: The decaying loss of pre-trained models. a biased in\ufb02ation of the performance metrics, such as precision and recall, the model was tested only on gold annotated data set comprising 202 documents (cf. Table 1) provided by the n2c2 2018 challenge. 3.2.5. Model evaluation In order to estimate the performance of the proposed named-entity recognition model, we used the evaluation schema proposed in SemEval\u201913 and outlined in Appendix A. The evaluation schema comprised a number of potential errors categories produced by the model and the model performance metrics, such as precision and recall were computed using the expressions A.1. Under the current evaluation schema, partial match was considered as an exact match between the gold-annotated and the predicted labels while no restriction was imposed on the boundaries of the tokens. The rationale behind this approach was obvious from the ambiguity in goldannotations examples corresponding to the same concept. For example, both sequences \u2019for 3 weeks\u2019 and \u20193 weeks\u2019 were labelled as \u2019Duration\u2019. In particular, 492 of 967 (71%) text spans labelled as \u2019Duration\u2019 started with the word \u2019for\u2019. We estimated both, strict and lenient metrics. Strict metrics accounts only for the exact match in both, surface strings and the corresponding labels, whereas the lenient metrics allow for partial matches. Speci\ufb01cally, strict and lenient metrics were obtained from A.1 with \u03b1 = 0 and \u03b1 = 1 correspondingly. We reported both, micro and macro averaged precision and recall and their corresponding F1 scores. 4. Results 4.1. Model pre-training The pre-training task was performed on the entire MIMIC-III data set for 350 epochs using a number of con\ufb01gurations of the width and depth of the convolutional layers. Each con\ufb01guration was trained on a single GTX 2080 Ti GPU. CNN dimensions, summary statistics of the pretraining text corpus, the average running time per epoch in minutes and the model size in MB are summarised in Table 2. The corresponding training losses, logarithmically scaled, are plotted in Fig. 1. 4.2. Rationale for collecting more training data 6 Fraction Accuracy Delta 0% 0.0 baseline 25% 90.66 +90.66 50% 91.93 +1.27 75% 92.42 +0.49 100% 92.63 +0.21 Table 3: Change in accuracy with more training data. Delta denotes a relative improvement. Generally, collecting more training data will improve the model accuracy and lead to better generalisation. We simulated, using the Prodigy library and \u2019train-curve\u2019 recipe, an acquisition of more data by training of NER model on fractions (25%, 50%, 75% and 100%) of the training set and evaluating on the test set. We indeed observed (Table 3) a steady upward trend in improvement of accuracy while using more training data, especially in the last fraction of data which indicates the advantages of further collecting more data. 4.3. Named-entity recognition model The developed Med7 clinical named-entity recognition model was trained in total on 1212 documents, comprising 303 silver training examples augmented with gold annotated data from the o\ufb03cial 303 documents from the n2c2 training data (cf. Table 1) and additionally manually gold annotated 606 documents, randomly sampled from discharge letters of MIMIC-III ensuring that there are no documents present from the testing data. The manual annotation was performed using Prodigy, an active learning annotation tool, following the general procedure outlined in [53]. The baseline NER model for the active-learning support containing all seven categories was trained on the o\ufb03cial 303 documents. The baseline NER model was used within the Prodigy \u2019human-in-the-loop\u2019 framework to suggest entities on unseen texts and a human annotator accepted or corrected model predictions, creating gold annotated examples. We obtained the inter-annotator agreement F1 score of 0.924 between the gold n2c2 annotations and of our two annotators and F1 score of 0.989 between our annotators. The explicit toke-level confusion matrices along with summary statistics are presented in Table B.11, Table B.12 and Table B.13 accordingly. For generating silver training data, we used spaCy python library for keyword phrase matching with \u2019EntityRuler\u2019 class along with linguistic pattern matching with exemplars from the training data set. Drug names, both generic and brand names, were sourced from publicly available online resources. Training results and evaluation statistics are summarised in Table 4 and Table 5 correspondingly. A more detailed token-level confusion matrix showing the exact model predictions is summarised in Table A.9. Gold (n2c2) Silver Prodigy Total Dosage 4227 2792 3437 10456 Drug 16257 10551 12687 39495 Duration 592 462 620 1674 Form 6657 4299 5056 16012 Frequency 6281 4317 5106 15704 Route 5460 3761 4554 13775 Strength 6694 4328 5246 16268 Number of documents 303 303 606 1212 Table 4: The distribution of annotated text spans in three data sets used for training of the NER model. 7 Strict Lenient Precision Recall F1 Precision Recall F1 Dosage 0.879 0.831 0.854 0.957 0.904 0.931 Drug 0.954 0.926 0.941 0.984 0.956 0.971 Duration 0.817 0.733 0.773 0.953 0.854 0.901 Form 0.921 0.886 0.903 0.983 0.947 0.965 Frequency 0.801 0.784 0.792 0.989 0.969 0.979 Route 0.961 0.943 0.952 0.973 0.954 0.964 Strength 0.927 0.781 0.848 0.992 0.836 0.907 Average (micro) 0.916 0.871 0.893 0.982 0.933 0.957 Average (macro) 0.897 0.844 0.869 0.977 0.919 0.947 Table 5: The evaluation results of the NER model on the test set with 202 documents. 4.4. Translation to UK-CRIS data One of the challenges in developing a robust clinical information extraction system, is in its generalisability beyond the data distribution it was trained on. Accurate algorithms developed using data from a small number of medical centres, have demonstrated their poor generalisability when applied within a similar context to other medical centres. For example, in a recent study on the algorithmic approach to early detection of sepsis [54], the training data were sourced from electronic health records of two hospitals, while the data from a third hospital were used for testing the developed algorithm. It has been demonstrated and discussed in details [55] that a highly accurate predictive algorithm, validated on a fraction of data from the same two hospitals, failed to achieve the same level of accuracy when tested on the data from the third hospital, not included in the training process. Poor performance using the out-of-distribution (OOD) data poses a signi\ufb01cant challenge on wider applications of the developed models and is highly important when algorithms inform real-world decisions [56]. Clinical concepts Train Test Total Dosage 298 48 346 Drug 3253 571 3824 Duration 1006 215 1221 Form 410 63 473 Frequency 1604 305 1909 Route 208 32 240 Strength 1338 276 1614 Number of texts 536 134 670 Table 6: Distribution of gold-annotated entities and text summary statistics of the OxCRIS training and test data sets. The number of unique tokens is computed by lowercasing words. We investigated how accurate the developed Med7 model, trained on MIMICIII electronic health records sourced from the Beth Israel Deaconess Medical Center in Massachusetts (United States), can be when applied to CRIS electronic health records in the United Kingdom. We selected a random sample of 670 documents from the Oxford Health NHS Foundation Trust (OFHT) instance of UK-CRIS Network and asked a clinician to annotate them for seven categories following the o\ufb03cial guidelines of the n2c2 challenge. The token-level confusion matrix and the performance metrics of the Med7 model trained on n2c2 data from MIMIC-III and applied to CRIS data from Oxford instance are presented in Table C.14 and in Table 7 correspondingly. Direct comparison to the results presented in Table 5 (F1=0.762 vs. F1=0.944) clearly shows the problem of direct transferability of 8 NER models trained on di\ufb00erent data sources. Before \ufb01ne-tuning on OxCRIS After \ufb01ne-tuning on OxCRIS Precision Recall F1 Precision Recall F1 Dosage 0.826 0.396 0.535 0.656 0.833 0.734 Drug 0.912 0.968 0.939 0.975 0.977 0.976 Duration 0.951 0.107 0.192 0.883 0.934 0.908 Form 0.554 0.611 0.581 0.924 0.968 0.946 Frequency 0.912 0.332 0.487 0.941 0.944 0.942 Route 0.348 0.719 0.469 0.882 0.938 0.909 Strength 0.938 0.877 0.906 0.996 0.917 0.955 Average (micro) 0.864 0.681 0.762 0.941 0.947 0.944 Average (macro) 0.778 0.586 0.609 0.901 0.932 0.914 Table 7: The lenient evaluation results of the Med7 model using 134 test documents sourced from OxCRIS the Oxford Health NHS Foundation Trust from within the UK-CRIS electronic health records Network. 5. Discussion The developed named-entity recognition model for clinical concepts in unstructured medical records was trained to recognise seven categories, such as drug names, including both generic and brand names, dosage of the drugs, their strength, the route of administration, prescription duration and the frequency. The data for model development and testing was sourced from the n2c2 challenge, comprising a collection of 303 and 202 documents for training and testing respectively, which represent a sample from the MIMIC-III electronic health records. We demonstrated (Section 4.2) that collecting more annotated examples would improve the model accuracy and therefore implemented two approaches for obtaining more annotations: noisy labelling and active learning with \u2019human-in-the-loop\u2019. For the noisy labelling, we create a list of unique patterns for each of the seven categories, sourced from the training corpus and from external resources available on the internet, and then used regular expression with string pattern matching to assign labels to tokens. Our two annotators were trained by closely following the o\ufb03cial 2018 n2c2 annotation guidelines and demonstrated a high level of inter-annotator agreement among themselves (F1=0.989) as well as a high-level of concordance (F1=0.924) with the gold-annotations provided by the organisers of 2018 n2c2 Challenge (cf. Table B.13). The overall (micro-averaged) performance of the NER model across all seven categories was F1=0.957 (0.893), with Precision=0.982 (0.916) and Recall=0.933 (0.871) for lenient (strict) estimates. More detailed breakdown of the performance for each of the categories is presented in Table 5. The performance for \u2019Duration\u2019 and \u2019Frequency\u2019 categories was poorer. There were intrinsically fewer cases of \u2019Duration\u2019 (\u223c1.5%) appeared in texts and these concepts were also ambiguously annotated as mentioned in Section 3.2.5. A similar situation was also observed for the \u2019Frequency\u2019 category, where in spite of a good number of the annotated examples (\u223c14%), the ambiguity in the presentation of text spans was higher, which resulted in a large number of partial matches (cf. Table A.9). Another reason for poor performance for both \u2019Duration\u2019 and \u2019Frequency\u2019 was due to inconsistent annotations, where the same text string appeared in both categories. 9 Self-supervised pre-training of deep learning models has shown its e\ufb03ciency in many NLP task. We experimented with a number of architectural variations of the width and depth of convolutional layers as well as the size of the embedding rows. Empirically, and as con\ufb01rmed by other studies [57], larger models, with more parameters, tend to achieve better results. Interestingly, the larger model (Width=256, Depth=16, Embeddings=10000) outperformed the default one (Width=96, Depth=4, Embeddings=2000) by a small margin (F1256=0.893 vs F196=0.884) however, the di\ufb00erences were more visible for \u2019Duration\u2019 (F1256=0.773 vs F196=0.729) and \u2019Strength\u2019 (F1256=0.848 vs F196=0.801). The better performance resulted at the expense of the training time, its size on a disk and the memory consumption. We publicly released the pretrained neural network weights for various architectures through the dedicated GitHub repository4. Another objective of this work was to estimate the degree of transferability of the developed information extraction model to another clinical domain. We evaluated how the Med7 model, trained on a collection of discharge letters from the intensive care unit in the US (MIMIC), performed on the secondary care mental health medical records in the UK (CRIS). The Med7 model was purposely designed to recognise non-context related medical concepts, such as drug names, strength, dosage, duration, route, form and frequency of administration and we expected to see a comparable level of the model performance across the both EHR systems. To consistently validate the transferability of the Med7 model, a random sample of 670 gold-annotated examples from OxCRIS were split into training (536) and test (134) data sets (cf. Table 6). We compared the performance of the Med7 model without and with \ufb01ne-tuning on OxCRIS. The direct application of Med7 on the testing set of 134 documents, resulted in a quite poor performance (F1=0.762). We investigated the cases where the model was predicting incorrectly and in the majority of them, the main reason for poor performance was due to di\ufb00erences in the language presentation of the concepts. For examples, the model largely missed concepts labelled as \u2019Frequency\u2019 in OxCRIS, such as \u201dON\u201d, (\u201devery night\u201d), \u201dOD\u201d (\u201devery day\u201d), \u201dBD\u201d (\u201dtwice daily\u201d), \u201dOM\u201d (\u201devery morning\u201d), \u201dmane\u201d and \u201dnocte\u201d. Then, we \ufb01ne-tuned the Med7 model on the training set of OxCRIS (536 documents) and evaluated on the same testing set as before of 134 documents. Despite the small number of training examples in OxCRIS, leveraging the transfer learning approach of re-using the pre-trained Med7 model on MIMIC, resulted in higher accuracy (F1=0.944) comparable with training and testing on the same domain (cf. Table 7). One strength on this project is in the interoperability of the developed model with other generic deep learning NLP libraries, such as HuggingFace and Thinc as well as straightforward integration with pipelines developed under the spaCy framework. This allows to customise the Med7 model and include other pipeline components, such as negation detection, entity relations extraction and to map the extracted concepts onto the universal medical language system (UMLS). Normalisation of concepts to UMLS categories will allow to systematically parse electronic medical records into structured and consistent tabular form which will be ready for downstream epidemiological analyses. Additionally, the developed model naturally integrates into the Prodigy annotation tool, which allows to e\ufb03ciently collect more gold-annotated examples. It is also worth mentioning that the Med7 model is designed to run on standard CPUs, rather than expensive GPUs. This fact will allow researchers without access to expensive and complex infrastructure to develop fast and robust pipelines for clinical natural language processing. However, two limitations should be noted. First, is that some of the categories are naturally underrepresented which impacts the accuracy of the NER model. It was observed empirically 4https://github.com/kormilitzin/med7 10 that the number of annotated \u2019Duration\u2019 entities was intrinsically skewed in the medical records, in contrast to drug names and strength, making it more challenging to train a robust model to accurately identify these entities. Interestingly, the same pattern of the number of reported mentions of the \u2019Duration\u2019 category persists in both, MIMIC and OxCRIS data, which might be indicative of a general clinical reporting pattern. A second limitation of this study is related to a low number of the manually-annotated examples in OxCRIS, in order to run more rigours evaluations of the transferability of the Med7 model across all seven categories. Future research into the robust clinical information extraction system will need to further address the feasibility of deploying the model in the UK-CRIS Network Trust members and evaluate its transferability. The aim is to furnish clinical researchers with an open source and a robust tool for structuring free-text patients\u2019 data for downstream analytical tasks. 6. Conclusion In this work we developed and validated a clinical named-entity recognition model for freetext electronic health records. The model was developed using the MIMIC-III free-text data and trained on a combination of the manually annotated data from the 2018 n2c2 challenge, on a random sample from MIMIC-III with noisy labels and manually annotated data using active learning with Prodigy. To maximise the utilisation of a large amount of unstructured free-text data and alleviate the problem of training from limited data, we used self-supervised learning to pre-train the weights of the NER neural network model. We demonstrated that transfer learning plays an essential role in developing a robust model applicable across di\ufb00erent clinical domains and the developed Med7 model does not require an expensive infrastructure and can be used on standard machines with CPU. Further research is needed to improve recognition of naturally underrepresented concepts and we are planning to address this problem, as well as extracted concepts normalisation and UMLS linkage in our future releases of the Med7 model. Acknowledgments The study was funded by the National Institute for Health Research\u2019s (NIHR) Oxford Health Biomedical Research Centre (BRC-1215-20005). This work was supported by the UK Clinical Records Interactive Search (UK-CRIS) system funded and developed by the NIHR Oxford Health BRC at Oxford Health NHS Foundation Trust and the Department of Psychiatry, University of Oxford. AK, NV, QL, ANH are funded by the MRC Path\ufb01nder Grant (MC-PC-17215). We are thankful to the organisers of the n2c2 2018 Challenge for providing annotated corpus and the annotation guidelines. The views expressed are those of the authors and not necessarily those of the UK National Health Service, the NIHR, or the UK Department of Health. We would also like to acknowledge the work and support of the Oxford CRIS Team: Tanya Smith, Head of Research Informatics and Biomedical Research Centre (BRC) CRIS Theme Lead and Lulu Kane, Adam Pill and Suzanne Fisher, CRIS Academic Support and Information Analysts. Appendix A. The evaluation schema for extracted concepts In order to evaluate the output of the NER system, we adopted the notations developed for different categories of errors [58] and the evaluation schema introduced in SemEval\u201913 (cf. Eq.A.1). 11 The following types of evaluation errors were considered (Table A.8): Error Type Gold Standard NER Prediction Text span Label Text span Label 1 Correct (COR) aspirin Drug aspirin Drug 2 Incorrect (INC) 25 Strength 25 Dosage 3 Partial (PAR) Augmentin Drug Augmentin XR Drug 4 Partial (PAR) for 3 weeks Duration 3 weeks Duration 5 Partial (PAR) p.r.n. Frequency prn Frequency 6 Missing (MIS) tablet Form 7 Spurious (SPU) Codeine Drug Table A.8: A list of examples of typical errors produced by the NER model. where Correct(COR) represents a complete match of both, the annotation boundary and the entity type. Incorrect(INC) is the case where at least one of the predicted boundary or the entity type do not match. Partial(PAR) match corresponds to predicted entity boundary which overlaps with ground-truth annotation, but they are not exactly the same. Missing(MIS) the case where the ground-truth annotated boundary is not predicted by the NER, but the ground-truth string is present in the gold-annotated corpus. Spurious(SPU) corresponds to predicted entity boundary which does not exist in the gold-annotated corpus. Possible (POS) = COR + INC + PAR + MIS = TP + FN Actual (ACT) = COR + INC + PAR + S PU = TP + FP Precision = (COR + \u03b1PAR)/ACT Recall = (COR + \u03b1PAR)/POS (A.1) The detailed token-level confusion matrix of the model predictions following the error types de\ufb01ned in A.1. Predicted categories Dosage Drug Duration Form Frequency Route Strength Missed Partial True categories Dosage 2225 0 6 10 24 1 16 200 199 Drug 2 9796 0 7 0 4 1 449 316 Duration 6 0 277 0 8 0 2 39 46 Form 38 31 0 3864 1 65 6 90 264 Frequency 1 3 4 5 3144 2 0 108 745 Route 3 4 0 43 1 3312 1 108 41 Strength 38 3 0 1 2 0 3304 650 232 Spurious 20 120 6 4 7 22 3 Table A.9: Token-level confusion matrix of the predicted entities versus the ground truth labels. Spurious examples correspond to predicted entity boundary and type which do not exist in ground-truth annotations and partial matches correspond to predicted entity boundary overlap with golden annotation, but they are not the same. Missing entities correspond to ground-truth annotation boundary which were not identi\ufb01ed. 12 Appendix B. Inter-annotator agreement analysis We estimated the level of concordance between the gold-annotated corpus from the n2c2 2018 challenge and two trained annotators. The annotators closely followed the same annotation guidelines as used in the challenge. Ten documents were sampled at random from 202 documents comprising the test set. The distribution of gold-annotated tokens and by two annotators is presented in Table B.10. Types of annotated entities Gold (n2c2) Annotator 1 Annotator 2 Dosage 128 139 139 Drug 519 530 526 Duration 28 31 32 Form 234 246 238 Frequency 193 196 201 Route 179 167 167 Strength 200 212 205 Number of documents 10 10 10 Table B.10: The number of the gold and manually annotated entities for the inter-annotator agreement evaluation corpus, comprising ten randomly sampled texts from the test set of 202 documents. Annotator 1 Dosage Drug Duration Form Frequency Route Strength Missed Partial Gold (n2c2) Dosage 104 0 1 3 0 0 2 17 4 Drug 0 473 0 3 0 1 0 27 21 Duration 0 0 19 0 0 0 0 2 7 Form 1 4 0 201 0 2 0 7 21 Frequency 1 0 0 0 172 0 1 2 17 Route 2 2 0 2 0 156 0 15 2 Strength 2 1 0 0 0 0 171 4 28 Spurious 25 29 4 16 7 6 10 Table B.11: Token-level confusion matrix of the annotator 1 versus the gold-standard annotations provided by 2018 n2c2 challenge. Annotator 2 Dosage Drug Duration Form Frequency Route Strength Missed Partial Gold (n2c2) Dosage 104 0 1 3 0 0 2 17 4 Drug 0 472 0 3 0 1 0 30 20 Duration 0 0 19 0 0 0 0 2 7 Form 0 3 0 201 0 2 0 9 21 Frequency 0 0 1 0 172 0 0 2 18 Route 2 2 0 2 0 156 0 15 2 Strength 3 1 0 0 4 0 171 3 21 Spurious 26 28 4 8 7 6 10 Table B.12: Token-level confusion matrix of the annotator 2 versus the gold-standard annotations provided by 2018 n2c2 challenge 13 Annot. 1 vs. Gold Annot. 2 vs. Gold Annot. 1 vs. Annot. 2 Pr Re F1 Pr Re F1 Pr Re F1 Dosage 0.777 0.824 0.801 0.777 0.824 0.801 0.986 0.986 0.986 Drug 0.935 0.935 0.935 0.935 0.935 0.935 0.998 0.991 0.994 Duration 0.812 0.923 0.867 0.812 0.929 0.867 0.969 1.000 0.984 Form 0.933 0.941 0.937 0.933 0.941 0.937 1.000 0.967 0.983 Frequency 0.945 0.984 0.964 0.945 0.984 0.964 0.975 1.000 0.987 Route 0.946 0.883 0.913 0.946 0.883 0.913 1.000 1.000 1.000 Strength 0.941 0.946 0.944 0.941 0.946 0.944 1.000 0.962 0.981 Average (micro) 0.921 0.928 0.924 0.921 0.928 0.924 0.994 0.985 0.989 Average (macro) 0.901 0.921 0.911 0.901 0.921 0.911 0.991 0.986 0.988 Table B.13: The evaluation results of the inter-annotator agreement on a random selection of ten documents from the 202 test texts. A pair-wise comparison between each of the annotators and the gold-annotated documents as well as the direct comparison between the both annotators. We examined the cases where our two annotators labelled the concepts of interests di\ufb00erently than those found in the gold-annotated data set provided by the n2c2 team. Appendix C. Fine-tuning on UK-CRIS Med7-predicted categories: before \ufb01ne-tuning on OxCRIS Dosage Drug Duration Form Frequency Route Strength Missed Partial Gold annotated Dosage 18 0 0 0 0 0 12 17 1 Drug 0 535 0 0 0 0 0 18 15 Duration 0 0 18 0 1 0 0 158 1 Form 0 2 0 34 0 1 0 20 2 Frequency 0 7 0 25 86 40 1 114 7 Route 0 0 0 3 3 23 0 6 0 Strength 3 0 0 0 0 0 238 31 4 Spurious 1 44 1 1 8 2 3 Table C.14: Token-level confusion matrix of the Med7 model trained on MIMIC-III and applied to 134 manually annotated documents from the Oxford instance (OxCRIS) of the UK-CRIS electronic medical records Network. Med7-predicted categories: after \ufb01ne-tuning on OxCRIS Dosage Drug Duration Form Frequency Route Strength Missed Partial Gold annotated Dosage 39 0 0 0 0 0 1 7 1 Drug 0 553 0 2 0 0 0 11 4 Duration 0 0 177 0 1 0 0 13 20 Form 0 0 0 61 1 1 0 0 0 Frequency 1 1 0 2 279 1 0 12 6 Route 0 0 0 0 0 30 0 2 0 Strength 16 1 0 0 0 0 242 6 11 Spurious 4 12 26 1 16 2 0 Table C.15: Token-level confusion matrix of the Med7 model trained on MIMIC-III and applied to 134 manually annotated documents from the Oxford instance (OxCRIS) of the UK-CRIS electronic medical records Network. 14",
                    "introduction": "Recent years have seen remarkable technological advances in digital platforms for medicine and healthcare. The majority of patients\u2019 medical records are now being collected electronically and represent unparalleled opportunities for research, delivering better health care and improv- ing patients\u2019 outcomes. However, a substantial amount of patients\u2019 information is contained in a free-text form as summarised by clinicians, nurses and caregivers through the interview and 1Corresponding author: andrey.kormilitzin@psych.ox.ac.uk Preprint submitted to Elsevier April 27, 2020 arXiv:2003.01271v2  [cs.CL]  24 Apr 2020 assessments. The textual medical records contain rich information about a patient\u2019s history as it is expressed in natural language and allows to re\ufb02ect nuanced details. However, free-texts pose certain challenges in their direct utilisation as opposed to structured and ready-to-use data sources. Manual processing of all patients\u2019 free-texts records severely limits the utilisation of unstructured data and makes the process of data mining extremely expensive. On the other hand, machine learning algorithms are well poised to process a large amount of data, spot unusual in- teractions and extract meaningful information. Recent lines of research in the \ufb01eld of natural language processing (NLP), such as deep contextualised word representations [1], Transformer- based architectures [2] and large language models [3], o\ufb00er new opportunities for clinical natural language processing with unstructured medical records [4]. However, despite recent technologi- cal advances, there are a number of challenges pertinent to the \ufb01eld of clinical NLP which should be addressed in order to develop trustworthy models for information extraction. One of the fore- most challenges is the dearth of high quality annotated examples to robustly train generalisable models. Large amounts of medical data cannot be made publicly available for crowdsourcing annotations, similar to ImageNet [5, 6] or by means of Amazon Mechanical Turk, due to ethical consideration of patients privacy preservation and information security [7]. Therefore, most of the data annotations are made by a limited amount of domain experts, such as clinicians or nurses, and cannot be shared. Since 2006, the Informatics for Integrating Biology and the Bedside (i2b2) initiative [8] has been organising regular challenges on clinical natural language processing and the organisers have been providing a sample of carefully selected for each particular task fully anonymised annotated data. The data were sourced from the Medical Information Mart for In- tensive Care (MIMIC) electronic health records (EHR) database [9]. Identi\ufb01cation of concepts of interest in free-texts is a sub-task of information extraction (IE), more commonly known as named-entity recognition (NER). The NER task seeks to classify words into prede\ufb01ned categories [10] and to assign labels to them. A robust and accurate NER model for identi\ufb01cation of medical concepts, such as drug names, strength, frequency of ad- ministration, reported symptoms, diagnoses, health score and many more, is an essential and foundational component of any clinical IE system. However, in order to develop a reliable and generalisable NER model for real-world observational data, one should \ufb01rst address a number of challenges. Despite the availability of both, annotated i2b2 data and the entire MIMIC electronic health records (EHR) database, the models developed using these data sources are not guaranteed to generalise robustly on other, yet similar EHR datasets, even on the same downstream tasks. Many supervised learning algorithms are based on the assumption that the training and test sets are sampled from the same distribution. However, when the target and the source domains are di\ufb00erent, it is expected that the model will underperform [11]. One of the potential solutions to transferability of a model trained to recognise concepts from labelled data in a source domain that also performs well on a di\ufb00erent but related target domain, regarded as domain adaptation [12, 13]. In this study we address the aforementioned problems by implementing three strategies. First, the underlying deep neural network language model was self-supervisedly pre-trained on the entire MIMIC-III corpora comprising more than 2 million documents using the cloze-style ap- proach [14]. Second, using the weak-supervision method [15], we developed synthetic training data with noisy labels. Lastly, we synergistically incorporated all ingredients into an active learn- ing with human-in-the-loop approach to maximise the accuracy of the NER model. Additionally, we demonstrated that the developed NER model trained on a source domain from the intensive care MIMIC EHR data in the US, failed to generalise well on the target domain 2 sourced from the secondary care mental health Clinical Record Interactive Search system (CRIS) in the United Kingdom. We also showed that using domain adaption, the NER model could be adequately transferred from MIMIC to CRIS."
