Daily Papers

Value functions are a central component of deep reinforcement learning (RL). These functions, parameterized by neural networks, are trained using a mean squared error regression objective to match bootstrapped target values. However, scaling value-based RL methods that use regression to large networks, such as high-capacity Transformers, has proven challenging. This difficulty is in stark contrast to supervised learning: by leveraging a cross-entropy classification loss, supervised methods have scaled reliably to massive networks. Observing this discrepancy, in this paper, we investigate whether the scalability of deep RL can also be improved simply by using classification in place of regression for training value functions. We demonstrate that value functions trained with categorical cross-entropy significantly improves performance and scalability in a variety of domains. These include: single-task RL on Atari 2600 games with SoftMoEs, multi-task RL on Atari with large-scale ResNets, robotic manipulation with Q-transformers, playing Chess without search, and a language-agent Wordle task with high-capacity Transformers, achieving state-of-the-art results on these domains. Through careful analysis, we show that the benefits of categorical cross-entropy primarily stem from its ability to mitigate issues inherent to value-based RL, such as noisy targets and non-stationarity. Overall, we argue that a simple shift to training value functions with categorical cross-entropy can yield substantial improvements in the scalability of deep RL at little-to-no cost.

Conventional wisdom holds that autoregressive models for image generation are typically accompanied by vector-quantized tokens. We observe that while a discrete-valued space can facilitate representing a categorical distribution, it is not a necessity for autoregressive modeling. In this work, we propose to model the per-token probability distribution using a diffusion procedure, which allows us to apply autoregressive models in a continuous-valued space. Rather than using categorical cross-entropy loss, we define a Diffusion Loss function to model the per-token probability. This approach eliminates the need for discrete-valued tokenizers. We evaluate its effectiveness across a wide range of cases, including standard autoregressive models and generalized masked autoregressive (MAR) variants. By removing vector quantization, our image generator achieves strong results while enjoying the speed advantage of sequence modeling. We hope this work will motivate the use of autoregressive generation in other continuous-valued domains and applications.

This abstract explores an RNN-based approach to online handwritten recognition problem. Our method uses data from an accelerometer and a gyroscope mounted on a handheld pen-like device to train and run a character pre-diction model. We have built a dataset of timestamped gyroscope and accelerometer data gathered during the manual process of handwriting Latin characters, labeled with the character being written; in total, the dataset con-sists of 1500 gyroscope and accelerometer data sequenc-es for 8 characters of the Latin alphabet from 6 different people, and 20 characters, each 1500 samples from Georgian alphabet from 5 different people. with each sequence containing the gyroscope and accelerometer data captured during the writing of a particular character sampled once every 10ms. We train an RNN-based neural network architecture on this dataset to predict the character being written. The model is optimized with categorical cross-entropy loss and RMSprop optimizer and achieves high accuracy on test data.

While language models have exceptional capabilities at text generation, they lack a natural inductive bias for emitting numbers and thus struggle in tasks involving reasoning over quantities, especially arithmetics. This has particular relevance in scientific datasets where combinations of text and numerical data are abundant. One fundamental limitation is the nature of the CE loss, which assumes a nominal (categorical) scale and thus cannot convey proximity between generated number tokens. As a remedy, we here present two versions of a number token loss. The first is based on an L_p loss between the ground truth token value and the weighted sum of the predicted class probabilities. The second loss minimizes the Wasserstein-1 distance between the distribution of the predicted output probabilities and the ground truth distribution. These regression-like losses can easily be added to any language model and extend the CE objective during training. We compare the proposed schemes on a mathematics dataset against existing tokenization, encoding, and decoding schemes for improving number representation in language models. Our results reveal a significant improvement in numerical accuracy when equipping a standard T5 model with the proposed loss schemes.

Diffusion models that are based on iterative denoising have been recently proposed and leveraged in various generation tasks like image generation. Whereas, as a way inherently built for continuous data, existing diffusion models still have some limitations in modeling discrete data, e.g., languages. For example, the generally used Gaussian noise can not handle the discrete corruption well, and the objectives in continuous spaces fail to be stable for textual data in the diffusion process especially when the dimension is high. To alleviate these issues, we introduce a novel diffusion model for language modeling, Masked-Diffuse LM, with lower training cost and better performances, inspired by linguistic features in languages. Specifically, we design a linguistic-informed forward process which adds corruptions to the text through strategically soft-masking to better noise the textual data. Also, we directly predict the categorical distribution with cross-entropy loss function in every diffusion step to connect the continuous space and discrete space in a more efficient and straightforward way. Through experiments on 5 controlled generation tasks, we demonstrate that our Masked-Diffuse LM can achieve better generation quality than the state-of-the-art diffusion models with better efficiency.

We propose a categorical semantics of gradient-based machine learning algorithms in terms of lenses, parametrised maps, and reverse derivative categories. This foundation provides a powerful explanatory and unifying framework: it encompasses a variety of gradient descent algorithms such as ADAM, AdaGrad, and Nesterov momentum, as well as a variety of loss functions such as as MSE and Softmax cross-entropy, shedding new light on their similarities and differences. Our approach to gradient-based learning has examples generalising beyond the familiar continuous domains (modelled in categories of smooth maps) and can be realized in the discrete setting of boolean circuits. Finally, we demonstrate the practical significance of our framework with an implementation in Python.

Markov categories are a novel framework to describe and treat problems in probability and information theory. In this work we combine the categorical formalism with the traditional quantitative notions of entropy, mutual information, and data processing inequalities. We show that several quantitative aspects of information theory can be captured by an enriched version of Markov categories, where the spaces of morphisms are equipped with a divergence or even a metric. As it is customary in information theory, mutual information can be defined as a measure of how far a joint source is from displaying independence of its components. More strikingly, Markov categories give a notion of determinism for sources and channels, and we can define entropy exactly by measuring how far a source or channel is from being deterministic. This recovers Shannon and R\'enyi entropies, as well as the Gini-Simpson index used in ecology to quantify diversity, and it can be used to give a conceptual definition of generalized entropy.

Categorical encoders transform categorical features into numerical representations that are indispensable for a wide range of machine learning models. Existing encoder benchmark studies lack generalizability because of their limited choice of (1) encoders, (2) experimental factors, and (3) datasets. Additionally, inconsistencies arise from the adoption of varying aggregation strategies. This paper is the most comprehensive benchmark of categorical encoders to date, including an extensive evaluation of 32 configurations of encoders from diverse families, with 36 combinations of experimental factors, and on 50 datasets. The study shows the profound influence of dataset selection, experimental factors, and aggregation strategies on the benchmark's conclusions -- aspects disregarded in previous encoder benchmarks.

We develop Markov categories as a framework for synthetic probability and statistics, following work of Golubtsov as well as Cho and Jacobs. This means that we treat the following concepts in purely abstract categorical terms: conditioning and disintegration; various versions of conditional independence and its standard properties; conditional products; almost surely; sufficient statistics; versions of theorems on sufficient statistics due to Fisher--Neyman, Basu, and Bahadur. Besides the conceptual clarity offered by our categorical setup, its main advantage is that it provides a uniform treatment of various types of probability theory, including discrete probability theory, measure-theoretic probability with general measurable spaces, Gaussian probability, stochastic processes of either of these kinds, and many others.

Autoregressive language models are trained by minimizing the cross-entropy of the model distribution Q relative to the data distribution P -- that is, minimizing the forward cross-entropy, which is equivalent to maximum likelihood estimation (MLE). We have observed that models trained in this way may "over-generalize", in the sense that they produce non-human-like text. Moreover, we believe that reverse cross-entropy, i.e., the cross-entropy of P relative to Q, is a better reflection of how a human would evaluate text generated by a model. Hence, we propose learning with MixCE, an objective that mixes the forward and reverse cross-entropies. We evaluate models trained with this objective on synthetic data settings (where P is known) and real data, and show that the resulting models yield better generated text without complex decoding strategies. Our code and models are publicly available at https://github.com/bloomberg/mixce-acl2023

Enhancing the intelligibility and interpretability of machine learning is a crucial task in responding to the demand for Explicability as an AI principle, and in promoting the better social implementation of AI. The aim of our research is to contribute to this improvement by reformulating machine learning models through the lens of category theory, thereby developing a semantic framework for structuring and understanding AI systems. Our categorical modeling in this paper clarifies and formalizes the structural interplay between residuals and parameters in supervised learning. The present paper focuses on the multiple linear regression model, which represents the most basic form of supervised learning. By defining two concrete categories corresponding to parameters and data, along with an adjoint pair of functors between them, we introduce our categorical formulation of supervised learning. We show that the essential structure of this framework is captured by what we call the Gauss-Markov Adjunction. Within this setting, the dual flow of information can be explicitly described as a correspondence between variations in parameters and residuals. The ordinary least squares estimator for the parameters and the minimum residual are related via the preservation of limits by the right adjoint functor. Furthermore, we position this formulation as an instance of extended denotational semantics for supervised learning, and propose applying a semantic perspective developed in theoretical computer science as a formal foundation for Explicability in AI.

Correctly dealing with categorical data in a supervised learning context is still a major issue. Furthermore, though some machine learning methods embody builtin methods to deal with categorical features, it is unclear whether they bring some improvements and how do they compare with usual categorical encoding methods. In this paper, we describe several well-known categorical encoding methods that are based on target statistics and weight of evidence. We apply them on a large and real credit card fraud detection database. Then, we train the encoded databases using state-of-the-art gradient boosting methods and evaluate their performances. We show that categorical encoding methods generally bring substantial improvements with respect to the absence of encoding. The contribution of this work is twofold: (1) we compare many state-of-the-art "lite" categorical encoding methods on a large scale database and (2) we use a real credit card fraud detection database.

Cross-entropy is a widely used loss function in applications. It coincides with the logistic loss applied to the outputs of a neural network, when the softmax is used. But, what guarantees can we rely on when using cross-entropy as a surrogate loss? We present a theoretical analysis of a broad family of loss functions, comp-sum losses, that includes cross-entropy (or logistic loss), generalized cross-entropy, the mean absolute error and other cross-entropy-like loss functions. We give the first H-consistency bounds for these loss functions. These are non-asymptotic guarantees that upper bound the zero-one loss estimation error in terms of the estimation error of a surrogate loss, for the specific hypothesis set H used. We further show that our bounds are tight. These bounds depend on quantities called minimizability gaps. To make them more explicit, we give a specific analysis of these gaps for comp-sum losses. We also introduce a new family of loss functions, smooth adversarial comp-sum losses, that are derived from their comp-sum counterparts by adding in a related smooth term. We show that these loss functions are beneficial in the adversarial setting by proving that they admit H-consistency bounds. This leads to new adversarial robustness algorithms that consist of minimizing a regularized smooth adversarial comp-sum loss. While our main purpose is a theoretical analysis, we also present an extensive empirical analysis comparing comp-sum losses. We further report the results of a series of experiments demonstrating that our adversarial robustness algorithms outperform the current state-of-the-art, while also achieving a superior non-adversarial accuracy.

From the Bayesian perspective, the category of conditional probabilities (a variant of the Kleisli category of the Giry monad, whose objects are measurable spaces and arrows are Markov kernels) gives a nice framework for conceptualization and analysis of many aspects of machine learning. Using categorical methods, we construct models for parametric and nonparametric Bayesian reasoning on function spaces, thus providing a basis for the supervised learning problem. In particular, stochastic processes are arrows to these function spaces which serve as prior probabilities. The resulting inference maps can often be analytically constructed in this symmetric monoidal weakly closed category. We also show how to view general stochastic processes using functor categories and demonstrate the Kalman filter as an archetype for the hidden Markov model.

Generalized Category Discovery (GCD) aims to discover novel categories in unlabelled datasets using knowledge learned from labelled samples. Previous studies argued that parametric classifiers are prone to overfitting to seen categories, and endorsed using a non-parametric classifier formed with semi-supervised k-means. However, in this study, we investigate the failure of parametric classifiers, verify the effectiveness of previous design choices when high-quality supervision is available, and identify unreliable pseudo-labels as a key problem. We demonstrate that two prediction biases exist: the classifier tends to predict seen classes more often, and produces an imbalanced distribution across seen and novel categories. Based on these findings, we propose a simple yet effective parametric classification method that benefits from entropy regularisation, achieves state-of-the-art performance on multiple GCD benchmarks and shows strong robustness to unknown class numbers. We hope the investigation and proposed simple framework can serve as a strong baseline to facilitate future studies in this field. Our code is available at: https://github.com/CVMI-Lab/SimGCD.

Categorical variables are a natural choice for representing discrete structure in the world. However, stochastic neural networks rarely use categorical latent variables due to the inability to backpropagate through samples. In this work, we present an efficient gradient estimator that replaces the non-differentiable sample from a categorical distribution with a differentiable sample from a novel Gumbel-Softmax distribution. This distribution has the essential property that it can be smoothly annealed into a categorical distribution. We show that our Gumbel-Softmax estimator outperforms state-of-the-art gradient estimators on structured output prediction and unsupervised generative modeling tasks with categorical latent variables, and enables large speedups on semi-supervised classification.

Markov categories are a recent categorical approach to the mathematical foundations of probability and statistics. Here, this approach is advanced by stating and proving equivalent conditions for second-order stochastic dominance, a widely used way of comparing probability distributions by their spread. Furthermore, we lay foundation for the theory of comparing statistical experiments within Markov categories by stating and proving the classical Blackwell-Sherman-Stein Theorem. Our version not only offers new insight into the proof, but its abstract nature also makes the result more general, automatically specializing to the standard Blackwell-Sherman-Stein Theorem in measure-theoretic probability as well as a Bayesian version that involves prior-dependent garbling. Along the way, we define and characterize representable Markov categories, within which one can talk about Markov kernels to or from spaces of distributions. We do so by exploring the relation between Markov categories and Kleisli categories of probability monads.

We apply category theory to extract multimodal document structure which leads us to develop information theoretic measures, content summarization and extension, and self-supervised improvement of large pretrained models. We first develop a mathematical representation of a document as a category of question-answer pairs. Second, we develop an orthogonalization procedure to divide the information contained in one or more documents into non-overlapping pieces. The structures extracted in the first and second steps lead us to develop methods to measure and enumerate the information contained in a document. We also build on those steps to develop new summarization techniques, as well as to develop a solution to a new problem viz. exegesis resulting in an extension of the original document. Our question-answer pair methodology enables a novel rate distortion analysis of summarization techniques. We implement our techniques using large pretrained models, and we propose a multimodal extension of our overall mathematical framework. Finally, we develop a novel self-supervised method using RLVR to improve large pretrained models using consistency constraints such as composability and closure under certain operations that stem naturally from our category theoretic framework.

We provide a construction for categorical representation learning and introduce the foundations of "categorifier". The central theme in representation learning is the idea of everything to vector. Every object in a dataset S can be represented as a vector in R^n by an encoding map E: Obj(S)toR^n. More importantly, every morphism can be represented as a matrix E: Hom(S)toR^{n}_{n}. The encoding map E is generally modeled by a deep neural network. The goal of representation learning is to design appropriate tasks on the dataset to train the encoding map (assuming that an encoding is optimal if it universally optimizes the performance on various tasks). However, the latter is still a set-theoretic approach. The goal of the current article is to promote the representation learning to a new level via a category-theoretic approach. As a proof of concept, we provide an example of a text translator equipped with our technology, showing that our categorical learning model outperforms the current deep learning models by 17 times. The content of the current article is part of the recent US patent proposal (patent application number: 63110906).

Inspired by the foundational works by Spivak and Fong and Cruttwell et al., we introduce a categorical framework to formalize Bayesian inference and learning. The two key ideas at play here are the notions of Bayesian inversions and the functor GL as constructed by Cruttwell et al.. In this context, we find that Bayesian learning is the simplest case of the learning paradigm. We then obtain categorical formulations of batch and sequential Bayes updates while also verifying that the two coincide in a specific example.

Knowledge distillation is a model compression technique in which a compact "student" network is trained to replicate the predictive behavior of a larger "teacher" network. In logit-based knowledge distillation, it has become the de facto approach to augment cross-entropy with a distillation term. Typically, this term is either a KL divergence that matches marginal probabilities or a correlation-based loss that captures intra- and inter-class relationships. In every case, it acts as an additional term to cross-entropy. This term has its own weight, which must be carefully tuned. In this paper, we adopt a choice-theoretic perspective and recast knowledge distillation under the Plackett-Luce model by interpreting teacher logits as "worth" scores. We introduce "Plackett-Luce Distillation (PLD)", a weighted list-wise ranking loss. In PLD, the teacher model transfers knowledge of its full ranking of classes, weighting each ranked choice by its own confidence. PLD directly optimizes a single "teacher-optimal" ranking. The true label is placed first, followed by the remaining classes in descending teacher confidence. This process yields a convex and translation-invariant surrogate that subsumes weighted cross-entropy. Empirically, across CIFAR-100, ImageNet-1K, and MS-COCO, PLD achieves consistent gains across diverse architectures and distillation objectives, including divergence-based, correlation-based, and feature-based methods, in both homogeneous and heterogeneous teacher-student pairs.

Click-through rate (CTR) prediction, which aims to predict the probability of a user clicking on an ad or an item, is critical to many online applications such as online advertising and recommender systems. The problem is very challenging since (1) the input features (e.g., the user id, user age, item id, item category) are usually sparse and high-dimensional, and (2) an effective prediction relies on high-order combinatorial features (a.k.a. cross features), which are very time-consuming to hand-craft by domain experts and are impossible to be enumerated. Therefore, there have been efforts in finding low-dimensional representations of the sparse and high-dimensional raw features and their meaningful combinations. In this paper, we propose an effective and efficient method called the AutoInt to automatically learn the high-order feature interactions of input features. Our proposed algorithm is very general, which can be applied to both numerical and categorical input features. Specifically, we map both the numerical and categorical features into the same low-dimensional space. Afterwards, a multi-head self-attentive neural network with residual connections is proposed to explicitly model the feature interactions in the low-dimensional space. With different layers of the multi-head self-attentive neural networks, different orders of feature combinations of input features can be modeled. The whole model can be efficiently fit on large-scale raw data in an end-to-end fashion. Experimental results on four real-world datasets show that our proposed approach not only outperforms existing state-of-the-art approaches for prediction but also offers good explainability. Code is available at: https://github.com/DeepGraphLearning/RecommenderSystems.

Categorical distributions are ubiquitous in machine learning, e.g., in classification, language models, and recommendation systems. However, when the number of possible outcomes is very large, using categorical distributions becomes computationally expensive, as the complexity scales linearly with the number of outcomes. To address this problem, we propose augment and reduce (A&R), a method to alleviate the computational complexity. A&R uses two ideas: latent variable augmentation and stochastic variational inference. It maximizes a lower bound on the marginal likelihood of the data. Unlike existing methods which are specific to softmax, A&R is more general and is amenable to other categorical models, such as multinomial probit. On several large-scale classification problems, we show that A&R provides a tighter bound on the marginal likelihood and has better predictive performance than existing approaches.

Categorical variables often appear in datasets for classification and regression tasks, and they need to be encoded into numerical values before training. Since many encoders have been developed and can significantly impact performance, choosing the appropriate encoder for a task becomes a time-consuming yet important practical issue. This study broadly classifies machine learning models into three categories: 1) ATI models that implicitly perform affine transformations on inputs, such as multi-layer perceptron neural network; 2) Tree-based models that are based on decision trees, such as random forest; and 3) the rest, such as kNN. Theoretically, we prove that the one-hot encoder is the best choice for ATI models in the sense that it can mimic any other encoders by learning suitable weights from the data. We also explain why the target encoder and its variants are the most suitable encoders for tree-based models. This study conducted comprehensive computational experiments to evaluate 14 encoders, including one-hot and target encoders, along with eight common machine-learning models on 28 datasets. The computational results agree with our theoretical analysis. The findings in this study shed light on how to select the suitable encoder for data scientists in fields such as fraud detection, disease diagnosis, etc.