                },
                {
                    "url": "http://arxiv.org/abs/1908.11399v1",
                    "title": "Deep Learning for Estimating Synaptic Health of Primary Neuronal Cell Culture",
                    "abstract": "Understanding the morphological changes of primary neuronal cells induced by\nchemical compounds is essential for drug discovery. Using the data from a\nsingle high-throughput imaging assay, a classification model for predicting the\nbiological activity of candidate compounds was introduced. The image\nrecognition model which is based on deep convolutional neural network (CNN)\narchitecture with residual connections achieved accuracy of 99.6$\\%$ on a\nbinary classification task of distinguishing untreated and treated rodent\nprimary neuronal cells with Amyloid-$\\beta_{(25-35)}$.",
                    "authors": "Andrey Kormilitzin, Xinyu Yang, William H. Stone, Caroline Woffindale, Francesca Nicholls, Elena Ribe, Alejo Nevado-Holgado, Noel Buckley",
                    "published": "2019-08-29",
                    "updated": "2019-08-29",
                    "primary_cat": "eess.IV",
                    "cats": [
                        "eess.IV",
                        "cs.LG",
                        "q-bio.QM",
                        "stat.ML"
                    ],
                    "main_content": "Recent years have seen an explosion of applications of the deep learning methods to medical imaging, including computer-aided diagnosis (CAD) in radiology and medical image analysis [6, 7, 8]. The \u2217Equal contribution. Preprint. Under review. arXiv:1908.11399v1  [eess.IV]  29 Aug 2019 ef\ufb01ciency of deep learning models for cytometry [9] has been widely recognised and applied to cell imaging [10], virtual staining with generative adversarial networks (GAN) [11, 12], \ufb02uorescence microscopy [13] and reconstructing cell cycles and disease progression [14]. However, despite the wide popularity and maturity of the deep learning approach, very little has been done to estimate the effect of biological activity of neuronal cells induced by compounds and searching for drugs that may protect against neurodegeneration and Alzheimer\u2019s disease. Simm et al. in [15] suggested to re-purpose high-throughput images assay to predict biological activity in drug discovery, however this approach depends on the features extracted from CellPro\ufb01ler [16] and lacks the \ufb02exibility of the CNN models [17] which learn features directly from raw pixels of images. 3 Materials and methods 3.1 The assay design Primary neuronal cells were seeded in 96 well plates and cultured for 21 days in vitro to allow them to establish neuronal connections and to synaptically mature. Cells are then pre-treated for one hour with one candidate compound in doses of either 10, 3 or 1 \u00b5M2 before the addition of 30 \u00b5M of A\u03b2(25\u221235) or a vehicle control. Cells are incubated for a further 48 hours before they are \ufb01xed and stained for various markers. The assay plate con\ufb01guration and the location of compounds and A\u03b2 at various doses (in \u00b5M) are presented in Fig. 1 and Tab. 1 respectively. For example, wells in column \u2019B\u2019 at rows 2, 3, 4 and wells in columns \u2019C\u2019 at rows 5,6,7 all contain zero dose of a compound and a zero dose of A\u03b2, which corresponds to a vehicle control. Wells in column \u2019D\u2019 and rows 2,3,4 and wells in column \u2019E\u2019 and rows 5,6,7 all contain a combination of 1 \u00b5M of a compound and 30 \u00b5M of A\u03b2. B  C  D  E  F  G  H  J  2  3  4  5  6  7  Figure 1: An assay plate with wells. Well position index Compound A\u03b2 B{2,3,4}, C{5,6,7} 0 0 C{2,3,4}, D{5,6,7} 0 30 D{2,3,4}, E{5,6,7} 1 0 E{2,3,4}, F{5,6,7} 1 30 F{2,3,4}, G{5,6,7} 3 0 G{2,3,4}, H{5,6,7} 3 30 H{2,3,4}, J{5,6,7} 10 0 F{2,3,4}, B{5,6,7} 10 30 Table 1: The position map of compounds and doses. To highlight speci\ufb01c cellular structure, four stains were used: MAP2 (neuronal cytoskeleton marker), PSD-95 (post-synaptic protein marker), Synaptophysin (pre-synaptic protein marker) and Hoescht 33342 (nucleic marker). Cells are then imaged at magni\ufb01cation of 40x using the high-content GE IN Cell Analyzer 6000TM imaging system. Each well was images 30 times (\u2019\ufb01eld views\u2019) using non-overlapping strides for each of the four channels; MAP2 (Cy5), Nucleus (DAPI), Synaptophysin (dsRed), PSD-95 (FITC). This resulted in 5760 images per plate used in the analysis. 3.2 The deep learning model The objective of this work was to develop a classi\ufb01cation model able to reliably recognise morphological changes in neuronal cells treated with A\u03b2(25\u221235) versus the vehicle control (\u2019untreated\u2019). Once trained to a satisfactory accuracy, the the model was applied to screen candidate compounds and determine whether images of cells treated with a compound + A\u03b2(25\u221235) were more similar to those treated with A\u03b2(25\u221235) alone. For this purpose, we developed a CNN-based [17] binary classi\ufb01er. The model used in classi\ufb01cation is based on the Resnet18 [18] architecture with weights pre-trained on the ImageNet data [19] and implemented in PyTorch [20] and fastai [21] python libraries. The model was \ufb01ne-tuned on a binary classi\ufb01cation task using 6480 of untreated and 6480 of treated images of neuronal cells of size 2048 by 2048 pixels. To mitigate the problem of over\ufb01tting, data augmentations with default settings of random cropping, \ufb02ipping both horizontally and vertically, small rotations and shearing were used. We used dropout [22] of 0.35, leading to stable convergence. The training was done using SGD with momentum of 0.9, slanted learning rate 2\u00b5M stands for micro molar, is a measure of the concentration of a chemical substance in a solution 2 [23, 24] with the optimal one [25]. The batch size of 4 was used due to memory limitation of NVIDIA 2080Ti GPU. The entire training procedure was split into two bits: \ufb01rst training the classi\ufb01cation head and then gradual unfreezing of convolutional layers. The classi\ufb01cation head comprised one fully connected layers of 512 neurons with ReLU activation function [26] and the \ufb01nal binary softmax function. No weight decay was used. In order to visualise individual pixels that supported the decision of the classi\ufb01cation model and for sanity check that the model\u2019s decisions are not due to image artefacts the weighted Grad-CAM [27] was implemented. The visualisation methods showed that the \u201cattention\u201d of the model was drawn towards speci\ufb01c neurites; providing assurance that the model \ufb01t true features of the data. A\u03b2 peptide has been found as a dominant mediator of neuronal dystrophy and synaptic loss [28] which is re\ufb02ected in the morphology of neuronal cytoskeleton structure. Therefore in the current work we focused only the Cy5 stain which highlights the cytoskeleton structure. However, we are planning on extending this approach and develop a multi-channel model which learns from all four stains simultaneously. We believe that further inclusion of all four channels (Cy5, DAPI, dsRed and FITC) will improve the detection capability and improve our understanding of morphological changes induced by compounds at various doses. 4 Results Of 36 assay plates, with a unique compound in each plate, 34 were randomly selected for training and the remaining 2 for testing. However, the model was trained only on images of neurons treated with vehicle controls and A\u03b2, whereas all remaining wells with various treatment regimes were unused. Therefore the unused images can be safely used for inference. The main reason behind setting aside two assay plates was to test the model performance on vehicle controls and A\u03b2. The list of 36 compounds is presented in Table 5 in A. and the distribution of predicted scored of vehicle controls and A\u03b2 are presented in Fig. 4 and Fig. 5. We applied data augmentation to training images including random scaling, \ufb02ipping, cropping, and other af\ufb01ne transformations using the package imgaug [29]. The model was trained for 10 epochs on the last convolution block and the fully connected layer with learning rate 1e-3, and another 10 epochs on all layers with learning rate 1e-4, all using the stochastic gradient descent (SGD) optimizer with momentum 0.9. The training results are summarised in Table 2. Training loss Training accuracy Validation loss Validation accuracy 0.012 99.68% 0.013 99.58% Table 2: Training and validation accuracies and losses. In the inference mode, the model prediction scores for each individual well were averaged over \ufb01eld views. The resulting prediction for each treatment regimen was averaged over six wells and the standard deviation computed. The results of model predictions for Raubasine and Thiamphenicol compounds are presented in Tables 3 and 4 respectively. The threshold of 0.5 was used to convert predicted scores to dichotomous categories (untreated and treated with 30 \u00b5M of A\u03b2(25\u221235)). compound dose (\u00b5M) 0 0 1 1 3 3 10 10 A\u03b2 dose (\u00b5M) 0 30 0 30 0 30 0 30 well1 0.0 0.87 0.01 0.92 0.01 0.93 0.01 0.69 well2 0.01 0.93 0.0 0.83 0.07 0.86 0.07 0.68 well3 0.21 0.87 0.04 0.7 0.47 0.94 0.01 0.87 well4 0.08 0.91 0.0 0.82 0.07 0.96 0.02 0.81 well5 0.03 0.93 0.06 0.87 0.01 0.84 0.03 0.91 well6 0.0 0.89 0.0 0.48 0.02 0.68 0.04 0.71 mean predicted score 0.05 0.9 0.02 0.77 0.10 0.87 0.03 0.78 standard deviation 0.11 0.21 0.07 0.27 0.14 0.18 0.09 0.29 Table 3: An example of screening of Raubasine compound at various doses. 3 The combination of zero dose of both a compound and A\u03b2 corresponds to a vehicle control. For example, the neuronal cells treated with Raubasine 1 \u00b5M and 30 \u00b5M of A\u03b2, were classi\ufb01ed as treated with A\u03b2 30 \u00b5M, which means there is a not signi\ufb01cant protective effect of Raubasine at this dose against synaptic loss induced by A\u03b2. Similarly, neuronal cells treated with larger doses of Raubasine (10 \u00b5M) were also classi\ufb01ed as treated with only A\u03b2. compound dose (\u00b5M) 0 0 1 1 3 3 10 10 A\u03b2 dose (\u00b5M) 0 30 0 30 0 30 0 30 well1 0.01 0.83 0.02 0.95 0.01 0.78 0.05 0.87 well2 0.02 0.83 0.01 0.96 0.01 0.76 0.03 0.79 well3 0.03 0.93 0.08 0.9 0.04 0.86 0.02 0.68 well4 0.0 0.84 0.18 0.76 0.01 0.81 0.01 0.85 well5 0.0 0.86 0.0 0.81 0.01 0.85 0.01 0.94 well6 0.0 0.88 0.01 0.85 0.06 0.97 0.02 0.98 mean predicted score 0.01 0.86 0.05 0.87 0.02 0.84 0.02 0.85 standard deviation 0.03 0.22 0.07 0.19 0.07 0.23 0.06 0.2 Table 4: An example of screening of Thiamphenicol compound at various doses. 5 Conclusions We report the validation accuracy of 99.58% on a binary images classi\ufb01cation problem using highthroughput images of neuronal cells that have been treated with vehicle control versus images treated with 30 \u00b5M of A\u03b2(25\u221235). Amyloid-\u03b2 is thought to induce synapse loss. The developed deep learning based high throughput method which is able to identify and measure this synapse loss and then use this technique to identify when compounds can rescue it. None of 36 screened compounds (Table 5) applied to neuronal cells at various doses was found as having a substantial protective effect against A\u03b2(25 \u221235). This result was con\ufb01rmed by screening the same assay plates of 36 compounds using the image processing pipeline of CellPro\ufb01ler followed by statistical hypothesis testing of the extracted features. In contrast to a deep CNN model, CellPro\ufb01ler [16] requires a substantial amount of computational resource to process the same number of images. For example, with 48 CPUs, a typical imaging processing of a single plate takes approximately 15 hours to complete in contrast to 60 seconds using the deep learning model in the inference mode. In addition to a long computation time, large scale screening of hundreds or thousands of compounds will result in a substantial carbon footprint compared to re-suing of pre-trained deep learning models. The visualisation of pixel-wise attention of the model using Grad-CAM is presented in B. The results demonstrated in Fig. 2 and Fig. 3 are randomly selected images from each of the treatment regimes for two compounds (Raubasine and Thiamphenicol) which were not used in the training (hold-out set). Various bits of the cytoskeleton structure found important for the classi\ufb01cation decision of the model. The Grad-CAM methods highlights the important regions in the image for predicting the class label. The predicted scores are predominantly distributed around zero or one, except for a few wells (C). This chart allows neurobiologists to manually inspect particular wells where the distribution of predicted scores is not clustered around zero or one. Such cases might be caused by contaminated wells, blurred imaging or other artefacts which may confuse the image classi\ufb01cation model. Learning synaptic features and segmentation of cytoskeleton structure have been explored previously [30, 31, 32]. Recently, a signature-based approach [33, 34] to learning from ordered data has been proposed and applied to various tasks in image and character recognition [35, 36, 37]. The signature transforms sequentially ordered data a path, into a succinct representation, effectively capturing global and local information. The signature transformation is used as feature representation in downstream machine learning tasks. The signature method was used in mental health [38, 39, 40], prediction of diagnosis of Alzheimer\u2019s disease [41, 42], \ufb01nance [43, 44, 45] and deep signature learning [46]. The cytoskeleton structure could be factorised into a collection of branching diagrams, 4 making it suitable for signature-based learning. We plan to investigate this approach to effective learning of morphological changes of neuronal cells in our future works. Although the images of neuronal cells were taken from rodents, potentially the developed method could be generalised in humans via transfer learning with the \ufb01nal goal of ef\ufb01ciently identifying novel compounds to reverse the effect of A\u03b2 and drug development for neurodegeneration and Alzheimer\u2019s disease. Acknowledgements AK is supported by the MRC under the Path\ufb01nder programme grant MC/PC/17215. The work of XY is supported in part by the Oxford Alzheimer\u2019s Researck UK (ARUK) Pilot Project Award.",
                    "introduction": "Alzheimer\u2019s disease is the third leading cause of death in the US and globally [1]. The economic cost of Alzheimer\u2019s disease is estimated to be $36.512 billion in the US alone and expected to rise to $2 trillion by 2030 globally [2]. It has been shown that the \u03b2-Amyloid (A\u03b2) peptide is involved in Alzheimer\u2019s disease [3] and found in the brains of Alzheimer patients [4, 5]. Searching for new chemical compounds, which moderate the previously identi\ufb01ed A\u03b2 driven DKK1-Wnt-PCP-JNK neurotoxic signalling pathway, may reverse the effect of toxic depositions of A\u03b2 plaques in the brain and will inform the development of novel therapeutic approaches for the treatment of Alzheimer\u2019s disease. We hypothesise that by reversing or preventing these changes in gene expression, this may protect against the toxic effects seen in primary rodent neuronal cultures following treatment with A\u03b2(25\u221235). The standard and laborious approach to assess whether a candidate compound may have a protective effect, is to perform a statistical hypothesis testing using the features extracted with CellPro\ufb02ier image processing tool across various treatment regimes. The proposed deep-learning approach eliminates the need for this statistical comparison and estimates the treatment effects from raw pixels of high-throughput images."
                },
                {
                    "url": "http://arxiv.org/abs/1708.01206v1",
                    "title": "Detecting early signs of depressive and manic episodes in patients with bipolar disorder using the signature-based model",
                    "abstract": "Recurrent major mood episodes and subsyndromal mood instability cause\nsubstantial disability in patients with bipolar disorder. Early identification\nof mood episodes enabling timely mood stabilisation is an important clinical\ngoal. Recent technological advances allow the prospective reporting of mood in\nreal time enabling more accurate, efficient data capture. The complex nature of\nthese data streams in combination with challenge of deriving meaning from\nmissing data mean pose a significant analytic challenge. The signature method\nis derived from stochastic analysis and has the ability to capture important\nproperties of complex ordered time series data. To explore whether the onset of\nepisodes of mania and depression can be identified using self-reported mood\ndata.",
                    "authors": "Andrey Kormilitzin, Kate E. A. Saunders, Paul J. Harrison, John R. Geddes, Terry Lyons",
                    "published": "2017-08-03",
                    "updated": "2017-08-03",
                    "primary_cat": "stat.ML",
                    "cats": [
                        "stat.ML"
                    ],
                    "main_content": "2.1. Data The data were collected as part of the OXTEXT-1 study (Bilderbeck et al., 2017). The participants completed standardised questionnaires on a weekly basis using the True Colours mood monitoring system after receiving a text or email prompt. The data were collected in an observational manner and independent from the clinical care. Self-reported mood data using the Quick Inventory of Depressive Symptoms (QIDS-SR16) (Rush et al., 2003) and Altman Self-Rating Mania scale (ASRM) (Altman et al., 1997). A depressive episode was defined as a QIDS score of above 11 for at least two consecutive weeks. A manic episode was defined as an AMRS score above a threshold 6 for at least one week (Kessler et al., 2005). 2.2. Demographics and Patient Selection The original cohort contained 286 subjects. Data collected from 01-Jan-2012 until 31-Dec-2016 was included in this analysis. We excluded 25 participants from the analysis: 22 participants had unconfirmed diagnoses and 3 participants withdrew consent. Of the 261 included participants 148 and 113 subjects were diagnosed with bipolar type I and type II, (denoted by BP-I and BP-II) respectively. All identical duplicate values were removed. If there were multiple responses within a week, only the first response was considered. Additionally, we excluded patients who stayed less than 5 weeks in self-monitoring and all of those who had no recorded mood episodes during the study period. From the exploratory analysis, we found that only 59% of patients (155/261) in this cohort had episodes of depression (spent at least two weeks in depression) and 69% (181/261) had manic episodes (at least one week). The reported ethnicity and education level in accordance with the standard classification. One male from the BP-II group did not report his ethnicity. One male from the BP-I group, one male from the BP-II group, two females, one BP-I and one BP-II did not report their education levels. Percents of relevant groups may not add up to 100 due to rounding errors. The adjusted adherence corresponds to the period of observations between the first and the last actual responses. The demographic data summarised in Table 1. 2.3. Signature-based Predictive Model We used a rolling window analysis to learn temporal dependencies in the data. This is a commonly used method to estimate changes and reveal patterns in sequential data over time (Zivot & Wang, 2007). The rolling window analysis allows to estimate the variability of data within certain time intervals and to compare between them. The proposed predictive model is based on logistic regression, which learns patterns in data within the window of size k-weeks to predict the future occurrence of an episode at one-week time horizon. Two linear logistic models were trained independently to predict depressive and manic episodes. Using the definition of depressive and manic episodes, we developed an algorithm which identifies episodes in patients data and marks the weekly observations with a binary label (0 or 1) corresponding to the absence or presence of an episode. The features used in logistic regression to predict outcomes, were extracted using the signature method (Chevyrev & Kormilitzin, 2016). The novel signature method, from stochastic analysis, has the ability to capture important properties of complex time-ordered data. It maps N unique data streams into a single piece-wise continuous path in N dimensions with the iterated integrals of such path representing a feature set (signature features) of the data. The signature is an infinite sequence of ordered iterated integrals and in practice. For machine learning applications and data analyses, we truncate the infinite sequence at some level L by taking only first terms and use them as features. The signature method allows missing responses to be incorporated into the analysis by introducing a new indicator binary variable, which takes values 1 or 0, indicates whether a response is missing or present respectively (Little & Rubin, 2014). The indicator variable stream is then combined with N data streams of interest and mapped into a lifted path in N+1 dimensions. Practically, we used the self-reported data streams (QIDS and Altman questionnaires) together with their missing responses indicator data streams. The detailed description, rigorous mathematical foundations and algorithms of the signature methods are beyond the scope of the current paper and have been extensively covered in (Kormilitzin et al., 2016; Levin et al., 2013; Gyurk\u00b4 o et al., 2013; Yang et al., 2015; Lyons, 2014; Kir\u00b4 aly & Oberhauser, 2016; Yin et al., 2013; Graham, 2013; Gyurk\u00b4 o et al., 2013; Yang et al., 2015; Lyons, 2014; Kir\u00b4 aly & Oberhauser, 2016; Yin et al., 2013; Graham, 2013; Chen, 1957; Lyons & Xu, 2011; Lyons et al., 2007; Kir aly & Oberhauser, 2016; Yin et al., 2013; Graham, 2013; Chen, 1957; Lyons & Xu, 2011; Lyons et al., 2007; Hambly & Lyons, 2010; Hairer, 2014; Yang et al., 2016; Xie et al., 2016; Lai et al., 2017) and references therein. In order to estimate the generalisation error of predictive models, we split the entire data set into two nonoverlapping groups of patients for training (67%) and testDetecting early signs of depressive and manic episodes in patients with bipolar disorder using the signature-based model ing (33%) data sets, while preserving the ratio of weeks in episodes to weeks without episodes in both sets. The strati\ufb01ed splitting strategy allowed the variance and bias of a model to be minimised (Kohavi et al., 1995; Cawley & Talbot, 2010). A model was trained and cross-validated using the data only from one group and then the data from the withheld second group of patients was used to assess the classi\ufb01cation metrics. The process of random splitting of patients into two disjoint groups was repeated 100 times to estimates the uncertainty of the metrics. The elastic net regularisation scheme (Zou & Hastie, 2005) was used to prevent the models from over\ufb01tting the data. The elastic net regularisation introduces the convex combination of L1 and L2 penalties, mitigating the problem of multicollinearity of features and improving the stability of a classi\ufb01er. As an additional preprocessing step, the signature features matrix was standardised along columns to have zero mean and unit variance. To account for the variability in longitudinal data, we used the lead-lag transformation, where the lead transform of the signal is paired with its lagged transform of the signal. To assess the performance of the classi\ufb01cation procedure we computed accuracy, sensitivity, speci\ufb01city, and positive predicted value (PPV). Additionally, we used the area under the receiver operating characteristic curve (AUC) to assess the performance of the classi\ufb01cation models at different values of a threshold. We compared the signature-based model (Sig) to four baseline models, where three of them based only on one of the mean value (Mean), variability (Rmssd) and a number of missing responses (MissRes) within the window predictors and the fourth model comprises all these three predictors simultaneously in a linear combination (MRM). The variability was computed, ignoring the missing responses, using the root mean square successive distance (RMSSD) (Electrophysiology, 1996), which captures the temporal dependencies in the data. 2.4. Parameters of the Model The longitudinal self-reported data were partitioned into kweek intervals, transformed into a set of features using the signature method and the resulting features were used as inputs to logistic regression to predict a binary outcome, presence or absence of an episodes, at the week following the interval. The intervals that precede the episodes (precursors to episodes) are labelled as positives (1). The data from QIDS and AMSR questionnaires were used to train models predicting respectively depressive and manic episodes. Intervals that precede missing responses or contain only one non-missing response were excluded. Additionally, we sought to optimise the classi\ufb01cation model using the hyperparameters of the penalised logistic regression during the 10-fold cross-validation phase with the parameter \u03bb \u2208{0, 0.1, 0.2, 0.3, ..., 1.0} that mixes L1 and L2 penalties. We used the Python Pandas package (version 0.20.1) (McKinney et al., 2010) for statistical analysis, data manipulations and processing, Python Scikit-learn package (version 0.18.1) (Pedregosa et al., 2011) for implementing machine learning tasks and Matplotlib for plotting and graphics (version 2.0.1) (Hunter, 2007). 3. Results 3.1. Predicting Depressive and Manic Episodes The performance of the signature-based model and comparison to the baseline models for depression and mania trained on corresponding test sets are summarised in Tables 2-3 respectively. Classi\ufb01cation results evaluated on the corresponding test sets of the models for depression and mania using 100 repetition of random splitting to train/test (67%,/33%) sets. The features used in the model are elements of a truncated signature at level 2. The repeated results of metrics were nearly normal distributed and following the suggested procedure (Salzberg, 1997; Dietterich, 1998), we used the corrected paired t-test to pair-wise compare the performance of all metrics of \ufb01ve models. We found a strong statistical signi\ufb01cance of their differences (p-value < 0.001), also for depression and mania models. The stability of the classi\ufb01cation metrics was estimated by repeating the training and testing the models 100 times and the results presented as mean and standard deviation. The classi\ufb01cation metrics of models for depression and mania as function of the size of the rolling window are presented in Figures 1-2. 3.2. Experimental Clinical Applications The proposed models for classi\ufb01cation of intervals are potentially useful for clinical insights and for identifying particular states, where a patient is in transition between the episodes. First, we are interested in examining whether it is possible to distinguish between the intervals which are close to an episode and those which are further away. For the sake of simplicity and demonstration of the conceptual approach, we consider intervals of \ufb01xed length of size 6 weeks. Two types of intervals are: a wellness and a precursor interval, which are spaced 14 and n weeks prior to the beginning of an episode respectively. By varying n = {0, 1, 2, 3, 4, 6}, and applying the developed models, we will measure the area under the ROC curve (AUC) to assess the classi\ufb01cation performance. We restrict the wellness and the precursor intervals from overlapping. For classi\ufb01cation procedure we considered only the signaturebased model. To estimate the variability due to split of Detecting early signs of depressive and manic episodes in patients with bipolar disorder using the signature-based model the data into training and testing sets (67% / 33%) we repeated the process 100 times. The results are presented as mean and standard deviation. The AUC estimations are summarised in Table 4. 4. Discussion 4.1. Principal Results In this study we have presented an application of the signature method for modelling and prediction of mood episodes in bipolar disorder. We demonstrated that the results of the signature-based model outperform four other models based on the manually selected predictors. The main advantage of the signature method is that it allows to systematically combine multimodal longitudinal data streams, including the distribution of missing responses, and to extract features used in predictive models, avoiding a complicated feature engineering process. The signature terms faithfully represent the underlying data, have an interpretable geometrical meaning as functions of data and should be used as canonical features in machine learning and data analysis tasks. Intuitively, one can think of the signature terms as of an ordered collection of the sample statistical moments. The lead-lag transformation naturally captures the successive variability in the data, avoiding the need for designing a special feature for that task as we did with the RMSSD. The plot of the classi\ufb01cation metrics (Figures 1-2) demonstrate the dependence of the predictive performance of the models on the size of the rolling window. For small values of the window size (k < 12) all models perform similar, while the signature-based model, MRM and MissRes, continue improving as the number of historical observations grows and the Mean and Rmssd models decline or saturate. The predictive performance does ultimately depend on the ability of models to account for the temporal dependencies. The signature model is based on the unique set of predictors derived from a trajectory (a path) of the longitudinal self-reported responses, where the predictors account for the sequential dependencies through the path integrals and thus more observations lead to a higher accuracy of predictions. The Mean model, in contrast with the others, strongly declines when used with a large number of historical observations. That manifests the fact, that the average score over a long interval of observations is a poor predictor of future episodes, because it does not take into account the temporal dependencies. Interestingly, it appears that the variability of the rating scale along is a very poor predictor of future episodes, even though it does account for the sequential dependencies in the data through the RMSSD metric. Another interesting observation is that the number of missing responses along within the window can predict with up to 80% accuracy the future episodes of depression and mania. Finally, we observed that the composite model (MRM) that comprises all three predictors linearly, underperforms the accuracy of the signature-based model on average by 2.36%. The developed models aim to discover the temporal patterns of mood episodes and accurately predict the possible future outcomes. The proposed algorithms can be potentially deployed in modern health-monitoring platforms and serve as a patient self-management tool. Detection of precursors to upcoming mood episodes and early intervention of the healthcare professionals can help to reduce the severity of symptoms in patients with bipolar disorder. However, the developed predictive models do not take into account the unique personal traits of patients, for example, the distribution of missing values and the item responses. The main problem of training an individual model is due to relatively small number of episodes each participant experiences during the self-monitoring. While the results of the current work have demonstrated the feasibility of building the predictive models based on the signature transformation of the self-reported data alone, more in-depth research is needed to re\ufb01ne the model. The current analysis considered only a relatively small number of patients who satis\ufb01ed the inclusion criteria and in order to develop robust models, in the future we are planning to replicated the proposed method using a larger cohort. It has been shown [40] that training a model on a selected subgroup of patients who share common traits leads to a signi\ufb01cant improvement of accuracy of the predictive models. We are planning to address the problem of clustering patient in our future works and retrain the predictive models for each cluster. Apart from the identifying early signs of deterioration, it is also clinically interesting to identify early signs of improvement. The approach to \ufb01nd precursors to wellness is conceptually similar to the one we presented in this work, but requires different labelling of intervals and retraining the models. The developed approach to interval classi\ufb01cation allows us potentially to identify the early signs of transitions between the mood states in patients. We tested whether the we can distinguish between an interval which is not in an episode and an interval which is n-weeks close to the beginning of an episode. The results presented in Table 4 indicate that intervals closer to an impeding are distinct than those which are far apart. However, the choice of the interval size (6-weeks) and the subjective de\ufb01nition of the wellness intervals (14 weeks prior to an episode) may not be optimal to conclude the results. Further investigation needed. In this work we used only linear models for prediction of future episodes. Linear models preferable over more complex and non-linear ones, especially with medical data, as Detecting early signs of depressive and manic episodes in patients with bipolar disorder using the signature-based model they allow to understand clearly which variables used as predictors and their in\ufb02uence on the dependent variable. However, the important clinical condition which has not yet been addressed through our research is the case of mixed episodes, where both depression and mania may occur simultaneously (Vieta & Valent\u00b4 \u0131, 2013). The signature method allows to combine and develop a model using both QIDS and AMSR data streams to predict the future states including the missing ones. We are planning to address this problem in a future work. 4.2. Limitations Notwithstanding the signature approach outperforms other models based on the manually created predictors, the full potential of the signature method, which has been shown to be superior to state-of-the-art methods in other \ufb01elds (Yang et al., 2017) has not yet been demonstrated on the longitudinal mood data. We refer the limited power of the proposed method to the challenging nature of the self-reported longitudinal data, e.g. presence of non-randomly distributed missing values and more importantly, to the diversity of the cohort and lack of regularly time-stamped records of exogenous factors (for example, medications and hospitalisations). The moderate accuracies of the models are also in\ufb02uenced by the assumption that all patients share the same patterns of early signs of deterioration, which might not be true. That assumption allowed us to train and test the models on randomly selected non-overlapping sets of patients from the entire cohort. With more data collected over longer period of the self-monitoring, we are interested in construction of individual models, to examine the diversity in patients. Additionally, the proposed method for incorporating of missing responses might not be optimal. In this work we laid a signi\ufb01cant groundwork with a lot of open questions for further research and are planning to address the aforementioned problems in subsequent publications. 4.3. Conclusions In this work we developed and compared several linear models for predicting the episodes of depression and mania in patients with bipolar disorders. We found that the accuracy of predictions depends on the length of historical observations (the size of the rolling window). The accuracy of the signature-based model is higher than all others by the amount of at least as 2.36% and 3.37% for depression and mania respectively. The signature method represents a systematic approach for feature extraction from and modelling functions on streams of data. We found that the linear combination of three predictors (Mean, Rmssd and MissRev) outperforms each of them individually for predicting the future episodes in both models for depression and mania. Ethics The study was approved by Oxfordshire Research Ethics Committee A (reference no: 10/H0604/13). All participants in gave written, informed consent. Data Accessibility Data can be requested from JRG Competing Interests PJH, AK, TJL, KEAS and JRG declare no competing interests. Authors Contributions JRG designed the trial. JRG coordinated the study. AK and TJL conducted the analysis. AK, TJL and KEAS drafted the paper, which was reviewed by all authors. Acknowledgements We thank Maarten De Vos, Guy Goodwin, Keltie McDonald, Nick Palmius and Athanasios Tsanas for valuable discussions. Funding AK, TJL, KEAS, JRG and PJH are supported by a Wellcome Trust Strategic Award CONBRIO: Collaborative Oxford Network for Bipolar Research to Improve Outcomes, Reference number 102616/Z. JRG, PH and KEAS are supported by the NIHR Oxford Health Biomedical Research Centre. TJL acknowledges the support of NCEO project NERC, ERC grant number 291244, EPSRC grant number EP/H000100/1 and by the Alan Turin Institute under the EPSRC grant EP/N510129/1. No funder had any role in the study design; data collection, analysis, or interpretation of data; writing of the report; or in the decision to submit the paper for publication. The views expressed are those of the authors and not necessarily those of the NHS, the NIHR or the Department of Health.",
                    "introduction": "1.1. Related Work Predicting the future outcomes on the basis of historical observations is a long standing challenge in many scien- ti\ufb01c areas. The accurate prediction of future symptoms in patients with bipolar disorder could facilitate timely clin- ical interventions enhancing patients quality of life, alter- ing the course of disease and could have economic bene- \ufb01ts for the national health service (Manning, 2005). Sev- eral predictive models have been proposed using the self- reported longitudinal mood data from psychometric ques- tionnaires. These models included: autoregressive linear models (Moore et al., 2012; 2014), relaxation oscillator framework (Bonsall et al., 2015), Kalman \ufb01lter with the data from geographic location (Tsanas et al., 2016; Palmius et al., 2017) and an effective subgroup selection among di- verse cohort of patients (Palmius & De Vos, 2016). How- ever, these methods focused only on predicting the numer- ical value of the rating scale In this work, we took a dif- ferent route in building a predictive model. In contrast to previous approaches, we aim to identify the precursors of upcoming episodes of depression and mania, using the self- arXiv:1708.01206v1  [stat.ML]  3 Aug 2017 Detecting early signs of depressive and manic episodes in patients with bipolar disorder using the signature-based model reported rating scale. In fact, we solve a binary classi\ufb01ca- tion problem, where our developed model, using an inter- val of k-consecutive self-reported observation, estimates a probability of being a precursor to an episode."
                }
            ],
            "Janet B. Pierrehumbert": [
                {
                    "url": "http://arxiv.org/abs/1408.1985v1",
                    "title": "A model of grassroots changes in linguistic systems",
                    "abstract": "Linguistic norms emerge in human communities because people imitate each\nother. A shared linguistic system provides people with the benefits of shared\nknowledge and coordinated planning. Once norms are in place, why would they\never change? This question, echoing broad questions in the theory of social\ndynamics, has particular force in relation to language. By definition, an\ninnovator is in the minority when the innovation first occurs. In some areas of\nsocial dynamics, important minorities can strongly influence the majority\nthrough their power, fame, or use of broadcast media. But most linguistic\nchanges are grassroots developments that originate with ordinary people. Here,\nwe develop a novel model of communicative behavior in communities, and identify\na mechanism for arbitrary innovations by ordinary people to have a good chance\nof being widely adopted.\n  To imitate each other, people must form a mental representation of what other\npeople do. Each time they speak, they must also decide which form to produce\nthemselves. We introduce a new decision function that enables us to smoothly\nexplore the space between two types of behavior: probability matching (matching\nthe probabilities of incoming experience) and regularization (producing some\nforms disproportionately often). Using Monte Carlo methods, we explore the\ninteractions amongst the degree of regularization, the distribution of biases\nin a network, and the network position of the innovator. We identify two\nregimes for the widespread adoption of arbritrary innovations, viewed as\ninformational cascades in the network. With moderate regularization of\nexperienced input, average people (not well-connected people) are the most\nlikely source of successful innovations. Our results shed light on a major\noutstanding puzzle in the theory of language change. The framework also holds\npromise for understanding the dynamics of other social norms.",
                    "authors": "Janet B. Pierrehumbert, Forrest Stonedahl, Robert Daland",
                    "published": "2014-08-08",
                    "updated": "2014-08-08",
                    "primary_cat": "cs.CL",
                    "cats": [
                        "cs.CL",
                        "nlin.AO",
                        "physics.soc-ph"
                    ],
                    "main_content": "1.1 Social network We consider N individuals in a community whose network structure is represented by a graph with adjacency matrix A. The matrix entry aij = 1 if individual i is a neighbor of individual j (e.g., individuals i and j are connected) and 0 otherwise. As explained above, the links are interpreted to mean that the two individuals communicate with each other and are disposed to imitate each other; social connections that lack this force are omitted. The number of neighbors of individual i, ni = \ufffd j aij, defines the individual\u2019s degree in the network. Individuals interact with their neighbors in the network, and these interactions are assumed to be bidirectional and uniformly weighted. Adjacency omitted. The number of neighbors of individual i, ni = \ufffd j aij, defines the individual\u2019s degree in the network. Individuals interact with their neighbors in the network, and these interactions are assumed to be bidirectional and uniformly weighted. Adjacency matrices are generated using preferential attachment [24], with an average degree of 4. This represents an intermediate degree of network connectivity that falls within the range for global cascades to occur [22]. Results for average degree 3 are similar, and are not reported here. 8 1.2 Social norms and signals Competing forms of expression are represented within the minds of individuals. With each communicative action, an individual elects to use one of them. For example, to express the past tense of slink, a speaker of English has a choice between slinked and slunk, but in each speci\ufb01c utterance, only one of these is used. The choice of signal is treated as a binary (Boolean) variable that assumes values of 0 (FALSE) or 1 (TRUE). In our simulations, 1 will always denote the innovation that may or may not cascade, and 0 will always denote the pre-existing consensus. This binary treatment of the available choices entails little loss of generality. If a new expression, such as snowpocalypse, competes against a variety of pre-existing expressions, such as blizzard, large snowstorm and massive snowfall, 0 denotes the use of any of the earlier forms. We de\ufb01ne the observable signal from individual i as a function of time as si(t). The signal is communicated to all of the neighbors in the network at the same time. This means that individuals with many neighbors (represented by nodes with high degrees) are heard by many more people than individuals with few neighbors; however, by the egalitarian assumptions of the model, these better-connected people also listen to more people. The mental state mi(t) of an individual i represents his or her private beliefs about norms of language, as these beliefs develop over time. The model is initialized with mi(0) = 0 for all individuals except a single innovator v, for whom mv(0) = 1. The innovator could deviate from the group consensus because his beliefs were formed before joining the network, or through a mutation process whose details fall outside of the scope of this paper. As individuals acquire experience over time, their mental states change because they are in\ufb02uenced by their impressions of their neighbors\u2019 norms. We next describe the learning rule that determines mi(t). We return later to the characterization of the relationship between mi(t) and the signal output at time t + 1. 1.3 Social assimilation In general, social learning is driven by general inclinations to assimilate one\u2019s opinions and behaviors to those of others in the community [16,23,28,29]. Applying these ideas to language, individuals estimate the community norm from the relative frequency of each signal type in their aggregate input. Taking Ni to be the set of neighbors of individual i (e.g. {j|aij = 1}) and ni to be number of neighbors, the input to that individual at each timepoint is thus the mean of the signals sj emanating from the members of Ni. inputi(t) = 1 ni X j|j\u2208Ni sj(t) (1) However, individuals do not instantaneously copy the current input as their new mental state. People\u2019s beliefs generally re\ufb02ect a combination of prior experience and current input. Standard learning models capture this by using a weighted average of the prior 9 mental state and the current input as the update rule, with a learning rate parameter 0 \u2264\u03b1 \u22641 [15,30]. mi(t) = \u03b1 \u00b7 inputi(t) + (1 \u2212\u03b1) \u00b7 mi(t \u22121) (2) The memory term (1 \u2212\u03b1) \u00b7 mi(t) holds individual i back from slavishly following the neighbors. \u03b1 has no \ufb01xed interpretation in relation to the time scale of learning, but rather re\ufb02ects the temporal granularity of a batch-processed approximation to social reality. We will report model runs for \u03b1 = 0.1, selected to give insightful results using the available computational resources. With this value of \u03b1, individuals give 9 times more weight to their existing knowledge than to the immediate input from their neighbors. 1.4 Unbiased decision rules The mental state mi and the learning rule Eq. 2 capture the way in which the individual\u2019s beliefs about the ambient social norm evolve as input arrives. Now we turn to the question of how individuals act on the basis of this knowledge, where action means making a choice of which signals to express. We \ufb01rst consider the case in which individuals act without any kind of preference or bias. 1.4.1 Criterion or threshold decision rules The criterion choice rule (also known as a threshold choice rule) maximizes the expected utility in the case of perfect knowledge [31, 32]. As a consequence of its mathematic de\ufb01nition, utility can assume values from \u2212\u221e(an in\ufb01nite loss) to \u221e(an in\ufb01nite gain). Considering a binary choice between mutually exclusive alternatives a and \u00aca, we de\ufb01ne Q(a) as the utility of a, and Q(\u00aca) as the utility of \u00aca. The criterion choice rule then takes the form: P(a) = \uf8f1 \uf8f4 \uf8f2 \uf8f4 \uf8f3 0 if Q(a) < Q(\u00aca) 0.5 if Q(a) = Q(\u00aca) 1 if Q(a) > Q(\u00aca) (3) An individual should choose a if it o\ufb00ers a net utility bene\ufb01t over \u00aca. The same equation can be also applied to perceptual decisions based on an in\ufb01nite scale of evidence; an individual should reach conclusion a if the total evidence for a is greater than the evidence for \u00aca. For language, let\u2019s imagine that the individual wants to produce the signal that is most likely to be accepted by any random member of the community. This means producing the signal that most other people use, on the assumption that what people use is what they will accept. This goal is similar to the goals of maximizing economic utility or reaching the best-supported conclusion, except that the input to the decision is not a utility or scale of evidence, but rather the mi, the mental estimate of community norms. The criterion choice rule can be put into following form. 10 P(si = 1) = \uf8f1 \uf8f4 \uf8f2 \uf8f4 \uf8f3 0 if mi < 0.5 0.5 if mi = 0.5 1 if mi > 0.5 (4) The individual i should choose s = 1 if, according to his beliefs, it is more likely than s = 0 to be the general norm. Eq. 3 and Eq. 4 are the same except for the range of the input variable. Q(a) and Q(\u00aca) can take values anywhere in the interval (\u2212\u221e, \u221e), whereas m can only take values in the interval [0, 1]. This di\ufb00erence in range has little importance if the decision function is a step function. However, for other decision functions the di\ufb00erence in range has important consequences. Eq. 4 is an absolutely categorical decision rule. Even if the input to the individual has been variable, the individual treats one of the competing forms as normative, and the other input as deviant, invariably producing the normative form as the output. This is not what people do. If linguistic norms vary amongst individuals in a group (as happens during periods of language change), then many individual speakers also vacillate in what form they choose to express [33,34]. In experiments where some regularization of the input is found, it is never absolute [35\u201337]. To model real linguistic behavior, a less categorical decision rule is needed. 1.4.2 The SoftMax and logistic functions In economics, a threshold decision rule is only guaranteed to be optimal in the case of perfect knowledge. It may not be optimal in the case of imperfect knowledge, because the threshold must be set on the basis of information already acquired, and it is possible that some information about the real optimum has not yet come to light. Speakers in a linguistic community also have imperfect knowledge of what other speakers do, because they only receive input from communications they are involved in. The statistical properties of communications that take place in more distant parts of their social networks are invisible to them, as are the communications that will take place in the future. These observations lead naturally to the conjecture that the cognitive system processes the frequencies of linguistic inputs in a manner that resembles reasoning under uncertainty in other areas of cognition. The theory of reinforcement learning provides a general framework for understanding how learning proceeds incrementally as more and more evidence becomes available from experience. The SoftMax equation contains a free temperature parameter \u03c4 that captures the extent to which the learner makes the optimal choice based on the evidence so far, or makes a random choice which may yield more information in the future [31]. If there are only two choices, the SoftMax reduces to the logistic function Eq. 5, which is a generalization of Eq. 3 and is expressed here in a form that emphasizes the parallelism. P(a) = eQ(a)/\u03c4 eQ(a)/\u03c4 + eQ(\u00aca)/\u03c4 (5) 11 The parameter \u03c4 captures the categoriality of the decision. As \u03c4 \u21920, the learning system becomes completely categorical, rigidly applying a threshold based on past evidence. This is the low temperature situation because the decision function can be viewed intuitively as a frozen re\ufb02ex of the past. As \u03c4 \u2192\u221e, the decision becomes random without regard to past evidence. The logistic function is a sigmoidal function that is widely used in analyzing cognitive, social, and biological processes that involve a competition between two states. Its many applications include not only decisions under uncertainty in economics, but also analysis of the time course of linguistic changes [38, 39], the categorization of perceptual inputs [40,41], and binary choices as a function of a continuous and unbounded scale of evidence [32]. The crux of the problem is whether it makes sense to add \u03c4 in just the same manner to a decision function that maps mental probabilities onto signaling actions, as shown in Eq. 6. P(s = 1) = em/\u03c4 em/\u03c4 + e(1\u2212m)/\u03c4 (6) The answer to this question rests on the behavior of Eq. 6 as it is iterated through repeated social interactions. Figure 2 graphs Eq. 6 as the temperature \u03c4 is varied over its full range. To understand the behavior of the function, it will be convenient to have an equation for the angle \u03c6 at the in\ufb02ection point. \u03c6 = arctan 1 2 \u00b7 \u03c4 (7) Varying \u03c4 is accomplished by varying \u03c6 from 90\u25e6to 0\u25e6. \u03c6 = 90\u25e6in the limit as \u03c4 \u21920 and \u03c6 = 0\u25e6in the limit as \u03c4 \u2192\u221e. The points of most interest are the \ufb01xed points, de\ufb01ned as the points for which the output and input are the same (eg. the points where Eq. 6 crosses the identity function P(si = 1) = mi). The stable \ufb01xed points act as attractors; that is, slight deviations in the vicinity of a stable \ufb01xed point push the result back onto the same point. The unstable \ufb01xed points act as repellers; slight deviations send the result away from the \ufb01xed point. Thus, the stable \ufb01xed points represent predictions about the possible long-term states for the system. The location and stability of the \ufb01xed points for Eq. 6 vary as \u03c6 is varied. For 45\u25e6< \u03c6 < 90\u25e6, there is an unstable \ufb01xed point at (0.5, 0.5), which means that for moderate temperatures, free variation between two competing forms is unstable towards a system in which one variant is preferred. This behavior is somewhat realistic, but not entirely so, because the location of the stable \ufb01xed points is problematic. No value of \u03c6 other than 90\u25e6has a stable \ufb01xed point at (0, 0) or (1, 1). For 45\u25e6< \u03c6 < 90\u25e6, there are indeed two stable \ufb01xed points. However, one is always located at 0 < mi < 0.5 and the other is always located at 0.5 < mi < 1. 12 \u25b2 Fixed points \u25b2 \u25b2 \u25b2 \u25b2 \u25b2 \u25b2 \u25b2 \u25b2 \u25b2 \u25b2 \u25b2 \u25b2 mental state (      ) mi i mental state (      ) mi (s  = 1) i P (s  = 1) i P \u25b2 \u25b2 \u25bc \u25bc \u25bc \u25bc Fixed points Fixed points stable stable unstable unstable Figure 2. Behavior of the logistic function as \u03c6 is varied. \u03c6 determines the location and nature of the \ufb01xed points. A: Except for \u03c6 = 90\u25e6, the function lacks \ufb01xed points at (0, 0) and (1, 1). For \u03c6 \u226445\u25e6, the unstable \ufb01xed point at (0.5, 0.5) becomes a stable \ufb01xed point. B: Detailed view of behavior in the lower-left quadrant. \u03c6 varied in 5\u25e6steps. For \u03c6 > 45\u25e6, there is an unstable \ufb01xed point at (0.5, 0.5). For \u03c6 \u226445\u25e6, the \ufb01xed point at (0.5, 0.5) is stable. This situation has the unfortunate consequence that inputs of mi = 0 and mi = 1 yield outputs that are shifted towards the center. It means that all binary competitions in language continue to the end of time; no form or expression can ever truly go extinct. To make a comparison to norms of attire, some 600 years ago, garments called chausses were in competition with garments called breeches; breeches eventually won out. If neither I nor anyone in my community has any knowledge or experience of chausses, then we have all adopted the innovative form and a model of our speech community has mi = 1 for all individuals i. A model using a logistic choice function would nonetheless predict that the archaic form chausses has a predictable and persistent tendency to reappear as a competitor to breeches, as we continue to interact with each other in the future. In fact in language, just as in biology, something that is extinct is gone forever. New competitions arise, but these are due to fresh innovations. The invention of trousers is what created later competition for breeches, and not the persistent return of chausses from the graveyard of fashion history. A further problem is revealed for 0\u25e6\u2264\u03c6 \u226445\u25e6. In this case, the \ufb01xed point at (0.5, 0.5) becomes stable. At high temperatures, the system is predicted to converge towards free 13 variation. For language systems, this asymptotic behavior is highly questionable. This would mean that if people weakly categorize the input they receive about two competing words or constructions, their output persistently reverts towards completely free variation. This would behavior would count as a tendency towards true synonymy (in which two forms completely share their denotation and their range of use). But, in the psycholinguistic literature, avoidance of true synonymy is documented in people of all ages, and it is argued to play a key role in the emergence of meaning categories in language [42\u201344]. The formalization of the concept of temperature in the context of language and collective opinions needs to be reconsidered. Note \ufb01nally that the logistic never falls on the line y = x. For \u03c6 = 45\u25e6, it tracks y = x in the middle of the range, but curves away from this line for more extreme values. This means that it cannot be used to model probability-matching behavior, which is widely assumed to be relevant for language [45\u201348]. 1.5 Introducing the clog function: categoriality and bias The problems with the applicability of Eq 6 arise from the fact that it converges to P(s = 1) = 0.5 as \u03c4 \u2192\u221e. Although Eq. 3 and Eq. 4 have similar behavior as formulations of a criterion (or expectation maximization) decision rule, this similarity disappears as soon as nonzero temperatures are introduced. This problem is solved if we assume that the sigmoidal function should instead approach P(si) = mi as \u03c4 \u2192\u221e. We now develop the mathematical apparatus to explore this assumption. We de\ufb01ne a new relative of the logistic, the clog (\u2018cognitive logistic\u2019) function that converges to the identity function as \u03c4 \u2192\u221e: clog\u03c4(m) = m \u00b7 em/\u03c4 m \u00b7 em/\u03c4 + (1 \u2212m) \u00b7 e(1\u2212m)/\u03c4 (8) Just as for the logistic, it will be convenient to characterize the degree of nonlinearity in the clog function in terms of the slope \u03c6 at the in\ufb02ection point, which we will denote as m\u2217. It is: \u03c6 = arctan (1 + 1 2 \u00b7 \u03c4 ) (9) In the limit of \u03c6 \u219245\u25e6(i.e. \u03c4 \u2192\u221e), clog reduces to the identity function; the production probabilities are exactly the same as the current mental state. As \u03c6 \u219290\u25e6 (i.e. \u03c4 \u21920), the function approaches a step function with the discontinuity at m\u2217. For all \u03c4 < \u221e(\u03c6 > 45\u25e6), Eq. 8 has attracting \ufb01xed points at (0, 0) and (1, 1). This means that uncertain opinions tend to become polarized in the course of repeated interactions towards more absolute opinions. The stability of these \ufb01xed points provides for the ultimate extinction of losing competitors. The in\ufb02ection point m\u2217in between m = 0 and m = 1 (located at m = 0.5) is a repelling \ufb01xed point. Because m\u2217is always unstable, there is never a regime in which the system is attracted towards free variation. 14 The limiting case represented by \u03c6 = 45\u25e6is studied in the literature under the name of a probability-matching rule, a relative goodness rule or Luce\u2019s Choice Rule [32]. Thus far, we have considered only unbiased decisions, which rest entirely on the balance of utility, evidence, or likelihood of the two alternatives. In practice, biased decisionmaking processes are frequently encountered. Such biases are normally accommodated in Eq. 5 for the logistic by introducing a second free parameter \u03b2. P(a) = e(Q(a)\u2212\u03b2)/\u03c4 e(Q(a)\u2212\u03b2)/\u03c4 + e(Q(\u00aca)+\u03b2)/\u03c4 (10) Varying \u03b2 has the e\ufb00ect of shifting the entire function. If \u03b2 < 0, the individual is more likely to pick the innovative variant than would be expected from its utility. If \u03b2 > 0, he is less likely to do so. Figure 3 illustrates the results of attempting to recast Eq. 10 as a function from mental probabilities to signaling actions, as shown in Eq. 11. P(s = 1) = e(m\u2212\u03b2)/\u03c4 e(m\u2212\u03b2)/\u03c4 + e(1\u2212m+\u03b2)/\u03c4 (11) mental state (      ) mi P (s  = 1) i \u25b2 \u25b2 \u25bc \u25b2 \u25b2 Fixed points \u25b2 \u25b2 \u25b2 Stable \u25bc Unstable \u03b2 = -0.2 \u03b2 = 0.0 \u03b2 = +0.2 \u03b2 = 0.0 Figure 3. Behavior of the logistic function for \u03c6 = 60\u25e6as \u03b2 is varied. The unstable \ufb01xed point at (0.5, 0.5) is lost for small biases \u03b2 = 0.2 and \u03b2 = \u22120.2. Each of these \u03b2 values results in a system with a single stable \ufb01xed point. 15 The shift in the function shifts the location of the in\ufb02ection point occurring in the unbiased case at mi = 0.5. The number and stability of the \ufb01xed points is greatly a\ufb00ected. A small positive bias gives rise to a single stable \ufb01xed point representing a high level of acceptance of the innovation, and a small negative bias yields a stable \ufb01xed point that represents a low level of acceptance of the innovation. In contrast to the logistic, the clog can incorporate a bias parameter without restructuring the \ufb01xed points. Including a bias parameter \u03b2 into the clog function yields the following fully elaborated form. clog\u03c4,\u03b2(m) = m \u00b7 e(m\u2212\u03b2)/\u03c4 m \u00b7 e(m\u2212\u03b2)/\u03c4 + (1 \u2212m) \u00b7 e(1\u2212m+\u03b2)/\u03c4 (12) For the clog, \u03b2 controls the location of the unstable \ufb01xed point m\u2217, which is always located at mi = 0.5 + \u03b2. If \u03b2i < 0, m\u2217 i < 0.5, and individual i has a greater propensity to produce 1 than the input from the neighbors would dictate. Similarly, if \u03b2i > 0, m\u2217 i > 0.5, and the individual has a disproportionate tendency to produce 0. The stable \ufb01xed points are una\ufb00ected by the value of \u03b2. The introduction of a function that smoothly interpolates between a criterion choice rule and a probability-matching choice rule, under under any choice of bias, while always having \ufb01xed points at (0, 0) and (1, 1), is a novel contribution of this paper. Heterogeneity amongst community members in \u03b2 is the primary type of heterogeneity that we explore. The di\ufb00erent scenarios for informational cascades depend on positive and negative values of \u03b2 being distributed in di\ufb00erent ways across the individuals in the network. Figure 4 illustrates the behavior of clog as \u03c6 and \u03b2 are varied. In this \ufb01gure, note particularly that varying \u03b2 has no e\ufb00ect on the \ufb01xed points at (0, 0) and (1, 1) for \u03c6 > 45\u25e6. This entails that the clog (unlike the logistic) cannot represent a uniform distribution on the closed interval [0, 1]. Note also that the e\ufb00ects of \u03b2 are neutralized if \u03c6 = 45\u25e6; the concept of bias is only meaningful if the choice rule is at least somewhat categorical. 1.6 Implementation The model is implemented in the NetLogo agent-based modeling environment [49]. It is initialized at time t = 0 with mi(0) = 0 for all individuals i in A, except for a single innovator v, for whom mv(0) = 1. During each model cycle t + 1, every individual \ufb01rst randomly produces an expression of opinion, 0 or 1, with probability: P(si(t) = 1) = clog\u03c4,\u03b2(mi(t)) (13) Then they update their mental state from mi(t) to mi(t + 1) on the basis of the set of signals emitted by their neighbors Ni (e.g. {sj(t)|j \u2208Ni}), using Eq. 2. Each model run is terminated when the population reaches a consensus (de\ufb01ned as mi < 10\u22128 or mi > 1 \u221210\u22128 for all i), or at the 10,000th iteration if no convergence has occurred. 16 \u25b2 \u25b2 \u25bc \u25bc \u25bc mental state (      ) mi (s  = 1) i P Fixed points Stable \u25b2 \u03b2  all Unstable \u25bc \u25bc \u25bc \u03b2 = -0.3 \u03b2 = 0.0 \u03b2 = +0.3 for \u03c6 > 45 Figure 4. Behavior of the clog function as \u03b2 and \u03c6 are varied. Blue: No bias. Magenta: Bias against the pre-existing consensus, equivalent to bias toward the innovation. Green: Bias toward the pre-existing consensus, equivalent to bias against the innovation. When \u03c6 = 45\u25e6, the clog reduces to the dashed line P(si = 1) = mi for all values of \u03b2. The probabilities of cascades as a function of innovator degree are estimated by a Monte Carlo method, in which innovator degrees from 2 to 55 are sampled equally in the form of 500 runs for each degree. Innovators with degrees of 1 and > 55 are not included because the preferential attachment rule for network construction does not generate nodes with such degrees frequently enough. A fresh network is generated for each run, and all individuals share a value of \u03c6. \u03c6 was smoothly varied from \u03c6 = 45\u25e6(linear) to \u03c6 = 90\u25e6 (categorical) by increments of 1\u25e6. In both baseline scenarios, all individuals are unbiased. (In the \ufb01rst baseline, this is because they follow a probability-matching decision rule. In the second baseline, the decision rule is more categorical and \u03b2i = 0). In all other scenarios, heterogenous values of \u03b2i are assigned, as described in the text. 1.7 Summarizing outcomes In our Monte Carlo simulations, we vary the categoriality, the degree of the innovator and the way that bias values are distributed across the community. Each model con\ufb01guration yields a distribution of cascade sizes; the size of a cascade is distinct from the likelihood 17 of a cascade. In order to summarize the results, however, we con\ufb02ate these two factors. We use the following classi\ufb01cations of the average mental state \u00af m of all the individuals in the network when the model run ends at time tfinal. \u2022 Survival: The innovation avoids extinction, de\ufb01ned as \u00af m(tfinal) > 10\u22124. \u2022 Dominance: The innovation becomes dominant by surpassing the established variant, i.e. \u00af m(tfinal) \u22650.5. \u2022 Completion: The innovation drives the previous consensus opinion to extinction i.e. \u00af m(tfinal) \u22651 \u221210\u22124. 2 Results in di\ufb00erent scenarios We \ufb01rst present two baseline cases in which all individuals are unbiased. Then, we compare three scenarios in which individuals have heterogeneous biases. 2.1 Baseline scenarios If \u03c6 = 45\u25e6, each individual expresses each opinion in direct proportion to their experience. The model instantiates the case of neutral evolution (also known as random drift [27]). For a fully continuous system, the population would converge to the average of the initial states of the individuals; however, because emitting a signal is a discrete probabilistic event, the mean state instead exhibits a random walk on the frequencies of the alternative signals 0 and 1 [27]. The probability of a complete cascade is low, and is directly proportional to the innovator\u2019s degree, as shown in Figure 5. If \u03c6 > 45\u25e6(e.g individuals have at least some tendency toward categorical behavior), and all individuals are unbiased (\u03b2i = 0 for all i), then the innovation always becomes extinct; no cascades of any size are found. This very strong result on the impossibility of change without bias heterogeneity occurs because memory is included in the model of learning. Eq. 2 entails that a single signal si = 1 from an innovator i can never cause the mental state of a neighbor j to increase from its initial value mj = 0 to a value greater than the repelling \ufb01xed point at m\u2217 j = 0.5. The innovator cannot convert anyone else, and is eventually reconverted to the original consensus. 2.2 Scenarios with heterogeneous biases To explore the role of heterogeneous biases while maintaining overall functional neutrality, bias values are generated through random sampling on a uniform distribution over the interval [0, 0.5]. Neutrality is enforced by taking both the +\u03b2 and \u2212\u03b2 for every |\u03b2| that is selected. The resulting set of values is distributed over the individuals in the social network according to one of three di\ufb00erent methods. In the hubs scenario, the 18 0 10 20 30 40 50 innovator degree 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 Probability survival dominance completion R2 \u22480.99 R2 \u22480.96 R2 \u22480.78 Figure 5. Relationship of innovator degree to cascade probability in the neutral evolution model. For all three summary cases, the relationship is linear. The probability of a complete cascade is extremely small. bias against the pre-existing consensus is preferentially allocated as a function of degree centrality. The highest degree individuals are most disposed to change, and the lowest degree individuals are least disposed to change. In the nearby scenario, the bias against the pre-existing consensus is allocated as a function of the distance from the innovator; individuals nearest to the innovator are the most disposed to change, and those farthest from the innovator are least disposed to change. In the random scenario, bias values are randomly distributed. The hubs and nearby scenarios idealize skewed patterns in the distribution of biases in the network. To motivate these idealizations, let us consider what the bias \u03b2 means. The case of negative bias generalizes the concept of early adopters, de\ufb01ned in [22, 23] as individuals who will adopt an innovation after encountering a single example of it. Negative bias means that an individual is inclined to abandon the old norm, even if most of the neighbors do not. Positive bias is a generalization of the concept of late adopters. It means that an individual is inclined to continue using the old expression, even if the neighbors use its more innovative competitor. Such individual biases could arise as a re\ufb02ex of personality traits such as levels of adventurousness and nonconformity, which are factors in the standard theory of personality [50] and are partially innate in people and other animals [51]. The di\ufb00erences could also arise from knowledge or habits that provide a latent potential or impediment to the adoption of the innovation. As a simple example, the use of text messaging provides a platform for the use of slang acronyms like lol (laughing out loud) and btw (by the way), and it would not be surprising if heavy users of text messaging were among the \ufb01rst to adopt these expressions upon encountering them. In modern linguistic theories, the adoption of one construction may also provide a foundation for further change through 19 its indirect impact on the encoding system [34]. It is possible to develop a connection between such individual biases and the concept of utility. We already provided an interpretation of \u03c4 in relation to the global value of addressing any member of the community in a cooperative manner, using a form they are likely to accept. \u03b2 encapsulates any sort of subjective personal utility that is independent from the utility to the community as a whole of having shared norms. The distribution of biases in the hubs scenario thus can be understood as one in which individuals with many social connections share any type of knowledge, practice, or experience that makes it easy for a speci\ufb01c linguistic innovation to take root. The nearby scenario is even more plausible, because people with shared traits tend to form social connections to each other [52]. Field studies of Belfast English indicate that feelings of group solidarity a\ufb00ect people\u2019s choice of modes of expression [53]. The rate of adoption of linguistic innovations peaks in adolescence [39]. In choices of language, music, and attire, adolescents tend to be most in\ufb02uenced by the central members of their immediate peer group (rather than by the highest status people in their whole world of experience) [54\u201356]. A group of young people who share rebellious attitudes and a love of novelty is indeed the very prototype of a group with innovative language. Results for the three scenarios are shown in Figure 6. 20 10 20 30 40 50 45 60 75 90 \u03c6 survival 10 20 30 40 50 dominance 10 20 30 40 50 completion 10 20 30 40 50 45 60 75 90 \u03c6 10 20 30 40 50 10 20 30 40 50 0.0 0.2 0.4 0.6 0.8 1.0 10 20 30 40 50 innovator degree 45 60 75 90 \u03c6 10 20 30 40 50 innovator degree 10 20 30 40 50 innovator degree A B C Figure 6. Interaction of bias distribution with innovator degree and categoriality in determining the likelihood of cascades. Non-zero likelihoods of a cascade in each of the three categories survival, dominance, completion are color-coded as shown. Black indicates the absence of any cascades in the simulation results. A: Bias values are assigned to individuals as a function of degree centrality under the hubs scenario. B: Bias values are assigned to individuals as a function of proximity to the innovator under the nearby scenario. C: Bias values are assigned randomly to individuals. 