We define the bicategory of Graph Convolutional Neural Networks GCNN_n for an arbitrary graph with n nodes. We show it can be factored through the already existing categorical constructions for deep learning called Para and Lens with the base category set to the CoKleisli category of the product comonad. We prove that there exists an injective-on-objects, faithful 2-functor GCNN_n to Para(CoKl(R^{n times n} times -)). We show that this construction allows us to treat the adjacency matrix of a GCNN as a global parameter instead of a a local, layer-wise one. This gives us a high-level categorical characterisation of a particular kind of inductive bias GCNNs possess. Lastly, we hypothesize about possible generalisations of GCNNs to general message-passing graph neural networks, connections to equivariant learning, and the (lack of) functoriality of activation functions.

We identify empirical scaling laws for the cross-entropy loss in four domains: generative image modeling, video modeling, multimodal imageleftrightarrowtext models, and mathematical problem solving. In all cases autoregressive Transformers smoothly improve in performance as model size and compute budgets increase, following a power-law plus constant scaling law. The optimal model size also depends on the compute budget through a power-law, with exponents that are nearly universal across all data domains. The cross-entropy loss has an information theoretic interpretation as S(True) + D_{KL}(True||Model), and the empirical scaling laws suggest a prediction for both the true data distribution's entropy and the KL divergence between the true and model distributions. With this interpretation, billion-parameter Transformers are nearly perfect models of the YFCC100M image distribution downsampled to an 8times 8 resolution, and we can forecast the model size needed to achieve any given reducible loss (ie D_{KL}) in nats/image for other resolutions. We find a number of additional scaling laws in specific domains: (a) we identify a scaling relation for the mutual information between captions and images in multimodal models, and show how to answer the question "Is a picture worth a thousand words?"; (b) in the case of mathematical problem solving, we identify scaling laws for model performance when extrapolating beyond the training distribution; (c) we finetune generative image models for ImageNet classification and find smooth scaling of the classification loss and error rate, even as the generative loss levels off. Taken together, these results strengthen the case that scaling laws have important implications for neural network performance, including on downstream tasks.

We present a novel application of category theory for deep learning. We show how category theory can be used to understand and work with the linear layer functions of group equivariant neural networks whose layers are some tensor power space of R^{n} for the groups S_n, O(n), Sp(n), and SO(n). By using category theoretic constructions, we build a richer structure that is not seen in the original formulation of these neural networks, leading to new insights. In particular, we outline the development of an algorithm for quickly computing the result of a vector that is passed through an equivariant, linear layer for each group in question. The success of our approach suggests that category theory could be beneficial for other areas of deep learning.

Model calibration aims to align confidence with prediction correctness. The Cross-Entropy (CE) loss is widely used for calibrator training, which enforces the model to increase confidence on the ground truth class. However, we find the CE loss has intrinsic limitations. For example, for a narrow misclassification, a calibrator trained by the CE loss often produces high confidence on the wrongly predicted class (e.g., a test sample is wrongly classified and its softmax score on the ground truth class is around 0.4), which is undesirable. In this paper, we propose a new post-hoc calibration objective derived from the aim of calibration. Intuitively, the proposed objective function asks that the calibrator decrease model confidence on wrongly predicted samples and increase confidence on correctly predicted samples. Because a sample itself has insufficient ability to indicate correctness, we use its transformed versions (e.g., rotated, greyscaled and color-jittered) during calibrator training. Trained on an in-distribution validation set and tested with isolated, individual test samples, our method achieves competitive calibration performance on both in-distribution and out-of-distribution test sets compared with the state of the art. Further, our analysis points out the difference between our method and commonly used objectives such as CE loss and mean square error loss, where the latters sometimes deviates from the calibration aim.

We give a conceptual treatment of the notion of joints, marginals, and independence in the setting of categorical probability. This is achieved by endowing the usual probability monads (like the Giry monad) with a monoidal and an opmonoidal structure, mutually compatible (i.e. a bimonoidal structure). If the underlying monoidal category is cartesian monoidal, a bimonoidal structure is given uniquely by a commutative strength. However, if the underlying monoidal category is not cartesian monoidal, a strength is not enough to guarantee all the desired properties of joints and marginals. A bimonoidal structure is then the correct requirement for the more general case. We explain the theory and the operational interpretation, with the help of the graphical calculus for monoidal categories. We give a definition of stochastic independence based on the bimonoidal structure, compatible with the intuition and with other approaches in the literature for cartesian monoidal categories. We then show as an example that the Kantorovich monad on the category of complete metric spaces is a bimonoidal monad for a non-cartesian monoidal structure.

Generalized Category Discovery (GCD) aims to identify a mix of known and novel categories within unlabeled data sets, providing a more realistic setting for image recognition. Essentially, GCD needs to remember existing patterns thoroughly to recognize novel categories. Recent state-of-the-art method SimGCD transfers the knowledge from known-class data to the learning of novel classes through debiased learning. However, some patterns are catastrophically forgot during adaptation and thus lead to poor performance in novel categories classification. To address this issue, we propose a novel learning approach, LegoGCD, which is seamlessly integrated into previous methods to enhance the discrimination of novel classes while maintaining performance on previously encountered known classes. Specifically, we design two types of techniques termed as Local Entropy Regularization (LER) and Dual-views Kullback Leibler divergence constraint (DKL). The LER optimizes the distribution of potential known class samples in unlabeled data, thus ensuring the preservation of knowledge related to known categories while learning novel classes. Meanwhile, DKL introduces Kullback Leibler divergence to encourage the model to produce a similar prediction distribution of two view samples from the same image. In this way, it successfully avoids mismatched prediction and generates more reliable potential known class samples simultaneously. Extensive experiments validate that the proposed LegoGCD effectively addresses the known category forgetting issue across all datasets, eg, delivering a 7.74% and 2.51% accuracy boost on known and novel classes in CUB, respectively. Our code is available at: https://github.com/Cliffia123/LegoGCD.

Modelling compositionality has been a longstanding area of research in the field of vector space semantics. The categorical approach to compositionality maps grammar onto vector spaces in a principled way, but comes under fire for requiring the formation of very high-dimensional matrices and tensors, and therefore being computationally infeasible. In this paper I show how a linear simplification of recursive neural tensor network models can be mapped directly onto the categorical approach, giving a way of computing the required matrices and tensors. This mapping suggests a number of lines of research for both categorical compositional vector space models of meaning and for recursive neural network models of compositionality.

Modern deep learning-based recommendation systems exploit hundreds to thousands of different categorical features, each with millions of different categories ranging from clicks to posts. To respect the natural diversity within the categorical data, embeddings map each category to a unique dense representation within an embedded space. Since each categorical feature could take on as many as tens of millions of different possible categories, the embedding tables form the primary memory bottleneck during both training and inference. We propose a novel approach for reducing the embedding size in an end-to-end fashion by exploiting complementary partitions of the category set to produce a unique embedding vector for each category without explicit definition. By storing multiple smaller embedding tables based on each complementary partition and combining embeddings from each table, we define a unique embedding for each category at smaller memory cost. This approach may be interpreted as using a specific fixed codebook to ensure uniqueness of each category's representation. Our experimental results demonstrate the effectiveness of our approach over the hashing trick for reducing the size of the embedding tables in terms of model loss and accuracy, while retaining a similar reduction in the number of parameters.

Objective functions that optimize deep neural networks play a vital role in creating an enhanced feature representation of the input data. Although cross-entropy-based loss formulations have been extensively used in a variety of supervised deep-learning applications, these methods tend to be less adequate when there is large intra-class variance and low inter-class variance in input data distribution. Deep Metric Learning seeks to develop methods that aim to measure the similarity between data samples by learning a representation function that maps these data samples into a representative embedding space. It leverages carefully designed sampling strategies and loss functions that aid in optimizing the generation of a discriminative embedding space even for distributions having low inter-class and high intra-class variances. In this chapter, we will provide an overview of recent progress in this area and discuss state-of-the-art Deep Metric Learning approaches.

We introduce the category of information structures, whose objects are suitable diagrams of measurable sets that encode the possible outputs of a given family of observables and their mutual relationships of refinement; they serve as mathematical models of contextuality in classical and quantum settings. Each information structure can be regarded as a ringed site with trivial topology; the structure ring is generated by the observables themselves and its multiplication corresponds to joint measurement. We extend Baudot and Bennequin's definition of information cohomology to this setting, as a derived functor in the category of modules over the structure ring, and show explicitly that the bar construction gives a projective resolution in that category, recovering in this way the cochain complexes previously considered in the literature. Finally, we study the particular case of a one-parameter family of coefficients made of functions of probability distributions. The only 1-cocycles are Shannon entropy or Tsallis alpha-entropy, depending on the value of the parameter.

Small sample sizes are common in many disciplines, which necessitates pooling roughly similar datasets across multiple institutions to study weak but relevant associations between images and disease outcomes. Such data often manifest shift/imbalance in covariates (i.e., secondary non-imaging data). Controlling for such nuisance variables is common within standard statistical analysis, but the ideas do not directly apply to overparameterized models. Consequently, recent work has shown how strategies from invariant representation learning provides a meaningful starting point, but the current repertoire of methods is limited to accounting for shifts/imbalances in just a couple of covariates at a time. In this paper, we show how viewing this problem from the perspective of Category theory provides a simple and effective solution that completely avoids elaborate multi-stage training pipelines that would otherwise be needed. We show the effectiveness of this approach via extensive experiments on real datasets. Further, we discuss how this style of formulation offers a unified perspective on at least 5+ distinct problem settings, from self-supervised learning to matching problems in 3D reconstruction.

Over the past two decades machine learning has permeated almost every realm of technology. At the same time, many researchers have begun using category theory as a unifying language, facilitating communication between different scientific disciplines. It is therefore unsurprising that there is a burgeoning interest in applying category theory to machine learning. We aim to document the motivations, goals and common themes across these applications. We touch on gradient-based learning, probability, and equivariant learning.

One-hot vectors, a common method for representing discrete/categorical data, in machine learning are widely used because of their simplicity and intuitiveness. However, one-hot vectors suffer from a linear increase in dimensionality, posing computational and memory challenges, especially when dealing with datasets containing numerous categories. In this paper, we focus on tabular data generation, and reveal the multinomial diffusion faces the mode collapse phenomenon when the cardinality is high. Moreover, due to the limitations of one-hot vectors, the training phase takes time longer in such a situation. To address these issues, we propose Residual Bit Vectors (ResBit), a technique for densely representing categorical data. ResBit is an extension of analog bits and overcomes limitations of analog bits when applied to tabular data generation. Our experiments demonstrate that ResBit not only accelerates training but also maintains performance when compared with the situations before applying ResBit. Furthermore, our results indicate that many existing methods struggle with high-cardinality data, underscoring the need for lower-dimensional representations, such as ResBit and latent vectors.

In this work we take a Category Theoretic perspective on the relationship between probabilistic modeling and function approximation. We begin by defining two extensions of function composition to stochastic process subordination: one based on the co-Kleisli category under the comonad (Omega x -) and one based on the parameterization of a category with a Lawvere theory. We show how these extensions relate to the category Stoch and other Markov Categories. Next, we apply the Para construction to extend stochastic processes to parameterized statistical models and we define a way to compose the likelihood functions of these models. We conclude with a demonstration of how the Maximum Likelihood Estimation procedure defines an identity-on-objects functor from the category of statistical models to the category of Learners. Code to accompany this paper can be found at https://github.com/dshieble/Categorical_Stochastic_Processes_and_Likelihood

Neural networks have become an increasingly popular tool for solving many real-world problems. They are a general framework for differentiable optimization which includes many other machine learning approaches as special cases. In this thesis we build a category-theoretic formalism around a class of neural networks exemplified by CycleGAN. CycleGAN is a collection of neural networks, closed under composition, whose inductive bias is increased by enforcing composition invariants, i.e. cycle-consistencies. Inspired by Functorial Data Migration, we specify the interconnection of these networks using a categorical schema, and network instances as set-valued functors on this schema. We also frame neural network architectures, datasets, models, and a number of other concepts in a categorical setting and thus show a special class of functors, rather than functions, can be learned using gradient descent. We use the category-theoretic framework to conceive a novel neural network architecture whose goal is to learn the task of object insertion and object deletion in images with unpaired data. We test the architecture on three different datasets and obtain promising results.

With infinitely many high-quality data points, infinite computational power, an infinitely large foundation model with a perfect training algorithm and guaranteed zero generalization error on the pretext task, can the model be used for everything? This question cannot be answered by the existing theory of representation, optimization or generalization, because the issues they mainly investigate are assumed to be nonexistent here. In this paper, we show that category theory provides powerful machinery to answer this question. We have proved three results. The first one limits the power of prompt-based learning, saying that the model can solve a downstream task with prompts if and only if the task is representable. The second one says fine tuning does not have this limit, as a foundation model with the minimum required power (up to symmetry) can theoretically solve downstream tasks for the category defined by pretext task, with fine tuning and enough resources. Our final result can be seen as a new type of generalization theorem, showing that the foundation model can generate unseen objects from the target category (e.g., images) using the structural information from the source category (e.g., texts). Along the way, we provide a categorical framework for supervised and self-supervised learning, which might be of independent interest.

We introduce a Parametric Information Maximization (PIM) model for the Generalized Category Discovery (GCD) problem. Specifically, we propose a bi-level optimization formulation, which explores a parameterized family of objective functions, each evaluating a weighted mutual information between the features and the latent labels, subject to supervision constraints from the labeled samples. Our formulation mitigates the class-balance bias encoded in standard information maximization approaches, thereby handling effectively both short-tailed and long-tailed data sets. We report extensive experiments and comparisons demonstrating that our PIM model consistently sets new state-of-the-art performances in GCD across six different datasets, more so when dealing with challenging fine-grained problems.

We define a probabilistic programming language for Gaussian random variables with a first-class exact conditioning construct. We give operational, denotational and equational semantics for this language, establishing convenient properties like exchangeability of conditions. Conditioning on equality of continuous random variables is nontrivial, as the exact observation may have probability zero; this is Borel's paradox. Using categorical formulations of conditional probability, we show that the good properties of our language are not particular to Gaussians, but can be derived from universal properties, thus generalizing to wider settings. We define the Cond construction, which internalizes conditioning as a morphism, providing general compositional semantics for probabilistic programming with exact conditioning.

Model overconfidence and poor calibration are common in machine learning and difficult to account for when applying standard empirical risk minimization. In this work, we propose a novel method to alleviate these problems that we call odd-k-out learning (OKO), which minimizes the cross-entropy error for sets rather than for single examples. This naturally allows the model to capture correlations across data examples and achieves both better accuracy and calibration, especially in limited training data and class-imbalanced regimes. Perhaps surprisingly, OKO often yields better calibration even when training with hard labels and dropping any additional calibration parameter tuning, such as temperature scaling. We demonstrate this in extensive experimental analyses and provide a mathematical theory to interpret our findings. We emphasize that OKO is a general framework that can be easily adapted to many settings and a trained model can be applied to single examples at inference time, without significant run-time overhead or architecture changes.

Data used for analytics and machine learning often take the form of tables with categorical entries. We introduce a family of lossless compression algorithms for such data that proceed in four steps: (i) Estimate latent variables associated to rows and columns; (ii) Partition the table in blocks according to the row/column latents; (iii) Apply a sequential (e.g. Lempel-Ziv) coder to each of the blocks; (iv) Append a compressed encoding of the latents. We evaluate it on several benchmark datasets, and study optimal compression in a probabilistic model for that tabular data, whereby latent values are independent and table entries are conditionally independent given the latent values. We prove that the model has a well defined entropy rate and satisfies an asymptotic equipartition property. We also prove that classical compression schemes such as Lempel-Ziv and finite-state encoders do not achieve this rate. On the other hand, the latent estimation strategy outlined above achieves the optimal rate.

Generative flows and diffusion models have been predominantly trained on ordinal data, for example natural images. This paper introduces two extensions of flows and diffusion for categorical data such as language or image segmentation: Argmax Flows and Multinomial Diffusion. Argmax Flows are defined by a composition of a continuous distribution (such as a normalizing flow), and an argmax function. To optimize this model, we learn a probabilistic inverse for the argmax that lifts the categorical data to a continuous space. Multinomial Diffusion gradually adds categorical noise in a diffusion process, for which the generative denoising process is learned. We demonstrate that our method outperforms existing dequantization approaches on text modelling and modelling on image segmentation maps in log-likelihood.

Markov categories are a recent category-theoretic approach to the foundations of probability and statistics. Here we develop this approach further by treating infinite products and the Kolmogorov extension theorem. This is relevant for all aspects of probability theory in which infinitely many random variables appear at a time. These infinite tensor products bigotimes_{i in J} X_i come in two versions: a weaker but more general one for families of objects (X_i)_{i in J} in semicartesian symmetric monoidal categories, and a stronger but more specific one for families of objects in Markov categories. As a first application, we state and prove versions of the zero-one laws of Kolmogorov and Hewitt-Savage for Markov categories. This gives general versions of these results which can be instantiated not only in measure-theoretic probability, where they specialize to the standard ones in the setting of standard Borel spaces, but also in other contexts.

In the presence of noisy labels, designing robust loss functions is critical for securing the generalization performance of deep neural networks. Cross Entropy (CE) loss has been shown to be not robust to noisy labels due to its unboundedness. To alleviate this issue, existing works typically design specialized robust losses with the symmetric condition, which usually lead to the underfitting issue. In this paper, our key idea is to induce a loss bound at the logit level, thus universally enhancing the noise robustness of existing losses. Specifically, we propose logit clipping (LogitClip), which clamps the norm of the logit vector to ensure that it is upper bounded by a constant. In this manner, CE loss equipped with our LogitClip method is effectively bounded, mitigating the overfitting to examples with noisy labels. Moreover, we present theoretical analyses to certify the noise-tolerant ability of LogitClip. Extensive experiments show that LogitClip not only significantly improves the noise robustness of CE loss, but also broadly enhances the generalization performance of popular robust losses.

Learning compact discrete representations of data is a key task on its own or for facilitating subsequent processing of data. In this paper we present a model that produces Discrete InfoMax Codes (DIMCO); we learn a probabilistic encoder that yields k-way d-dimensional codes associated with input data. Our model's learning objective is to maximize the mutual information between codes and labels with a regularization, which enforces entries of a codeword to be as independent as possible. We show that the infomax principle also justifies previous loss functions (e.g., cross-entropy) as its special cases. Our analysis also shows that using shorter codes, as DIMCO does, reduces overfitting in the context of few-shot classification. Through experiments in various domains, we observe this implicit meta-regularization effect of DIMCO. Furthermore, we show that the codes learned by DIMCO are efficient in terms of both memory and retrieval time compared to previous methods.

This work considers the category distribution heterogeneity in federated learning. This issue is due to biased labeling preferences at multiple clients and is a typical setting of data heterogeneity. To alleviate this issue, most previous works consider either regularizing local models or fine-tuning the global model, while they ignore the adjustment of aggregation weights and simply assign weights based on the dataset size. However, based on our empirical observations and theoretical analysis, we find that the dataset size is not optimal and the discrepancy between local and global category distributions could be a beneficial and complementary indicator for determining aggregation weights. We thus propose a novel aggregation method, Federated Learning with Discrepancy-aware Collaboration (FedDisco), whose aggregation weights not only involve both the dataset size and the discrepancy value, but also contribute to a tighter theoretical upper bound of the optimization error. FedDisco also promotes privacy-preservation, communication and computation efficiency, as well as modularity. Extensive experiments show that our FedDisco outperforms several state-of-the-art methods and can be easily incorporated with many existing methods to further enhance the performance. Our code will be available at https://github.com/MediaBrain-SJTU/FedDisco.

Speech emotion recognition (SER) has received a great deal of attention in recent years in the context of spontaneous conversations. While there have been notable results on datasets like the well known corpus of naturalistic dyadic conversations, IEMOCAP, for both the case of categorical and dimensional emotions, there are few papers which try to predict both paradigms at the same time. Therefore, in this work, we aim to highlight the performance contribution of multi-task learning by proposing a multi-task, multi-modal system that predicts categorical and dimensional emotions. The results emphasise the importance of cross-regularisation between the two types of emotions. Our approach consists of a multi-task, multi-modal architecture that uses parallel feature refinement through self-attention for the feature of each modality. In order to fuse the features, our model introduces a set of learnable bridge tokens that merge the acoustic and linguistic features with the help of cross-attention. Our experiments for categorical emotions on 10-fold validation yield results comparable to the current state-of-the-art. In our configuration, our multi-task approach provides better results compared to learning each paradigm separately. On top of that, our best performing model achieves a high result for valence compared to the previous multi-task experiments.