21 2.2.1 Results for the hubs scenario In the hubs scenario (Figure 6A), cascading is frequent and consistent for high-degree innovators and high \u03c6 values. As the innovator degree decreases, the likelihood of success also decreases. Furthermore, cascading is basically an all-or-nothing phenomenon; if a cascade avoids extinction, it is very likely to go all the way to completion. Intuitively, if an innovation survives the initial stage in this scenario, it has done so by spreading to a backbone of high-degree adopters. These in turn can dominate the overall signal to the rest of the network, because each of their expressions of opinion is sent to many neighbors. Interestingly, when the input-output relation is not strongly categorical (i.e., \u03c6 \u2a8575\u25e6), assigning the favorable bias values to the hubs is not e\ufb00ective for causing cascades (regardless of innovator degree). As seen in Figure 6A, a phase transition occurs in the high-\u03c6 regime (\u03c6 > 75\u25e6). As categoriality increases, the outcome passes from invariable cascade extinction, through degree-sensitive all-or-nothing cascades, to complete cascades (apart from very low-degree innovators). Just visible in blue at the bottom of the graph is a sporadic set of cascades arising from neutral evolution (\u03c6 = 45\u25e6), corresponding to those displayed in Figure 5. 2.2.2 Results for the nearby scenario We identify three regimes in the nearby scenario (Figure 6B). For 45\u25e6\u2264\u03c6 \u2a8555\u25e6, no cascades occur, apart from the few previously discussed for the \u03c6 = 45\u25e6neutral evolution model. For 55\u25e6\u2a85\u03c6 \u2a8565\u25e6, cascades are more frequent, and often go to completion. For 65\u25e6\u2a85\u03c6 \u226490\u25e6, cascades become increasingly likely, but do not go to completion even if they succeed in dominating the network. In particular, in the fully categorical limit, where \u03c6 = 90\u25e6, the cascade proceeds only a little further than halfway: \u00af m(tfinal) = 0.56 (with the standard deviation \u03c3 = 0.069). The network already displayed in Figure 1 is a \ufb01nal con\ufb01guration (at the 10,000th time step) for this partial cascade situation. It shows how the novel opinion di\ufb00uses through some (but not all) of the network, leaving an entrenched opposition elsewhere. This means that for innovations occurring in a social network with a nearby bias distribution, a highly categorical decision rule tends to split the social network into subgroups with di\ufb00erent norms. In-depth examination of the case \u03c6 = 60\u25e6(Figure 7) reveals another striking point. The likelihood of success in triggering a cascade peaks in the vicinity of innovator degrees 7 \u2264ni \u226415 for this level of categoriality. The individuals with degrees in this range are more likely to succeed than very low-degree individuals, an e\ufb00ect also visible for other values of \u03c6 at the left edge of the panels in Figure 6B. Surprisingly, they are also somewhat more likely to succeed than high-degree individuals. With this combination of categoriality and bias, it is clearly not appropriate to describe the best-connected nodes as in\ufb02uentials; their in\ufb02uence is actually constrained by the variability of their many neighbors. Taking the network\u2019s degree distribution into account, we can also calculate the probability of the innovator degree, given that a cascade occurred. As Figure 7 shows, 22 this probability peaks at innovator degree ni = 4, which is by construction the average degree of the network. Thus in this scenario, a successful innovation is most likely to have originated from Joe or Jane Average. 0 10 20 30 40 50 innovator degree 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Probability P(cascade|degree) P(degree|cascade) Figure 7. Relationship of innovator degree to complete cascades for the nearby scenario with \u03c6=60\u25e6. Red: The probability of a complete cascade, given the degree of the innovator. Blue: The probability of the innovator degree, given that a complete cascade occurred. Each data point is estimated from the 500 runs per degree in the Monte Carlos simulation. Results are highly similar for cascade survival and dominance. 2.2.3 Results for the random scenario The hubs and nearby scenarios are highly idealized, and yield exorbitantly high success rates for innovation. In reality, the bias distribution is probably less stringently tied to network position, and very many innovations fail. A perspective on this reality is provided by results on the random scenario in Figure 6C. Survival of an innovation is fairly common when \u03c6 \u2a8670\u25e6. The rate of survival is notably higher than in the neutral evolution model as shown in Figure 5, also visible in this \ufb01gure panel as a blue line at \u03c6 = 45\u25e6. Dominating cascades are more rare. In addition to the few dominating cascades found for \u03c6 = 45\u25e6, a small cluster of dominating cascades is found for degree ni \u2a8610 and \u03c6 \u2a8680\u25e6. Thus, moderate categoriality in combination with heterogeneity permits a moderate to high degree innovator to have some chance of seeing an innovation widely adopted. This likelihood becomes attenuated as \u03c6 approaches 90\u25e6. Qualitatively, the pattern suggests a mixture of cases skewed towards the nearby scenario and cases skewed towards the hubs scenario. Complete cascades were not observed at all above \u03c6 = 45\u25e6. Of course, a complete cascade could occur if the random bias distribution happened to distribute the bias in exactly the same way as in one of the more favorable scenarios in 23 Figure 6AB. The fact that this outcome is too rare to occur at all in our simulations suggests that bias heterogeneity alone cannot fully explain how neutral innovations may come to be adopted by an entire community. Instead, systematic patterns are needed in the distribution of decision biases across individuals. Discussion We have presented a framework for exploring the interaction of categoriality, bias, and innovator degree in permitting arbitrary linguistic innovations to succeed in a social network. As anticipated from prior related models [23,26,27], model con\ufb01gurations in which individuals are homogeneous and unbiased exhibit negligible success rates for innovations. We identi\ufb01ed two regimes involving heterogeneous biases that are conducive to change. Under the hubs scenario, a highly categorical decision rule supports a mechanism for the widespread adoption of innovations initiated by highly connected people. Under the nearby scenario, a moderately categorical decision rule leads to a mechanism for the grassroots changes to succeeed. This second regime, which was previously unsuspected in research on informational cascades, is highly relevant to linguistic change because linguistic changes typically originate with ordinary people. Previous models of language dynamics have explored the ways that functional factors can have major impacts on the linguistic structures through their iterated e\ufb00ects in language acquisition, perception, and production [46, 57]. Here we have shown that such functional factors are not necessary for global changes to occur. Our results connect the understanding of language dynamics with classic observations about the arbitrariness of many words and expressions in human languages [1,2]. Statistical variability in language is pervasive and often persists through language learning from one generation to the next [45]. Many researchers have assumed that the cognitive system for language uses probability-matching decision rules [47,48]. However, tendencies toward regularization of observed frequencies have been found in the area of phonotactics [58, 59], and in some experiments involving learning of arti\ufb01cial languages [35,36]. It has been argued that people discount ambiguous evidence in the acquisition of morphology and syntax [60,61]. Ambiguity and vacillation may be cognitively costly for linguistic processing. Categorical processing is argued to support fast, accurate encoding and decoding, as well as the ability to create new words and sentences by recombining basic elements [7]. Our results reconcile these disparate threads in the literature by developing a formal apparatus for analyzing regularization as the categorization of experienced frequencies. We then suggest that the cognitive processing of frequencies in language is moderately categorical. The regime in which we observe grassroots changes has \u03c6 \u224860\u25e6. As shown in Figure 4, this is a level of categoriality that deviates only moderately from a probabilitymatching decision rule. Although this moderate nonlinearity is su\ufb03cient to completely 24 change the prospects for an innovation to succeed, it is probably too weak to be detected in a typical psycholinguistics experiment. Very large scale data collection over the entire range of input probabilities would also be needed to assess the heterogeneity in individual biases that also plays a key role in our model. In short, the statistical power needed to rigorously compare a probability-matching (or neutral evolution) model with the regime for complete cascades in the nearby scenario is much higher than has been available in many classic experimental studies. Why isn\u2019t language processing strongly categorical? A probability-matching decision rule can be optimal at the group level when coordinated actions are needed to divide up resources [45]. Language presents a related case, because coordinated actions are needed for a group to maintain a mutually intelligible language, which bene\ufb01ts the group as a whole by permitting knowledge to be transmitted from any person to any other. In the nearby scenario, a completely categorical decision rule jeopardizes mutual intelligibility. For 65\u25e6\u2a85\u03c6 \u226490\u25e6, arbitrary innovations dominate the system but do not go to completion. This outcome means that the social group has split into subgroups with distinct norms. In contrast, the regime 55\u25e6\u2a85\u03c6 \u2a8565\u25e6yields a greater likelihood that mutual intelligibility will be maintained through periods of change. Assuming that the distribution of biases in the nearby scenario is empirically well-founded, language processing can be understood as striking a balance between fast, accurate processing and the maintenance of a shared linguistic code. In research on opinion dynamics, an early and prominent hypothesis held that a small number of individuals with high degree in a social network had disproportionate importance in triggering global cascades. That is, hubs in the network were thought to have special importance as so-called in\ufb02uentials [23]. Some previous models of language change achieve realistic cascade rates by assuming that people weight positively the input from highly-connected people, who are also assumed to be high-status [3, 4]. In the extreme, these assumptions lead to the conjecture that broadcast media should be a major factor in language change, since the media transmit the linguistic patterns of political leaders and celebrities to such large numbers of people. This conjecture is not well supported. For example, establishing any e\ufb00ect whatsoever of television on local dialects has been an elusive goal, and only recently has such an e\ufb00ect been found. In a detailed \ufb01eld study of Glaswegian English, some TV watchers were found to be in\ufb02uenced by the East End dialect of London, but only if they had personal ties to the East End or felt strong psychological engagement with characters in a popular TV soap drama that is set there [62]. In our model of egalitarian changes (the nearby scenario), informational cascades occur without any positive weighting of input from highly connected individuals. These individuals do play an important role, in that successful innovations succeed in part by being adopted by one or more highly connected individuals, who then broadcast them to many people. On the average, however, the highest degree individuals are somewhat conservative compared to less connected individuals, because their linguistic patterns are stabilized by the large number of incoming signals. Individuals who are far from the 25 innovator, and biased against the change, eventually adopt it with some probability simply because a core of positively biased individuals near the innovator allows the change to gain traction and in some cases eventually dominate the signal to the whole community. Some previous work has argued that the concept of covert prestige (understood as an implicit value system that countervails overt norms) is necessary to explain why high status people often adopt stigmatized expressions originating in lower status circles [63]. However e\ufb00orts to substantiate this notion in terms of perceived lower-class attributes such as toughness or friendliness have enjoyed mixed success [18]. Our model can explain why high degree or high status people eventually adopt grassroots linguistic innovations without recourse to a covert value system. Overall, our results support claims that social solidarity, and not di\ufb00erences in status, is the dominant factor in the adoption of linguistic innovations [53,55]. We saw that categorical decisions in the hubs scenario permit a well-connected group of people to e\ufb00ect a rapid and complete change that it favors. Less well-connected people may be initially biased against the change, but are swept along. This scenario does not appear to be relevant for linguistic changes. Is the model appropriate for some other type of change in social norms or collective opinions? A categorical decision function maximizes an individual\u2019s statistical expectations [32] in the case of perfect knowledge. This low-temperature decision rule is normally used in economic models [32], a re\ufb02ex of economists\u2019 assumption that individuals have complete information and make independent and rational decisions to maximize their gains. A recent example of a shift in public opinion in the economic domain was the 1999 repeal of Glass-Steagall Act provisions that separated investment banking from commercial banking. Our model shows how a wellconnected network of investment bankers who were biased in favor of opportunities for investment banking could cause this change to be widely accepted (even if other people held the opposite bias). More generally, a categorical decision rule is adaptive if the utility of the competing options is well-de\ufb01ned and generally known, or if the cost of waiting for more information is great. In times of revolution or war, it may be clear that people who delay or vacillate in their allegiances are less safe than people who take a side. Insofar as political behavior re\ufb02ects this perception of the risks, our model predicts people would apply a highly categorical decision process, be strongly in\ufb02uenced by a slight advantage of one option over the other, and that as a result public opinion in a time of crisis could be e\ufb00ectively controlled by a well-connected minority with shared biases. Insofar as political behavior strikes a balance between taking a stand and waiting for more information, our model suggests that grassroots political changes could take place without any de\ufb01nitive evidence about their ultimate utility. 26 Acknowledgments We thank L.A.N Amaral for time on his computing cluster. We are also grateful to P.J. Lamberson and Daniel Lassiter for useful discussions about decision functions, and to Simon Todd for incisive feedback on the mathematical exposition. We are also grateful for \ufb01nancial support from JSMF Grant No. 21002061 and John Templeton Foundation Award No. 36617 . The opinions expressed in this publication are those of the authors and do not necessarily re\ufb02ect the views of the John Templeton Foundation.",
                    "introduction": "Many human needs and goals are shared by people in di\ufb00erent cultures. But the social norms for addressing them can be highly arbitrary in their details. This is especially true for norms that promote communication and social cohesion. The value of such norms may arise more from the existence of a consensus than from its speci\ufb01cs. A fax machine has value only insofar as other people also have compatible fax machines. Facebook supports social contact only insofar as one\u2019s friends and relations are also on Facebook. This situation is epitomized in the most complex and highly evolved communication system of all, namely human language. Relationships between word forms and word meanings are very idiosyncratic across languages, and hence must be learned for any individual language [1, 2]. The usefulness of language comes about because people come to agree on ways to refer to entities, events, and abstractions. Agreement enables them to pool individual knowledge and bene\ufb01t from cooperative activities over great expanses of time and space. Once a linguistic consensus is in place in a community, why and how can it ever change? This question, the central focus of our paper, is a major challenge for models of language dynamics. It is widely agreed that linguistic systems emerge through innate propensities for people to imitate others in their communities [3\u20139]. Frequent forms, and forms produced by many di\ufb00erent speakers, are at an advantage in being learned, remembered, and used [10\u201313]. In contrast, infrequent forms are vulnerable to loss over time [12, 14]. These basic \ufb01ndings all mitigate against linguistic innovations, which by de\ufb01nition are rare and poorly disseminated when they \ufb01rst occur. Nonetheless, natural languages are never perfectly stable. They change at a wide range of time scales, and the fastest changes (such as the adoption of new slang expressions and jargon) are exhibited on time-scales of a few months or less within the speech of individual adults. In this regard, linguistic systems resemble cultural norms in other domains such as fashion, dancing, politics, and religion. In these domains as well, people are strongly in\ufb02uenced by the consensus of their neighbors, but norms still evolve over time. Complex patterns of variation across groups emerge when distinct groups follow di\ufb00erent trajectories of cultural evolution. Here, we develop a new model of how linguistic innovations can become widely adopted in a community. We focus on a type of changes that are particularly challenging to model: changes that we characterize as fast, arbitrary, and egalitarian. By fast changes, we mean ones that occur through learning and adaptation by individual speakers in the course of repeated interaction with their peers, without any generational replacement. Ref [15] characterizes within-generation changes in social norms as cases of horizontal transmis- sion. The slow changes that occur during cross-generational transmission of language fall outside of the scope of this paper; modeling them requires distinct mechanisms [6,16]. By arbitrary changes, we mean changes that involve no global functional advantage. They may be neutral, o\ufb00ering no identi\ufb01able functional advantage at all. Or, if there is any 3 advantage to some people from adopting them, it is balanced by some equal disadvantage to others. We do not deny that some changes in language may be globally advantageous. For example, human languages are shaped by a persistent bias to encode more predictable information using shorter expressions, which improves the e\ufb03ciency of communication [17]. However, prior work in language evolution, drawing on evolutionary biology, already reveals how positive utility can cause an innovation to spread. In contrast, for many linguistic changes, no global advantage is apparent. Explaining how arbitrary changes can take hold is essential to explain the vast profusion of apparently arbitrary detail that is observed synchronically [1]. We use the term egalitarian to highlight our interest in changes that originate with ordinary people and spread without regard to social status. Sociolinguistic \ufb01eld work has shown that people at the forefront of linguistic change typically belong to the lower middle class or upper working class. Although imitation of upper-class people may play a role in some conscious choices, such as product purchases, it cannot be the fundamental mechanism for linguistic changes. Typically, upper-class speakers eventually adopt pat- terns set by lower classes, rather than the other way around [18]. This pervasive pattern could not arise if imitating the few people at the top of the social hierarchy (perhaps in an e\ufb00ort to increase social capital) is the engine of linguistic change. However, the em- pirical \ufb01ndings do not necessarily indicate that people preferentially imitate lower-class people. Ordinary people are far more numerous than upper-class people, and this factor alone might explain the results. We thus take as a starting point the null hypothesis by which listeners weight input from all speakers equally, without assigning more value or prestige to some speakers than to others. Unlike Refs [3,4], we do not assume that people with many social connections have more status than others, or are preferentially taken as linguistic models. This null hypothesis takes us surprisingly far. We identify a con\ufb02uence of social and cognitive factors that enables fast, arbitrary, and egalitarian innovations to propagate with considerable probability. The key cognitive factor is the decision rule relating the perception of linguistic norms to the choice of what form to produce on any particular occasion. The key social factor is the distribution of biases over the members of the community. If some people are conservative, and others love novelty, the linguistic system is more likely to change than if nobody is biased in either direction. These \ufb01nd- ings challenge previous claims [3,4,19] that di\ufb00erences in social prestige are a necessary component in a theory of how linguistic innovations can spread. Our model of how innovations propagate integrates technical ingredients from work in several disciplines. Following recent work in network theory, we consider the linguistic community to be a social network in which nodes represent people and links represent social relationships. Speci\ufb01cally, a link between two nodes means that the two communi- cate with each other and are disposed to imitate each other in their choices of expression. Social ties that do not involve this level of mutual in\ufb02uence exist of course, but these ties are omitted from the model. Next, we draw a careful distinction between the mental state of a node and the signals 4 that the node emits. We assume that signals are categorical. For example, on each individual occasion when some speaker wishes to quote someone else, she either uses the conservative form (e.g. he said) or an innovative form (e.g. he was like). Mental states, in contrast, are numbers on a continuous scale of probabilities, representing the speaker\u2019s current estimate of the linguistic norm. They take values from 0 (\u201cI don\u2019t believe anybody uses that expression\u201d) to 1 (\u201cI believe everybody uses that expression\u201d). The value 0 will be used here for the conservative norm, and 1 for the innovation, so that in this example, a mental state of 0.6 would represent the speaker\u2019s belief that people in general use like to express quotation with P = 0.6. The model is applicable to any linguistic innovation that can be described as a new category competing with a pre-existing one. Examples include novel slang, such as lol in competition with ha-ha; novel a\ufb03xes such as uber- in competition with super-, as well as new constructions, such as gonna in competition with will for expressing the future. It does not encompass gradient changes in the signals themselves, such as the gradual shifts in vowel quality explored in Ref [20]. Signals and mental states are linked by a decision function, whose input is the mental state and whose output is the probability of emitting di\ufb00erent signals. This decision process is unconscious, but it is not trivial. To characterize variability in the decision function, we adopt the concepts of temperature and bias from the \ufb01eld of reinforcement learning. The bias captures the extent to which an individual generally favors conservative norms versus innovations. Temperature characterizes the extent to which the individual chooses the optimal production based on input received so far, versus exploring other options. A higher temperature means that individuals make more random choices, an analogy to the behavior of gas molecules, which exhibit more random motion under higher temperatures. In this application, we construe the optimal signal to be the one that others are most likely to accept as the norm. A central innovation of our model is a novel mathematical treatment of the decision function. In standard treatments of temperature, the decision function is the SoftMax function, which reduces to the logistic in the case of binary choices. The logistic is a sigmoidal function that maps inputs on the interval (\u2212\u221e, \u221e) to values on the interval (0, 1). Varying the free temperature parameter \u03c4 causes its form to vary between a step function as \u03c4 \u21920 and a constant function as \u03c4 \u2192\u221e. We analyze the behavior of the logistic function in the context of the emergence of linguistic norms, and identify serious problems with its behavior and interpretability. Linguistic norms resemble other application areas for reinforcement learning, because people learn them incrementally from experiences over time. However, a critical di\ufb00erence is that the signals produced by each individual provide the input for the neighbors, so that repeated signaling gives rise to positive feedback loops in the community. The logistic equation does not display sensible behavior under such iteration. For any temperature \u03c4 > 0, it cannot characterize the situation in which an absolute agreement in the linguistic community is stable. It is also unable to capture probability-matching behavior, in which people produce linguistic variants with the same relative frequencies that they experience them. Since probability-matching behavior and stable agreement are two of the principle 5 phenomena we need to characterize, we develop a new sigmoidal decision function that incorporates the broad insights behind the logistic, while also avoiding these problems. This is the clog (\u2018cognitive logistic\u2019) function. Like the logistic, the clog is a sigmoidal function that reduces to a step function as \u03c4 \u21920. Unlike the logistic, it is designed to map probabilities onto probabilities. It converges to the line y = x, and not a constant function, as \u03c4 \u2192\u221e. Variation in \u03c4 is usefully viewed as variation in the categoriality of the decision process. As \u03c4 \u21920, the output approaches two categories, y = 1 (or Boolean TRUE) and y = 0 (or Boolean FALSE). The variation in the input is completely regularized in the output. As \u03c4 \u2192\u221e, the categorization vanishes as all experienced probabilities become equally available to the production system. The output faithfully re\ufb02ects the input, without any regularization at all. Finally, these ingredients come together in our treatment of the di\ufb00usion of innova- tions as informational cascades [21]. Informational cascades occur in a social system when a local change propagates through a large group as a result of people\u2019s repeated interac- tions and tendencies to conform to each other. Initially developed in the area of opinion dynamics and product adoption [21\u201323], the concept is applicable to language dynamics under the assumption that linguistic norms are collective opinions about how to express concepts [4]. Figure 1, the result of one run of our model, illustrates a partial informa- tional cascade in a social network in which people vary in their biases. At the beginning of the run, the innovator (at the left edge) is the only person in the network who has adopted the novel expression. Although the innovator is directly connected to only three other people, the expression is adopted by many others in the network to varying degrees after a large number of communicative interactions have occurred. To explore the behavior of the clog in relation to likelihood of informational cascades in social networks, we report simulations on networks of 256 nodes. This size corresponds to a village, social club, or adolescent peer group that might adopt a new opinion, fashion, or linguistic expression in a short time. The social network is idealized as a scale-free network generated by a preferential attachment rule [24]. We have already said that bias heterogenity is a key factor in the successful propagation of linguistic innovations. Variation in individual biases is generated by sampling from a uniform distribution. However, values are sampled in pairs to ensure the overall functional neutrality of the innovative variant: each individual who is biased toward the innovation is balanced by a di\ufb00erent individual in the same run with an equal but opposite bias. In the \ufb01eld of opinion dynamics, the adoption of an innovation is typically treated as absolute and irreversible (c.f. [16, 25]). Under these assumptions, bias heterogeneity has already proven to be an important factor in the propagation of innovations [26]. In contrast to these models, we treat individual changes as reversible, in the interests of empirical realism in the language domain. Reversibility does not a\ufb00ect which end states can be reached by the system, but it does impact the likelihoods of the di\ufb00erent end states, which is our primary interest. The previous observations about the importance of bias heterogeneity generalize to this new model structure. 6 Figure 1. A partial cascade of a novel form of expression originating from a low-degree innovator. For each individual i, the degree of preference m for the novel opinion is represented as a probability from blue (mi = 0) to red (mi = 1). The network layout is governed by the distance from the innovator. Heterogeneous individual biases are assigned on the basis of this distance as described in the text for the nearby scenario. The decision rule is absolutely categorical (model parameter \u03c4 = 0). Our Monte Carlo simulation, implemented as an agent-based model, systematically explores the interaction between categoriality, innovator degree, and the distribution of biases in the population. We contrast two baseline scenarios, for which we expect rather stable norms, to three novel scenarios in which change is more likely. In one baseline scenario, people simply reproduce the frequencies they encounter. This scenario is compa- rable to neutral evolution in evolutionary biology, and is already known to make incorrect predictions about rates of language change [27]. In a second baseline, people categorize the frequencies they encounter (to greater or lesser extents), but no one has any bias for or against the change; the only heterogeneity in the population is in the number of social connections in the network. This setup is known to be highly stable if the decision function is a step function [22,26], and we will extend this result to less categorical decision func- tions. Of greatest interest are the three other scenarios, in which people in the network both categorize frequencies, and vary in their biases. We designate these as the random, hubs, and nearby scenarios. In the random scenario, bias values are distributed randomly 7 in the community. In the hubs scenario, innovation-favoring bias is preferentially allocated to high degree nodes (hubs), and bias against the innovation is allocated to low degree nodes. In the nearby scenario, innovation-favoring bias is preferentially allocated to the individuals topologically nearest to the innovator (regardless of the innovator\u2019s degree), and bias against the innovation is allocated to the individuals that are furthest from the innovation. Cascading is rare in the random scenario, though this scenario does support some partial cascades beyond those that are observed in a neutral evolution model. Two dif- ferent regimes in which change is far more likely are identi\ufb01ed. In the hubs scenario, the probability of a cascade increases monotonically with categoriality and innovator degree; total cascades become certain for su\ufb03ciently high categoriality and innovator degree. This regime may be relevant for social phenomena in which a few highly connected individuals are able to trigger sudden changes in collective opinion through their ability to broadcast their preferences to a large number of people at once. However, it is less relevant to lan- guage change than the nearby scenario. In the nearby scenario, cascades are most likely at a moderate level of categoriality, and are most likely to be initiated by individuals with low to middle degrees of connectivity. This novel result captures the phenomenon of changes that are fast, arbitrary and egalitarian. It represents a previously unsuspected regime for informational cascades. The discovery of this regime is due to our model\u2019s ability to formalize the concept of moderate categoriality and explore the interaction of categoriality with heterogeneity in the population."
                }
            ],
            "Qiang Liu": [
                {
                    "url": "http://arxiv.org/abs/2402.03916v2",
                    "title": "Can Large Language Models Detect Rumors on Social Media?",
                    "abstract": "In this work, we investigate to use Large Language Models (LLMs) for rumor\ndetection on social media. However, it is challenging for LLMs to reason over\nthe entire propagation information on social media, which contains news\ncontents and numerous comments, due to LLMs may not concentrate on key clues in\nthe complex propagation information, and have trouble in reasoning when facing\nmassive and redundant information. Accordingly, we propose an LLM-empowered\nRumor Detection (LeRuD) approach, in which we design prompts to teach LLMs to\nreason over important clues in news and comments, and divide the entire\npropagation information into a Chain-of-Propagation for reducing LLMs' burden.\nWe conduct extensive experiments on the Twitter and Weibo datasets, and LeRuD\noutperforms several state-of-the-art rumor detection models by 3.2% to 7.7%.\nMeanwhile, by applying LLMs, LeRuD requires no data for training, and thus\nshows more promising rumor detection ability in few-shot or zero-shot\nscenarios.",
                    "authors": "Qiang Liu, Xiang Tao, Junfei Wu, Shu Wu, Liang Wang",
                    "published": "2024-02-06",
                    "updated": "2024-02-08",
                    "primary_cat": "cs.IR",
                    "cats": [
                        "cs.IR",
                        "cs.CL"
                    ],
                    "main_content": "Rumor detection on social media is a major text mining task for automatically distinguishing untrustworthy information and maintaining the healthy development of the internet and society. Extensive works have been done to detect rumors from different perspectives (Castillo et al., 2011; Islam et al., 2020). Early attempts on rumor detection mainly focus on extracting statistical features of the propagation process (Kwon et al., 2013; Ma et al., 2015). Then, deep neural networks for modeling sequential data have been widely applied in aggregating propagation information and detecting rumors on social media. Among them, detection models based on recurrent neural networks (Ma et al., 2016, 2018), convolutional neural networks (Yu et al., 2017), attentive networks (Liu et al., 2018) and generative adversarial networks (Ma et al., 2019) have been extensively studied. Meanwhile, their combinations have also been investigated for rumor detection (Liu and Wu, 2018; Yu et al., 2019). Recently, detection models based on graph neural networks (Bian et al., 2020; Lu and Li, 2020; Nguyen et al., 2020; Xu et al., 2022) have achieved stateof-the-art performances. Furthermore, some works investigate incorporate graph contrastive learning for better rumor detection performances (Sun et al., 2022b; Wu et al., 2023). For better interpretability, reasoning over subgraph has been proposed (Jin et al., 2022; Yang et al., 2022). Meanwhile, for capturing temporal characteristics, dynamic graph has been constructed and applied in rumor detection (Sun et al., 2022a). Nowadays, considering practical applications, rumor detection in debiasing, few-shot or zero-shot scenarios have drawn much attention (Zhu et al., 2022; Xu et al., 2023; Yue et al., 2023; Lin et al., 2023; Liu et al., 2023). As LLMs have achieved great success, they also bring opportunities and challenges to misinformation identification (Chen and Shu, 2023). LLMs are able to easily generate misinformation (Vykopal et al., 2023; Chen and Shu, 2024), which is hard to be distinguished by human or LLMs solely based Vanilla Prompt There is a piece of news: \u201cSamsung paid Apple one-billion fine, with 20 billion coins in 30 trucks!\u201d Verify the credibility of the news. Please choose the answer from the following options: A. Fake, B. Real. Output I cannot verify the credibility of real-time or specific news events as my training only includes information up until January 2022, and I do not have the capability to access the internet for real-time updates. Rational Prompt There is a piece of news: \u201cSamsung paid Apple one-billion fine, with 20 billion coins in 30 trucks!\u201d Based on the writing style and the commonsense knowledge, estimate the credibility of the news. Based on above results, please choose the answer from the following options: A. Fake, B. Real. Output The news about Samsung paying Apple a one-billion fine with 20 billion coins in 30 trucks seems highly implausible and unrealistic. It lacks specific details, and the use of such an unconventional method for payment raises doubts about the credibility of the information. Therefore, the most appropriate answer would be: A. Fake. Vanilla Prompt There is a piece of news: \u201cAround 7 o\u2019clock this morning, a major traffic accident occurred on the Yuncheng to Houma section of the Shanxi Dayun Expressway, 9.3 kilometers away from Houma. A total of 47 vehicles collided in a series, resulting in 3 deaths and 7 injuries.\u201d Verify the credibility of the news. Please choose the answer from the following options: A. Fake, B. Real. Output I cannot verify the credibility of real-time or specific news events as my training only includes information up until January 2022, and I do not have the capability to access the internet for real-time updates. Rational Prompt There is a piece of news: \u201cAround 7 o\u2019clock this morning, a major traffic accident occurred on the Yuncheng to Houma section of the Shanxi Dayun Expressway, 9.3 kilometers away from Houma. A total of 47 vehicles collided in a series, resulting in 3 deaths and 7 injuries.\u201d Based on the writing style and the commonsense knowledge, estimate the credibility of the news. Based on above results, please choose the answer from the following options: A. Fake, B. Real. Output The provided news about a major traffic accident on the Yuncheng to Houma section of the Shanxi Dayun Expressway appears to be presented in a straightforward and factual manner. It includes specific details such as the time of the incident, the location, and the number of vehicles involved, as well as the reported casualties (3 deaths and 7 injuries). While I cannot independently verify the information, the news seems plausible and is presented in a manner consistent with typical reporting of traffic accidents. Therefore, based on the writing style and common sense, it appears to be: B. Real. Table 1: Analyzing news contents with GPT 3.5 on two samples. Without proper prompts, it is hard for the LLM to judge the credibility of the news. Thus, we design prompts (in red italicized words) to teach the LLM to concentrate on the writing styles and commonsense mistakes, which enable the LLM to find important clues in writing details and conduct commonsense reasoning. Key clues during reasoning are highlighted with red underlined words. on textual features (Chen and Shu, 2024). CICAN (Yang et al., 2023) uses GPT 3.5 as an auxiliary tool, for extracting entities from news and comments, and constructing relational graph. ARG (Hu et al., 2024) uses LLMs for analyzing the news contents, and conclude that, LLMs are hard to beat finetuned small models on detecting fake news. Thus, ARG incorporates insights generated by LLMs in small models for fake news detection. 3 Methodology In this section, we detail our proposed LeRuD approach, which consists of prompts for reasoning over news and comments, as well as the Chain-ofPropagation reasoning process. The whole procedure of LeRuD is demonstrated in Fig. 3. 3.1 Problem Formulation For a piece of news spreading on social media, we denote the news content as n, which is a paragraph of text. During spreading, the news receives comments, denoted as C = {(c1, t1), (c2, t2), ......}, in which ci denotes the textual content of the i-th comment, and ti means the relative posting time compared with the original news. We aim to utilize LLMs for modeling both the news n and comments C, and detecting rumors, i.e., identifying whether the news is fake or real. 3.2 RP: Rational Prompts for News We need design proper prompts to teach LLMs for analyzing news contents for rumor detection. Here, we apply the widely-used GPT 3.5 as the LLM used in our proposed approach. As shown in the two cases in Tab. 1, we try the vanilla prompts, which directly ask the LLM to infer the credibility of the news contents. However, without proper prompts, it is hard for the LLM to make guesses about veracity. The LLM does not know how to reason over the content that it has no knowledge about the described fact. This is mainly because that, the LLM can not concentrate on some key clues in the news contents. Accordingly to some previous study, writing styles of news are highlighted for misinformation identification (Przybyla, 2020), and commonsense reasoning is essential for distinguish fake news (Hu et al., 2024). Thus, we need to teach LLMs to reason from these aspect. Accordingly, we design Rational Prompts, which ask the LLM to answer \u201cBased on the writing style and the commonsense knowledge, estimate the credibility of the news.\u201d As shown in Tab. 1, with Rational Prompts, the LLM is able to find important clues in writing details and conduct commonsense reasoning, and give judgement on the veracity of news contents. In the first case, the LLM correctly predicts the news is fake, Vanilla Prompt There is a piece of news: \u201cAround 7 o\u2019clock this morning, a major traffic accident occurred on the Yuncheng to Houma section of the Shanxi Dayun Expressway, 9.3 kilometers away from Houma. A total of 47 vehicles collided in a series, resulting in 3 deaths and 7 injuries.\u201d There are comments for the news: \u201cMy god!\u201d \u201cBlessing...\u201d \u201cWhy isn\u2019t the highway closed on such a foggy day?\u201d \u201cRepost\u201d \u201cCherishing life!\u201d \u201cHow scary!\u201d \u201cBlessing.\u201d \u201cDrive carefully and pay attention to safety.\u201d \u201cShocking...\u201d Based on the comments, verify the authenticity of the news. Please choose the answer from the following options: A. Fake, B. Real. Output Based on the provided comments, it\u2019s challenging to determine the authenticity of the news directly. The comments express shock, concern, and questioning regarding the incident, but they don\u2019t provide concrete evidence or information about the news source. Therefore, the answer is: A. Fake. Conflicting Prompt There is a piece of news: \u201cAround 7 o\u2019clock this morning, a major traffic accident occurred on the Yuncheng to Houma section of the Shanxi Dayun Expressway, 9.3 kilometers away from Houma. A total of 47 vehicles collided in a series, resulting in 3 deaths and 7 injuries.\u201d There are comments for the news: \u201cMy god!\u201d \u201cBlessing...\u201d \u201cWhy isn\u2019t the highway closed on such a foggy day?\u201d \u201cRepost\u201d \u201cCherishing life!\u201d \u201cHow scary!\u201d \u201cBlessing.\u201d \u201cDrive carefully and pay attention to safety.\u201d \u201cShocking...\u201d Based on the comments, analyze whether there are any rebuttals or conflicts, and accordingly verify the authenticity of the news. Based on above results, please choose the answer from the following options: A. Fake, B. Real. Output The comments mainly express shock, concern, and questions about the responsibility for the accident. Some comments criticize the decision not to close the expressway in thick fog, suggesting potential negligence. There is also a call for attention to safety in such weather conditions. There doesn\u2019t seem to be any direct rebuttal or conflict among the comments. Instead, the comments generally focus on expressing emotions, seeking information about the incident, and questioning the decision-making around highway closure during foggy conditions. Based on the analysis of comments, there is no clear evidence of conflicting viewpoints that would cast doubt on the authenticity of the news. The concerns raised by commenters align with the details provided in the news report. Therefore, the answer is: B. Real. Table 2: Analyzing comments with GPT 3.5 on a sample. Without proper prompts, the LLM tends to say the news is fake when there lacks clear supporting materials. However, in most cases, is it hard to have clear evidences, especially in early stage of propagation. Thus, we design prompts (in red italicized words) to teach the LLM to concentrate on rebuttals or conflicts in comments, which lead the LLM to use crowd wisdom for judging the veracity of information. Key clues during reasoning are highlighted with red underlined words. by noticing that the event is not plausible from a commonsense perspective. In the second case, the LLM correctly predicts the news is real, via noticing some accident details, and concluding that the writing style is consistent with typical reports. 3.3 CP: Conflicting Prompts for Comments Furthermore, we need to design prompts to teach LLMs to reason over comments in propagation. As shown in Tab. 2, we try the vanilla prompts, which directly ask the LLM to verify the authenticity of news based on given comments. However, with such prompts, the LLM tends to predict the news is fake when there lacks clear supporting materials. In most cases, is it hard to have enough clear evidences, especially in the early stage of propagation. This makes it easy for the LLM to mistakenly recognize real news as fake news. Conflicts, rebuttals and skepticism in comments have been proven to be key features for distinguish misinformation (Ma et al., 2016; Liu et al., 2018; Ma et al., 2018; Lu and Li, 2020; Yu et al., 2017; Yang et al., 2022; Jin et al., 2022). Considering the difficulty of having sufficient supporting materials, we design Conflicting Prompts, which ask the LLM to answer \u201cBased on the comments, analyze whether there are any rebuttals or conflicts, and accordingly verify the authenticity of the news.\u201d As shown in Tab. 2, with Conflicting Prompts, the LLM correctly predicts the news is real, via noticing that people are all discussing about the event 1.0 0.4 [0,100]  (100,200]  (200,300]  (300,) #Comments  (a) Results on Twitter. (b) Results on Weibo. Figure 2: LLMs have trouble with too many comments. itself, and no conflicting information is posted. 3.4 CoP: Chain-of-Propagation Though Rational and Conflicting Prompts can teach LLMs to reason for rumor detection, LLMs still have trouble when facing too many comments. In real social media scenarios, the number of comments is usually very large. However, LLMs usually have limitations in input length. And more seriously, LLMs can not well reason over long contexts or redundant information (Huang et al., 2023; Xie, 2023). We test above Rational and Conflicting Prompts with GPT 3.5 on the Twitter and Weibo datasets (Sec. 4.1), and results are shown in Fig. 2. When the input length of a sample exceeds the limit, we randomly select part comments belonging to the sample as input. It is clear that, when a sample has too many comments, the detection accuracy drops sharply, which means the LLM can not well reason over excessive information. Prompt There is a piece of news: \"Famous actor Morgan  Freeman passed away in Los Angeles due to a  heart attack.\" There are comments for the news: \"A great  actor!\" \"Blessing.\" \"So suddenly.\" \"One of my  favorite actors...\" \u2026\u2026 You need to do: (1) Based on the writing style  and the commonsense knowledge, estimate the  credibility of the news. (2) Based on the  comments, analyze whether there are any  rebuttals or conflicts, and then accordingly  verify the authenticity of the news. Based on  above results, please choose the answer from the  following options: A. Fake, B. Real. Output The news itself seems straightforward, reporting  the death of Morgan Freeman in Los Angeles  due to a heart attack. However, the credibility  cannot be determined solely based on writing  style or common sense knowledge. The  comments seem to express condolences,  admiration for Morgan Freeman, and surprise at  the sudden nature of his passing. There are no  apparent rebuttals or conflicts in the comments.  Therefore, the answer is: B. Real. \u2026\u2026 Prompt There is a piece of news: \"Famous actor Morgan  Freeman passed away in Los Angeles due to a  heart attack.\" There are comments for the news: \"Morgan  Freeman is said to be died again?\" \"Who can tell  me if this is really true or not!\" \"I hope it's not  true.\" \"Oh my goodness, I really like him!\u201c \u2026\u2026 You need to do: (1) Based on the writing style  and the commonsense knowledge, estimate the  credibility of the news. (2) Based on the  comments, analyze whether there are any  rebuttals or conflicts, and then accordingly  verify the authenticity of the news. Based on  above results, please choose the answer from the  following options: A. Fake, B. Real. Output The news itself seems straightforward, reporting  the death of Morgan Freeman in Los Angeles  due to a heart attack. However, the credibility  cannot be determined solely based on writing  style or common sense knowledge. The  comment \"Morgan Freeman is said to be died  again?\" directly questions the veracity of the  news, indicating a potential conflict or doubt.  The comment \"I hope it's not true\" also reflects  uncertainty about the news. Therefore, the  answer is: A. Fake. Prompt There is a piece of news: \"Famous actor Morgan  Freeman passed away in Los Angeles due to a  heart attack.\" There are comments for the news: \"It's fake!\"  \"Will never see his works again.\" \"I haven't  found any news reports about his death, but  rather the news that he will dub for Apple SIRI  is going viral.\" \"What a pity...\" \u2026\u2026 You need to do: (1) Based on the writing style  and the commonsense knowledge, estimate the  credibility of the news. (2) Based on the  comments, analyze whether there are any  rebuttals or conflicts, and then accordingly  verify the authenticity of the news. Based on  above results, please choose the answer from the  following options: A. Fake, B. Real. Output The news itself seems straightforward, reporting  the death of Morgan Freeman in Los Angeles  due to a heart attack. However, the credibility  cannot be determined solely based on writing  style or common sense knowledge. The  comment \"It's fake!\" is a clear rebuttal to the  news, indicating a conflict in the information.  The comment about the absence of news reports  and the viral news about Morgan Freeman  dubbing for Apple SIRI adds to the conflicting  nature of the information. Therefore, the answer  is: A. Fake. \ud835\udc501, \u2026 , \ud835\udc50\ud835\udc58 \ud835\udc50\ud835\udc58+1, \u2026 , \ud835\udc502\ud835\udc58 The news is fake. \u2026\u2026 Chain-of-Propagation \ud835\udc50 \ud835\udc56\ud835\udc5b\ud835\udc61 \ud835\udc36\u22121 \ud835\udc58 \ud835\udc58+1, \u2026 , \ud835\udc50|\ud835\udc36| Figure 3: The procedure of the LeRuD approach. LeRuD divide the entire propagation information into a Chainof-propagation with easy comment information for reasoning in each step. In each reasoning step, Rational and Conflicting Prompts, which are written in red italicized words, are performed. Key findings during LeRuD\u2019s reasoning process are highlighted with red underlined words. In recent research of LLMs, a complex task, which is hard for LLMs, is divided into a series of easy tasks for LLMs to execute (Wei et al., 2022; Wang et al., 2023; Yao et al., 2023; Besta et al., 2024). This enhances LLMs\u2019 ability for complex tasks. Thus, we propose to divide the proposition information into a Chain-of-Propagation (CoP), which enables LLMs to conduct reasoning more easily. Considering comments in a time period usually share similar attitudes, we construct CoP in order of comments\u2019 posting time, and select k comments in each reasoning step. As shown in Fig. 2, the LLM can deal with up to 100 comments easily, so we set k = 100. Reasoning steps in a CoP are run in the same session of LLM, so that latter reasoning steps can refer to the results of former reasoning steps. Moreover, we use the result in the last step as the final estimation, considering the last step aggregates all the information. 4 Experiments In this section, we conduct extensive experiments, to verify whether LLMs can detect rumors on social media with our efforts. 4.1 Data Preparation Firstly, we introduce the data preparation process, which enables us to conduct sufficient evaluation. Datasets: For evaluation, we combine Twitter15 and Twitter16 as the Twitter dataset (Ma et al., 2017), and also incorporate the Weibo dataset (Ma et al., 2018). They are collected from two popular social media platforms, i.e., Twitter and Weibo. The average numbers of comments of each news in Twitter and Weibo are 232 and 816 respectively. We only use the verified false rumors (fake news) and non-rumors (real news) in Twitter. Data Filtering: For smooth and low-cost usage of GPT 3.5, we filter samples with ethics issues (such as violence, pornography and discrimination) and repeated news contents. We also filter samples containing mainly subjective expressions, for they are not factually real or fake. Meanwhile, for fair comparison, we need to filter samples with data leakage risks raised by the usage of LLMs, in which GPT 3.5 already exactly knows about the facts in the news. Thus, we direly ask GPT 3.5 to verify the veracity of each news with the Vanilla Table 3: Results of performance comparison and ablation study. Approach Twitter Weibo Accuracy Precision Recall F1-score Accuracy Precision Recall F1-score BIGCN 0.8882 0.8739 0.8940 0.8838 0.9258 0.9133 0.9335 0.9233 DDGCN 0.8982 0.8834 0.9078 0.8954 0.9414 0.9390 0.9483 0.9436 GACL 0.9042 0.8884 0.9171 0.9025 0.9354 0.9294 0.9409 0.9351 CICAN 0.9082 0.8855 0.9263 0.9054 0.9390 0.9298 0.9458 0.9377 ARG 0.8902 0.8628 0.8986 0.8803 0.9043 0.9022 0.9089 0.9055 LeRuD 0.9401 0.9156 0.9493 0.9321 0.9809 0.9732 0.9852 0.9792 w/o RP 0.9261 0.9107 0.9401 0.9252 0.9689 0.9635 0.9754 0.9694 w/o CP 0.9142 0.8525 0.9585 0.9024 0.9342 0.8777 0.9901 0.9306 w/o CoP 0.9281 0.9148 0.9401 0.9273 0.9330 0.9249 0.9409 0.9328 Prompts in Tab. 1, and only keep samples in which GPT 3.5 has no idea about the facts and can not give answers. In contrast, when GPT 3.5 knows about the fact in a piece of news, it will detail the fact and clearly judge the veracity. 4.2 Settings The, we detail the settings of our experiments. Baselines: Firstly, we compare with some stateof-the-art rumor detection models based graph neural networks: BIGCN (Bian et al., 2020), DDGCN (Sun et al., 2022a) and GACL (Sun et al., 2022b). Secondly, we also compare with two rumor detection models with LLMs: CICAN (Yang et al., 2023) and ARG (Hu et al., 2024). Metrics: We use Accuracy, Precision, Recall and F1-score for performance evaluation. Precision, Recall and F1-score are calculated according to the rumor detection results. Zero-shot Setting: LeRuD is performed in zeroshot setting, in which no training data is needed, and the evaluation is done with all samples in the dataset. We use GPT 3.5 as the LLM in LeRuD. 5-fold Cross-validation Setting: For other compared baselines, we perform 5-fold cross-validation. The whole process is run for 5 times, and in each time, 3 folds of samples are used for training, 1 fold of samples are used for validation, and 1 fold of samples are used for testing. After 5-time running, all samples have been used for testing, which stays the same as in the zero-shot setting. 4.3 Performance Comparison In Tab. 3, we compare LeRuD with several stateof-the-art rumor detection models. Among the three graph-based detection models, DDGCN and GACL obviously outperform BIGCN. With the help of GPT 3.5 for extracting entities, CICAN achieves similar or better performances compared to the graph-based models. ARG considers only news contents, so it underperforms other detection models which capture both news and comments. However, with insights generated by LLMs, ARG still achieves high accuracy of about 90%. Meanwhile, our proposed LeRuD approach achieves the best performances on both dataset evaluated by all metrics. Specifically, LeRuD outperforms the best baselines on Twitter and Weibo by 3.19% and 3.95% respectively. These results strongly demonstrate the superiority of LeRuD. Moreover, LeRuD requires no data for training, so it can consistently achieve promising rumor detection performances in few-shot or zero-shot scenarios, and thus is more suitable for real-world rumor detection. 4.4 Ablation Study In Tab. 3, we also demonstrate the ablation study of LeRuD, including three variants: LeRuD w/o RP, LeRuD w/o CP and LeRuD w/o CoP. LeRuD w/o RP denotes LeRuD without Rational Prompts. It decreases the performances of LeRuD by approximately 1%, but still outperforms other baselines. LeRuD w/o CP denotes LeRuD without Conflicting Prompts. The declines of accuracy and f1-score are 2.5% to 4.8%. LeRuD w/o CP achieves the highest recall values, but also achieves the lowest precision values. This is because that, without Conflicting Prompts, LLMs may mistakenly classify real news as fake news. LeRuD w/o CoP Denotes LeRuD without Chain-of-Propagation. The declines of accuracy and f1-score are about 1% and 4.5% on Twitter and Weibo respectively. The Prompt There is a piece of news: \u201cSamsung paid Apple one-billion fine, with 20 billion coins in 30 trucks!\u201d Verify the credibility of the news. Please choose the answer from the following options: A. Fake, B. Real. Output I cannot verify the credibility of real-time or specific news events as my training only includes information up until January 2022, and I do not have the capability to access the internet for real-time updates. Table 4: When asked to estimate the veracity of Sample \u201c3484403570896812\u201d in the Weibo dataset, GPT 3.5 has no idea about the fact. Prompt There is a piece of news: \u201cEx-New York Giants safety Tyler Sash, who died at 27, found to have degenerative brain disease.\u201d Verify the credibility of the news. Please choose the answer from the following options: A. Fake, B. Real. Output As of my last update in January 2022, the information you provided was accurate. Tyler Sash, a former New York Giants safety, passed away at the age of 27 and was found to have chronic traumatic encephalopathy (CTE), a degenerative brain disease often associated with head trauma in contact sports. Therefore, the answer is: B. Real. Table 5: When asked to estimate the veracity of sample \u201c692142338890661888\u201d in the Twitter dataset, GPT 3.5 provides details about the fact, and confirms the news is real. (a) Results on Twitter. (b) Results on Weibo. Figure 4: Early rumor detection results evaluated by accuracy with different detection deadlines. performance declines on Weibo are much larger, because the average number of comments in the Weibo dataset is much larger, according to the statistics in Sec. 4.1. This strongly proves that, LLMs have trouble in reasoning on excessive information. Above observations demonstrate the necessity of the three modules proposed in LeRuD. 4.5 Early Detection As shown in Fig. 4, we conduct early rumor detection with different detection deadlines. ARG is not included, for it does not model the propagation information. LeRuD constantly and significantly outperforms all the baselines with all the detection deadlines. This shows that, LeRuD can perform well during early stage of propagation, and does not rely on the sufficiency of comment information. 