In this work, we tackle the problem of structured text generation, specifically academic paper generation in $, inspired by the surprisingly good results of basic character-level language models. Our motivation is using more recent and advanced methods of language modeling on a more complex dataset of source files to generate realistic academic papers. Our first contribution is preparing a dataset with source files on recent open-source computer vision papers. Our second contribution is experimenting with recent methods of language modeling and text generation such as Transformer and Transformer-XL to generate consistent code. We report cross-entropy and bits-per-character (BPC) results of the trained models, and we also discuss interesting points on some examples of the generated $ code.

Anomaly detection plays an important role in modern data-driven security applications, such as detecting suspicious access to a socket from a process. In many cases, such events can be described as a collection of categorical values that are considered as entities of different types, which we call heterogeneous categorical events. Due to the lack of intrinsic distance measures among entities, and the exponentially large event space, most existing work relies heavily on heuristics to calculate abnormal scores for events. Different from previous work, we propose a principled and unified probabilistic model APE (Anomaly detection via Probabilistic pairwise interaction and Entity embedding) that directly models the likelihood of events. In this model, we embed entities into a common latent space using their observed co-occurrence in different events. More specifically, we first model the compatibility of each pair of entities according to their embeddings. Then we utilize the weighted pairwise interactions of different entity types to define the event probability. Using Noise-Contrastive Estimation with "context-dependent" noise distribution, our model can be learned efficiently regardless of the large event space. Experimental results on real enterprise surveillance data show that our methods can accurately detect abnormal events compared to other state-of-the-art abnormal detection techniques.

The reverse derivative is a fundamental operation in machine learning and automatic differentiation. This paper gives a direct axiomatization of a category with a reverse derivative operation, in a similar style to that given by Cartesian differential categories for a forward derivative. Intriguingly, a category with a reverse derivative also has a forward derivative, but the converse is not true. In fact, we show explicitly what a forward derivative is missing: a reverse derivative is equivalent to a forward derivative with a dagger structure on its subcategory of linear maps. Furthermore, we show that these linear maps form an additively enriched category with dagger biproducts.

This paper discusses a simple and explicit toy-model example of the categorical Hopfield equations introduced in previous work of Manin and the author. These describe dynamical assignments of resources to networks, where resources are objects in unital symmetric monoidal categories and assignments are realized by summing functors. The special case discussed here is based on computational resources (computational models of neurons) as objects in a category of DNNs, with a simple choice of the endofunctors defining the Hopfield equations that reproduce the usual updating of the weights in DNNs by gradient descent.

Generalized Category Discovery (GCD) is an intriguing open-world problem that has garnered increasing attention. Given a dataset that includes both labelled and unlabelled images, GCD aims to categorize all images in the unlabelled subset, regardless of whether they belong to known or unknown classes. In GCD, the common practice typically involves applying a spherical projection operator at the end of the self-supervised pretrained backbone, operating within Euclidean or spherical space. However, both of these spaces have been shown to be suboptimal for encoding samples that possesses hierarchical structures. In contrast, hyperbolic space exhibits exponential volume growth relative to radius, making it inherently strong at capturing the hierarchical structure of samples from both seen and unseen categories. Therefore, we propose to tackle the category discovery challenge in the hyperbolic space. We introduce HypCD, a simple Hyperbolic framework for learning hierarchy-aware representations and classifiers for generalized Category Discovery. HypCD first transforms the Euclidean embedding space of the backbone network into hyperbolic space, facilitating subsequent representation and classification learning by considering both hyperbolic distance and the angle between samples. This approach is particularly helpful for knowledge transfer from known to unknown categories in GCD. We thoroughly evaluate HypCD on public GCD benchmarks, by applying it to various baseline and state-of-the-art methods, consistently achieving significant improvements.

We introduce the Structured Knowledge Accumulation (SKA) framework, which reinterprets entropy as a dynamic, layer-wise measure of knowledge alignment in neural networks. Instead of relying on traditional gradient-based optimization, SKA defines entropy in terms of knowledge vectors and their influence on decision probabilities across multiple layers. This formulation naturally leads to the emergence of activation functions such as the sigmoid as a consequence of entropy minimization. Unlike conventional backpropagation, SKA allows each layer to optimize independently by aligning its knowledge representation with changes in decision probabilities. As a result, total network entropy decreases in a hierarchical manner, allowing knowledge structures to evolve progressively. This approach provides a scalable, biologically plausible alternative to gradient-based learning, bridging information theory and artificial intelligence while offering promising applications in resource-constrained and parallel computing environments.

Separating a singing voice from its music accompaniment remains an important challenge in the field of music information retrieval. We present a unique neural network approach inspired by a technique that has revolutionized the field of vision: pixel-wise image classification, which we combine with cross entropy loss and pretraining of the CNN as an autoencoder on singing voice spectrograms. The pixel-wise classification technique directly estimates the sound source label for each time-frequency (T-F) bin in our spectrogram image, thus eliminating common pre- and postprocessing tasks. The proposed network is trained by using the Ideal Binary Mask (IBM) as the target output label. The IBM identifies the dominant sound source in each T-F bin of the magnitude spectrogram of a mixture signal, by considering each T-F bin as a pixel with a multi-label (for each sound source). Cross entropy is used as the training objective, so as to minimize the average probability error between the target and predicted label for each pixel. By treating the singing voice separation problem as a pixel-wise classification task, we additionally eliminate one of the commonly used, yet not easy to comprehend, postprocessing steps: the Wiener filter postprocessing. The proposed CNN outperforms the first runner up in the Music Information Retrieval Evaluation eXchange (MIREX) 2016 and the winner of MIREX 2014 with a gain of 2.2702 ~ 5.9563 dB global normalized source to distortion ratio (GNSDR) when applied to the iKala dataset. An experiment with the DSD100 dataset on the full-tracks song evaluation task also shows that our model is able to compete with cutting-edge singing voice separation systems which use multi-channel modeling, data augmentation, and model blending.

Given a large number of low-level heterogeneous categorical alerts from an anomaly detection system, how to characterize complex relationships between different alerts, filter out false positives, and deliver trustworthy rankings and suggestions to end users? This problem is motivated by and generalized from applications in enterprise security and attack scenario reconstruction. While existing techniques focus on either reconstructing abnormal scenarios or filtering out false positive alerts, it can be more advantageous to consider the two perspectives simultaneously in order to improve detection accuracy and better understand anomaly behaviors. In this paper, we propose CAR, a collaborative alerts ranking framework that exploits both temporal and content correlations from heterogeneous categorical alerts. CAR first builds a tree-based model to capture both short-term correlations and long-term dependencies in each alert sequence, which identifies abnormal action sequences. Then, an embedding-based model is employed to learn the content correlations between alerts via their heterogeneous categorical attributes. Finally, by incorporating both temporal and content dependencies into one optimization framework, CAR ranks both alerts and their corresponding alert patterns. Our experiments, using real-world enterprise monitoring data and real attacks launched by professional hackers, show that CAR can accurately identify true positive alerts and successfully reconstruct attack scenarios at the same time.

The learnable, linear neural network layers between tensor power spaces of R^{n} that are equivariant to the orthogonal group, O(n), the special orthogonal group, SO(n), and the symplectic group, Sp(n), were characterised in arXiv:2212.08630. We present an algorithm for multiplying a vector by any weight matrix for each of these groups, using category theoretic constructions to implement the procedure. We achieve a significant reduction in computational cost compared with a naive implementation by making use of Kronecker product matrices to perform the multiplication. We show that our approach extends to the symmetric group, S_n, recovering the algorithm of arXiv:2303.06208 in the process.

Transfer entropy (TE) is an information theoretic measure that reveals the directional flow of information between processes, providing valuable insights for a wide range of real-world applications. This work proposes Transfer Entropy Estimation via Transformers (TREET), a novel attention-based approach for estimating TE for stationary processes. The proposed approach employs Donsker-Varadhan representation to TE and leverages the attention mechanism for the task of neural estimation. We propose a detailed theoretical and empirical study of the TREET, comparing it to existing methods on a dedicated estimation benchmark. To increase its applicability, we design an estimated TE optimization scheme that is motivated by the functional representation lemma, and use it to estimate the capacity of communication channels with memory, which is a canonical optimization problem in information theory. We further demonstrate how an optimized TREET can be used to estimate underlying densities, providing experimental results. Finally, we apply TREET to feature analysis of patients with Apnea, demonstrating its applicability to real-world physiological data. Our work, applied with state-of-the-art deep learning methods, opens a new door for communication problems which are yet to be solved.

Knowledge Distillation (KD) has been validated as an effective model compression technique for learning compact object detectors. Existing state-of-the-art KD methods for object detection are mostly based on feature imitation. In this paper, we present a general and effective prediction mimicking distillation scheme, called CrossKD, which delivers the intermediate features of the student's detection head to the teacher's detection head. The resulting cross-head predictions are then forced to mimic the teacher's predictions. This manner relieves the student's head from receiving contradictory supervision signals from the annotations and the teacher's predictions, greatly improving the student's detection performance. Moreover, as mimicking the teacher's predictions is the target of KD, CrossKD offers more task-oriented information in contrast with feature imitation. On MS COCO, with only prediction mimicking losses applied, our CrossKD boosts the average precision of GFL ResNet-50 with 1x training schedule from 40.2 to 43.7, outperforming all existing KD methods. In addition, our method also works well when distilling detectors with heterogeneous backbones. Code is available at https://github.com/jbwang1997/CrossKD.

Generalized category discovery (GCD) is a pragmatic but underexplored problem, which requires models to automatically cluster and discover novel categories by leveraging the labeled samples from old classes. The challenge is that unlabeled data contain both old and new classes. Early works leveraging pseudo-labeling with parametric classifiers handle old and new classes separately, which brings about imbalanced accuracy between them. Recent methods employing contrastive learning neglect potential positives and are decoupled from the clustering objective, leading to biased representations and sub-optimal results. To address these issues, we introduce a unified and unbiased prototype learning framework, namely ProtoGCD, wherein old and new classes are modeled with joint prototypes and unified learning objectives, {enabling unified modeling between old and new classes}. Specifically, we propose a dual-level adaptive pseudo-labeling mechanism to mitigate confirmation bias, together with two regularization terms to collectively help learn more suitable representations for GCD. Moreover, for practical considerations, we devise a criterion to estimate the number of new classes. Furthermore, we extend ProtoGCD to detect unseen outliers, achieving task-level unification. Comprehensive experiments show that ProtoGCD achieves state-of-the-art performance on both generic and fine-grained datasets. The code is available at https://github.com/mashijie1028/ProtoGCD.

Learning high-quality feature embeddings efficiently and effectively is critical for the performance of web-scale machine learning systems. A typical model ingests hundreds of features with vocabularies on the order of millions to billions of tokens. The standard approach is to represent each feature value as a d-dimensional embedding, introducing hundreds of billions of parameters for extremely high-cardinality features. This bottleneck has led to substantial progress in alternative embedding algorithms. Many of these methods, however, make the assumption that each feature uses an independent embedding table. This work introduces a simple yet highly effective framework, Feature Multiplexing, where one single representation space is used across many different categorical features. Our theoretical and empirical analysis reveals that multiplexed embeddings can be decomposed into components from each constituent feature, allowing models to distinguish between features. We show that multiplexed representations lead to Pareto-optimal parameter-accuracy tradeoffs for three public benchmark datasets. Further, we propose a highly practical approach called Unified Embedding with three major benefits: simplified feature configuration, strong adaptation to dynamic data distributions, and compatibility with modern hardware. Unified embedding gives significant improvements in offline and online metrics compared to highly competitive baselines across five web-scale search, ads, and recommender systems, where it serves billions of users across the world in industry-leading products.

Diffusion models have emerged as a promising alternative to autoregressive models in modeling discrete categorical data. Yet diffusion models that directly work on discrete data space do not fully exploit the power of iterative refinement, as the signals are lost during the transition between discrete states. Existing continuous diffusion models for discrete data have limited performance compared to discrete approaches, and the unclear link between them restricts the development of diffusion models for discrete data. In this work, we propose a continuous diffusion model for language modeling that incorporates the geometry of the underlying categorical distribution. We establish a connection between the discrete diffusion and continuous flow on the statistical manifold, and building on the analogy, we introduce a simple design for the diffusion process that generalizes previous discrete diffusion models. We further propose a simulation-free training framework based on radial symmetry and a simple technique to address the high dimensionality of the manifold. Comprehensive experiments on language modeling benchmarks and other modalities show that our method outperforms existing discrete diffusion models and approaches the performance of autoregressive models. Codes available at https://github.com/harryjo97/RDLM{https://github.com/harryjo97/RDLM}.

In this paper, we address the problem of generalized category discovery (GCD), \ie, given a set of images where part of them are labelled and the rest are not, the task is to automatically cluster the images in the unlabelled data, leveraging the information from the labelled data, while the unlabelled data contain images from the labelled classes and also new ones. GCD is similar to semi-supervised learning (SSL) but is more realistic and challenging, as SSL assumes all the unlabelled images are from the same classes as the labelled ones. We also do not assume the class number in the unlabelled data is known a-priori, making the GCD problem even harder. To tackle the problem of GCD without knowing the class number, we propose an EM-like framework that alternates between representation learning and class number estimation. We propose a semi-supervised variant of the Gaussian Mixture Model (GMM) with a stochastic splitting and merging mechanism to dynamically determine the prototypes by examining the cluster compactness and separability. With these prototypes, we leverage prototypical contrastive learning for representation learning on the partially labelled data subject to the constraints imposed by the labelled data. Our framework alternates between these two steps until convergence. The cluster assignment for an unlabelled instance can then be retrieved by identifying its nearest prototype. We comprehensively evaluate our framework on both generic image classification datasets and challenging fine-grained object recognition datasets, achieving state-of-the-art performance.

We introduce Reverse Derivative Ascent: a categorical analogue of gradient based methods for machine learning. Our algorithm is defined at the level of so-called reverse differential categories. It can be used to learn the parameters of models which are expressed as morphisms of such categories. Our motivating example is boolean circuits: we show how our algorithm can be applied to such circuits by using the theory of reverse differential categories. Note our methodology allows us to learn the parameters of boolean circuits directly, in contrast to existing binarised neural network approaches. Moreover, we demonstrate its empirical value by giving experimental results on benchmark machine learning datasets.

The conventional wisdom behind learning deep classification models is to focus on bad-classified examples and ignore well-classified examples that are far from the decision boundary. For instance, when training with cross-entropy loss, examples with higher likelihoods (i.e., well-classified examples) contribute smaller gradients in back-propagation. However, we theoretically show that this common practice hinders representation learning, energy optimization, and margin growth. To counteract this deficiency, we propose to reward well-classified examples with additive bonuses to revive their contribution to the learning process. This counterexample theoretically addresses these three issues. We empirically support this claim by directly verifying the theoretical results or significant performance improvement with our counterexample on diverse tasks, including image classification, graph classification, and machine translation. Furthermore, this paper shows that we can deal with complex scenarios, such as imbalanced classification, OOD detection, and applications under adversarial attacks because our idea can solve these three issues. Code is available at: https://github.com/lancopku/well-classified-examples-are-underestimated.

Generalized Continual Category Discovery (GCCD) tackles learning from sequentially arriving, partially labeled datasets while uncovering new categories. Traditional methods depend on feature distillation to prevent forgetting the old knowledge. However, this strategy restricts the model's ability to adapt and effectively distinguish new categories. To address this, we introduce a novel technique integrating a learnable projector with feature distillation, thus enhancing model adaptability without sacrificing past knowledge. The resulting distribution shift of the previously learned categories is mitigated with the auxiliary category adaptation network. We demonstrate that while each component offers modest benefits individually, their combination - dubbed CAMP (Category Adaptation Meets Projected distillation) - significantly improves the balance between learning new information and retaining old. CAMP exhibits superior performance across several GCCD and Class Incremental Learning scenarios. The code is available at https://github.com/grypesc/CAMP.

Constantly discovering novel concepts is crucial in evolving environments. This paper explores the underexplored task of Continual Generalized Category Discovery (C-GCD), which aims to incrementally discover new classes from unlabeled data while maintaining the ability to recognize previously learned classes. Although several settings are proposed to study the C-GCD task, they have limitations that do not reflect real-world scenarios. We thus study a more practical C-GCD setting, which includes more new classes to be discovered over a longer period, without storing samples of past classes. In C-GCD, the model is initially trained on labeled data of known classes, followed by multiple incremental stages where the model is fed with unlabeled data containing both old and new classes. The core challenge involves two conflicting objectives: discover new classes and prevent forgetting old ones. We delve into the conflicts and identify that models are susceptible to prediction bias and hardness bias. To address these issues, we introduce a debiased learning framework, namely Happy, characterized by Hardness-aware prototype sampling and soft entropy regularization. For the prediction bias, we first introduce clustering-guided initialization to provide robust features. In addition, we propose soft entropy regularization to assign appropriate probabilities to new classes, which can significantly enhance the clustering performance of new classes. For the harness bias, we present the hardness-aware prototype sampling, which can effectively reduce the forgetting issue for previously seen classes, especially for difficult classes. Experimental results demonstrate our method proficiently manages the conflicts of C-GCD and achieves remarkable performance across various datasets, e.g., 7.5% overall gains on ImageNet-100. Our code is publicly available at https://github.com/mashijie1028/Happy-CGCD.

Recent advances in artificial intelligence reveal the limits of purely predictive systems and call for a shift toward causal and collaborative reasoning. Drawing inspiration from the revolution of Grothendieck in mathematics, we introduce the relativity of causal knowledge, which posits structural causal models (SCMs) are inherently imperfect, subjective representations embedded within networks of relationships. By leveraging category theory, we arrange SCMs into a functor category and show that their observational and interventional probability measures naturally form convex structures. This result allows us to encode non-intervened SCMs with convex spaces of probability measures. Next, using sheaf theory, we construct the network sheaf and cosheaf of causal knowledge. These structures enable the transfer of causal knowledge across the network while incorporating interventional consistency and the perspective of the subjects, ultimately leading to the formal, mathematical definition of relative causal knowledge.

Since the introduction of deep learning, a wide scope of representation properties, such as decorrelation, whitening, disentanglement, rank, isotropy, and mutual information, have been studied to improve the quality of representation. However, manipulating such properties can be challenging in terms of implementational effectiveness and general applicability. To address these limitations, we propose to regularize von Neumann entropy~(VNE) of representation. First, we demonstrate that the mathematical formulation of VNE is superior in effectively manipulating the eigenvalues of the representation autocorrelation matrix. Then, we demonstrate that it is widely applicable in improving state-of-the-art algorithms or popular benchmark algorithms by investigating domain-generalization, meta-learning, self-supervised learning, and generative models. In addition, we formally establish theoretical connections with rank, disentanglement, and isotropy of representation. Finally, we provide discussions on the dimension control of VNE and the relationship with Shannon entropy. Code is available at: https://github.com/jaeill/CVPR23-VNE.

Hallucination in large language models (LLMs) can be detected by assessing the uncertainty of model outputs, typically measured using entropy. Semantic entropy (SE) enhances traditional entropy estimation by quantifying uncertainty at the semantic cluster level. However, as modern LLMs generate longer one-sentence responses, SE becomes less effective because it overlooks two crucial factors: intra-cluster similarity (the spread within a cluster) and inter-cluster similarity (the distance between clusters). To address these limitations, we propose a simple black-box uncertainty quantification method inspired by nearest neighbor estimates of entropy. Our approach can also be easily extended to white-box settings by incorporating token probabilities. Additionally, we provide theoretical results showing that our method generalizes semantic entropy. Extensive empirical results demonstrate its effectiveness compared to semantic entropy across two recent LLMs (Phi3 and Llama3) and three common text generation tasks: question answering, text summarization, and machine translation. Our code is available at https://github.com/BigML-CS-UCLA/SNNE.

Machine learning models are often personalized with categorical attributes that are protected, sensitive, self-reported, or costly to acquire. In this work, we show models that are personalized with group attributes can reduce performance at a group level. We propose formal conditions to ensure the "fair use" of group attributes in prediction tasks by training one additional model -- i.e., collective preference guarantees to ensure that each group who provides personal data will receive a tailored gain in performance in return. We present sufficient conditions to ensure fair use in empirical risk minimization and characterize failure modes that lead to fair use violations due to standard practices in model development and deployment. We present a comprehensive empirical study of fair use in clinical prediction tasks. Our results demonstrate the prevalence of fair use violations in practice and illustrate simple interventions to mitigate their harm.

User journeys in e-commerce routinely violate the one-to-one assumption that a clicked item on an advertising platform is the same item later purchased on the merchant's website/app. For a significant number of converting sessions on our platform, users click product A but buy product B -- the Click A, Buy B (CABB) phenomenon. Training recommendation models on raw click-conversion pairs therefore rewards items that merely correlate with purchases, leading to biased learning and sub-optimal conversion rates. We reframe conversion prediction as a multi-task problem with separate heads for Click A Buy A (CABA) and Click A Buy B (CABB). To isolate informative CABB conversions from unrelated CABB conversions, we introduce a taxonomy-aware collaborative filtering weighting scheme where each product is first mapped to a leaf node in a product taxonomy, and a category-to-category similarity matrix is learned from large-scale co-engagement logs. This weighting amplifies pairs that reflect genuine substitutable or complementary relations while down-weighting coincidental cross-category purchases. Offline evaluation on e-commerce sessions reduces normalized entropy by 13.9% versus a last-click attribution baseline. An online A/B test on live traffic shows +0.25% gains in the primary business metric.

The analysis of emotions expressed in text has numerous applications. In contrast to categorical analysis, focused on classifying emotions according to a pre-defined set of common classes, dimensional approaches can offer a more nuanced way to distinguish between different emotions. Still, dimensional methods have been less studied in the literature. Considering a valence-arousal dimensional space, this work assesses the use of pre-trained Transformers to predict these two dimensions on a continuous scale, with input texts from multiple languages and domains. We specifically combined multiple annotated datasets from previous studies, corresponding to either emotional lexica or short text documents, and evaluated models of multiple sizes and trained under different settings. Our results show that model size can have a significant impact on the quality of predictions, and that by fine-tuning a large model we can confidently predict valence and arousal in multiple languages. We make available the code, models, and supporting data.

The design of modern recommender systems relies on understanding which parts of the feature space are relevant for solving a given recommendation task. However, real-world data sets in this domain are often characterized by their large size, sparsity, and noise, making it challenging to identify meaningful signals. Feature ranking represents an efficient branch of algorithms that can help address these challenges by identifying the most informative features and facilitating the automated search for more compact and better-performing models (AutoML). We introduce OutRank, a system for versatile feature ranking and data quality-related anomaly detection. OutRank was built with categorical data in mind, utilizing a variant of mutual information that is normalized with regard to the noise produced by features of the same cardinality. We further extend the similarity measure by incorporating information on feature similarity and combined relevance. The proposed approach's feasibility is demonstrated by speeding up the state-of-the-art AutoML system on a synthetic data set with no performance loss. Furthermore, we considered a real-life click-through-rate prediction data set where it outperformed strong baselines such as random forest-based approaches. The proposed approach enables exploration of up to 300% larger feature spaces compared to AutoML-only approaches, enabling faster search for better models on off-the-shelf hardware.

Ensuring equitable treatment (fairness) across protected attributes (such as gender or ethnicity) is a critical issue in machine learning. Most existing literature focuses on binary classification, but achieving fairness in regression tasks-such as insurance pricing or hiring score assessments-is equally important. Moreover, anti-discrimination laws also apply to continuous attributes, such as age, for which many existing methods are not applicable. In practice, multiple protected attributes can exist simultaneously; however, methods targeting fairness across several attributes often overlook so-called "fairness gerrymandering", thereby ignoring disparities among intersectional subgroups (e.g., African-American women or Hispanic men). In this paper, we propose a distance covariance regularisation framework that mitigates the association between model predictions and protected attributes, in line with the fairness definition of demographic parity, and that captures both linear and nonlinear dependencies. To enhance applicability in the presence of multiple protected attributes, we extend our framework by incorporating two multivariate dependence measures based on distance covariance: the previously proposed joint distance covariance (JdCov) and our novel concatenated distance covariance (CCdCov), which effectively address fairness gerrymandering in both regression and classification tasks involving protected attributes of various types. We discuss and illustrate how to calibrate regularisation strength, including a method based on Jensen-Shannon divergence, which quantifies dissimilarities in prediction distributions across groups. We apply our framework to the COMPAS recidivism dataset and a large motor insurance claims dataset.

We present a neural framework for learning conditional optimal transport (OT) maps between probability distributions. Our approach introduces a conditioning mechanism capable of processing both categorical and continuous conditioning variables simultaneously. At the core of our method lies a hypernetwork that generates transport layer parameters based on these inputs, creating adaptive mappings that outperform simpler conditioning methods. Comprehensive ablation studies demonstrate the superior performance of our method over baseline configurations. Furthermore, we showcase an application to global sensitivity analysis, offering high performance in computing OT-based sensitivity indices. This work advances the state-of-the-art in conditional optimal transport, enabling broader application of optimal transport principles to complex, high-dimensional domains such as generative modeling and black-box model explainability.

Disentangling the factors of variation in data is a fundamental concept in machine learning and has been studied in various ways by different researchers, leading to a multitude of definitions. Despite the numerous empirical studies, more theoretical research is needed to fully understand the defining properties of disentanglement and how different definitions relate to each other. This paper presents a meta-analysis of existing definitions of disentanglement, using category theory as a unifying and rigorous framework. We propose that the concepts of the cartesian and monoidal products should serve as the core of disentanglement. With these core concepts, we show the similarities and crucial differences in dealing with (i) functions, (ii) equivariant maps, (iii) relations, and (iv) stochastic maps. Overall, our meta-analysis deepens our understanding of disentanglement and its various formulations and can help researchers navigate different definitions and choose the most appropriate one for their specific context.

We show that the way inference is performed in few-shot segmentation tasks has a substantial effect on performances -- an aspect often overlooked in the literature in favor of the meta-learning paradigm. We introduce a transductive inference for a given query image, leveraging the statistics of its unlabeled pixels, by optimizing a new loss containing three complementary terms: i) the cross-entropy on the labeled support pixels; ii) the Shannon entropy of the posteriors on the unlabeled query-image pixels; and iii) a global KL-divergence regularizer based on the proportion of the predicted foreground. As our inference uses a simple linear classifier of the extracted features, its computational load is comparable to inductive inference and can be used on top of any base training. Foregoing episodic training and using only standard cross-entropy training on the base classes, our inference yields competitive performances on standard benchmarks in the 1-shot scenarios. As the number of available shots increases, the gap in performances widens: on PASCAL-5i, our method brings about 5% and 6% improvements over the state-of-the-art, in the 5- and 10-shot scenarios, respectively. Furthermore, we introduce a new setting that includes domain shifts, where the base and novel classes are drawn from different datasets. Our method achieves the best performances in this more realistic setting. Our code is freely available online: https://github.com/mboudiaf/RePRI-for-Few-Shot-Segmentation.

Effective cross-modal retrieval requires robust alignment of heterogeneous data types. Most existing methods focus on bi-modal retrieval tasks and rely on distributional alignment techniques such as Kullback-Leibler divergence, Maximum Mean Discrepancy, and correlation alignment. However, these methods often suffer from critical limitations, including numerical instability, sensitivity to hyperparameters, and their inability to capture the full structure of the underlying distributions. In this paper, we introduce the Cauchy-Schwarz (CS) divergence, a hyperparameter-free measure that improves both training stability and retrieval performance. We further propose a novel Generalized CS (GCS) divergence inspired by H\"older's inequality. This extension enables direct alignment of three or more modalities within a unified mathematical framework through a bidirectional circular comparison scheme, eliminating the need for exhaustive pairwise comparisons. Extensive experiments on six benchmark datasets demonstrate the effectiveness of our method in both bi-modal and tri-modal retrieval tasks. The code of our CS/GCS divergence is publicly available at https://github.com/JiahaoZhang666/CSD.

Knowledge distillation (KD) is a general neural network training approach that uses a teacher model to guide the student model. Existing works mainly study KD from the network output side (e.g., trying to design a better KD loss function), while few have attempted to understand it from the input side. Especially, its interplay with data augmentation (DA) has not been well understood. In this paper, we ask: Why do some DA schemes (e.g., CutMix) inherently perform much better than others in KD? What makes a "good" DA in KD? Our investigation from a statistical perspective suggests that a good DA scheme should reduce the covariance of the teacher-student cross-entropy. A practical metric, the stddev of teacher's mean probability (T. stddev), is further presented and well justified empirically. Besides the theoretical understanding, we also introduce a new entropy-based data-mixing DA scheme, CutMixPick, to further enhance CutMix. Extensive empirical studies support our claims and demonstrate how we can harvest considerable performance gains simply by using a better DA scheme in knowledge distillation.

We study a family of loss functions named label-distributionally robust (LDR) losses for multi-class classification that are formulated from distributionally robust optimization (DRO) perspective, where the uncertainty in the given label information are modeled and captured by taking the worse case of distributional weights. The benefits of this perspective are several fold: (i) it provides a unified framework to explain the classical cross-entropy (CE) loss and SVM loss and their variants, (ii) it includes a special family corresponding to the temperature-scaled CE loss, which is widely adopted but poorly understood; (iii) it allows us to achieve adaptivity to the uncertainty degree of label information at an instance level. Our contributions include: (1) we study both consistency and robustness by establishing top-k (forall kgeq 1) consistency of LDR losses for multi-class classification, and a negative result that a top-1 consistent and symmetric robust loss cannot achieve top-k consistency simultaneously for all kgeq 2; (2) we propose a new adaptive LDR loss that automatically adapts the individualized temperature parameter to the noise degree of class label of each instance; (3) we demonstrate stable and competitive performance for the proposed adaptive LDR loss on 7 benchmark datasets under 6 noisy label and 1 clean settings against 13 loss functions, and on one real-world noisy dataset. The code is open-sourced at https://github.com/Optimization-AI/ICML2023_LDR.

Relational databases are the de facto standard for storing and querying structured data, and extracting insights from structured data requires advanced analytics. Deep neural networks (DNNs) have achieved super-human prediction performance in particular data types, e.g., images. However, existing DNNs may not produce meaningful results when applied to structured data. The reason is that there are correlations and dependencies across combinations of attribute values in a table, and these do not follow simple additive patterns that can be easily mimicked by a DNN. The number of possible such cross features is combinatorial, making them computationally prohibitive to model. Furthermore, the deployment of learning models in real-world applications has also highlighted the need for interpretability, especially for high-stakes applications, which remains another issue of concern to DNNs. In this paper, we present ARM-Net, an adaptive relation modeling network tailored for structured data, and a lightweight framework ARMOR based on ARM-Net for relational data analytics. The key idea is to model feature interactions with cross features selectively and dynamically, by first transforming the input features into exponential space, and then determining the interaction order and interaction weights adaptively for each cross feature. We propose a novel sparse attention mechanism to dynamically generate the interaction weights given the input tuple, so that we can explicitly model cross features of arbitrary orders with noisy features filtered selectively. Then during model inference, ARM-Net can specify the cross features being used for each prediction for higher accuracy and better interpretability. Our extensive experiments on real-world datasets demonstrate that ARM-Net consistently outperforms existing models and provides more interpretable predictions for data-driven decision making.

In the latest advancements in multimodal learning, effectively addressing the spatial and semantic losses of visual data after encoding remains a critical challenge. This is because the performance of large multimodal models is positively correlated with the coupling between visual encoders and large language models. Existing approaches often face issues such as vector gaps or semantic disparities, resulting in information loss during the propagation process. To address these issues, we propose MAGE (Multimodal Alignment and Generation Enhancement), a novel framework that bridges the semantic spaces of vision and text through an innovative alignment mechanism. By introducing the Intelligent Alignment Network (IAN), MAGE achieves dimensional and semantic alignment. To reduce the gap between synonymous heterogeneous data, we employ a training strategy that combines cross-entropy and mean squared error, significantly enhancing the alignment effect. Moreover, to enhance MAGE's "Any-to-Any" capability, we developed a fine-tuning dataset for multimodal tool-calling instructions to expand the model's output capability boundaries. Finally, our proposed multimodal large model architecture, MAGE, achieved significantly better performance compared to similar works across various evaluation benchmarks, including MME, MMBench, and SEED. Complete code and appendix are available at: https://github.com/GTCOM-NLP/MAGE.

In this work we present a new method for the estimation of Mutual Information (MI) between random variables. Our approach is based on an original interpretation of the Girsanov theorem, which allows us to use score-based diffusion models to estimate the Kullback Leibler divergence between two densities as a difference between their score functions. As a by-product, our method also enables the estimation of the entropy of random variables. Armed with such building blocks, we present a general recipe to measure MI, which unfolds in two directions: one uses conditional diffusion process, whereas the other uses joint diffusion processes that allow simultaneous modelling of two random variables. Our results, which derive from a thorough experimental protocol over all the variants of our approach, indicate that our method is more accurate than the main alternatives from the literature, especially for challenging distributions. Furthermore, our methods pass MI self-consistency tests, including data processing and additivity under independence, which instead are a pain-point of existing methods.

Entropy and mutual information in neural networks provide rich information on the learning process, but they have proven difficult to compute reliably in high dimensions. Indeed, in noisy and high-dimensional data, traditional estimates in ambient dimensions approach a fixed entropy and are prohibitively hard to compute. To address these issues, we leverage data geometry to access the underlying manifold and reliably compute these information-theoretic measures. Specifically, we define diffusion spectral entropy (DSE) in neural representations of a dataset as well as diffusion spectral mutual information (DSMI) between different variables representing data. First, we show that they form noise-resistant measures of intrinsic dimensionality and relationship strength in high-dimensional simulated data that outperform classic Shannon entropy, nonparametric estimation, and mutual information neural estimation (MINE). We then study the evolution of representations in classification networks with supervised learning, self-supervision, or overfitting. We observe that (1) DSE of neural representations increases during training; (2) DSMI with the class label increases during generalizable learning but stays stagnant during overfitting; (3) DSMI with the input signal shows differing trends: on MNIST it increases, while on CIFAR-10 and STL-10 it decreases. Finally, we show that DSE can be used to guide better network initialization and that DSMI can be used to predict downstream classification accuracy across 962 models on ImageNet. The official implementation is available at https://github.com/ChenLiu-1996/DiffusionSpectralEntropy.

We present an empirical study of scaling properties of encoder-decoder Transformer models used in neural machine translation (NMT). We show that cross-entropy loss as a function of model size follows a certain scaling law. Specifically (i) We propose a formula which describes the scaling behavior of cross-entropy loss as a bivariate function of encoder and decoder size, and show that it gives accurate predictions under a variety of scaling approaches and languages; we show that the total number of parameters alone is not sufficient for such purposes. (ii) We observe different power law exponents when scaling the decoder vs scaling the encoder, and provide recommendations for optimal allocation of encoder/decoder capacity based on this observation. (iii) We also report that the scaling behavior of the model is acutely influenced by composition bias of the train/test sets, which we define as any deviation from naturally generated text (either via machine generated or human translated text). We observe that natural text on the target side enjoys scaling, which manifests as successful reduction of the cross-entropy loss. (iv) Finally, we investigate the relationship between the cross-entropy loss and the quality of the generated translations. We find two different behaviors, depending on the nature of the test data. For test sets which were originally translated from target language to source language, both loss and BLEU score improve as model size increases. In contrast, for test sets originally translated from source language to target language, the loss improves, but the BLEU score stops improving after a certain threshold. We release generated text from all models used in this study.

We develop tools for explicitly constructing categories enriched over generating data and that compose via ordinary scalar and matrix arithmetic arithmetic operations. We characterize meaningful size maps, weightings, and magnitude that reveal features analogous to outliers that these same notions have previously been shown to reveal in the context of metric spaces. Throughout, we provide examples of such "outlier detection" relevant to the analysis of computer programs, neural networks, cyber-physical systems, and networks of communications channels.

For safety-related applications, it is crucial to produce trustworthy deep neural networks whose prediction is associated with confidence that can represent the likelihood of correctness for subsequent decision-making. Existing dense binary classification models are prone to being over-confident. To improve model calibration, we propose Adaptive Stochastic Label Perturbation (ASLP) which learns a unique label perturbation level for each training image. ASLP employs our proposed Self-Calibrating Binary Cross Entropy (SC-BCE) loss, which unifies label perturbation processes including stochastic approaches (like DisturbLabel), and label smoothing, to correct calibration while maintaining classification rates. ASLP follows Maximum Entropy Inference of classic statistical mechanics to maximise prediction entropy with respect to missing information. It performs this while: (1) preserving classification accuracy on known data as a conservative solution, or (2) specifically improves model calibration degree by minimising the gap between the prediction accuracy and expected confidence of the target training label. Extensive results demonstrate that ASLP can significantly improve calibration degrees of dense binary classification models on both in-distribution and out-of-distribution data. The code is available on https://github.com/Carlisle-Liu/ASLP.

As the scale of training corpora for large language models (LLMs) grows, model developers become increasingly reluctant to disclose details on their data. This lack of transparency poses challenges to scientific evaluation and ethical deployment. Recently, pretraining data detection approaches, which infer whether a given text was part of an LLM's training data through black-box access, have been explored. The Min-K\% Prob method, which has achieved state-of-the-art results, assumes that a non-training example tends to contain a few outlier words with low token probabilities. However, the effectiveness may be limited as it tends to misclassify non-training texts that contain many common words with high probabilities predicted by LLMs. To address this issue, we introduce a divergence-based calibration method, inspired by the divergence-from-randomness concept, to calibrate token probabilities for pretraining data detection. We compute the cross-entropy (i.e., the divergence) between the token probability distribution and the token frequency distribution to derive a detection score. We have developed a Chinese-language benchmark, PatentMIA, to assess the performance of detection approaches for LLMs on Chinese text. Experimental results on English-language benchmarks and PatentMIA demonstrate that our proposed method significantly outperforms existing methods. Our code and PatentMIA benchmark are available at https://github.com/zhang-wei-chao/DC-PDD.

Generalized Category Discovery (GCD) aims to classify unlabelled images from both `seen' and `unseen' classes by transferring knowledge from a set of labelled `seen' class images. A key theme in existing GCD approaches is adapting large-scale pre-trained models for the GCD task. An alternate perspective, however, is to adapt the data representation itself for better alignment with the pre-trained model. As such, in this paper, we introduce a two-stage adaptation approach termed SPTNet, which iteratively optimizes model parameters (i.e., model-finetuning) and data parameters (i.e., prompt learning). Furthermore, we propose a novel spatial prompt tuning method (SPT) which considers the spatial property of image data, enabling the method to better focus on object parts, which can transfer between seen and unseen classes. We thoroughly evaluate our SPTNet on standard benchmarks and demonstrate that our method outperforms existing GCD methods. Notably, we find our method achieves an average accuracy of 61.4% on the SSB, surpassing prior state-of-the-art methods by approximately 10%. The improvement is particularly remarkable as our method yields extra parameters amounting to only 0.117% of those in the backbone architecture. Project page: https://visual-ai.github.io/sptnet.

Many learning algorithms have invariances: when their training data is transformed in certain ways, the function they learn transforms in a predictable manner. Here we formalize this notion using concepts from the mathematical field of category theory. The invariances that a supervised learning algorithm possesses are formalized by categories of predictor and target spaces, whose morphisms represent the algorithm's invariances, and an index category whose morphisms represent permutations of the training examples. An invariant learning algorithm is a natural transformation between two functors from the product of these categories to the category of sets, representing training datasets and learned functions respectively. We illustrate the framework by characterizing and contrasting the invariances of linear regression and ridge regression.