4.6 Impact of Comment Amount In Fig. 5, we illustrate the accuracy of LeRuD under different numbers of comments. With the help of CoP, LeRuD has no more trouble in conducting reasoning when facing great amount of comments. Meanwhile, with more comments, LeRuD has even higher rumor detection accuracy, as there is more (a) Results on Twitter. (b) Results on Weibo. Figure 5: Accuracy of LeRuD under different numbers of comments. More comments, better performances. information available for analysis. Above observations are totally different from those in Fig. 2. In a word, dividing the propagation information into Chain-of-Propagation helps LLMs to conduct reasoning more easily. 4.7 The Data Leakage Risk As in Sec. 4.1, we filter samples with data leakage risks, in which GPT 3.5 already exactly knows about the facts in the news. Examples with and without data leakage risks are shown in Tab. 4 and 5 respectively. More examples can be found in App. A. According to these examples, we can clearly observe totally different outputs by the LLM between samples with and without data leakage risks. This makes us easy to distinguish samples with and without data leakage risks. That is to say, after filtering these samples, we can avoid the data leakage risk, and experimental comparison can be fairly done among LeRuD and the baselines. 4.8 Explanations We can further refer to the explanations generated by the LLM, to ensure that LeRuD does not take use of the exact factual knowledge for detecting rumors. An example is shown in Tab. 6, and more Prompt of Step 1 There is a piece of news: \u201cSamsung paid Apple one-billion fine, with 20 billion coins in 30 trucks!\u201d There are comments for the news: \u201cNaughty!\u201d \u201cIt\u2019s funny!\u201d \u201cWeigh it \u201d \u201cSamsung has to count first!\u201d \u201cHow creativity!\u201d \u201cVerification needed.\u201d . .. . . . You need to do: (1) Based on the writing style and the commonsense knowledge, estimate the credibility of the news. (2) Based on the comments, analyze whether there are any rebuttals or conflicts, and then accordingly verify the authenticity of the news. Based on above results, please choose the answer from the following options: A. Fake, B. Real. Output of Step 1 Based on the writing style and commonsense knowledge, the news seems highly unlikely and lacks credibility. Paying a fine with 20 billion coins in 30 trucks sounds more like a creative or satirical piece rather than a factual event. Additionally, such a method of payment raises practical concerns and seems impractical. Analyzing the comments, we can observe a mix of skepticism, humor, and requests for verification. Comments like \u201cNaughty!,\u201d \u201cWeigh it,\u201d and \u201cSamsung has to count first!\u201d suggest doubts and a need for verification. The comment \u201cHow creativity!\u201d acknowledges the imaginative aspect, and \u201cVerification needed\u201d explicitly calls for confirmation. Therefore, the answer is: A. Fake. Prompt of Step 2 There is a piece of news: \u201cSamsung paid Apple one-billion fine, with 20 billion coins in 30 trucks!\u201d There are comments for the news: \u201cIt\u2019s hard to say whether it is true or not.\u201d \u201cUsing $1 billion in cash is illegal.\u201d \u201cRepost\u201d \u201cA truck with a load capacity of 3000 tons is impossible.\u201d \u201cWell done!\u201d ...... You need to do: (1) Based on the writing style and the commonsense knowledge, estimate the credibility of the news. (2) Based on the comments, analyze whether there are any rebuttals or conflicts, and then accordingly verify the authenticity of the news. Based on above results, please choose the answer from the following options: A. Fake, B. Real. Output of Step 2 Based on the writing style and commonsense knowledge, the news still appears unlikely and lacks credibility. Paying a one-billion dollar fine with 20 billion coins in 30 trucks seems impractical and raises legal and logistical issues. Analyzing the comments, there are several expressions of doubt and skepticism. Comments like \u201cIt\u2019s hard to say whether it is true or not,\u201d \u201cUsing $1 billion in cash is illegal,\u201d and \u201cA truck with a load capacity of 3000 tons is impossible\u201d highlight concerns about the feasibility and legality of the described scenario. The comment \u201cWell done!\u201d seems to be sarcastic or ironic, suggesting a lack of belief in the news. Therefore, the answer is: A. Fake. Final Output The final estimation of the veracity of the news is: The news is fake. Table 6: Prompts and outputs of performing the LeRuD approach on sample \u201c3484403570896812\u201d in the Weibo dataset. Key clues during LeRuD\u2019s reasoning process are highlighted with red underlined words. LeRuD correctly identifies the sample as fake, and the explanations are pretty reasonable from the commonsense perspective. examples can be found in App. B. According to these explanations, we can summarize the key clues in the reasoning process of LeRuD as follows: The regularity of writing: When the writing is informal, or the tone seems suspicions, LeRuD tends to judge the samples as fake (Tab. 21 and 24). When the writing is formal, or consistent with typical reporting styles, LeRuD tends to judge the samples as real (Tab. 25 and 27-30). The adequacy of details: When there lacks enough details of events in the news, LeRuD tends to judge the samples as fake (Tab. 17, 21, 22 and 24). When details are rich, LeRuD tends to judge the samples as real (Tab. 27, 28 and 31). The plausibility of contents: When the contents seem impractical, or there are conflicts within the contents, or the events do not conform to commonsense logic, LeRuD tends to judge the samples as fake (Tab. 6 and 24). When the contents seem plausible and rational from the commonsense perspective, or the events have large chances to occur in certain circumstances, LeRuD tends to judge the samples as real (Tab. 27 29). The attitudes of public: When the attitudes in the comments contains massive skepticism, questioning and rebuttals, or even some comments directly claim the news is fake, LeRuD tends to judge the samples as fake (Tab. 6 and 17 24). When comments seldom express skepticism or rebuttals, and people are discussing and commenting on the news events themselves, LeRuD tends to judge the samples as real (Tab. 25 32). The consistency of comments: When details in the comments conflict with the news events, or demonstrates the irrationality of the news, LeRuD tends to judge the samples as fake (Tab. 6, 17, 19 and 20). When details in the comments conform to the news, LeRuD tends to judge the samples as real (Tab. 25 and 26). In summary, LeRuD detects rumor on social media via reasoning from commonsense perspectives, and does not take usage of the LLM\u2019s exact prior knowledge about news facts. 5 Conclusion In this paper, we investigate to use LLMs for rumor detection on social media, and propose a novel approach called LeRuD. LeRuD designs proper prompts to teach LLMs to reason over important clues in news and comments. Meanwhile, we divide the entire propagation information of a piece of news into a Chain-of-Propagation for leading LLMs to conduct reasoning step-by-step with reasonable amount of information in each time. Then, we implement LeRud with the widely-used GPT 3.5, and conduct extensive experiments on the Twitter and Weibo datasets. LeRud can outperform several state-of-the-art rumor detection models with large margins. In summary, with our efforts, LLMs can well detect rumors on social media. Limitations In this paper, though we have taught LLMs to detect rumors on social media, our work still has limitations in the following two aspects. Firstly, running LLMs for rumor detection requires relatively high costs, such as the usage of high-performance GPUs, or the calls of APIs, or inputs of web interfaces. Secondly, graph neural networks have great ability for modeling structural data, while structural data is hard to be well described in texts. Thus, using LLMs for analyzing complex propagation structures, or combining the abilities of LLMs and graph neural networks, has not been explored. In the future, we shall put more efforts to overcome above limitations.",
                    "introduction": "With the development of social media, users can access to information more easily, and messages can be spread more rapidly. However, at the same time, rumors can also be spread to the public more easily and widely. It is necessary to conduct re- search on automatic rumor detection on social me- dia (Castillo et al., 2011; Islam et al., 2020), which is still very challenging. Recently, Large Language Models (LLMs) (Zhao et al., 2023) have achieved success and applied widely. This brings great con- venience to people. However, people can also use LLMs to intentionally generate great amount of unidentified information (Vykopal et al., 2023; Chen and Shu, 2024), which aggravate the propaga- tion situation of rumor on social media. Thus, the success of LLMs makes automatic rumor detection more challenging and urgent. News Samsung paid Apple one-billion fine, with 20  billion coins in 30 trucks! Comments Naughty! It\u2019s funny! Weigh it~ Verification needed. Samsung has to count first! No way~ Samsung has creativity. \u2026\u2026 It's hard to say whether it is true or not. Using $1 billion in cash is illegal. A truck with a load capacity of 3000 tons is  impossible. \u2026\u2026 Rumor? Figure 1: Can LLMs detect rumors on social media? The key of rumor detection lies in the modeling of propagation patterns on social media, i.e., aggre- gating the features of original news and user com- ments. Early approaches regards news and com- ments as sequences of texts, and applies recurrent networks (Ma et al., 2016), convolutional networks (Yu et al., 2017) or attention networks (Liu et al., 2018) for feature extraction. Then, rumor detection models based on graph neural networks (Lu and Li, 2020; Bian et al., 2020) have been widely proposed and achieved state-of-the-art performances. Recently, some research works attempt to apply LLMs in identifying the veracity of information (Chen and Shu, 2023). They mostly use LLMs to extract knowledge from texts (Yang et al., 2023) or solely analyzing the news contents (Hu et al., 2024). The power of LLMs for analyzing the prop- agation information, which contains both news and comments, on social media has not been explored. Meanwhile, as introduced by (Hu et al., 2024; Chen and Shu, 2024), solely relying on textual features of news, it is hard to obtain promising detection results by LLMs. This requires us to investigate the ability of LLMs for modeling the entire propa- gation information on social media. However, using LLMs for modeling the prop- agation information is not easy. Firstly, we find arXiv:2402.03916v2  [cs.IR]  8 Feb 2024 LLMs can not concentrate on the key clues in the propagation information, and thus may produce wrong predictions (Sec. 3.2 and 3.3). Secondly, the amount of comments is usually large, which brings great burden for LLMs to reason (Sec. 3.4), as LLMs usually have input length limitations, and have trouble when facing long contexts or redun- dant information (Huang et al., 2023; Xie, 2023). To teach LLMs to conduct reasoning over propa- gation information and overcome above shortcom- ings, we propose an LLM-empowered Rumor Detection approach, called LeRuD. Firstly, we draw experience from previous rumor detection models (Ma et al., 2016; Liu et al., 2018; Ma et al., 2018; Yang et al., 2022; Jin et al., 2022; Hu et al., 2024; Przybyla, 2020), in which useful informa- tion for distinguish rumors has been highlighted. We design proper prompts to teach LLMs to con- centrate on the writing styles and commonsense mistakes of news, as well as rebuttals or conflicts in comments. Secondly, we divide the propagation information into a Chain-of-Propagation, which en- ables LLMs to reason step-by-step in time order with a reasonable number of comments. Then, to evaluate the effectiveness of the LeRuD approach on detecting rumors, we conduct experi- ments on the Twitter and Weibo datasets (Sec. 4). We use the widely-applied GPT 3.5 1 in our imple- mentation. For smooth usage of GPT 3.5, we filter samples with ethics issues. Meanwhile, to avoid data leakage, we also filter samples in which GPT 3.5 already knows about the facts in the news. On the filtered datasets, LeRuD outperforms several state-of-the-art rumor detection models by 3.2% to 7.7%. To be noted, LeRuD achieves these results in zero-shot setting, while other models require training data. In a word, with our efforts, LLMs can well detect rumors on social media. Our main contributions can be listed as follows: \u2022 We propose to apply LLMs in detecting ru- mors on social media with the entire propaga- tion information, which contains both news and comments. \u2022 We design proper prompts to teach LLMs to concentrate on the key clues in news and com- ments, which enable LLMs to conduct reason- ing from multiple views. \u2022 We divide the propagation information of a piece of news into a Chain-of-Propagation, which enables LLMs to conduct reasoning 1https://chat.openai.com/ step-by-step with reasonable amount of infor- mation in each time. \u2022 We conduct extensive experiments, in which several state-of-the-art rumor detection mod- els are compared. Results demonstrate the superiority of our LeRuD approach."
                }
            ],
            "Hao Ni": [
                {
                    "url": "http://arxiv.org/abs/2308.03322v2",
                    "title": "Part-Aware Transformer for Generalizable Person Re-identification",
                    "abstract": "Domain generalization person re-identification (DG-ReID) aims to train a\nmodel on source domains and generalize well on unseen domains. Vision\nTransformer usually yields better generalization ability than common CNN\nnetworks under distribution shifts. However, Transformer-based ReID models\ninevitably over-fit to domain-specific biases due to the supervised learning\nstrategy on the source domain. We observe that while the global images of\ndifferent IDs should have different features, their similar local parts (e.g.,\nblack backpack) are not bounded by this constraint. Motivated by this, we\npropose a pure Transformer model (termed Part-aware Transformer) for DG-ReID by\ndesigning a proxy task, named Cross-ID Similarity Learning (CSL), to mine local\nvisual information shared by different IDs. This proxy task allows the model to\nlearn generic features because it only cares about the visual similarity of the\nparts regardless of the ID labels, thus alleviating the side effect of\ndomain-specific biases. Based on the local similarity obtained in CSL, a\nPart-guided Self-Distillation (PSD) is proposed to further improve the\ngeneralization of global features. Our method achieves state-of-the-art\nperformance under most DG ReID settings. Under the Market$\\to$Duke setting, our\nmethod exceeds state-of-the-art by 10.9% and 12.8% in Rank1 and mAP,\nrespectively. The code is available at\nhttps://github.com/liyuke65535/Part-Aware-Transformer.",
                    "authors": "Hao Ni, Yuke Li, Lianli Gao, Heng Tao Shen, Jingkuan Song",
                    "published": "2023-08-07",
                    "updated": "2023-09-18",
                    "primary_cat": "cs.CV",
                    "cats": [
                        "cs.CV",
                        "cs.AI"
                    ],
                    "main_content": "2.1. Domain Generalizable Person ReID. Supervised and unsupervised domain adaptation person ReID have achieved great success. But DG ReID is still a challenging task. It requires the model to train a model on source domains yet generalize to unseen target domains. Due to its huge practical value, it has been widely studied in recent years. The concept of DG ReID was first proposed in [29]. [21, 9] applied meta-learning to learn domaininvariant features. [11] proposed to disentangle identityirrelevant information. Last but not the least, [20] proposed IBN-net to explore the effect of combining instance and batch normalization, which was widely used in later DG ReID methods due to its good transferability and effectiveness. However, pure Transformer does use batch normalization, so IBN cannot bring gain to our model. But even without using IBN, our method still outperforms the existing CNN-based state-of-the-art in DG ReID. 2.2. Transformer-related Person ReID. The original Transformer is proposed in [25] for natural language processing (NLP) tasks. Based on ViT [4], [8] applies pure Transformer to supervised ReID for the first time, which introduces side information to improve the robustness of features. [17] further proposed self-supervised pretraining for Transformer-based person ReID, which mitigates the gap between the pre-training and ReID datasets from the perspective of data and model structure. Recently, some work investigate the generalization of vision Transformers [30]. In DG ReID, TransMatcher [15] employs hard attention to cross-matching similarity computing, which is more efficient for image matching. However, it still uses CNN as the main feature extractor, and the role of the Transformer is mainly reflected in image matching. Our method is the first to investigate the generalization ability of pure Transformer in DG ReID. 2.3. Proxy Task and Self-Distillation. Proxy Task and Self-Distillation have been extensively studied, and we only discuss their contribution to generalization here. Proxy Task is referred to as learning with free labels generated from the data itself, such as solving Jigsaw puzzles [19], predicting rotations [6] or reconstruction [5]. Since these tasks are not related to the target task (such as image classification), they can guide the model to learn generic features, which leads to less over-fitting to domainspecific biases [1]. CSL picks similar parts from the entire dataset without using ID labels, thus encouraging the model to learn the discriminative information shared by different IDs. Self-Distillation (SD) uses soft labels containing \u201cricher dark knowledge\u201d, which can reduce the difficulty of learning the mapping and further improve the generalization ability of the model [26]. Besides, [31] found that SD can help models converge to flat minima, improving the generalization of features. However, traditional SD methods are not suitable for ReID. Because it is a fine-grained retrieval task. So we propose PSD to replace traditional methods. 3. Methodology We proposed a pure Transformer-based framework, named Part-aware Transformer (PAT), to learn generalizable features, as shown in Figure 3. In the following, we describe the main components of our method. First, we introduce our Transformer encoder composed of L blocks, which simultaneously extracts global and local features (Sec. 3.1). Next, we design a proxy task, named CrossID Similarity Learning (CSL), to learn the generic features (3.2). It mines local similarity shared by different IDs and encourages model to learn generic features, thereby reducing over-fitting on source datasets. Finally, a Part-guided Self-Distillation module (PSD) is proposed to further improve the generalization of global features (Sec. 3.3). It constructs soft labels based on the similarity of local features, which solves the problems existing in traditional selfdistillation methods on ReID. CSL and PSD are jointly trained in an end-to-end manner (Sec. 3.4). 3.1. Transformer Encoder Our Transformer encoder f consists of L blocks. Each block contains global attention, part-aware attention and a feed-forward network. Global/Part-aware attention is used to extract global/local features. Input of Transformer Encoder. We split an input image x \u2208RH\u00d7W \u00d7C into non-overlapping N patches by a patch embedding module. Each patch is treated as an \u201cimage token\u201d {xi|i = 1, 2, . . . , N}. Besides, a learnable \u201cclass token\u201d xcls and three \u201cpart tokens\u201d{xpi|i = 1, 2, 3} are concatenated with all \u201cimage tokens\u201d. Then, the input to the Transformer encoder can be expressed as: Z = [xcls, xp1, xp2, xp3, x1, . . . , xN] + P (1) where Z represents input sequence embeddings, P \u2208 R(N+4)\u00d7D is position embedding. D is the number of channels. The attention mechanism is based on a trainable associative memory with query Q, key K, and value V . They are all computed from the vector sequence Z, which can be formulated as: Q = ZWQ = [qcls, qp1, qp2, qp3, q1, . . . , qN] K = ZWK = [kcls, kp1, kp2, kp3, k1, . . . , kN] V = ZWV = [vcls, vp1, vp2, vp3, v1, . . . , vN] (2) where WQ, WK, WV are different linear transformations. Global Attention. To extract global features, we use \u201cclass token\u201d and all \u201cimage tokens\u201d to perform global attention. The output matrix of global attention can be obtained by: Attention( Qcls,Kcls,Vcls)=Softmax(QclsKT cls \u221a D )Vcls (3) where Qcls = [qcls, q1, . . . , qN], Kcls = [kcls, k1, . . . , kN] and Vcls = [qcls, q1, . . . , qN]. Then the outputs of global attention are sent to FFN network. Repeat this process L times and we get a global feature f(xcls). \u2026 \u2026 \u2026 F F N Global  Attention Part-aware Attention \u00d7 \ufffd Cross-ID  Similarity Learning update \u2026 \u2026 \u2026 Memory Bank Hard  Label Cross-entropy Loss  Triplet Loss  Part-guided Self-Distillation Transformer Encoder Soft  Label N Image Tokens \ufffd\ufffd\ufffd\ufffd \ufffd(\ufffd\ufffd\ufffd\ufffd) \ufffd\ufffd1 \ufffd\ufffd2 \ufffd\ufffd3 \ufffd(\ufffd\ufffd) Figure 3. Illustration of our proposed method. FFN is a feed-forward network. We split an input image into N non-overlapping patches as \u201cimage tokens\u201d. The input of the model includes a \u201cclass token\u201d (xcls), three \u201cpart tokens\u201d ({xpi|i \u22081, 2, 3}) and N \u201cimage tokens\u201d. The \u201cclass token\u201d concatenates all \u201cimage tokens\u201d to get a global feature through global attention. For each \u201cpart token\u201d, it concatenates \u201cimage tokens\u201d of the region of interest to obtain the local feature belonging to this region. The output of the L Transformer block includes a global feature f(xcls) and three local features {f(xpi)|i \u22081, 2, 3}. We use three local representations and samples in the memory bank to solve a proxy task, named Cross-ID Similarity Learning (CSL). The results of the CSL guide the global representation to perform Part-guided Self-Distillation (PSD). Part-aware Attention. To learn local similarity from data themselves, we need to extract local features using partaware attention. For each \u201cpart token\u201d xpi, we use xpi and \u201cimage tokens\u201d belonging to a special region to perform part-aware attention. the output matrix of part-ware attention can be obtained by: Attention(Qpi, Kpi, Vpi)=Softmax(QpiKT pi \u221a D )Vpi (4) where Qpi = [qpi, qki, . . . , qki+m] and {ki, . . . , ki + m} represent the serial number of (m + 1) \u201cimage tokens\u201d associated with the part token xpi. Qpi and Kpi are handled in the same way. That is, \u201cpart tokens\u201d will only interact with \u201cimage tokens\u201d in the region of interest. In this work, We take three overlapping square areas along the vertical direction, as shown in the figure 3. The outputs of part-ware attention are sent to the FFN network. Repeating this process L times we get Three local features {f(xpi)|i = 1, 2, 3}. 3.2. Cross-ID Similarity Learning Existing Transformer-based ReID models perform representation learning based on global attention with annotated images, which leads the models to focus too much on domain-specific information, thus models get over-fitted on source domains. Besides, transformer-based ReID models ignore local similarities between different IDs, which can be helpful for generic representation learning. Specifically, cross-ID local similarities are ID-irrelevant, they offer visual knowledge to the models regardless of labels. Just like self-supervised learning, it provides the model with additional visual knowledge from the images themselves, not their labels. To learn generic features, we propose a proxy task named Cross-ID Similarity Learning (CSL). Our method is based on the observation that although the entire images of different IDs are quite different, the local regions of some IDs are similar, such as red short sleeves, white skirts, and many more (see Figure 2). The above information is not enough to discriminate ID on the source domain, but it is helpful to learn generic features. Just like other self-supervised learning methods in DG, such as solving jigsaw puzzles and predicting rotations, solving proxy tasks allow our model to learn generic features regardless of ReID task, and hence less over-fitting to domain-specific biases. Since it is difficult to find local similarities shared by different IDs in a mini-batch, we need to compare as many samples as possible in one gradient descent. To this end, we maintain a momentum-updated memory bank {wpi|i = 1, . . . , M} for each part token xpi during learning, which can be expressed as: wj pi = ( f \u0000xj pi \u0001 t = 0, (1 \u2212m) \u00d7 wj pi + m \u00d7 f \u0000xj pi \u0001 t > 0 (5) where t is the training epoch, m is the momentum and j = 1, . . . , K. K is the number of samples in the source dataset. For each local feature f(xj pi) in current mini-batch, we compare it with the entire memory bank. We select k local features closest to f(xj pi) from {wpi}K to form a set {Kj pi}k j=1 of positive samples. Then, the distance between positive samples and f(xj pi) is minimized by softmaxclustering loss , which can be formulated as: Lj pi = \u2212log P wm pi\u2208{Kj pi}k j=1 exp( f(xj pi)wm pi \u03c4 ) PK n=1 exp( f(xj pi)wn pi \u03c4 ) (6) where \u03c4 is a temperature coefficient. Minimizing Lpi encourages the model to pull similar patches {Kj pi}k j=1 close to f(xj pi) while pushing dissimilar patches away from f(xj pi) in feature space. In this way, the model can learn those visually similar patches in different IDs and make the Transformer notice the regions where this useful information is located. 3.3. Part-guided Self-Distillation Self-distillation has been shown to help improve generalization. For example, it can learn visual similarities beyond hard labels and make the model converges easier to the flat minima [26, 31, 22]. However, our experiments found that the traditional self-distillation method could not improve the generalization of ReID. Because traditional selfdistillation method relies on the output of the classifier to get the similarity between different categories. This is effective in image classification because of the large visual differences between different classes. For example, cats and dogs are visually similar, but cats and tables are very dissimilar. Such information can be utilized to facilitate learning. However, ReID is a fine-grained retrieval task, and the differences between different IDs are insignificant. So there is no useful information in the classification results. To this end, we propose Part-guided Self-Distillation (PSD), which uses the visual similarity of local parts to implement self-distillation. In Section 3.2, each local representation f(xj pi) gets k positive samples, and an image includes three part. Therefore, there are 3k positive samples in total for the global representation. We regard the IDs {Ii}3k i=1 corresponding to these 3k part as similar IDs. Soft labels Y j s of f(xj cls) are constructed as follows: Y j s |i = \uf8f1 \uf8f4 \uf8f2 \uf8f4 \uf8f3 1 \u2212\u03b1 i = yj s \u03b1 3kni i \u2208{Ii}3k i=1, 0 i / \u2208{Ii}3k i=1 \u222a{yj s} (7) where \u03b1 is the weight of similar categories, ni is the number of the i-th ID in {Ii}3k i=1 and yj s is ground truth of f(xj cls). That is, the more similar parts, the greater the probability of the ID to which these parts belong. Then, the part-guided self-distillation loss can be formulated as: Lj s =\u2212 \u03bbY j s logP \u0010 f(xj cls) \u0011 \u2212(1\u2212\u03bb)Y j log P \u0010 f(xj cls) \u0011 (8) where Y j is the one-hot hard label, \u03bb is the coefficient to balance soft label and P is the classifier that predicts probability distribution on source dataset. Since the apparent similarity is obtained by comparing the local representations of the current sample with the entire dataset. Therefore, it reflects the similarity between IDs better than the classification result of the classifier. 