The behavior of neural networks still remains opaque, and a recently widely noted phenomenon is that networks often achieve similar performance when initialized with different random parameters. This phenomenon has attracted significant attention in measuring the similarity between features learned by distinct networks. However, feature similarity could be vague in describing the same feature since equivalent features hardly exist. In this paper, we expand the concept of equivalent feature and provide the definition of what we call functionally equivalent features. These features produce equivalent output under certain transformations. Using this definition, we aim to derive a more intrinsic metric for the so-called feature complexity regarding the redundancy of features learned by a neural network at each layer. We offer a formal interpretation of our approach through the lens of category theory, a well-developed area in mathematics. To quantify the feature complexity, we further propose an efficient algorithm named Iterative Feature Merging. Our experimental results validate our ideas and theories from various perspectives. We empirically demonstrate that the functionally equivalence widely exists among different features learned by the same neural network and we could reduce the number of parameters of the network without affecting the performance.The IFM shows great potential as a data-agnostic model prune method. We have also drawn several interesting empirical findings regarding the defined feature complexity.

As new products are emerging daily, recommendation systems are required to quickly adapt to possible new domains without needing extensive retraining. This work presents ``X-Cross'' -- a novel cross-domain sequential-recommendation model that recommends products in new domains by integrating several domain-specific language models; each model is fine-tuned with low-rank adapters (LoRA). Given a recommendation prompt, operating layer by layer, X-Cross dynamically refines the representation of each source language model by integrating knowledge from all other models. These refined representations are propagated from one layer to the next, leveraging the activations from each domain adapter to ensure domain-specific nuances are preserved while enabling adaptability across domains. Using Amazon datasets for sequential recommendation, X-Cross achieves performance comparable to a model that is fine-tuned with LoRA, while using only 25% of the additional parameters. In cross-domain tasks, such as adapting from Toys domain to Tools, Electronics or Sports, X-Cross demonstrates robust performance, while requiring about 50%-75% less fine-tuning data than LoRA to make fine-tuning effective. Furthermore, X-Cross achieves significant improvement in accuracy over alternative cross-domain baselines. Overall, X-Cross enables scalable and adaptive cross-domain recommendations, reducing computational overhead and providing an efficient solution for data-constrained environments.

The analysis of scientific data and complex multivariate systems requires information quantities that capture relationships among multiple random variables. Recently, new information-theoretic measures have been developed to overcome the shortcomings of classical ones, such as mutual information, that are restricted to considering pairwise interactions. Among them, the concept of information synergy and redundancy is crucial for understanding the high-order dependencies between variables. One of the most prominent and versatile measures based on this concept is O-information, which provides a clear and scalable way to quantify the synergy-redundancy balance in multivariate systems. However, its practical application is limited to simplified cases. In this work, we introduce SOmegaI, which allows for the first time to compute O-information without restrictive assumptions about the system. Our experiments validate our approach on synthetic data, and demonstrate the effectiveness of SOmegaI in the context of a real-world use case.

We investigate causal computations taking sequences of inputs to sequences of outputs where the nth output depends on the first n inputs only. We model these in category theory via a construction taking a Cartesian category C to another category St(C) with a novel trace-like operation called "delayed trace", which misses yanking and dinaturality axioms of the usual trace. The delayed trace operation provides a feedback mechanism in St(C) with an implicit guardedness guarantee. When C is equipped with a Cartesian differential operator, we construct a differential operator for St(C) using an abstract version of backpropagation through time, a technique from machine learning based on unrolling of functions. This obtains a swath of properties for backpropagation through time, including a chain rule and Schwartz theorem. Our differential operator is also able to compute the derivative of a stateful network without requiring the network to be unrolled.

Data-Free Knowledge Distillation (DFKD) enables the knowledge transfer from the given pre-trained teacher network to the target student model without access to the real training data. Existing DFKD methods focus primarily on improving image recognition performance on associated datasets, often neglecting the crucial aspect of the transferability of learned representations. In this paper, we propose Category-Aware Embedding Data-Free Knowledge Distillation (CAE-DFKD), which addresses at the embedding level the limitations of previous rely on image-level methods to improve model generalization but fail when directly applied to DFKD. The superiority and flexibility of CAE-DFKD are extensively evaluated, including: \textbf{i.)} Significant efficiency advantages resulting from altering the generator training paradigm; \textbf{ii.)} Competitive performance with existing DFKD state-of-the-art methods on image recognition tasks; \textbf{iii.)} Remarkable transferability of data-free learned representations demonstrated in downstream tasks.

There has been a recent surge of interest in time series modeling using the Transformer architecture. However, forecasting multivariate time series with Transformer presents a unique challenge as it requires modeling both temporal (cross-time) and variate (cross-variate) dependencies. While Transformer-based models have gained popularity for their flexibility in capturing both sequential and cross-variate relationships, it is unclear how to best integrate these two sources of information in the context of the Transformer architecture while optimizing for both performance and efficiency. We re-purpose the Transformer architecture to effectively model both cross-time and cross-variate dependencies. Our approach begins by embedding each variate independently into a variate-wise representation that captures its cross-time dynamics, and then models cross-variate dependencies through attention mechanisms on these learned embeddings. Gating operations in both cross-time and cross-variate modeling phases regulate information flow, allowing the model to focus on the most relevant features for accurate predictions. Our method achieves state-of-the-art performance across 13 real-world datasets and can be seamlessly integrated into other Transformer-based and LLM-based forecasters, delivering performance improvements up to 20.7\% over original models. Code is available at this repository: https://github.com/nyuolab/Gateformer.

We present our position on the elusive quest for a general-purpose framework for specifying and studying deep learning architectures. Our opinion is that the key attempts made so far lack a coherent bridge between specifying constraints which models must satisfy and specifying their implementations. Focusing on building a such a bridge, we propose to apply category theory -- precisely, the universal algebra of monads valued in a 2-category of parametric maps -- as a single theory elegantly subsuming both of these flavours of neural network design. To defend our position, we show how this theory recovers constraints induced by geometric deep learning, as well as implementations of many architectures drawn from the diverse landscape of neural networks, such as RNNs. We also illustrate how the theory naturally encodes many standard constructs in computer science and automata theory.

Recent studies on Graph Convolutional Networks (GCNs) reveal that the initial node representations (i.e., the node representations before the first-time graph convolution) largely affect the final model performance. However, when learning the initial representation for a node, most existing work linearly combines the embeddings of node features, without considering the interactions among the features (or feature embeddings). We argue that when the node features are categorical, e.g., in many real-world applications like user profiling and recommender system, feature interactions usually carry important signals for predictive analytics. Ignoring them will result in suboptimal initial node representation and thus weaken the effectiveness of the follow-up graph convolution. In this paper, we propose a new GCN model named CatGCN, which is tailored for graph learning when the node features are categorical. Specifically, we integrate two ways of explicit interaction modeling into the learning of initial node representation, i.e., local interaction modeling on each pair of node features and global interaction modeling on an artificial feature graph. We then refine the enhanced initial node representations with the neighborhood aggregation-based graph convolution. We train CatGCN in an end-to-end fashion and demonstrate it on semi-supervised node classification. Extensive experiments on three tasks of user profiling (the prediction of user age, city, and purchase level) from Tencent and Alibaba datasets validate the effectiveness of CatGCN, especially the positive effect of performing feature interaction modeling before graph convolution.

Multimodal foundation models are prone to hallucination, generating outputs that either contradict the input or are not grounded by factual information. Given the diversity in architectures, training data and instruction tuning techniques, there can be large variations in systems' susceptibility to hallucinations. To assess system hallucination robustness, hallucination ranking approaches have been developed for specific tasks such as image captioning, question answering, summarization, or biography generation. However, these approaches typically compare model outputs to gold-standard references or labels, limiting hallucination benchmarking for new domains. This work proposes "CrossCheckGPT", a reference-free universal hallucination ranking for multimodal foundation models. The core idea of CrossCheckGPT is that the same hallucinated content is unlikely to be generated by different independent systems, hence cross-system consistency can provide meaningful and accurate hallucination assessment scores. CrossCheckGPT can be applied to any model or task, provided that the information consistency between outputs can be measured through an appropriate distance metric. Focusing on multimodal large language models that generate text, we explore two information consistency measures: CrossCheck-explicit and CrossCheck-implicit. We showcase the applicability of our method for hallucination ranking across various modalities, namely the text, image, and audio-visual domains. Further, we propose the first audio-visual hallucination benchmark, "AVHalluBench", and illustrate the effectiveness of CrossCheckGPT, achieving correlations of 98% and 89% with human judgements on MHaluBench and AVHalluBench, respectively.

This paper is the second in the series Commutative Scaling of Width and Depth (WD) about commutativity of infinite width and depth limits in deep neural networks. Our aim is to understand the behaviour of neural functions (functions that depend on a neural network model) as width and depth go to infinity (in some sense), and eventually identify settings under which commutativity holds, i.e. the neural function tends to the same limit no matter how width and depth limits are taken. In this paper, we formally introduce and define the commutativity framework, and discuss its implications on neural network design and scaling. We study commutativity for the neural covariance kernel which reflects how network layers separate data. Our findings extend previous results established in [55] by showing that taking the width and depth to infinity in a deep neural network with skip connections, when branches are suitably scaled to avoid exploding behaviour, result in the same covariance structure no matter how that limit is taken. This has a number of theoretical and practical implications that we discuss in the paper. The proof techniques in this paper are novel and rely on tools that are more accessible to readers who are not familiar with stochastic calculus (used in the proofs of WD(I))).

Modern deep neural networks have achieved impressive performance on tasks from image classification to natural language processing. Surprisingly, these complex systems with massive amounts of parameters exhibit the same structural properties in their last-layer features and classifiers across canonical datasets when training until convergence. In particular, it has been observed that the last-layer features collapse to their class-means, and those class-means are the vertices of a simplex Equiangular Tight Frame (ETF). This phenomenon is known as Neural Collapse (NC). Recent papers have theoretically shown that NC emerges in the global minimizers of training problems with the simplified "unconstrained feature model". In this context, we take a step further and prove the NC occurrences in deep linear networks for the popular mean squared error (MSE) and cross entropy (CE) losses, showing that global solutions exhibit NC properties across the linear layers. Furthermore, we extend our study to imbalanced data for MSE loss and present the first geometric analysis of NC under bias-free setting. Our results demonstrate the convergence of the last-layer features and classifiers to a geometry consisting of orthogonal vectors, whose lengths depend on the amount of data in their corresponding classes. Finally, we empirically validate our theoretical analyses on synthetic and practical network architectures with both balanced and imbalanced scenarios.

Contrastive self-supervised learning (CSL) has attracted increasing attention for model pre-training via unlabeled data. The resulted CSL models provide instance-discriminative visual features that are uniformly scattered in the feature space. During deployment, the common practice is to directly fine-tune CSL models with cross-entropy, which however may not be the best strategy in practice. Although cross-entropy tends to separate inter-class features, the resulting models still have limited capability for reducing intra-class feature scattering that exists in CSL models. In this paper, we investigate whether applying contrastive learning to fine-tuning would bring further benefits, and analytically find that optimizing the contrastive loss benefits both discriminative representation learning and model optimization during fine-tuning. Inspired by these findings, we propose Contrast-regularized tuning (Core-tuning), a new approach for fine-tuning CSL models. Instead of simply adding the contrastive loss to the objective of fine-tuning, Core-tuning further applies a novel hard pair mining strategy for more effective contrastive fine-tuning, as well as smoothing the decision boundary to better exploit the learned discriminative feature space. Extensive experiments on image classification and semantic segmentation verify the effectiveness of Core-tuning.

In this paper, we delve into the foundational principles of tensor categories, harnessing the universal property of the tensor product to pioneer novel methodologies in deep network architectures. Our primary contribution is the introduction of the Tensor Attention and Tensor Interaction Mechanism, a groundbreaking approach that leverages the tensor category to enhance the computational efficiency and the expressiveness of deep networks, and can even be generalized into the quantum realm.

A number of different architectures and loss functions have been applied to the problem of self-supervised learning (SSL), with the goal of developing embeddings that provide the best possible pre-training for as-yet-unknown, lightly supervised downstream tasks. One of these SSL criteria is to maximize the entropy of a set of embeddings in some compact space. But the goal of maximizing the embedding entropy often depends--whether explicitly or implicitly--upon high dimensional entropy estimates, which typically perform poorly in more than a few dimensions. In this paper, we motivate an effective entropy maximization criterion (E2MC), defined in terms of easy-to-estimate, low-dimensional constraints. We demonstrate that using it to continue training an already-trained SSL model for only a handful of epochs leads to a consistent and, in some cases, significant improvement in downstream performance. We perform careful ablation studies to show that the improved performance is due to the proposed add-on criterion. We also show that continued pre-training with alternative criteria does not lead to notable improvements, and in some cases, even degrades performance.

Robust loss functions are essential for training accurate deep neural networks (DNNs) in the presence of noisy (incorrect) labels. It has been shown that the commonly used Cross Entropy (CE) loss is not robust to noisy labels. Whilst new loss functions have been designed, they are only partially robust. In this paper, we theoretically show by applying a simple normalization that: any loss can be made robust to noisy labels. However, in practice, simply being robust is not sufficient for a loss function to train accurate DNNs. By investigating several robust loss functions, we find that they suffer from a problem of underfitting. To address this, we propose a framework to build robust loss functions called Active Passive Loss (APL). APL combines two robust loss functions that mutually boost each other. Experiments on benchmark datasets demonstrate that the family of new loss functions created by our APL framework can consistently outperform state-of-the-art methods by large margins, especially under large noise rates such as 60% or 80% incorrect labels.

Understanding geometric properties of natural language processing models' latent spaces allows the manipulation of these properties for improved performance on downstream tasks. One such property is the amount of data spread in a model's latent space, or how fully the available latent space is being used. In this work, we define data spread and demonstrate that the commonly used measures of data spread, Average Cosine Similarity and a partition function min/max ratio I(V), do not provide reliable metrics to compare the use of latent space across models. We propose and examine eight alternative measures of data spread, all but one of which improve over these current metrics when applied to seven synthetic data distributions. Of our proposed measures, we recommend one principal component-based measure and one entropy-based measure that provide reliable, relative measures of spread and can be used to compare models of different sizes and dimensionalities.

We explore the problem of Incremental Generalized Category Discovery (IGCD). This is a challenging category incremental learning setting where the goal is to develop models that can correctly categorize images from previously seen categories, in addition to discovering novel ones. Learning is performed over a series of time steps where the model obtains new labeled and unlabeled data, and discards old data, at each iteration. The difficulty of the problem is compounded in our generalized setting as the unlabeled data can contain images from categories that may or may not have been observed before. We present a new method for IGCD which combines non-parametric categorization with efficient image sampling to mitigate catastrophic forgetting. To quantify performance, we propose a new benchmark dataset named iNatIGCD that is motivated by a real-world fine-grained visual categorization task. In our experiments we outperform existing related methods

We propose Equiangular Basis Vectors (EBVs) for classification tasks. In deep neural networks, models usually end with a k-way fully connected layer with softmax to handle different classification tasks. The learning objective of these methods can be summarized as mapping the learned feature representations to the samples' label space. While in metric learning approaches, the main objective is to learn a transformation function that maps training data points from the original space to a new space where similar points are closer while dissimilar points become farther apart. Different from previous methods, our EBVs generate normalized vector embeddings as "predefined classifiers" which are required to not only be with the equal status between each other, but also be as orthogonal as possible. By minimizing the spherical distance of the embedding of an input between its categorical EBV in training, the predictions can be obtained by identifying the categorical EBV with the smallest distance during inference. Various experiments on the ImageNet-1K dataset and other downstream tasks demonstrate that our method outperforms the general fully connected classifier while it does not introduce huge additional computation compared with classical metric learning methods. Our EBVs won the first place in the 2022 DIGIX Global AI Challenge, and our code is open-source and available at https://github.com/NJUST-VIPGroup/Equiangular-Basis-Vectors.

Reverse derivative categories (RDCs) have recently been shown to be a suitable semantic framework for studying machine learning algorithms. Whereas emphasis has been put on training methodologies, less attention has been devoted to particular model classes: the concrete categories whose morphisms represent machine learning models. In this paper we study presentations by generators and equations of classes of RDCs. In particular, we propose polynomial circuits as a suitable machine learning model. We give an axiomatisation for these circuits and prove a functional completeness result. Finally, we discuss the use of polynomial circuits over specific semirings to perform machine learning with discrete values.

Detecting out-of-distribution inputs for visual recognition models has become critical in safe deep learning. This paper proposes a novel hierarchical visual category modeling scheme to separate out-of-distribution data from in-distribution data through joint representation learning and statistical modeling. We learn a mixture of Gaussian models for each in-distribution category. There are many Gaussian mixture models to model different visual categories. With these Gaussian models, we design an in-distribution score function by aggregating multiple Mahalanobis-based metrics. We don't use any auxiliary outlier data as training samples, which may hurt the generalization ability of out-of-distribution detection algorithms. We split the ImageNet-1k dataset into ten folds randomly. We use one fold as the in-distribution dataset and the others as out-of-distribution datasets to evaluate the proposed method. We also conduct experiments on seven popular benchmarks, including CIFAR, iNaturalist, SUN, Places, Textures, ImageNet-O, and OpenImage-O. Extensive experiments indicate that the proposed method outperforms state-of-the-art algorithms clearly. Meanwhile, we find that our visual representation has a competitive performance when compared with features learned by classical methods. These results demonstrate that the proposed method hasn't weakened the discriminative ability of visual recognition models and keeps high efficiency in detecting out-of-distribution samples.

We present FOLD-SE, an efficient, explainable machine learning algorithm for classification tasks given tabular data containing numerical and categorical values. FOLD-SE generates a set of default rules-essentially a stratified normal logic program-as an (explainable) trained model. Explainability provided by FOLD-SE is scalable, meaning that regardless of the size of the dataset, the number of learned rules and learned literals stay quite small while good accuracy in classification is maintained. A model with smaller number of rules and literals is easier to understand for human beings. FOLD-SE is competitive with state-of-the-art machine learning algorithms such as XGBoost and Multi-Layer Perceptrons (MLP) wrt accuracy of prediction. However, unlike XGBoost and MLP, the FOLD-SE algorithm is explainable. The FOLD-SE algorithm builds upon our earlier work on developing the explainable FOLD-R++ machine learning algorithm for binary classification and inherits all of its positive features. Thus, pre-processing of the dataset, using techniques such as one-hot encoding, is not needed. Like FOLD-R++, FOLD-SE uses prefix sum to speed up computations resulting in FOLD-SE being an order of magnitude faster than XGBoost and MLP in execution speed. The FOLD-SE algorithm outperforms FOLD-R++ as well as other rule-learning algorithms such as RIPPER in efficiency, performance and scalability, especially for large datasets. A major reason for scalable explainability of FOLD-SE is the use of a literal selection heuristics based on Gini Impurity, as opposed to Information Gain used in FOLD-R++. A multi-category classification version of FOLD-SE is also presented.

This paper studies the emergence of interpretable categorical features within large language models (LLMs), analyzing their behavior across training checkpoints (time), transformer layers (space), and varying model sizes (scale). Using sparse autoencoders for mechanistic interpretability, we identify when and where specific semantic concepts emerge within neural activations. Results indicate clear temporal and scale-specific thresholds for feature emergence across multiple domains. Notably, spatial analysis reveals unexpected semantic reactivation, with early-layer features re-emerging at later layers, challenging standard assumptions about representational dynamics in transformer models.

Previous knowledge distillation methods have shown their impressive performance on model compression tasks, however, it is hard to explain how the knowledge they transferred helps to improve the performance of the student network. In this work, we focus on proposing a knowledge distillation method that has both high interpretability and competitive performance. We first revisit the structure of mainstream CNN models and reveal that possessing the capacity of identifying class discriminative regions of input is critical for CNN to perform classification. Furthermore, we demonstrate that this capacity can be obtained and enhanced by transferring class activation maps. Based on our findings, we propose class attention transfer based knowledge distillation (CAT-KD). Different from previous KD methods, we explore and present several properties of the knowledge transferred by our method, which not only improve the interpretability of CAT-KD but also contribute to a better understanding of CNN. While having high interpretability, CAT-KD achieves state-of-the-art performance on multiple benchmarks. Code is available at: https://github.com/GzyAftermath/CAT-KD.