3.4. Loss Function and Discussion Loss function. In addition to the softmax-clustering loss and part-guided self-distillation loss used in 3.2 and 3.3, we also use the triplet loss with soft-margin to constrain the distance between positive and negative sample pairs. it can be formulated as follows: Ltri = log[1 + exp(||fa \u2212fp||2 2 \u2212||fa \u2212fn||2 2)] (9) where {fa, fp, fn} are the features of a triplet set. For a mini-batch with Nb samples, our entire loss function can be expressed as: L = Ltri + Nb X j=1 ( M X i=1 Lj pi + Lj s) (10) Discussion about occlusion and cloth-changing. Since CSL and PSD mine the local similarity shared by different IDs, it may aggravate the negative impact of occlusion or cloth-changing. Below we briefly explain why our method is still valid. (1) We do not fuse local features (cascaded or weighted with global features) during inference, so local features with only occlusion information would not degrade performance. See Section 1 of the Appendix for details. (2) Since there is still a large gap between DG ReID and supervised ReID, the impact of cloth-changing can be ignored compared to improving generalization. 4. Experiments 4.1. Datasets and Evaluation Metrics As shown in Table 2, we conduct experiments on four large-scale person re-identification datasets: Market1501[34], DukeMTMC-reID[37], MSMT17[27] and CUHK03-NP[38]. For simplicity, we denote the datasets above as M, D, MS, and C, respectively. We adopt the detected subset of the new protocol of CUHK03[13] (767 IDs for training and 700 IDs for evaluation), which is more challenging than the original CUHK03 protocol. To evaluate the generalization of our models, we adopt a single-source protocol [14] and a multi-source protocol Table 1. Performance comparisons between ours and the state-of-the-art in single-source DG ReID on Market1501, DukeMTMC-reID, MSMT17, and CUHK03-NP. Our results are highlighted in bold and others\u2019 best results are underlined. The subscripts 50 and 152 denote using IBNNet50 and IBNNet152 as backbone, respectively. Method Reference Duke MSMT CUHK-NP R1 mAP R1 mAP R1 mAP SNR [11] CVPR2020 Source: 55.1 33.6 QAConv50 [14] ECCV2020 Market 48.8 28.7 22.6 7.0 9.9 8.6 QAConv152 [14] 54.4 33.6 25.6 8.2 14.1 11.8 TransMatcher [15] NeurIPS2021 47.3 18.4 22.2 21.4 MetaBIN [3] CVPR2021 55.2 33.1 QAConv-GS [16] CVPR2022 45.9 17.2 19.1 18.1 MDA [18] CVPR2022 56.7 34.4 33.5 11.8 DTIN-Net[10] ECCV2022 57.0 36.1 PAT Ours 67.9 48.9 42.8 18.2 25.4 26.0 Method Reference Market MSMT CUHK-NP R1 mAP R1 mAP R1 mAP SNR [11] CVPR2020 Source: 66.7 33.9 QAConv50 [14] ECCV2020 Duke 58.6 27.2 29.0 8.9 7.9 6.8 QAConv152 [14] 62.8 31.6 32.7 10.4 11.0 9.4 MetaBIN [3] CVPR2021 69.2 35.9 MDA [18] CVPR2022 70.3 38.0 39.8 13.6 DTIN-Net[10] ECCV2022 69.8 37.4 PAT Ours 71.9 45.2 43.9 19.2 18.8 18.9 Table 2. Statistics of Person ReID Datasets. Dataset # IDs # images # cameras Market1501[34] 1,501 32,217 6 DukeMTMC-reID[37] 1,812 36,411 8 MSMT17[27] 4,101 126,441 15 CUHK03-NP[38] 1,467 28,192 2 [32]. Under the setting of single-source, we use one dataset mentioned above for training (only the training set) and another one for testing (only the testing set). Under the multisource protocol, we select one domain from M+D+C3+MS for testing(only the testing set in this domain) and all the remaining domains for training (only the training set). For evaluation metrics, the performance is evaluated quantitatively by mean average precision (mAP) and cumulative matching characteristic (CMC) at Rank-1 (R1). 4.2. Implementation Details We use ViT-base with stride = 16 [4] pre-trained on ImageNet as our backbone (denoted as ViT-B/16 for short). The batch size is set to 64 and images are resized to 256 \u00d7 128. We adopt random flipping and local grayscale transformation [7] for data augmentation. To optimize the model, we use SGD optimizer with a weight decay of 10\u22124. The learning rate increases linearly from 0 to 10\u22123 in the first 10 epochs then it decays in the following 50 epochs. The total training stage takes 60 epochs. For hyper-parameters, we conduct comprehensive experiments on the temperature parameter \u03c4 in section 4.4. Unless otherwise specified, we set \u03b1 (the weight of similar categories), \u03bb (the coefficient to balance soft label and hard label), and k (the number of clusters) to 0.5, 0.5, and 10, respectively. Besides, the label-smoothing parameter is 0.1. As for baseline, we use TransReID-B/16 [8] without SIE and JPM for a fair comparison. 4.3. Comparison with State-of-the-art Methods Single-source DG ReID To validate the performance of our model, we evaluate our framework on the singlesource generalization ReID benchmark. Specifically, we use Market-train and Duke-train as the training sets, and use Market-test, Duke-test, MSMT-test, and CUHK03-test as the testing sets. The experimental results are shown in Table 1. Our model outperforms the SOTA model under most settings and achieves a comparable performance with the SOTA model under the rest settings. In particular, under M\u2192D and D\u2192M settings, our model\u2019s mAPs outperform the state-of-the-art model by 10.3% on average. When trained on Market, our model surpasses the SOTA model (DTINNET[10]) by 10.9% and 12.8% (test on Duke), 3.2% and Table 3. Comparison with the State-of-the-Arts DG models on four large-scale person ReID benchmarks: Market-1501 (M), DukeMTMCreID (D), MSMT17 (MS) and CUHK03 (C). Our results are highlighted in bold and others\u2019 best results are underlined. Method MSMT Duke Market CUHK R1 mAP R1 mAP R1 mAP R1 mAP QACONV50* [14] Source: 29.9 10.0 Source: 64.9 43.4 Source: 68.6 39.5 Source: 22.9 19.2 M3L [32] M+D+C 33.0 12.9 MS+M+C 69.4 50.5 MS+D+C 74.5 48.1 MS+M+D 30.7 29.9 M3LIBN [32] 36.9 14.7 69.2 51.1 75.9 50.2 33.1 32.1 PAT 45.6 21.6 71.8 56.5 75.2 51.7 31.1 31.5 * represents the results reimplemented by M3L. Table 4. Improvements of our method (PAT) on different Transformers. The training set is Market. Method Duke CUHK MSMT R1 mAP R1 mAP R1 mAP DeiT-Tiny[24] 39.0 23.4 9.1 9.5 14.2 4.5 PAT 48.5 29.9 13.5 14.2 19.2 7.0 DeiT-Small[24] 53.0 34.0 14.1 14.5 23.5 8.4 PAT 56.9 37.4 18.4 18.2 27.1 10.0 ViT-Small[4] 51.9 33.1 12.9 14.0 24.8 9.2 PAT 54.4 35.9 15.1 15.2 26.9 10.0 DeiT-base[24] 59.3 41.3 18.1 18.8 32.9 12.8 PAT 61.3 42.6 20.3 21.0 36.2 14.9 ViT-Base[4] 65.9 46.5 23.1 23.6 38.6 16.2 PAT 67.9 48.9 25.4 26.0 42.8 18.2 4.6% (test on CUHK03-NP) in R1 and mAP. When trained on Duke, our model outperforms the SOTA by 1.6% and 7.2% (test on Market), 4.1% and 5.6% (test on MSMT) for R1 and mAP, respectively. This demonstrates the superiority of our model. Multi-source DG ReID To further validate the generalization of our model, we also conduct the experiments under the multi-source protocol. We follow the protocol proposed in M3L [32] which we have introduced in section 4.1. We use three of Market1501 (M), DukeMTMC-reID (D), MSMT17 (MS) and CUHK03-NP (C) as our source domain and the rest as our target domain. Note that, we follow the performance of QAConv reimplemented by M3L. As shown in Table 3, our method outperforms the SOTA model on all datasets. Specifically, our model\u2019s mAP is 6.9% higher than the current best model (M3L) under the M+D+C\u2192MS setting and reaches 56.5% under the MS+M+C\u2192D setting, which exceeds M3L by 5.4%. When training on MS+D+C or MS+M+D, our model still shows quite a similar performance compared with M3L. 4.4. Ablation Study Improvement on Transformer. To investigate the improvement of our method on original Transformers (baseTable 5. Ablation studies on the effectiveness of CSL and PSD. All methods are trained on Market and evaluated on Duke, MSMT, and CUHK03-NP. Method M\u2192D M\u2192MS R1 mAP R1 mAP Baseline (B) 65.9 46.5 38.6 16.2 B+SD [22] 64.1 44.9 35.6 14.6 B+CSL 67.1 48.3 40.2 17.0 B+CSL+PSD (ours) 67.9 48.9 42.8 18.2 line), we conduct extensive experiments on different Transformers. As shown in Tab 4, our approach can improve the generalization of various Transformers on ReID task, especially when model size is small. For example, our method surpasses baseline by 9.5% and 6.5% in R1 and mAP (Market \u2192Duke) when using DeiT-Tiny as the backbone. Ablation study of main components of our model. To ensure that all components promote our model, we conduct an ablation study. All models are trained on Market and then tested on Duke, MSMT, and CUHK03-NP, respectively. We choose the following models: (1) Baseline, namely TransReID-B/16 without SIE and JPM which is introduced in 4.1; (2) Baseline with conventional selfdistillation (B + SD). We follow the self-distillation way designed for domain generalization [22]; (3) our model without PSD (B + CSL); (4) our model with all components, including CSL and PSD. As shown in Table 5, Baseline + SD (self-distillation) results in a descent, which means that traditional selfdistillation fails to improve the generalization of ReID. Since ReID is a fine-grained retrieval task, it is not suitable to use conventional self-distillation which usually requires large inter-class distances. The results of (3) and (4) demonstrate our contribution. Firstly, our CSL module brings significant improvement. Secondly, PSD using the visual similarity of local parts to construct soft labels is effective. Visualization of attention maps. To better understand the part tokens, we conduct illustrative experiments on viimage cls part1 part2 part3 image cls part1 part2 part3 Figure 4. Attention map visualization. Original images are selected from the target domain (Duke). We exhibit the visualizations of the class token and three part tokens. Figure 5. Ablation study on \u03c4 of softmax-clustering loss. sualizing the attention maps. The size of attention maps in each head is N\u00d7N (N is the number of patches). We obtain the first four rows of an attention map, which denote the attention on each image patch of the class token and the part tokens. We resize these four attentions to H\u00d7W (H and W denote the height and width of the input), then we turn them into heat maps with the original image. We fuse the attention results of the shallow layers, which contain more visual information than the deep ones. As shown in Figure 4, the class token mainly focuses on the whole images, while the \u201cpart tokens\u201d pay attention to local areas like the upper body, legs, and backpacks. It shows that \u201cpart tokens\u201d broaden the scope of attention, and provide more comprehensive multi-view information to the class token. To put it another way, our model learns a more generic representation by utilizing local similarities. Ablation study on hyperparameters. (1) \u03c4: As shown in Figure 5, it is apparent that when trained on Market, setting \u03c4 to 0.02 is optimum. Softmax-clustering loss raises when \u03c4 decreases. If we set \u03c4 too large, the effect of softmaxclustering loss will be inappreciable. On the contrary, if \u03c4 is too small, the training stage will become quite unstable due to the increasing effect of softmax-clustering loss. Based on our experimental observation, we hold the opinion that using a larger \u03c4 is more suitable when the scale of the training set increases. (2) Number of parts: Dividing into three parts is the most intuitive and the most effective. The results of Table 6. Ablation study for the number of parts. Number of parts M\u2192D M\u2192C M\u2192MS mAP R1 mAP R1 mAP R1 2 47.0 66.7 24.5 23.6 16.7 39.3 3 48.9 67.9 26.0 25.4 18.2 42.8 4 48.6 67.1 25.1 25.1 18.1 41.7 5 47.9 66.1 25.0 25.6 17.0 40.5 Figure 6. Visualization of local features\u2019 ranking list in CSL. other numbers are shown in Table 6. For analysis of other hyperparameters (such as \u03b1, \u03bb), see Appendix. Visualization of local features\u2019 ranking list. To verify whether CSL has mined local similarities, we show those samples that are closest to the current local feature, that is, the samples belonging to {Kj pi}k j=1 in Section 3.2. As shown in Figure 6, the model can find samples with apparent similarity to the current sample in a specific area. For example, in the area attended by part token 1, not only people wearing dark red shirts but also backpacks were found. The above similarity is not dependent on the labels but completely derived from the data itself, which guides the model to learn generic features. 5. Conclusion In this paper, we propose a pure Transformer-based framework (termed Part-aware transformer) for DG ReID for the first time. Specifically, we design a proxy task, named Cross-ID Similarity Learning (CSL), to mine local visual information shared by different IDs. This proxy task allows the model to learn generic features because it only cares about the visual similarity of the parts regardless of the ID labels, thus alleviating the side effect of domainspecific biases. Furthermore, we propose a part-guided selfdistillation module to further improve the generalization of the global representation. Experimental results on multisource and single-source DG ReID show that our method achieves state-of-the-art in DG ReID.",
                    "introduction": "Person Re-Identification (ReID) [33, 2, 36, 35] aims to find persons with the same identity from multiple disjoint cameras. Thanks to the great success of Convolutional Neu- ral Network (CNN) in the field of computer vision [12, 23], supervised, unsupervised person ReID has made significant progress. However, a more challenging task, domain gen- eralization (DG) ReID [29] which trains a model on source *Jingkuan Song is the corresponding author. Target Source R1 (a) (b) Vision transformers CNNs DeiT-tiny ResNet18 ResNet34 DeiT-small ResNet50 ResNet101 ViT-small ResNet152 DeiT-base ViT-base 25  30  35  40  45  50  55  60  65  70  5.9 11.6 21.7 22.3 25.1 44 49.3 59.7 87.1 87.1 Parameters(M) Figure 1. (a) We applied different Transformers to DG ReID. Mod- els are trained on Market and tested on Duke. Results show Vi- sion transformers (blue bars) are better than CNNs (orange bars) even with fewer parameters. (b) Visualization of attention maps of \u201cclass token\u201d on source domain (Market) and target domain (Duke). We use ViT [4] as the backbone and fuse the attention results of the shallow layers. However, the attention to discrimi- native information is still limited on target domain. domains yet generalizes well on unseen target domains, still lags far behind the performance of supervised ReID model. Thus, many DG methods are proposed to learn generic features. These methods explore the generalization of CNN based on disentanglement [11] or meta-learning [3, 18]. Recently, Transformer has gained increasing attention in computer vision. It is a neural network based on attention mechanisms [25]. Vision Transformer usually yields better generalization ability than common CNN networks under distribution shift[30]. However, existing pure transformer- based ReID models are only used in supervised and pre- trained ReID [17, 8]. The generalization of Transformer is still unknown in DG ReID. arXiv:2308.03322v2  [cs.CV]  18 Sep 2023 ID\uff1a1 ID\uff1a2 ID\uff1a3 ID\uff1a4 ID\uff1a5 ID\uff1a6 ID\uff1a7 ID\uff1a8 Figure 2. Local similarity among parts with different IDs. It comes from the visual data themselves, not from ID labels. To investigate the performance of Transformer in DG ReID, we use different Transformers and CNNs as back- bones to test their cross-domain performance from Market to Duke. The results show that Vision Transformers are much better than common CNNs, as shown in Figure 1 (a). Even with fewer parameters, Transformers still outperform CNNs. For instance, DeiT-tiny [24] with 5.9M parameters is much better than ResNet18 with 11.6M parameters. De- spite the great performance of ViT [4], we still experimen- tally find that the attention to discriminative information is limited on unseen target domain. As shown in Figure 1(b), some discriminative information on the target domain is ig- nored, such as the black backpack and grey coat. The above phenomenon shows that Transformer- based ReID models inevitably over-fit to domain-specific biases due to the supervised learning strategy on the source do- main. It is manifested in the insufficient learning of local in- formation on unseen target domains. We observe that while the global images of different IDs should have different fea- tures, their similar local parts (e.g., White skirt, red T-shirt) are not bounded by this constraint, as shown in Figure 2. And these ID-independent local similarities can provide ex- tra visual knowledge from the images themselves. Ignoring this similarity leads the Transformer to focus on the ReID task instead of learning generic features, resulting in more over-fitting to domain-specific biases. To this end, we design a proxy task, named Cross-ID Similarity Learning (CSL), to mine local similarities shared by different IDs and learn generic features without using ID labels. CSL is based on part-aware attention to learn discriminative information across different IDs. The part- aware attention concatenates the \u201cpart token\u201d and the \u201cim- age tokens\u201d in the region of interest to learn local represen- tations. In each mini-batch, we use a memory bank to cal- culate the distance between the current local features and the samples of the entire dataset to mine apparent local sim- ilarity. The apparent similarity is learned not from ID an- notations, but from the visual data themselves [28]. Thus it allows the model to learn generic features because it only cares about the visual similarity of the parts regardless of the ID labels, thus alleviating the side effect of domain-specific biases. Part-guided Self-Distillation (PSD) is proposed to fur- ther improve the generalization of the global representa- tion. Self-distillation has been proven effective in DG im- age classification [26, 31]. It can learn visual similarities beyond hard labels and make the model converges easier to the flat minima. However, we experimentally find that the traditional self-distillation method would reduce the gener- alization in DG ReID. The reason is that ReID is a fine- grained retrieval task, and the difference between different categories is not significant. It is difficult to mine useful information from the classification results. Therefore, PSD uses the results of CSL to construct soft labels for global representation. In general, the motivation of self-distillation is similar to CSL, which is to learn generic features by data themselves regardless of the ID labels. Extensive experiments have proved that CSL and PSD can improve the generalization of the model. Specifically, our method achieves state-of-the-art performance under most DG ReID settings, especially when using small source datasets. Under the Market\u2192Duke setting, our method ex- ceeds state-of-the-art by 10.9% and 12.8% in Rank1 and mAP, respectively. The contributions of this work are three- fold: a) We propose a pure Transformer-based framework for DG ReID for the first time. Specifically, we design a proxy task, named Cross-ID Similarity Learning module (CSL), to learn generic features. b) We design part-guided self-distillation (PSD) for DG ReID, which learns visual similarities beyond hard labels to further improve the generalization. c) Extensive experiments have proved that our Part- aware Transformer achieves state-of-the-art of DG ReID."
                },
                {
                    "url": "http://arxiv.org/abs/2111.01207v1",
                    "title": "Sig-Wasserstein GANs for Time Series Generation",
                    "abstract": "Synthetic data is an emerging technology that can significantly accelerate\nthe development and deployment of AI machine learning pipelines. In this work,\nwe develop high-fidelity time-series generators, the SigWGAN, by combining\ncontinuous-time stochastic models with the newly proposed signature $W_1$\nmetric. The former are the Logsig-RNN models based on the stochastic\ndifferential equations, whereas the latter originates from the universal and\nprincipled mathematical features to characterize the measure induced by time\nseries. SigWGAN allows turning computationally challenging GAN min-max problem\ninto supervised learning while generating high fidelity samples. We validate\nthe proposed model on both synthetic data generated by popular quantitative\nrisk models and empirical financial data. Codes are available at\nhttps://github.com/SigCGANs/Sig-Wasserstein-GANs.git.",
                    "authors": "Hao Ni, Lukasz Szpruch, Marc Sabate-Vidales, Baoren Xiao, Magnus Wiese, Shujian Liao",
                    "published": "2021-11-01",
                    "updated": "2021-11-01",
                    "primary_cat": "cs.LG",
                    "cats": [
                        "cs.LG",
                        "60L10",
                        "I.6; G.3"
                    ],
                    "main_content": "When working with time-series data, especially sampled at high frequency and/or with irregular time stamps, it is useful to take a continuous-time perspective and view data as unknown continuous-time dynamics samples. In particular, rough path theory offers a mathematically principled and universal way of describing the continuous-time data trajectories (paths), which in turn allows designing computationally efficient algorithms. We briefly summarise these ideas below. 2.1 Signature of a path Let E := Rd and J be a compact time interval. Let X : J \u2192E denote a continuous path endowed with a norm denoted by | \u00b7 |. We first introduce the p-variation as a measure of the roughness of a path. The larger p-variation is, the rougher a path is. Definition 2.0.1 (p-variation) Let p \u22651 be a real number. Let X : J \u2192E be a continuous path. The p-variation of  on the interval is defined by \ufffd\ufffdr\u22121 p\ufffd1 p , where the supremum is taken over any Definition 2.0.1 (p-variation) Let p \u22651 be a real number. Let X : J \u2192E be X on the interval J is defined by \u2225X\u2225p,J = supD\u2208J \ufffd\ufffdr\u22121 j=0 |Xtj+1 \u2212Xtj|p\ufffd1 p finite time partition of J, i.e. D = (t1, t2, \u00b7 \u00b7 \u00b7 , tr). be a continuous path. The p-variation of 1 p , where the supremum is taken over any \u2225\u2225D\u2208 finite time partition of J, i.e. D = (t1, t2, \u00b7 \u00b7 \u00b7 , tr). Definition 2.0.2 (The signature of a path) Let X : J \u2192E be a continuous path of finite p-variation such that the following integration makes sense. The signature of X denoted by S(X) is defined as an infinite series of Xk J, i.e. S(X)J = (1, X1 J, \u00b7 \u00b7 \u00b7 , Xk J, \u00b7 \u00b7 \u00b7 ), where \ufffd \ufffd \u00b7 Xk J = \ufffd \u00b7 \u00b7 \u00b7 \ufffd u1<\u00b7\u00b7\u00b7<uk;u1,\u00b7\u00b7 \ufffd \u00b7 \u00b7 \u00b7 \ufffd u1<\u00b7\u00b7\u00b7<uk;u1,\u00b7\u00b7\u00b7 ,uk\u2208J dXu1 \u2297\u00b7 \u00b7 \u00b7 \u2297dXuk, \u2200k \u22651. Let Sk(X)J denote the truncated signature of X of degree k, i.e. Sk(X)J = (1, X1 J, ..., Xk J). Path augumentations There are a few commonly used path augumentations methods to accompany with the signature feature to retain good properties of the signature. In our work, we use three augumentation methods (a) Time augumentation, (b) Visiability transformation, and (c) Lead-lag transformation, which add the extra feature dimension to encode the information on the time stamps, the starting point of the path and the lagged process respectively. We refer [14] for the precise definition of the above path augmentations. For ease of notation, we denote the space of the time-augmented and visibility transformed paths of finite p-variation by \u2126p 0(J, E). Such augumented path has the path dimension 2d + 1 where d is the dimension of the original path. Intuitively the signature of a path plays a role of a non-commutative polynomial on the path space. With appropriate path augmentations, the signature of a path has the uniqueness and universality, which make the signature a useful candidate for the feature set of a path: Uniqueness: The signature of a path determines the path up to tree-like equivalence [15, 16]. More specifically, when restricted the path space to \u21261 0(J, Rd), the signature map is bijective. In other words, the signature of an augumented path by time augmentation and visibility transformation determines the path completely. Universality: Any continuous functional on the paths in \u21261 0(J, Rd) can be arbitrarily well approximated by a linear functional of truncated signatures when the degree of the signature is high enough. To state it more precisely we have: Theorem 2.1 Consider a compact set K \u2282\u21261 0(J, Rd). Let f : K \u2192R be any continuous function. Then, for any \u03f5 > 0, there exists an integer M > 0, and a linear functional l \u2208T (M)(R2d+1)\u2217acting on the truncated signature of degree M such that sup X\u2208K |f(X) \u2212\u27e8l, SM(X)\u27e9| < \u03f5 (1) 2 Sig-Wasserstein GANs for Time Series Generation A PREPRINT 2.2 Log-signature of a path The log-signature is a parsimonious representation for the signature feature. To de\ufb01ne the log-signature, we introduce the logarithm of an element in the tensor algebra space, i.e. T((E)) = \u2295E\u2297n. Let a = (a0, a1, \u00b7 \u00b7 \u00b7 , an) \u2208T((E)) be such that a0 = 1 and t = a \u22121. Then the logarithm map is de\ufb01ned as follows: log(a) = log(1 + t) = \u221e X n=1 (\u22121)n\u22121 n t\u2297n, \u2200a \u2208T((E)). (2) De\ufb01nition 2.1.1 The log signature of path X is the logarithm of the signature of the path X, denoted by LogSig(X). Let LogSigk(X) denote the truncated log signature of a path X of degree k. Uniqueness: Like the signature, the log-signature has the uniqueness as there is one-to-one correspondence between the signature and the log-signature. Dimension reduction When truncated by the same degree, the log-signature is of lower dimension compared with the signature feature in general. It be used for signi\ufb01cant dimension reduction when the path dimension d and the truncated degree of the (log)-signature k is large. See the comparison \ufb01gure of the dimension of the signature and log-signature. k d 2 3 4 5 6 7 1 3 2 4 3 5 4 6 5 7 6 8 7 2 7 3 13 6 21 10 31 15 43 21 57 28 3 15 5 40 14 85 30 156 55 259 91 400 140 4 31 8 121 32 341 90 781 205 1555 406 2801 728 5 63 14 364 80 1365 294 3906 829 9331 1960 19608 4088 Table 1: The left integer is the signature dimension whereas the right integer (in bold) is the log-signature dimension. 2.3 Expected signature of a stochastic process Let us consider a E-valued stochastic process X under the probability space. Assume that the signature of X is well de\ufb01ned almost surely, and S(X) has \ufb01nite expectation. We call E[S(X)] the expected signature of X. Intuitively the expected signatures serves the moment generating function, which can characterize the law induced by a stochastic process under some regularity condition. More concretely, an immediate consequence of Proposition 6.1 in [17] on the uniqueness of the expected signature is summarized in the below theorem: Theorem 2.2 Let X and Y be two \u21261 0(J, E)-valued random variables. If E[S(X)] = E[S(Y )] and E[S(X)] has the in\ufb01nite radius of convergence, then X = Y in the distribution sense. 