This paper studies the prediction of a target z from a pair of random variables (x,y), where the ground-truth predictor is additive E[z mid x,y] = f_star(x) +g_{star}(y). We study the performance of empirical risk minimization (ERM) over functions f+g, f in F and g in G, fit on a given training distribution, but evaluated on a test distribution which exhibits covariate shift. We show that, when the class F is "simpler" than G (measured, e.g., in terms of its metric entropy), our predictor is more resilient to heterogenous covariate shifts in which the shift in x is much greater than that in y. These results rely on a novel H\"older style inequality for the Dudley integral which may be of independent interest. Moreover, we corroborate our theoretical findings with experiments demonstrating improved resilience to shifts in "simpler" features across numerous domains.

As an important modeling paradigm in click-through rate (CTR) prediction, the Deep & Cross Network (DCN) and its derivative models have gained widespread recognition primarily due to their success in a trade-off between computational cost and performance. This paradigm employs a cross network to explicitly model feature interactions with linear growth, while leveraging deep neural networks (DNN) to implicitly capture higher-order feature interactions. However, these models still face several key limitations: (1) The performance of existing explicit feature interaction methods lags behind that of implicit DNN, resulting in overall model performance being dominated by the DNN; (2) While these models claim to capture high-order feature interactions, they often overlook potential noise within these interactions; (3) The learning process for different interaction network branches lacks appropriate supervision signals; and (4) The high-order feature interactions captured by these models are often implicit and non-interpretable due to their reliance on DNN. To address the identified limitations, this paper proposes a novel model, called Fusing Cross Network (FCN), along with two sub-networks: Linear Cross Network (LCN) and Exponential Cross Network (ECN). FCN explicitly captures feature interactions with both linear and exponential growth, eliminating the need to rely on implicit DNN. Moreover, we introduce the Self-Mask operation to filter noise layer by layer and reduce the number of parameters in the cross network by half. To effectively train these two cross networks, we propose a simple yet effective loss function called Tri-BCE, which provides tailored supervision signals for each network. We evaluate the effectiveness, efficiency, and interpretability of FCN on six benchmark datasets. Furthermore, by integrating LCN and ECN, FCN achieves a new state-of-the-art performance.

Optics and lenses are abstract categorical gadgets that model systems with bidirectional data flow. In this paper we observe that the denotational definition of optics - identifying two optics as equivalent by observing their behaviour from the outside - is not suitable for operational, software oriented approaches where optics are not merely observed, but built with their internal setups in mind. We identify operational differences between denotationally isomorphic categories of cartesian optics and lenses: their different composition rule and corresponding space-time tradeoffs, positioning them at two opposite ends of a spectrum. With these motivations we lift the existing categorical constructions and their relationships to the 2-categorical level, showing that the relevant operational concerns become visible. We define the 2-category 2-Optic(C) whose 2-cells explicitly track optics' internal configuration. We show that the 1-category Optic(C) arises by locally quotienting out the connected components of this 2-category. We show that the embedding of lenses into cartesian optics gets weakened from a functor to an oplax functor whose oplaxator now detects the different composition rule. We determine the difficulties in showing this functor forms a part of an adjunction in any of the standard 2-categories. We establish a conjecture that the well-known isomorphism between cartesian lenses and optics arises out of the lax 2-adjunction between their double-categorical counterparts. In addition to presenting new research, this paper is also meant to be an accessible introduction to the topic.

Class-incremental learning (CIL) has achieved remarkable successes in learning new classes consecutively while overcoming catastrophic forgetting on old categories. However, most existing CIL methods unreasonably assume that all old categories have the same forgetting pace, and neglect negative influence of forgetting heterogeneity among different old classes on forgetting compensation. To surmount the above challenges, we develop a novel Heterogeneous Forgetting Compensation (HFC) model, which can resolve heterogeneous forgetting of easy-to-forget and hard-to-forget old categories from both representation and gradient aspects. Specifically, we design a task-semantic aggregation block to alleviate heterogeneous forgetting from representation aspect. It aggregates local category information within each task to learn task-shared global representations. Moreover, we develop two novel plug-and-play losses: a gradient-balanced forgetting compensation loss and a gradient-balanced relation distillation loss to alleviate forgetting from gradient aspect. They consider gradient-balanced compensation to rectify forgetting heterogeneity of old categories and heterogeneous relation consistency. Experiments on several representative datasets illustrate effectiveness of our HFC model. The code is available at https://github.com/JiahuaDong/HFC.

We propose causal isotonic calibration, a novel nonparametric method for calibrating predictors of heterogeneous treatment effects. Furthermore, we introduce cross-calibration, a data-efficient variant of calibration that eliminates the need for hold-out calibration sets. Cross-calibration leverages cross-fitted predictors and generates a single calibrated predictor using all available data. Under weak conditions that do not assume monotonicity, we establish that both causal isotonic calibration and cross-calibration achieve fast doubly-robust calibration rates, as long as either the propensity score or outcome regression is estimated accurately in a suitable sense. The proposed causal isotonic calibrator can be wrapped around any black-box learning algorithm, providing robust and distribution-free calibration guarantees while preserving predictive performance.

Quantifying the similarity between two mathematical structures or datasets constitutes a particularly interesting and useful operation in several theoretical and applied problems. Aimed at this specific objective, the Jaccard index has been extensively used in the most diverse types of problems, also motivating some respective generalizations. The present work addresses further generalizations of this index, including its modification into a coincidence index capable of accounting also for the level of relative interiority between the two compared entities, as well as respective extensions for sets in continuous vector spaces, the generalization to multiset addition, densities and generic scalar fields, as well as a means to quantify the joint interdependence between two random variables. The also interesting possibility to take into account more than two sets has also been addressed, including the description of an index capable of quantifying the level of chaining between three structures. Several of the described and suggested eneralizations have been illustrated with respect to numeric case examples. It is also posited that these indices can play an important role while analyzing and integrating datasets in modeling approaches and pattern recognition activities, including as a measurement of clusters similarity or separation and as a resource for representing and analyzing complex networks.

Recent advancements in deep learning have significantly improved performance on computer vision tasks. Previous image classification methods primarily modify model architectures or add features, and they optimize models using cross-entropy loss on class logits. Since they focus on classifying images with considering class labels, these methods may struggle to learn various aspects of classes (e.g., natural positions and shape changes). Rethinking the previous approach from a novel view, we propose a multi-aspect knowledge distillation method using Multimodal Large Language Models (MLLMs). Our approach involves: 1) querying Large Language Model with multi-aspect questions relevant to the knowledge we want to transfer to the model, 2) extracting corresponding logits from MLLM, and 3) expanding the model's output dimensions to distill these multi-aspect logits. We then apply cross-entropy loss to class logits and binary cross-entropy loss to multi-aspect logits. Through our method, the model can learn not only the knowledge about visual aspects but also the abstract and complex aspects that require a deeper understanding. We primarily apply our method to image classification, and to explore the potential for extending our model, we expand it to other tasks, such as object detection. In all experimental results, our method improves the performance of the baselines. Additionally, we analyze the effect of multi-aspect knowledge distillation. These results demonstrate that our method can transfer knowledge about various aspects to the model and the aspect knowledge can enhance model performance in computer vision tasks. This paper demonstrates the great potential of multi-aspect knowledge distillation, and we believe it offers a promising direction for future research in computer vision and beyond.

A fundamental question in modern machine learning is why large, over-parameterized models, such as deep neural networks and transformers, tend to generalize well, even when their number of parameters far exceeds the number of training samples. We investigate this phenomenon through the lens of information theory, grounded in universal learning theory. Specifically, we study a Bayesian mixture learner with log-loss and (almost) uniform prior over an expansive hypothesis class. Our key result shows that the learner's regret is not determined by the overall size of the hypothesis class, but rather by the cumulative probability of all models that are close, in Kullback-Leibler divergence distance, to the true data-generating process. We refer to this cumulative probability as the weight of the hypothesis. This leads to a natural notion of model simplicity: simple models are those with large weight and thus require fewer samples to generalize, while complex models have small weight and need more data. This perspective provides a rigorous and intuitive explanation for why over-parameterized models often avoid overfitting: the presence of simple hypotheses allows the posterior to concentrate on them when supported by the data. We further bridge theory and practice by recalling that stochastic gradient descent with Langevin dynamics samples from the correct posterior distribution, enabling our theoretical learner to be approximated using standard machine learning methods combined with ensemble learning. Our analysis yields non-uniform regret bounds and aligns with key practical concepts such as flat minima and model distillation. The results apply broadly across online, batch, and supervised learning settings, offering a unified and principled understanding of the generalization behavior of modern AI systems.

Scientific studies of consciousness rely on objects whose existence is assumed to be independent of any consciousness. On the contrary, we assume consciousness to be fundamental, and that one of the main features of consciousness is characterized as being other-dependent. We set up a framework which naturally subsumes this feature by defining a compact closed category where morphisms represent conscious processes. These morphisms are a composition of a set of generators, each being specified by their relations with other generators, and therefore co-dependent. The framework is general enough and fits well into a compositional model of consciousness. Interestingly, we also show how our proposal may become a step towards avoiding the hard problem of consciousness, and thereby address the combination problem of conscious experiences.

A new approach to linguistic watermarking of language models is presented in which information is imperceptibly inserted into the output text while preserving its readability and original meaning. A cross-attention mechanism is used to embed watermarks in the text during inference. Two methods using cross-attention are presented that minimize the effect of watermarking on the performance of a pretrained model. Exploration of different training strategies for optimizing the watermarking and of the challenges and implications of applying this approach in real-world scenarios clarified the tradeoff between watermark robustness and text quality. Watermark selection substantially affects the generated output for high entropy sentences. This proactive watermarking approach has potential application in future model development.

Bayes' rule tells us how to invert a causal process in order to update our beliefs in light of new evidence. If the process is believed to have a complex compositional structure, we may observe that the inversion of the whole can be computed piecewise in terms of the component processes. We study the structure of this compositional rule, noting that it relates to the lens pattern in functional programming. Working in a suitably general axiomatic presentation of a category of Markov kernels, we see how we can think of Bayesian inversion as a particular instance of a state-dependent morphism in a fibred category. We discuss the compositional nature of this, formulated as a functor on the underlying category and explore how this can used for a more type-driven approach to statistical inference.

In this paper, we study the semi-supervised semantic segmentation problem via exploring both labeled data and extra unlabeled data. We propose a novel consistency regularization approach, called cross pseudo supervision (CPS). Our approach imposes the consistency on two segmentation networks perturbed with different initialization for the same input image. The pseudo one-hot label map, output from one perturbed segmentation network, is used to supervise the other segmentation network with the standard cross-entropy loss, and vice versa. The CPS consistency has two roles: encourage high similarity between the predictions of two perturbed networks for the same input image, and expand training data by using the unlabeled data with pseudo labels. Experiment results show that our approach achieves the state-of-the-art semi-supervised segmentation performance on Cityscapes and PASCAL VOC 2012. Code is available at https://git.io/CPS.

Large language models exhibit exceptional generalization capabilities, primarily attributed to the utilization of diversely sourced data. However, conventional practices in integrating this diverse data heavily rely on heuristic schemes, lacking theoretical guidance. This research tackles these limitations by investigating strategies based on low-cost proxies for data mixtures, with the aim of streamlining data curation to enhance training efficiency. Specifically, we propose a unified scaling law, termed BiMix, which accurately models the bivariate scaling behaviors of both data quantity and mixing proportions. We conduct systematic experiments and provide empirical evidence for the predictive power and fundamental principles of BiMix. Notably, our findings reveal that entropy-driven training-free data mixtures can achieve comparable or even better performance than more resource-intensive methods. We hope that our quantitative insights can shed light on further judicious research and development in cost-effective language modeling.

The input space of a neural network with ReLU-like activations is partitioned into multiple linear regions, each corresponding to a specific activation pattern of the included ReLU-like activations. We demonstrate that this partition exhibits the following encoding properties across a variety of deep learning models: (1) {\it determinism}: almost every linear region contains at most one training example. We can therefore represent almost every training example by a unique activation pattern, which is parameterized by a {\it neural code}; and (2) {\it categorization}: according to the neural code, simple algorithms, such as K-Means, K-NN, and logistic regression, can achieve fairly good performance on both training and test data. These encoding properties surprisingly suggest that {\it normal neural networks well-trained for classification behave as hash encoders without any extra efforts.} In addition, the encoding properties exhibit variability in different scenarios. {Further experiments demonstrate that {\it model size}, {\it training time}, {\it training sample size}, {\it regularization}, and {\it label noise} contribute in shaping the encoding properties, while the impacts of the first three are dominant.} We then define an {\it activation hash phase chart} to represent the space expanded by {model size}, training time, training sample size, and the encoding properties, which is divided into three canonical regions: {\it under-expressive regime}, {\it critically-expressive regime}, and {\it sufficiently-expressive regime}. The source code package is available at https://github.com/LeavesLei/activation-code.

Open-vocabulary semantic segmentation is a challenging task that requires segmenting novel object categories at inference time. Recent studies have explored vision-language pre-training to handle this task, but suffer from unrealistic assumptions in practical scenarios, i.e., low-quality textual category names. For example, this paradigm assumes that new textual categories will be accurately and completely provided, and exist in lexicons during pre-training. However, exceptions often happen when encountering ambiguity for brief or incomplete names, new words that are not present in the pre-trained lexicons, and difficult-to-describe categories for users. To address these issues, this work proposes a novel attribute decomposition-aggregation framework, AttrSeg, inspired by human cognition in understanding new concepts. Specifically, in the decomposition stage, we decouple class names into diverse attribute descriptions to complement semantic contexts from multiple perspectives. Two attribute construction strategies are designed: using large language models for common categories, and involving manually labeling for human-invented categories. In the aggregation stage, we group diverse attributes into an integrated global description, to form a discriminative classifier that distinguishes the target object from others. One hierarchical aggregation architecture is further proposed to achieve multi-level aggregations, leveraging the meticulously designed clustering module. The final results are obtained by computing the similarity between aggregated attributes and images embeddings. To evaluate the effectiveness, we annotate three types of datasets with attribute descriptions, and conduct extensive experiments and ablation studies. The results show the superior performance of attribute decomposition-aggregation.

Training classifiers is difficult with severe class imbalance, but many rare events are the culmination of a sequence with much more common intermediate outcomes. For example, in online marketing a user first sees an ad, then may click on it, and finally may make a purchase; estimating the probability of purchases is difficult because of their rarity. We show both theoretically and through data experiments that the more abundant data in earlier steps may be leveraged to improve estimation of probabilities of rare events. We present PRESTO, a relaxation of the proportional odds model for ordinal regression. Instead of estimating weights for one separating hyperplane that is shifted by separate intercepts for each of the estimated Bayes decision boundaries between adjacent pairs of categorical responses, we estimate separate weights for each of these transitions. We impose an L1 penalty on the differences between weights for the same feature in adjacent weight vectors in order to shrink towards the proportional odds model. We prove that PRESTO consistently estimates the decision boundary weights under a sparsity assumption. Synthetic and real data experiments show that our method can estimate rare probabilities in this setting better than both logistic regression on the rare category, which fails to borrow strength from more abundant categories, and the proportional odds model, which is too inflexible.

A critical barrier to learning an accurate decision rule for outlier detection is the scarcity of outlier data. As such, practitioners often turn to the use of similar but imperfect outlier data from which they might transfer information to the target outlier detection task. Despite the recent empirical success of transfer learning approaches in outlier detection, a fundamental understanding of when and how knowledge can be transferred from a source to a target outlier detection task remains elusive. In this work, we adopt the traditional framework of Neyman-Pearson classification -- which formalizes supervised outlier detection -- with the added assumption that one has access to some related but imperfect outlier data. Our main results are as follows: We first determine the information-theoretic limits of the problem under a measure of discrepancy that extends some existing notions from traditional balanced classification; interestingly, unlike in balanced classification, seemingly very dissimilar sources can provide much information about a target, thus resulting in fast transfer. We then show that, in principle, these information-theoretic limits are achievable by adaptive procedures, i.e., procedures with no a priori information on the discrepancy between source and target outlier distributions.

We prove theoretically that generalization improves not only through data scaling but also by compressing internal representations. To operationalize this insight, we introduce the Information Bottleneck Language Modeling (IBLM) objective, which reframes language modeling as a constrained optimization problem: minimizing representation entropy subject to optimal prediction performance. Empirically, we observe an emergent memorization-compression cycle during LLM pretraining, evidenced by oscillation positive/negative gradient alignment between cross-entropy and Matrix-Based Entropy (MBE), a measure of representation entropy. This pattern closely mirrors the predictive-compressive trade-off prescribed by IBLM and also parallels the biological alternation between awake learning and sleep consolidation. Motivated by this observation, we propose Gated Phase Transition (GAPT), a training algorithm that adaptively switches between memorization and compression phases. When applied to GPT-2 pretraining on FineWeb dataset, GAPT reduces MBE by 50% and improves cross-entropy by 4.8%. GAPT improves OOD generalizatino by 35% in a pretraining task on arithmetic multiplication. In a setting designed to simulate catastrophic forgetting, GAPT reduces interference by compressing and separating representations, achieving a 97% improvement in separation - paralleling the functional role of sleep consolidation.

Auto-regressive language models factorize sequence probabilities and are trained by minimizing the negative log-likelihood (NLL) objective. While empirically powerful, a deep theoretical understanding of why this simple objective yields such versatile representations remains elusive. This work introduces a unifying analytical framework using Markov Categories (MCs) to deconstruct the AR generation process and the NLL objective. We model the single-step generation map as a composition of Markov kernels in the category Stoch. This compositional view, when enriched with statistical divergences, allows us to dissect information flow and learned geometry. Our framework makes three main contributions. First, we provide a formal, information-theoretic rationale for the success of modern speculative decoding methods like EAGLE, quantifying the information surplus in hidden states that these methods exploit. Second, we formalize how NLL minimization forces the model to learn not just the next token, but the data's intrinsic conditional stochasticity, a process we analyze using categorical entropy. Third, and most centrally, we prove that NLL training acts as an implicit form of spectral contrastive learning. By analyzing the information geometry of the model's prediction head, we show that NLL implicitly forces the learned representation space to align with the eigenspectrum of a predictive similarity operator, thereby learning a geometrically structured space without explicit contrastive pairs. This compositional and information-geometric perspective reveals the deep structural principles underlying the effectiveness of modern LMs. Project Page: https://github.com/asiresearch/lm-theory

In this paper, we consider a real-world scenario where a model that is trained on pre-defined classes continually encounters unlabeled data that contains both known and novel classes. The goal is to continually discover novel classes while maintaining the performance in known classes. We name the setting Continual Generalized Category Discovery (C-GCD). Existing methods for novel class discovery cannot directly handle the C-GCD setting due to some unrealistic assumptions, such as the unlabeled data only containing novel classes. Furthermore, they fail to discover novel classes in a continual fashion. In this work, we lift all these assumptions and propose an approach, called MetaGCD, to learn how to incrementally discover with less forgetting. Our proposed method uses a meta-learning framework and leverages the offline labeled data to simulate the testing incremental learning process. A meta-objective is defined to revolve around two conflicting learning objectives to achieve novel class discovery without forgetting. Furthermore, a soft neighborhood-based contrastive network is proposed to discriminate uncorrelated images while attracting correlated images. We build strong baselines and conduct extensive experiments on three widely used benchmarks to demonstrate the superiority of our method.

The Automunge open source python library platform for tabular data pre-processing automates feature engineering data transformations of numerical encoding and missing data infill to received tidy data on bases fit to properties of columns in a designated train set for consistent and efficient application to subsequent data pipelines such as for inference, where transformations may be applied to distinct columns in "family tree" sets with generations and branches of derivations. Included in the library of transformations are methods to extract structure from bounded categorical string sets by way of automated string parsing, in which comparisons between entries in the set of unique values are parsed to identify character subset overlaps which may be encoded by appended columns of boolean overlap detection activations or by replacing string entries with identified overlap partitions. Further string parsing options, which may also be applied to unbounded categoric sets, include extraction of numeric substring partitions from entries or search functions to identify presence of specified substring partitions. The aggregation of these methods into "family tree" sets of transformations are demonstrated for use to automatically extract structure from categoric string compositions in relation to the set of entries in a column, such as may be applied to prepare categoric string set encodings for machine learning without human intervention.