3 Wassersetein Generative Adversarial Network (WGAN) Let (\u2126, F, P) be a probability space, under which \u00b5 and \u03bd are two distributions induced by X-valued stochastic process. The Kantorovich-Rubinstein dual representation of Wassersetein-1 (W1) metric de\ufb01nes a distance between two measures \u00b5 and \u03bd, denoted by W1(\u00b5, \u03bd) as follows: W1(\u00b5, \u03bd) = sup \u2225f\u2225Lip\u22641 EX\u223c\u00b5[f(X)] \u2212EX\u223c\u03bd[f(X)], (3) where the supremum is over all the 1-Lipschitz functions f : X \u2192R with its Lipschitz norm smaller than 1, i.e. for all x1, x2 \u2208X, |f(x1) \u2212f(x2)| \u2264|x1 \u2212x2|. In the context of generative modelling, let Z denote a latent space and Z \u2208Z denote a variable with the known distribution \u00b5Z \u2208P(Z). Let \u00b5 \u2208P(X) denote a target distribution of observed data. The aim of Wassersetein Generative Adversarial Network (WGAN) is to train a model that induces distribution \u03bd, so that W1(\u00b5, \u03bd) is small. The WGAN is composed of the generator G and the discriminator D. The generator G\u03b8 : Z \u2192X is a parameterized map transporting the latent distribution \u00b5Z to the model distribution \u03bd, i.e. the distribution induced by G\u03b8(Z), where \u03b8 \u2208\u0398g is a parameter set. To discriminate between real and synthetic samples, one parameterises the test function f 3 Sig-Wasserstein GANs for Time Series Generation A PREPRINT in de\ufb01nition of W1 metric (Eqn. (3)) by a network f\u03b7 with the parameter set \u03b7 \u2208\u0398d. Training the generator entails solving min-max problem. Indeed, to \ufb01nd optimal (\u03b8\u22c6, \u03b7\u22c6), one needs to solve min \u03b8 max \u2225f\u03b7\u2225Lip\u22641 E[f\u03b7(X)] \u2212E[f\u03b7(G\u03b8(Z))]. In practice, the min-max problem is solved by iterating gradient descent-ascent algorithms and it convergence can be studied using tools from game theory [18, 19]. It is well known that \ufb01rst order methods that are typically used in practice to solve the min-max problem might not converge, even if the convex-concave case, [20, 21, 22]. Consequently the adversarial training is notoriously dif\ufb01cult to tune, [23, 18], and generalisation error is very sensitive to the choice of discriminator and hype-parameters as it was demonstrated in large scale study in [24]. 4 Sig-Wassersetein Generative Adversarial Network (Sig-WGAN) In this work we design algorithms for generating time-series data. Let x1:T := (x1, \u00b7 \u00b7 \u00b7 , xT ) \u2208X \u2286Rd\u00d7T denotes a sample, or trajectory, of a time series data and assume that x1:T is distributed according to some unknown target distribution \u03bd \u2208P(X). Unlike majority of work in the literature, we don\u2019t assume that the data points are equidistant from each other. Given N independent trajectories (xi 1:T )N i=1 sampled from \u03bd \u2208P(X) or given one long trajectory (xiT,(i+1)T )N i=0 of stationary data, the aim of generative modelling is to learn a model capable of producing high \ufb01delity data samples from \u03bd \u2208P(X), without explicitly modelling the target distribution. 4.1 Signature Wassersetein-1 (Sig-W1) metric We propose a new Signature Wasserstein-1 (Sig-W1) metric on the measures on the path space X = \u21261 0(J, Rd) by combining the signature feature and the W1 metric to achieve better computation ef\ufb01ciency. Let \u00b5 and \u03bd be two measures on the path space X. When using W1 with. discrete time series, one needs to \ufb01x the time dimension of time series a prior. Here we (linearly) interpolate the data and compute its signature, possibly using appropriate path augmentation methods without information loss. The signature, as a universal and principled feature, encodes the temporal information regardless of the sampling frequency and variable length. Hence one may consider using the W1 metric on the signature space to de\ufb01ne a distance between the measure induced by two measures on the path space \u00b5 and \u03bd, i.e. W Sig space 1 (\u00b5, \u03bd) = sup \u2225f\u2225Lip\u22641 EX\u223c\u00b5[f(S(X))] \u2212EX\u223c\u03bd[f(S(X))] (4) While the use of signature features space W Sig space 1 signi\ufb01cantly reduces the time dimension of the problem, practical challenges of solving min-max problem remains. By working with the signature feature, one can reduce the computation of W Sig space 1 distance over the class of Lipschitz functionals to the linear functionals on the signature space thanks to the universality property of the signature. This motivates us to consider the proposed Signature Wasserstein-1 metric between \u00b5 and \u03bd de\ufb01ned by Sig-W1(\u00b5, \u03bd) := sup L is linear, \u2225L\u2225\u22641 EX\u223c\u00b5[L(S(X))] \u2212EX\u223c\u03bd[L(S(X))] . (5) Hence, by using Sig-W1 we reduced the nonlinear optimisation task to the linear problem with constraints. In practice, one needs to truncate the in\ufb01nite dimensional signature to a \ufb01nite degree for numerical computation of W Sig space 1 and Sig-W1(\u00b5, \u03bd). The factorial decay of the signature enables us to approximate the signature in Eqn. (5) by its truncated signature up to degree M for a suf\ufb01ciently large M. Therefore we propose to de\ufb01ne the truncated Sig-W1(\u00b5, \u03bd) metric up to a degree M as follows: Sig-W(M) 1 (\u00b5, \u03bd) := sup \u2225L\u2225\u22641,L is linear L(EX\u223c\u00b5[SM(X)] \u2212EX\u223c\u03bd[SM(X)]), (6) When the norm of L is chosen as the l2 norm of the linear coef\ufb01cients of L, this reduced optimization problem admits the analytic solution Sig-W(M) 1 (\u00b5, \u03bd) := |E\u00b5[SM(X)] \u2212E\u03bd[SM(X)]| (7) where |.| is l2 norm. In [25], if one chooses the truncated signature up to degree M as the feature map, then the corresponding Maximum Mean Discrepancy (Sig-MMD) is the square of Sig-W(M)(\u00b5, \u03bd). 4 Sig-Wasserstein GANs for Time Series Generation A PREPRINT The following toy example illustrates the relationship between the Sig-W1 distance and the W1 distance between two path distributions. Let X = (Xt)t\u2208[0,T ], \u02c6 X = ( \u02c6 Xt)t\u2208[0,T ] two 1-dimensional GBMs given by, dXt = \u03b81Xtdt + \u03c3XtdWt, X0 = 1; d \u02c6 Xt = \u03b82 \u02c6 Xtdt + \u03c3 \u02c6 Xtd \u02c6 Wt, \u02c6 X0 = 1, with the same volatility but with possibly different drifts \u03b81, \u03b82. Let \u00b5, \u03bd be the laws of X, \u02c6 X. We \ufb01x \u03c3 = 0.1, \u03b81 = 0.02, and for \u03b82 = 0.02 + j0.025, j = 0, . . . , 4. When \u03b82 is increasing, the discrepancy between X and \u02c6 X is increasing. We calculate three distances, i.e. W path space 1 , W Sig space 1 and Sig-W1 to quantify the distance between X and \u02c6 X for different \u03b82, which all increase when enlarging \u03b82 as expected. Since Sig-W(M) 1 (\u00b5, \u03bd) admits an analytic solution, it is cheaper to calculate than W path space 1 (\u00b5, \u03bd) and W Sig space 1 (\u00b5, \u03bd), where one needs to parametrise f by a neural network and optimise its weights. We observe in Figure 1 how these three values increase with similar rate as \u03b82 increases. 0 5 10 15 0.6 0.8 1.0 1.2 1.4 1.6 1.8 1=0.02;  2=0.020 0 5 10 15 1=0.02;  2=0.045 0 5 10 15 1=0.02;  2=0.070 0 5 10 15 1=0.02;  2=0.095 0 5 10 15 1=0.02;  2=0.120 0.02 0.04 0.06 0.08 0.10 0.12 2 10 4 10 3 10 2 10 1 Distance between gbm processes with  1 = 0.02 fixed w1-dist path space w1-dist sig space sigw1-dist Figure 1: The top row displays blue and red samples from X, \u02c6 X respectively for \ufb01xed \u03b81, and different values of \u03b82 4.2 LogSig-RNN Generator In this section, we introduce two generators of continuous type, which both are motivated by the numerical approximation of stochastic differential equations (SDEs). The \ufb01rst generator is the Neural SDE, which approximates the vector \ufb01eld by a feed-forward neural network in the Euler scheme, while the second generator \u2013 the Logsig-RNN resembles the high-order Taylor approximation of SDEs by combining the recurrent neural network with the log-signature. Fix a \ufb01ltered probability space (\u2126, F, {Ft}t\u22650, P), under which W = (Wt)t\u2208[0,T ] be a d-dimensional Brownian motion. Let W = (Wt)t\u2208[0,T ] denote the time-augmented Brownian motion, where Wt = (t, Wt) for ease of the 5 Sig-Wasserstein GANs for Time Series Generation A PREPRINT notation. Consider a Re-valued process X = (Xt)t\u2208[0,T ], which satis\ufb01es the following time-homogeneous SDEs driven by the Brownian motion W with the drift term \u00b5 and the volatility term \u03c3, i.e. dXt = \u00b5(Xt)dt + \u03c3(Xt)dWt := f(Xt)dWt, (8) where the stochastic integral is taken in the stratonovich sense and the vector \ufb01eld f : x\u00d7(s, \u03c9) 7\u2192\u00b5(x)s+\u03c3(x)\u03c9, \u2200x \u2208 Re, s \u2208R and \u03c9 \u2208Rd. 1 One can approximate the solution X de\ufb01ned by (8) via the step-M Taylor expansion locally; when s and t are close, Xt \u2212Xs \u2248 M X m=1 f \u25e6k(Xs) Z s<s1<\u00b7\u00b7\u00b7<sm<t dWs1 \u2297\u00b7 \u00b7 \u00b7 \u2297dWsm, (9) where 0 < s < t < T, f \u25e6m : Re \u2192L((Rd+1)\u2297m, Re) is de\ufb01ned inductively by f \u25e61 = f; f \u25e6m+1 = D(f \u25e6m)f with D(g) denoting the differential of the function g. This leads to the numerical approximation scheme by pasting the local step-M Taylor approximation together. Indeed, \ufb01x time partitions \u03a0h = (uj)N1 j=0 and \u03a0X = (tk)N2 k=0 of [0, T], which are time partition of Taylor expansion and the time discretization of the solution X respectively. Without loss of generality, \u03a0h \u2282\u03a0X. We de\ufb01ne \u02c6 X evaluated at the time partition \u03a0X inductively; let \u02c6 X0 = x0. For any tk \u2208\u03a0X \ufb01nd j such that tk \u2208(uj\u22121, uj], we apply the Taylor approximation of Xtk around the reference time point t = uj\u22121 \u2208\u03a0h, and hence obtain \u02c6 Xtk = \u02c6 Xuj\u22121 + M X m=1 f \u25e6m( \u02c6 Xuj\u22121) Z uj\u22121<s1<\u00b7\u00b7\u00b7<sm<tk dWs1 \u2297\u00b7 \u00b7 \u00b7 \u2297dWsk := F( \u02c6 Xuj\u22121, SM(Wuj\u22121,tk)) = \u02dc F( \u02c6 Xuj\u22121, LogSigM(Wuj\u22121,tk)). (10) Motivated by [26], we approximate \u02dc F in (10) by using a recurrent neural network. This leads to generalized LogsigRNN model, which maps a d-dimensional Brownian motion W[0,T ] to (otk)N2 k=1 \u2208RN2\u00d7e as the generator of Re-valued stochastic process: \u2200j \u2208{1, \u00b7 \u00b7 \u00b7 , N1} and \u2200k \u2208{1, \u00b7 \u00b7 \u00b7 , N2}, htk = \u03c31(\u03b81huj\u22121 + \u03b82LogSigM(Wuj\u22121,tk)); (11) otk = \u03c32(\u03b83htk). where \u03c31, \u03c32 are two activation functions and \u0398 = {\u03b81, \u03b82, \u03b83} is the learnable parameter set. When \u03a0h = \u03a0X, this is exactly the Logsig-RNN model in [26] Figure 2: The pictorial illustration of the generalized Logsig-RNN model. 1The time-inhomogeneous SDE can be viewed as the projection of the solution to time-homogeneous SDE by lifting X to its time-augmented process. 6 Sig-Wasserstein GANs for Time Series Generation A PREPRINT 5 Numerical results To validate the performance of the proposed Sig-Wasserstein GANs (SigWGANs), we consider three datasets, i.e. (1) synthetic data generated by multi-dimensional Geometric Brownian motion (GBM); (2) synthetic data generated by the rough volatility model; (3) stock price and realized volatility data. The former two datasets are representatives of commonly-used Markovian and non-Markovian model for the underlying price process. For each dataset, we compare the proposed SigWGANs with WGANs to demonstrate the advantages of Sig-Wasserstein metric in terms of the accuracy and ef\ufb01ciency. Besides for the SigWGANs, we benchmark the proposed Logsig-RNN generators of continuous type against the Long short-term memory (LSTM) model. To assess the quality of generated data, we consider the following test metrics: 1. Sig-W1 metric. 2. Marginal distribution metric. To assess the \ufb01tting of the marginal distribution, we compute the average of Wasserstein distance (also called earth mover\u2019s distance, EMD for short) between each marginal distribution X(i) t of the real time series and fake time series over all time t and feature channel i as the marginal distribution metric. 3. Correlation metric. To quantify the \ufb01tting of spatial and temporal dependence, we consider how close the correlation of X(i) t and X(j) s for any feature coordinate i and j and any time s and t. The correlation metric of X and \u02c6 X is de\ufb01ned as cor(X, \u02c6 X) = PT s,t=1 Pd i,j=1 \f \f \f\u03c1(X(i) s , X(j) t ) \u2212\u03c1( \u02c6 X(i) s , \u02c6 X(j) t ) \f \f \f, where \u03c1(X, Y ) denotes the correlation of two real-valued random variables X and Y . The smaller test metrics indicates better performance. Moreover, on the synthetic dataset, we test the predictive performance of the generative model, which is trained on the dataset of one time frequency and is tested on another time frequency. The better \ufb01tting performance on the test time frequency shows the robustness and generalization of the trained generative model against variation in sampling time. 5.1 Multi-dimensional Geometric Brownian motion (GBM) As a motivating example, we consider a d-dimensional GBM X = (Xt)t\u2208[0,T ] satisfying the following SDE: for i \u2208{1, \u00b7 \u00b7 \u00b7 , d}, dX(i) t = \u00b5iX(i) t dt + \u03c3iX(i) t d \u02dc W (i) t where Xt \u2208Rd, \u00b5 \u2208Rd, \u03c3 \u2208Rd and \u02dc W is a d-dimensional correlated Brownian motions with correlation matrix (\u03c1ij)i,j\u2208{1,\u00b7\u00b7\u00b7 ,d}. In this example, we set \u00b5i = 0.1, \u03c3i = 0.2, \u2200i \u2208{1, ..., d} and \u03c1ij = 0.5, for i \u0338= j. We use the equally spaced time partition of the time interval [0, 1] with step size \u2206t = 10\u22123, and simulate 4000 samples of the solution X to the SDE (5.1) using the analytic formula: X(i) tn = X(i) tn\u22121 exp[(\u00b5i \u22121 2\u03c32 i )\u2206t + \u03c3i( \u02dc W (i) tn \u2212\u02dc W (i) tn\u22121)] where tn = n\u2206t and i \u2208{1, \u00b7 \u00b7 \u00b7 , d}. Here we specify d = 3. 5.1.1 Performance comparison of SigWGAN v.s WGAN Figure 3 shows that by replacing the W1 discriminator by Sig-W1 discriminator, three test metrics drop more quickly at the beginning of training period, which indicates that the Sig-WGAN is more ef\ufb01cient to train. Besides, regardless of the generator, the Sig-WGAN outperforms the WGAN in terms of the three test metrics during the training. 5.1.2 Sensitively analysis in terms of number of time steps Table 2. As shown in Table 2, the Sig-W1 GAN with the LSTM generator works best when NT is small (e.g. 10 or 20). However, when increasing the number of time step NT , it gets more challenging for the LSTM generator to learn the joint path distribution in terms of correlation metric. In contrast to the LSTM, the performance of the LogsigRNN is much robust in terms of high frequency sampling of the data. In particular, combined with Sig-W1 metric, the Logsig-RNN generator achieves the correlation metric and marginal distribution of narrow range [0.045, 0.050] and [0.919, 1.032] for each NT \u2208{10, 20, 50, 100} respectively. For NT = 100, when using the SigWGAN, the test metrics of the LSTM generator is about four times of that of the Logsig-generator. For a \ufb01xed generator, we observe the consistent performance improvement of using Sig-W1 over the W1 metric as the discriminator. 7 Sig-Wasserstein GANs for Time Series Generation A PREPRINT 0 20 40 60 80 100 Time 10 2 10 1 Marginal Distribution Metric 0 20 40 60 80 100 Time 2 4 Correlation Metric(10 1) 0 20 40 60 80 100 Time 10 3 10 2 10 1 SigW1 Metric SigWGAN WGAN (a) LogsigRNN 0 20 40 60 80 100 Time 10 1 Marginal Distribution Metric 0 20 40 60 80 100 Time 1 2 3 Correlation Metric(10 1) 0 20 40 60 80 100 Time 10 3 10 2 SigW1 Metric SigWGAN WGAN (b) LSTM Figure 3: The upper/lower panel are the evolution of the test metrics of the Logsig-RNN/LSTM generator during training for the \ufb01rst 100 seconds. From left to right, the test metrics are Marginal distribution metric (Left), Correlation metric (Middle) and SigW1 metric (Right). The results are trained on 3-dimensional Geometric Brownian motion. W1 Sig-W1 NT 10 20 50 100 10 20 50 100 SigW1 Metric(1e-1) LSTM 0.140 0.125 0.677 0.651 0.096 0.064 0.020 0.196 LogsigRNN 0.264 0.128 0.162 0.160 0.047 0.040 0.042 0.037 Correlation Metrics (1e-3) LSTM 1.057 0.862 5.512 2.658 0.478 0.852 0.9698 3.391 LogsigRNN 2.125 1.811 9.277 2.219 0.962 1.032 0.967 0.919 Marginal Distribution Metric LSTM 0.052 0.065 0.132 0.082 0.026 0.043 0.036 0.140 LogsigRNN 0.122 0.059 0.317 0.067 0.050 0.047 0.050 0.045 Training time (seconds) LSTM 376.55 374.78 375.44 375.53 134.33 134.66 134.71 135.89 LogsigRNN 682.21 718.21 721.21 781.21 261.23 322.33 371.21 472.21 Table 2: Evaluation for 3-dimensional GBM with various numbers of timesteps NT \u2208{10, 20, 50, 100}. 5.2 Rough Volatility model We consider a rough stochastic volatility model for an asset price process St, which satis\ufb01es the below SDE: dSt = \u221avtStdZt vt := \u03be(t) exp \u0012 \u03b7W H t \u22121 2\u03b72t2H \u0013 (12) where \u03be(t) denotes the forward variance and W H t denotes the fBM given by W H t := Z t 0 K(t \u2212s)dWs, K(r) := \u221a 2HrH\u22121/2 where Zt, Wt are (possibly correlated) Brownian motions. In our experiments, the synthetic dataset is sampled from (12) with t \u2208[0, 1], H = 0.25, \u03be(t) = 0.25, \u03b7 = 0.5, \u03c1 = 0 where \u03c1dt = d\u27e8W, Z\u27e9t. Each sampled path is a stream of data of 20 points sampled uniformly between [0, 1]. For the training details, we train the generators to learn \u2022 the log price distribution, 8 Sig-Wasserstein GANs for Time Series Generation A PREPRINT \u2022 the log price and the log volatility joint distributions using WGAN and Sig-W1 GAN. In both learning algorithms we scale the log-price paths by 2 and the log-volatiliy by 0.5 so that they have similar variance. In addition, in the SigWGAN we augment the paths by adding time dimension and visibility transformation before computing the expected signature up to degree 4. For a fair comparison, we train the Wasserstein GAN and the Sig-W1 GAN for 2 500 iterations of the generator. The Sig-W1 GAN provides an explicit form for the Sig-W1 distance between two path distributions, which implies that the overall number of gradient steps is 2 500. However, training the Wasserstein GAN involves training the generator and the discriminator; in our settings, for every gradient step of the generator, we take three gradient steps on the discriminator, thus the overall number of gradient steps is 10 000. Table 3 shows the evaluation metrics of the trained generators. W1 Sig-W1 Data (Xt)t (St) (St, vt) (St) (St, vt) SigW1 Metric LSTM 0.29 0.42 0.07 0.17 LogsigRNN 0.20 1.43 0.11 0.32 Correlation Metric(1e-3) LSTM 4.76 5.21 1.58 8.23 LogsigRNN 2.19 8.19 1.09 4.82 Marginal Distribution Metric(1e-2) LSTM 2.37 1.95 1.62 4.83 LogsigRNN 1.17 9.25 1.38 4.03 Training time(seconds) LSTM 158 205 164 256 LogsigRNN 814 845 352 452 Table 3: The test metrics of the trained models on a one dimensional price data (St)t\u2208[0,T ] and two dimensional price and volatility data (St, vt)t\u2208[0,T ] respectively. Sig-W1 GANs outperform GANs in all evaluation metrics, except for the training time in the case of the LSTM generator. The LSTM and the LogSigRNN generators have similar performances in terms of correlation metric, SigW1 metric and Marginal Distribution metric. Regarding the training time, the LSTM generator is marginally cheaper to train with the W1-GAN algorithm, even if the training of the W1-GAN involves 4x more gradient steps than the Sig-W1 GAN. This is due to the fact that calculating the signature of the augmented path in the Sig-W1 GAN algorithm accounts for the additional iterations taken to train the W1-GAN. However, for a more complex generator as is the case of the LogSigRNN, the Sig-W1 GAN is 2x cheaper than the W1-GAN in terms of training time. 5.2.1 Correlation metric comparison The error plot of the covariance matrix \u0010 cov(X(i) s , X(j) t ) \u0011 i,j\u2208{1,2},s,t\u2208{1,\u00b7\u00b7\u00b7 ,NT } in Figure 4 clearly shows that the combination of the Logsig-RNN and SigW1 metric are able to capture the temporal and spatial dependency of the rough volatility data best. The WGAN struggles to the temporal covariance of the volatility data. 5.2.2 Robustness to the variable sampling frequency We test the robustness of the trained generator by generating data streams with a different frequency than the frequency used for training and we test them on synthetic data generated from (12) with the same new frequency. Namely, we generate data streams of 30 points on [0, 1], whilst training was performed on data streams of 20 points on [0, 1]. Table 4 shows how in this new setting Sig-W1 GANs outperform GANs by two orders of magnitude. It is also veri\ufb01ed qualitatively and visually by comparing the sample trajectories of the real paths and the synthetic path generated by the SigWGAN and WGAN using the same LogsigRNN generator in Figure 5. 5.3 S&P 500 and DJI Market Data We validate our proposed SigWGAN model on the empirical \ufb01nancial data. Here we choose daily spot-prices of the S&P 500 and DJI from January 1st 2005 to June 1st 2020. This dataset is from the Oxford MAN Realized Library. We 9 Sig-Wasserstein GANs for Time Series Generation A PREPRINT 0 10 20 30 0 5 10 15 20 25 30 35 Cov error SigWGAN 0.000 0.002 0.004 0.006 0.008 0.010 0 10 20 30 0 5 10 15 20 25 30 35 Cov error WGAN 0.000 0.002 0.004 0.006 0.008 0.010 0.012 (a) LogsigRNN 0 10 20 30 0 5 10 15 20 25 30 35 Cov error SigWGAN 0.000 0.002 0.004 0.006 0.008 0.010 0 10 20 30 0 5 10 15 20 25 30 35 Cov error WGAN 0.000 0.001 0.002 0.003 0.004 0.005 (b) LSTM Figure 4: The upper/lower \ufb01gures are the covariance error plots of the Logsig-RNN/LSTM generators for each dimension (St, vt) and each timestep. From Left to Right, each heatmap displays the covariance error of the Sig-WGAN and the WGAN respectively. W1 Sig-W1 Data (Xt)t (St, vt) (St, vt) Correlation Metric(1e-4) LSTM 358.84 8.32 LogsigRNN 411.39 5.02 Table 4: The test metrics of the trained models on two dimensional price and volatility data (St, vt)t\u2208[0,T ]. Models are trained on data streams sampled every T 20 units of time, and evaluated on data streams sampled every T 30 units of time. compute the log return series from the close price of both S&P 500 and DJI, then apply rolling window to get 3856 samples of log return paths of 10 time steps. We use 80% samples as the training set and the rest 20% as the test set. To train the SigWGAN, we use the basepoint path augmentation, cumulative sum and the lead-lag transformation. According to Table 5, for a \ufb01xed generator (LSTM/LogsigRNN), the SigWGAN improves the WGAN in terms of both the correlation metric and marginal distribution metrics. Besides, SigWGAN is more ef\ufb01cient than WGAN, which is illustrated by the half reduced training time when using the Logsig-RNN generator. Although the SigWGAN with the Logsig-RNN generator takes a bit longer to train than the other models, it can signi\ufb01cantly reduce the correlation metric from 0.5982 to 0.5031 and the marginal distribution metric from 0.1752 to 0.1304 compared with the second best model. 5.3.1 Correlation metric comparison The error plot of the correlation matrix in Figure 6 clearly shows that the combination of the Logsig-RNN and SigW1 metric are able to capture the temporal and spatial dependency of the stock data best. However, the error plot of correlation matrix of Logsig-RNN and W1 metric shows more dark areas. Hence the combination of Logsig-RNN and W1 metric struggles to the temporal correlation of the volatility data. 10 Sig-Wasserstein GANs for Time Series Generation A PREPRINT 0 5 10 15 20 25 30 Number of time steps in time discretisation 0.5 1.0 1.5 2.0 2.5 (a) Real paths of new frequency 0 5 10 15 20 25 30 Number of time steps in time discretisation 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 (b) SigWGAN+LogsigRNN 0 5 10 15 20 25 30 Number of time steps in time discretisation 0.5 1.0 1.5 2.0 2.5 3.0 (c) WGAN+LogSigRNN Figure 5: From left to right, generated paths with new frequency (i.e. 30 time steps), generated paths using the trained LogSigRNN with Sig-W1 GAN on the old frequency (20 time steps), generated paths using the trained LogSigRNN with Wasserstein-GAN on the old frequency. Type W1 Sig-W1 SigW1 Metric(1e-4) LSTM 5.0632 2.7510 LogsigRNN 5.6269 2.8161 Correlation Metric(1e-1) LSTM 0.6422 0.5161 LogsigRNN 0.5982 0.5031 Marginal Distribution Metric(1e-2) LSTM 0.2001 0.1513 LogsigRNN 0.1752 0.1304 Training time(seconds) LSTM 0.138882 0.103918 LogsigRNN 0.472448 0.210008 Table 5: The test metrics of the trained models on the log price of S&P 500 index and S&P 500 and DJI index. 0 1 2 3 4 5 6 7 8 9 10111213141516171819 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 (a) SigWGAN + LogsigRNN 0 1 2 3 4 5 6 7 8 9 10111213141516171819 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 (b) WGAN + LogsigRNN Figure 6: The correlation error of synthetic data generated by LogsigRNN using SigWGAN and WGAN resp. for stock data. 11 Sig-Wasserstein GANs for Time Series Generation A PREPRINT",
                    "introduction": "The ability to model time-series data accurately is critical for numerous applications in the \ufb01nance industry. In particular, synthetically generated time-series datasets can facilitate training and validation of data-driven risk models and enable data sharing by respecting the demand for privacy constraints. We refer the reader to [1, 2] for the overview of the applications and challenges for synthetic data generation and to [3, 4, 5, 6, 7, 8] for generative modelling perspective of some of the classical problems in quantitative risk management. While generative modelling has been highly successful in generating samples from seemingly high dimensional probability measures, off-the-shelf techniques, such as generative adversarial network\u2019s (GAN) [9], struggle to capture the temporal dependence of joint probability distributions induced by time-series data. Furthermore, the min-max objective function of classical GANs make them notoriously dif\ufb01cult to tune. In this paper, we use mathematically principled feature extraction machinery that emerged from the theory of rough paths to reduce the min-max formulation of GANs to an optimization problem. The proposed method, called Sig-Wasserstein GAN, can handle irregularly spaced data streams of variable lengths and is poetically ef\ufb01cient for data sampled at high frequency. Related work It is by now well documented that popular machine learning frameworks enhanced with path signatures achieve the state of the art performance across many time series learning tasks. For example, the combination of rough path theory and variational autoencoder showed the strength in simulating \ufb01nancial time series in small data environment [4]. In [10] authors showed that by combining signatures with classical quantitative \ufb01nance models provide arXiv:2111.01207v1  [cs.LG]  1 Nov 2021 Sig-Wasserstein GANs for Time Series Generation A PREPRINT novel perspective on neural SDEs and lead to ef\ufb01cient calibration procedure. Related results have been obtained in [11]. The most related to this work is [12]. There authors developed the conditional Sig-Wasserstein GAN to simulate time series that mimics the conditional law of the future time series given the past. This work focuses on the unconditional case instead. Our Logsig-RNN generator extends the work of [13], as we do not require the equal time dimension of input data and output data. The article is structured as follows. In Section 2 we overview the key elements of rough path theory. In Section 3 we present classical GAN framework which we then extend to Sig-Wasserstein GAN in Section 4. Section 5 contains numerical examples."
                }
            ]
        },
        "edge_feat": {}
    }
}