In this paper, we present a novel framework for the analysis of Riemann Hypothesis [27], which is composed of three key components: a) probabilistic modeling with cross entropy optimization and reasoning; b) the application of the law of large numbers; c) the application of mathematical inductions. The analysis is mainly conducted by virtue of probabilistic modeling of cross entropy optimization and reasoning with rare event simulation techniques. The application of the law of large numbers [2, 3, 6] and the application of mathematical inductions make the analysis of Riemann Hypothesis self-contained and complete to make sure that the whole complex plane is covered as conjectured in Riemann Hypothesis. We also discuss the method of enhanced top-p sampling with large language models (LLMs) for reasoning, where next token prediction is not just based on the estimated probabilities of each possible token in the current round but also based on accumulated path probabilities among multiple top-k chain of thoughts (CoTs) paths. The probabilistic modeling of cross entropy optimization and reasoning may suit well with the analysis of Riemann Hypothesis as Riemann Zeta functions are inherently dealing with the sums of infinite components of a complex number series. We hope that our analysis in this paper could shed some light on some of the insights of Riemann Hypothesis. The framework and techniques presented in this paper, coupled with recent developments with chain of thought (CoT) or diagram of thought (DoT) reasoning in large language models (LLMs) with reinforcement learning (RL) [1, 7, 18, 21, 24, 34, 39-41], could pave the way for eventual proof of Riemann Hypothesis [27].

Generalized Category Discovery (GCD) is a practical and challenging open-world task that aims to recognize both known and novel categories in unlabeled data using limited labeled data from known categories. Due to the lack of supervision, previous GCD methods face significant challenges, such as difficulty in rectifying errors for confusing instances, and inability to effectively uncover and leverage the semantic meanings of discovered clusters. Therefore, additional annotations are usually required for real-world applicability. However, human annotation is extremely costly and inefficient. To address these issues, we propose GLEAN, a unified framework for generalized category discovery that actively learns from diverse and quality-enhanced LLM feedback. Our approach leverages three different types of LLM feedback to: (1) improve instance-level contrastive features, (2) generate category descriptions, and (3) align uncertain instances with LLM-selected category descriptions. Extensive experiments demonstrate the superior performance of \MethodName over state-of-the-art models across diverse datasets, metrics, and supervision settings. Our code is available at https://github.com/amazon-science/Glean.

Nearly all practical neural models for classification are trained using cross-entropy loss. Yet this ubiquitous choice is supported by little theoretical or empirical evidence. Recent work (Hui & Belkin, 2020) suggests that training using the (rescaled) square loss is often superior in terms of the classification accuracy. In this paper we propose the "squentropy" loss, which is the sum of two terms: the cross-entropy loss and the average square loss over the incorrect classes. We provide an extensive set of experiments on multi-class classification problems showing that the squentropy loss outperforms both the pure cross entropy and rescaled square losses in terms of the classification accuracy. We also demonstrate that it provides significantly better model calibration than either of these alternative losses and, furthermore, has less variance with respect to the random initialization. Additionally, in contrast to the square loss, squentropy loss can typically be trained using exactly the same optimization parameters, including the learning rate, as the standard cross-entropy loss, making it a true "plug-and-play" replacement. Finally, unlike the rescaled square loss, multiclass squentropy contains no parameters that need to be adjusted.

The optimal transport problem for measures supported on non-Euclidean spaces has recently gained ample interest in diverse applications involving representation learning. In this paper, we focus on circular probability measures, i.e., probability measures supported on the unit circle, and introduce a new computationally efficient metric for these measures, denoted as Linear Circular Optimal Transport (LCOT). The proposed metric comes with an explicit linear embedding that allows one to apply Machine Learning (ML) algorithms to the embedded measures and seamlessly modify the underlying metric for the ML algorithm to LCOT. We show that the proposed metric is rooted in the Circular Optimal Transport (COT) and can be considered the linearization of the COT metric with respect to a fixed reference measure. We provide a theoretical analysis of the proposed metric and derive the computational complexities for pairwise comparison of circular probability measures. Lastly, through a set of numerical experiments, we demonstrate the benefits of LCOT in learning representations of circular measures.

Understanding how semantic meaning is encoded in the representation spaces of large language models is a fundamental problem in interpretability. In this paper, we study the two foundational questions in this area. First, how are categorical concepts, such as {'mammal', 'bird', 'reptile', 'fish'}, represented? Second, how are hierarchical relations between concepts encoded? For example, how is the fact that 'dog' is a kind of 'mammal' encoded? We show how to extend the linear representation hypothesis to answer these questions. We find a remarkably simple structure: simple categorical concepts are represented as simplices, hierarchically related concepts are orthogonal in a sense we make precise, and (in consequence) complex concepts are represented as polytopes constructed from direct sums of simplices, reflecting the hierarchical structure. We validate these theoretical results on the Gemma large language model, estimating representations for 957 hierarchically related concepts using data from WordNet.

Federated Learning (FL) is a distributed learning paradigm that enables different parties to train a model together for high quality and strong privacy protection. In this scenario, individual participants may get compromised and perform backdoor attacks by poisoning the data (or gradients). Existing work on robust aggregation and certified FL robustness does not study how hardening benign clients can affect the global model (and the malicious clients). In this work, we theoretically analyze the connection among cross-entropy loss, attack success rate, and clean accuracy in this setting. Moreover, we propose a trigger reverse engineering based defense and show that our method can achieve robustness improvement with guarantee (i.e., reducing the attack success rate) without affecting benign accuracy. We conduct comprehensive experiments across different datasets and attack settings. Our results on eight competing SOTA defense methods show the empirical superiority of our method on both single-shot and continuous FL backdoor attacks. Code is available at https://github.com/KaiyuanZh/FLIP.

The escalating reliance on revolutionary online web services has introduced heightened security risks, with persistent challenges posed by phishing despite extensive security measures. Traditional phishing systems, reliant on machine learning and manual features, struggle with evolving tactics. Recent advances in deep learning offer promising avenues for tackling novel phishing challenges and malicious URLs. This paper introduces a two-phase stack generalized model named AntiPhishStack, designed to detect phishing sites. The model leverages the learning of URLs and character-level TF-IDF features symmetrically, enhancing its ability to combat emerging phishing threats. In Phase I, features are trained on a base machine learning classifier, employing K-fold cross-validation for robust mean prediction. Phase II employs a two-layered stacked-based LSTM network with five adaptive optimizers for dynamic compilation, ensuring premier prediction on these features. Additionally, the symmetrical predictions from both phases are optimized and integrated to train a meta-XGBoost classifier, contributing to a final robust prediction. The significance of this work lies in advancing phishing detection with AntiPhishStack, operating without prior phishing-specific feature knowledge. Experimental validation on two benchmark datasets, comprising benign and phishing or malicious URLs, demonstrates the model's exceptional performance, achieving a notable 96.04% accuracy compared to existing studies. This research adds value to the ongoing discourse on symmetry and asymmetry in information security and provides a forward-thinking solution for enhancing network security in the face of evolving cyber threats.

We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of smaller parts. However, neither their theoretical justification nor their implementation reflects this modularity. We show how to conceptualise and analyse such inference algorithms as manipulating intermediate representations of probabilistic programs using higher-order functions and inductive types, and their denotational semantics. Semantic accounts of continuous distributions use measurable spaces. However, our use of higher-order functions presents a substantial technical difficulty: it is impossible to define a measurable space structure over the collection of measurable functions between arbitrary measurable spaces that is compatible with standard operations on those functions, such as function application. We overcome this difficulty using quasi-Borel spaces, a recently proposed mathematical structure that supports both function spaces and continuous distributions. We define a class of semantic structures for representing probabilistic programs, and semantic validity criteria for transformations of these representations in terms of distribution preservation. We develop a collection of building blocks for composing representations. We use these building blocks to validate common inference algorithms such as Sequential Monte Carlo and Markov Chain Monte Carlo. To emphasize the connection between the semantic manipulation and its traditional measure theoretic origins, we use Kock's synthetic measure theory. We demonstrate its usefulness by proving a quasi-Borel counterpart to the Metropolis-Hastings-Green theorem.

We present a formulation of flow matching as variational inference, which we refer to as variational flow matching (VFM). Based on this formulation we develop CatFlow, a flow matching method for categorical data. CatFlow is easy to implement, computationally efficient, and achieves strong results on graph generation tasks. In VFM, the objective is to approximate the posterior probability path, which is a distribution over possible end points of a trajectory. We show that VFM admits both the CatFlow objective and the original flow matching objective as special cases. We also relate VFM to score-based models, in which the dynamics are stochastic rather than deterministic, and derive a bound on the model likelihood based on a reweighted VFM objective. We evaluate CatFlow on one abstract graph generation task and two molecular generation tasks. In all cases, CatFlow exceeds or matches performance of the current state-of-the-art models.

LoRA (Low-Rank Adaptation) is a widely used model fine-tuning method. In fine-tuning, the law among model performance, model parameters, and data complexity has been a focal issue in the field. Existing methods often leverage external metrics (such as cross-entropy or perplexity) to evaluate model performance. In the fine-tuning process for large models, two types of knowledge are typically involved: the frozen, general knowledge acquired by the model during pre-training and the new knowledge learned through the LoRA module from the current data. Generally, the less LoRA's learned knowledge relies on the large model, the more it captures the specific knowledge of new data, thereby enhancing its adaptability to new tasks. However, external metrics do not readily capture the dependency relationship between these two types of knowledge. Therefore, we designed an internal metric based on the Mutual Information Upper Bound (MIUB) theory to investigate the scaling law of large-model LoRA fine-tuning. In our experiments, we validated this approach on benchmark datasets, using the Llama3-8B and Phi3-3B models. The results show that the proposed MIUB metric aligns more accurately and stably with the scaling law of LoRA fine-tuning compared to cross-entropy and perplexity.

In recent years, Wi-Fi sensing has garnered significant attention due to its numerous benefits, such as privacy protection, low cost, and penetration ability. Extensive research has been conducted in this field, focusing on areas such as gesture recognition, people identification, and fall detection. However, many data-driven methods encounter challenges related to domain shift, where the model fails to perform well in environments different from the training data. One major factor contributing to this issue is the limited availability of Wi-Fi sensing datasets, which makes models learn excessive irrelevant information and over-fit to the training set. Unfortunately, collecting large-scale Wi-Fi sensing datasets across diverse scenarios is a challenging task. To address this problem, we propose CrossFi, a siamese network-based approach that excels in both in-domain scenario and cross-domain scenario, including few-shot, zero-shot scenarios, and even works in few-shot new-class scenario where testing set contains new categories. The core component of CrossFi is a sample-similarity calculation network called CSi-Net, which improves the structure of the siamese network by using an attention mechanism to capture similarity information, instead of simply calculating the distance or cosine similarity. Based on it, we develop an extra Weight-Net that can generate a template for each class, so that our CrossFi can work in different scenarios. Experimental results demonstrate that our CrossFi achieves state-of-the-art performance across various scenarios. In gesture recognition task, our CrossFi achieves an accuracy of 98.17% in in-domain scenario, 91.72% in one-shot cross-domain scenario, 64.81% in zero-shot cross-domain scenario, and 84.75% in one-shot new-class scenario. The code for our model is publicly available at https://github.com/RS2002/CrossFi.

Although deep neural networks achieve tremendous success on various classification tasks, the generalization ability drops sheer when training datasets exhibit long-tailed distributions. One of the reasons is that the learned representations (i.e. features) from the imbalanced datasets are less effective than those from balanced datasets. Specifically, the learned representation under class-balanced distribution will present the Neural Collapse (NC) phenomena. NC indicates the features from the same category are close to each other and from different categories are maximally distant, showing an optimal linear separable state of classification. However, the pattern differs on imbalanced datasets and is partially responsible for the reduced performance of the model. In this work, we propose two explicit feature regularization terms to learn high-quality representation for class-imbalanced data. With the proposed regularization, NC phenomena will appear under the class-imbalanced distribution, and the generalization ability can be significantly improved. Our method is easily implemented, highly effective, and can be plugged into most existing methods. The extensive experimental results on widely-used benchmarks show the effectiveness of our method

As multimodal learning finds applications in a wide variety of high-stakes societal tasks, investigating their robustness becomes important. Existing work has focused on understanding the robustness of vision-and-language models to imperceptible variations on benchmark tasks. In this work, we investigate the robustness of multimodal classifiers to cross-modal dilutions - a plausible variation. We develop a model that, given a multimodal (image + text) input, generates additional dilution text that (a) maintains relevance and topical coherence with the image and existing text, and (b) when added to the original text, leads to misclassification of the multimodal input. Via experiments on Crisis Humanitarianism and Sentiment Detection tasks, we find that the performance of task-specific fusion-based multimodal classifiers drops by 23.3% and 22.5%, respectively, in the presence of dilutions generated by our model. Metric-based comparisons with several baselines and human evaluations indicate that our dilutions show higher relevance and topical coherence, while simultaneously being more effective at demonstrating the brittleness of the multimodal classifiers. Our work aims to highlight and encourage further research on the robustness of deep multimodal models to realistic variations, especially in human-facing societal applications. The code and other resources are available at https://claws-lab.github.io/multimodal-robustness/.

In this paper we show how tensor networks help in developing explainability of machine learning algorithms. Specifically, we develop an unsupervised clustering algorithm based on Matrix Product States (MPS) and apply it in the context of a real use-case of adversary-generated threat intelligence. Our investigation proves that MPS rival traditional deep learning models such as autoencoders and GANs in terms of performance, while providing much richer model interpretability. Our approach naturally facilitates the extraction of feature-wise probabilities, Von Neumann Entropy, and mutual information, offering a compelling narrative for classification of anomalies and fostering an unprecedented level of transparency and interpretability, something fundamental to understand the rationale behind artificial intelligence decisions.

Cross-entropy loss and focal loss are the most common choices when training deep neural networks for classification problems. Generally speaking, however, a good loss function can take on much more flexible forms, and should be tailored for different tasks and datasets. Motivated by how functions can be approximated via Taylor expansion, we propose a simple framework, named PolyLoss, to view and design loss functions as a linear combination of polynomial functions. Our PolyLoss allows the importance of different polynomial bases to be easily adjusted depending on the targeting tasks and datasets, while naturally subsuming the aforementioned cross-entropy loss and focal loss as special cases. Extensive experimental results show that the optimal choice within the PolyLoss is indeed dependent on the task and dataset. Simply by introducing one extra hyperparameter and adding one line of code, our Poly-1 formulation outperforms the cross-entropy loss and focal loss on 2D image classification, instance segmentation, object detection, and 3D object detection tasks, sometimes by a large margin.

Misclassification detection is an important problem in machine learning, as it allows for the identification of instances where the model's predictions are unreliable. However, conventional uncertainty measures such as Shannon entropy do not provide an effective way to infer the real uncertainty associated with the model's predictions. In this paper, we introduce a novel data-driven measure of uncertainty relative to an observer for misclassification detection. By learning patterns in the distribution of soft-predictions, our uncertainty measure can identify misclassified samples based on the predicted class probabilities. Interestingly, according to the proposed measure, soft-predictions corresponding to misclassified instances can carry a large amount of uncertainty, even though they may have low Shannon entropy. We demonstrate empirical improvements over multiple image classification tasks, outperforming state-of-the-art misclassification detection methods.

We approach the problem of improving robustness of deep learning algorithms in the presence of label noise. Building upon existing label correction and co-teaching methods, we propose a novel training procedure to mitigate the memorization of noisy labels, called CrossSplit, which uses a pair of neural networks trained on two disjoint parts of the labelled dataset. CrossSplit combines two main ingredients: (i) Cross-split label correction. The idea is that, since the model trained on one part of the data cannot memorize example-label pairs from the other part, the training labels presented to each network can be smoothly adjusted by using the predictions of its peer network; (ii) Cross-split semi-supervised training. A network trained on one part of the data also uses the unlabeled inputs of the other part. Extensive experiments on CIFAR-10, CIFAR-100, Tiny-ImageNet and mini-WebVision datasets demonstrate that our method can outperform the current state-of-the-art in a wide range of noise ratios.

Class Incremental Semantic Segmentation~(CISS), within Incremental Learning for semantic segmentation, targets segmenting new categories while reducing the catastrophic forgetting on the old categories.Besides, background shifting, where the background category changes constantly in each step, is a special challenge for CISS. Current methods with a shared background classifier struggle to keep up with these changes, leading to decreased stability in background predictions and reduced accuracy of segmentation. For this special challenge, we designed a novel background adaptation mechanism, which explicitly models the background residual rather than the background itself in each step, and aggregates these residuals to represent the evolving background. Therefore, the background adaptation mechanism ensures the stability of previous background classifiers, while enabling the model to concentrate on the easy-learned residuals from the additional channel, which enhances background discernment for better prediction of novel categories. To precisely optimize the background adaptation mechanism, we propose Pseudo Background Binary Cross-Entropy loss and Background Adaptation losses, which amplify the adaptation effect. Group Knowledge Distillation and Background Feature Distillation strategies are designed to prevent forgetting old categories. Our approach, evaluated across various incremental scenarios on Pascal VOC 2012 and ADE20K datasets, outperforms prior exemplar-free state-of-the-art methods with mIoU of 3.0% in VOC 10-1 and 2.0% in ADE 100-5, notably enhancing the accuracy of new classes while mitigating catastrophic forgetting. Code is available in https://andyzaq.github.io/barmsite/.

Knowledge Graphs (KGs) are symbolically structured storages of facts. The KG embedding contains concise data used in NLP tasks requiring implicit information about the real world. Furthermore, the size of KGs that may be useful in actual NLP assignments is enormous, and creating embedding over it has memory cost issues. We represent KG as a 3rd-order binary tensor and move beyond the standard CP decomposition by using a data-specific generalized version of it. The generalization of the standard CP-ALS algorithm allows obtaining optimization gradients without a backpropagation mechanism. It reduces the memory needed in training while providing computational benefits. We propose a MEKER, a memory-efficient KG embedding model, which yields SOTA-comparable performance on link prediction tasks and KG-based Question Answering.

We characterize the statistical efficiency of knowledge transfer through n samples from a teacher to a probabilistic student classifier with input space mathcal S over labels mathcal A. We show that privileged information at three progressive levels accelerates the transfer. At the first level, only samples with hard labels are known, via which the maximum likelihood estimator attains the minimax rate {|{mathcal S||{mathcal A}|}/{n}}. The second level has the teacher probabilities of sampled labels available in addition, which turns out to boost the convergence rate lower bound to {{|{mathcal S}||{mathcal A}|}/{n}}. However, under this second data acquisition protocol, minimizing a naive adaptation of the cross-entropy loss results in an asymptotically biased student. We overcome this limitation and achieve the fundamental limit by using a novel empirical variant of the squared error logit loss. The third level further equips the student with the soft labels (complete logits) on {mathcal A} given every sampled input, thereby provably enables the student to enjoy a rate {|{mathcal S}|}/{n} free of |{mathcal A}|. We find any Kullback-Leibler divergence minimizer to be optimal in the last case. Numerical simulations distinguish the four learners and corroborate our theory.

The cross-entropy objective has proved to be an all-purpose training objective for autoregressive language models (LMs). However, without considering the penalization of problematic tokens, LMs trained using cross-entropy exhibit text degeneration. To address this, unlikelihood training has been proposed to reduce the probability of unlikely tokens predicted by LMs. But unlikelihood does not consider the relationship between the label tokens and unlikely token candidates, thus showing marginal improvements in degeneration. We propose a new contrastive token learning objective that inherits the advantages of cross-entropy and unlikelihood training and avoids their limitations. The key idea is to teach a LM to generate high probabilities for label tokens and low probabilities of negative candidates. Comprehensive experiments on language modeling and open-domain dialogue generation tasks show that the proposed contrastive token objective yields much less repetitive texts, with a higher generation quality than baseline approaches, achieving the new state-of-the-art performance on text degeneration.

With the rapid advancement of synthetic dataset generation techniques, evaluating the quality of synthetic data has become a critical research focus. Robust evaluation not only drives innovations in data generation methods but also guides researchers in optimizing the utilization of these synthetic resources. However, current evaluation studies for synthetic datasets remain limited, lacking a universally accepted standard framework. To address this, this paper proposes a novel evaluation framework integrating generalized cross-validation experiments and domain transfer learning principles, enabling generalizable and comparable assessments of synthetic dataset quality. The framework involves training task-specific models (e.g., YOLOv5s) on both synthetic datasets and multiple real-world benchmarks (e.g., KITTI, BDD100K), forming a cross-performance matrix. Following normalization, a Generalized Cross-Validation (GCV) Matrix is constructed to quantify domain transferability. The framework introduces two key metrics. One measures the simulation quality by quantifying the similarity between synthetic data and real-world datasets, while another evaluates the transfer quality by assessing the diversity and coverage of synthetic data across various real-world scenarios. Experimental validation on Virtual KITTI demonstrates the effectiveness of our proposed framework and metrics in assessing synthetic data fidelity. This scalable and quantifiable evaluation solution overcomes traditional limitations, providing a principled approach to guide synthetic dataset optimization in artificial intelligence research.

State-of-the-art methods for conditional average treatment effect (CATE) estimation make widespread use of representation learning. Here, the idea is to reduce the variance of the low-sample CATE estimation by a (potentially constrained) low-dimensional representation. However, low-dimensional representations can lose information about the observed confounders and thus lead to bias, because of which the validity of representation learning for CATE estimation is typically violated. In this paper, we propose a new, representation-agnostic framework for estimating bounds on the representation-induced confounding bias that comes from dimensionality reduction (or other constraints on the representations) in CATE estimation. First, we establish theoretically under which conditions CATEs are non-identifiable given low-dimensional (constrained) representations. Second, as our remedy, we propose to perform partial identification of CATEs or, equivalently, aim at estimating of lower and upper bounds of the representation-induced confounding bias. We demonstrate the effectiveness of our bounds in a series of experiments. In sum, our framework is of direct relevance in practice where the validity of CATE estimation is of importance.

Compact convolutional neural networks (CNNs) have witnessed exceptional improvements in performance in recent years. However, they still fail to provide the same predictive power as CNNs with a large number of parameters. The diverse and even abundant features captured by the layers is an important characteristic of these successful CNNs. However, differences in this characteristic between large CNNs and their compact counterparts have rarely been investigated. In compact CNNs, due to the limited number of parameters, abundant features are unlikely to be obtained, and feature diversity becomes an essential characteristic. Diverse features present in the activation maps derived from a data point during model inference may indicate the presence of a set of unique descriptors necessary to distinguish between objects of different classes. In contrast, data points with low feature diversity may not provide a sufficient amount of unique descriptors to make a valid prediction; we refer to them as random predictions. Random predictions can negatively impact the optimization process and harm the final performance. This paper proposes addressing the problem raised by random predictions by reshaping the standard cross-entropy to make it biased toward data points with a limited number of unique descriptive features. Our novel Bias Loss focuses the training on a set of valuable data points and prevents the vast number of samples with poor learning features from misleading the optimization process. Furthermore, to show the importance of diversity, we present a family of SkipNet models whose architectures are brought to boost the number of unique descriptors in the last layers. Our Skipnet-M can achieve 1% higher classification accuracy than MobileNetV3 Large.

We consider the problem of zero-shot recognition: learning a visual classifier for a category with zero training examples, just using the word embedding of the category and its relationship to other categories, which visual data are provided. The key to dealing with the unfamiliar or novel category is to transfer knowledge obtained from familiar classes to describe the unfamiliar class. In this paper, we build upon the recently introduced Graph Convolutional Network (GCN) and propose an approach that uses both semantic embeddings and the categorical relationships to predict the classifiers. Given a learned knowledge graph (KG), our approach takes as input semantic embeddings for each node (representing visual category). After a series of graph convolutions, we predict the visual classifier for each category. During training, the visual classifiers for a few categories are given to learn the GCN parameters. At test time, these filters are used to predict the visual classifiers of unseen categories. We show that our approach is robust to noise in the KG. More importantly, our approach provides significant improvement in performance compared to the current state-of-the-art results (from 2 ~ 3% on some metrics to whopping 20% on a few).

The Koopman operator provides a powerful framework for modeling dynamical systems and has attracted growing interest from the machine learning community. However, its infinite-dimensional nature makes identifying suitable finite-dimensional subspaces challenging, especially for deep architectures. We argue that these difficulties come from suboptimal representation learning, where latent variables fail to balance expressivity and simplicity. This tension is closely related to the information bottleneck (IB) dilemma: constructing compressed representations that are both compact and predictive. Rethinking Koopman learning through this lens, we demonstrate that latent mutual information promotes simplicity, yet an overemphasis on simplicity may cause latent space to collapse onto a few dominant modes. In contrast, expressiveness is sustained by the von Neumann entropy, which prevents such collapse and encourages mode diversity. This insight leads us to propose an information-theoretic Lagrangian formulation that explicitly balances this tradeoff. Furthermore, we propose a new algorithm based on the Lagrangian formulation that encourages both simplicity and expressiveness, leading to a stable and interpretable Koopman representation. Beyond quantitative evaluations, we further visualize the learned manifolds under our representations, observing empirical results consistent with our theoretical predictions. Finally, we validate our approach across a diverse range of dynamical systems, demonstrating improved performance over existing Koopman learning methods. The implementation is publicly available at https://github.com/Wenxuan52/InformationKoopman.

The present work explores the theoretical limits of Machine Learning (ML) within the framework of Kolmogorov's theory of Algorithmic Probability, which clarifies the notion of entropy as Expected Kolmogorov Complexity and formalizes other fundamental concepts such as Occam's razor via Levin's Universal Distribution. As a fundamental application, we develop Maximum Entropy methods that allow us to derive the Erdos--Kac Law in Probabilistic Number Theory, and establish the impossibility of discovering a formula for primes using Machine Learning via the Prime Coding Theorem.

Semantic segmentation usually suffers from a long-tail data distribution. Due to the imbalanced number of samples across categories, the features of those tail classes may get squeezed into a narrow area in the feature space. Towards a balanced feature distribution, we introduce category-wise variation into the network predictions in the training phase such that an instance is no longer projected to a feature point, but a small region instead. Such a perturbation is highly dependent on the category scale, which appears as assigning smaller variation to head classes and larger variation to tail classes. In this way, we manage to close the gap between the feature areas of different categories, resulting in a more balanced representation. It is noteworthy that the introduced variation is discarded at the inference stage to facilitate a confident prediction. Although with an embarrassingly simple implementation, our method manifests itself in strong generalizability to various datasets and task settings. Extensive experiments suggest that our plug-in design lends itself well to a range of state-of-the-art approaches and boosts the performance on top of them.

Large language models perform near-Bayesian inference yet violate permutation invariance on exchangeable data. We resolve this by showing transformers minimize expected conditional description length (cross-entropy) over orderings, E_pi[ell(Y mid Gamma_pi(X))], which admits a Kolmogorov-complexity interpretation up to additive constants, rather than the permutation-invariant description length ell(Y mid X). This makes them Bayesian in expectation, not in realization. We derive (i) a Quantified Martingale Violation bound showing order-induced deviations scale as O(log n) with constants; (ii) the Expectation-level Decompression Law linking information budgets to reliability for Bernoulli predicates; and (iii) deployable planners (B2T/RoH/ISR) for answer/abstain decisions. Empirically, permutation dispersion follows a+bln n (Qwen2-7B b approx 0.377, Llama-3.1-8B b approx 0.147); permutation mixtures improve ground-truth likelihood/accuracy; and randomized dose-response shows hallucinations drop by sim 0.13 per additional nat. A pre-specified audit with a fixed ISR=1.0 achieves near-0\% hallucinations via calibrated refusal at 24\% abstention. The framework turns hallucinations into predictable compression failures and enables principled information budgeting.

We propose a general method for measuring complex variables on a continuous, interval spectrum by combining supervised deep learning with the Constructing Measures approach to faceted Rasch item response theory (IRT). We decompose the target construct, hate speech in our case, into multiple constituent components that are labeled as ordinal survey items. Those survey responses are transformed via IRT into a debiased, continuous outcome measure. Our method estimates the survey interpretation bias of the human labelers and eliminates that influence on the generated continuous measure. We further estimate the response quality of each labeler using faceted IRT, allowing responses from low-quality labelers to be removed. Our faceted Rasch scaling procedure integrates naturally with a multitask deep learning architecture for automated prediction on new data. The ratings on the theorized components of the target outcome are used as supervised, ordinal variables for the neural networks' internal concept learning. We test the use of an activation function (ordinal softmax) and loss function (ordinal cross-entropy) designed to exploit the structure of ordinal outcome variables. Our multitask architecture leads to a new form of model interpretation because each continuous prediction can be directly explained by the constituent components in the penultimate layer. We demonstrate this new method on a dataset of 50,000 social media comments sourced from YouTube, Twitter, and Reddit and labeled by 11,000 U.S.-based Amazon Mechanical Turk workers to measure a continuous spectrum from hate speech to counterspeech. We evaluate Universal Sentence Encoders, BERT, and RoBERTa as language representation models for the comment text, and compare our predictive accuracy to Google Jigsaw's Perspective API models, showing significant improvement over this standard benchmark.

Recently, self-supervised learning has attracted great attention, since it only requires unlabeled data for model training. Contrastive learning is one popular method for self-supervised learning and has achieved promising empirical performance. However, the theoretical understanding of its generalization ability is still limited. To this end, we define a kind of (sigma,delta)-measure to mathematically quantify the data augmentation, and then provide an upper bound of the downstream classification error rate based on the measure. It reveals that the generalization ability of contrastive self-supervised learning is related to three key factors: alignment of positive samples, divergence of class centers, and concentration of augmented data. The first two factors are properties of learned representations, while the third one is determined by pre-defined data augmentation. We further investigate two canonical contrastive losses, InfoNCE and cross-correlation, to show how they provably achieve the first two factors. Moreover, we conduct experiments to study the third factor, and observe a strong correlation between downstream performance and the concentration of augmented data.

Knowledge distillation (KD) has shown potential for learning compact models in dense object detection. However, the commonly used softmax-based distillation ignores the absolute classification scores for individual categories. Thus, the optimum of the distillation loss does not necessarily lead to the optimal student classification scores for dense object detectors. This cross-task protocol inconsistency is critical, especially for dense object detectors, since the foreground categories are extremely imbalanced. To address the issue of protocol differences between distillation and classification, we propose a novel distillation method with cross-task consistent protocols, tailored for the dense object detection. For classification distillation, we address the cross-task protocol inconsistency problem by formulating the classification logit maps in both teacher and student models as multiple binary-classification maps and applying a binary-classification distillation loss to each map. For localization distillation, we design an IoU-based Localization Distillation Loss that is free from specific network structures and can be compared with existing localization distillation losses. Our proposed method is simple but effective, and experimental results demonstrate its superiority over existing methods. Code is available at https://github.com/TinyTigerPan/BCKD.

Identifying risky traders with high profits in financial markets is crucial for market makers, such as trading exchanges, to ensure effective risk management through real-time decisions on regulation compliance and hedging. However, capturing the complex and dynamic behaviours of individual traders poses significant challenges. Traditional classification and anomaly detection methods often establish a fixed risk boundary, failing to account for this complexity and dynamism. To tackle this issue, we propose a profit-aware risk ranker (PA-RiskRanker) that reframes the problem of identifying risky traders as a ranking task using Learning-to-Rank (LETOR) algorithms. Our approach features a Profit-Aware binary cross entropy (PA-BCE) loss function and a transformer-based ranker enhanced with a self-cross-trader attention pipeline. These components effectively integrate profit and loss (P&L) considerations into the training process while capturing intra- and inter-trader relationships. Our research critically examines the limitations of existing deep learning-based LETOR algorithms in trading risk management, which often overlook the importance of P&L in financial scenarios. By prioritising P&L, our method improves risky trader identification, achieving an 8.4% increase in F1 score compared to state-of-the-art (SOTA) ranking models like Rankformer. Additionally, it demonstrates a 10%-17% increase in average profit compared to all benchmark models.

Deep neural networks have demonstrated remarkable performance in supervised learning tasks but require large amounts of labeled data. Self-supervised learning offers an alternative paradigm, enabling the model to learn from data without explicit labels. Information theory has been instrumental in understanding and optimizing deep neural networks. Specifically, the information bottleneck principle has been applied to optimize the trade-off between compression and relevant information preservation in supervised settings. However, the optimal information objective in self-supervised learning remains unclear. In this paper, we review various approaches to self-supervised learning from an information-theoretic standpoint and present a unified framework that formalizes the self-supervised information-theoretic learning problem. We integrate existing research into a coherent framework, examine recent self-supervised methods, and identify research opportunities and challenges. Moreover, we discuss empirical measurement of information-theoretic quantities and their estimators. This paper offers a comprehensive review of the intersection between information theory, self-supervised learning, and deep neural networks.

Misinformation is a complex societal issue, and mitigating solutions are difficult to create due to data deficiencies. To address this problem, we have curated the largest collection of (mis)information datasets in the literature, totaling 75. From these, we evaluated the quality of all of the 36 datasets that consist of statements or claims. We assess these datasets to identify those with solid foundations for empirical work and those with flaws that could result in misleading and non-generalizable results, such as insufficient label quality, spurious correlations, or political bias. We further provide state-of-the-art baselines on all these datasets, but show that regardless of label quality, categorical labels may no longer give an accurate evaluation of detection model performance. We discuss alternatives to mitigate this problem. Overall, this guide aims to provide a roadmap for obtaining higher quality data and conducting more effective evaluations, ultimately improving research in misinformation detection. All datasets and other artifacts are available at https://misinfo-datasets.complexdatalab.com/.

This paper addresses the problem of formalizing and quantifying the concept of "intensional inheritance" between two concepts. We begin by conceiving the intensional inheritance of W from F as the amount of information the proposition "x is F " provides about the proposition "x is W. To flesh this out, we consider concepts F and W defined by sets of properties left{F_{1}, F_{2}, ldots, F_{n}right} and left{W_{1}, W_{2}, ldots, W_{m}right} with associated degrees left{d_{1}, d_{2}, ldots, d_{n}right} and left{e_{1}, e_{2}, ldots, e_{m}right}, respectively, where the properties may overlap. We then derive formulas for the intensional inheritance using both Shannon information theory and algorithmic information theory, incorporating interaction information among properties. We examine a special case where all properties are mutually exclusive and calculate the intensional inheritance in this case in both frameworks. We also derive expressions for P(W mid F) based on the mutual information formula. Finally we consider the relationship between intensional inheritance and conventional set-theoretic "extensional" inheritance, concluding that in our information-theoretic framework, extensional inheritance emerges as a special case of intensional inheritance.

Recognizing the prevalence of domain shift as a common challenge in machine learning, various domain generalization (DG) techniques have been developed to enhance the performance of machine learning systems when dealing with out-of-distribution (OOD) data. Furthermore, in real-world scenarios, data distributions can gradually change across a sequence of sequential domains. While current methodologies primarily focus on improving model effectiveness within these new domains, they often overlook fairness issues throughout the learning process. In response, we introduce an innovative framework called Counterfactual Fairness-Aware Domain Generalization with Sequential Autoencoder (CDSAE). This approach effectively separates environmental information and sensitive attributes from the embedded representation of classification features. This concurrent separation not only greatly improves model generalization across diverse and unfamiliar domains but also effectively addresses challenges related to unfair classification. Our strategy is rooted in the principles of causal inference to tackle these dual issues. To examine the intricate relationship between semantic information, sensitive attributes, and environmental cues, we systematically categorize exogenous uncertainty factors into four latent variables: 1) semantic information influenced by sensitive attributes, 2) semantic information unaffected by sensitive attributes, 3) environmental cues influenced by sensitive attributes, and 4) environmental cues unaffected by sensitive attributes. By incorporating fairness regularization, we exclusively employ semantic information for classification purposes. Empirical validation on synthetic and real-world datasets substantiates the effectiveness of our approach, demonstrating improved accuracy levels while ensuring the preservation of fairness in the evolving landscape of continuous domains.

Machine learning models are often personalized with information that is protected, sensitive, self-reported, or costly to acquire. These models use information about people but do not facilitate nor inform their consent. Individuals cannot opt out of reporting personal information to a model, nor tell if they benefit from personalization in the first place. We introduce a family of classification models, called participatory systems, that let individuals opt into personalization at prediction time. We present a model-agnostic algorithm to learn participatory systems for personalization with categorical group attributes. We conduct a comprehensive empirical study of participatory systems in clinical prediction tasks, benchmarking them with common approaches for personalization and imputation. Our results demonstrate that participatory systems can facilitate and inform consent while improving performance and data use across all groups who report personal data.

Model diffing is the study of how fine-tuning changes a model's representations and internal algorithms. Many behaviors of interest are introduced during fine-tuning, and model diffing offers a promising lens to interpret such behaviors. Crosscoders are a recent model diffing method that learns a shared dictionary of interpretable concepts represented as latent directions in both the base and fine-tuned models, allowing us to track how concepts shift or emerge during fine-tuning. Notably, prior work has observed concepts with no direction in the base model, and it was hypothesized that these model-specific latents were concepts introduced during fine-tuning. However, we identify two issues which stem from the crosscoders L1 training loss that can misattribute concepts as unique to the fine-tuned model, when they really exist in both models. We develop Latent Scaling to flag these issues by more accurately measuring each latent's presence across models. In experiments comparing Gemma 2 2B base and chat models, we observe that the standard crosscoder suffers heavily from these issues. Building on these insights, we train a crosscoder with BatchTopK loss and show that it substantially mitigates these issues, finding more genuinely chat-specific and highly interpretable concepts. We recommend practitioners adopt similar techniques. Using the BatchTopK crosscoder, we successfully identify a set of chat-specific latents that are both interpretable and causally effective, representing concepts such as false information and personal question, along with multiple refusal-related latents that show nuanced preferences for different refusal triggers. Overall, our work advances best practices for the crosscoder-based methodology for model diffing and demonstrates that it can provide concrete insights into how chat-tuning modifies model behavior.

Cross-modal metric learning is a prominent research topic that bridges the semantic heterogeneity between vision and language. Existing methods frequently utilize simple cosine or complex distance metrics to transform the pairwise features into a similarity score, which suffers from an inadequate or inefficient capability for distance measurements. Consequently, we propose a Generalized Structural Sparse Function to dynamically capture thorough and powerful relationships across modalities for pair-wise similarity learning while remaining concise but efficient. Specifically, the distance metric delicately encapsulates two formats of diagonal and block-diagonal terms, automatically distinguishing and highlighting the cross-channel relevancy and dependency inside a structured and organized topology. Hence, it thereby empowers itself to adapt to the optimal matching patterns between the paired features and reaches a sweet spot between model complexity and capability. Extensive experiments on cross-modal and two extra uni-modal retrieval tasks (image-text retrieval, person re-identification, fine-grained image retrieval) have validated its superiority and flexibility over various popular retrieval frameworks. More importantly, we further discover that it can be seamlessly incorporated into multiple application scenarios, and demonstrates promising prospects from Attention Mechanism to Knowledge Distillation in a plug-and-play manner. Our code is publicly available at: https://github.com/Paranioar/GSSF.

As the field of representation learning grows, there has been a proliferation of different loss functions to solve different classes of problems. We introduce a single information-theoretic equation that generalizes a large collection of modern loss functions in machine learning. In particular, we introduce a framework that shows that several broad classes of machine learning methods are precisely minimizing an integrated KL divergence between two conditional distributions: the supervisory and learned representations. This viewpoint exposes a hidden information geometry underlying clustering, spectral methods, dimensionality reduction, contrastive learning, and supervised learning. This framework enables the development of new loss functions by combining successful techniques from across the literature. We not only present a wide array of proofs, connecting over 23 different approaches, but we also leverage these theoretical results to create state-of-the-art unsupervised image classifiers that achieve a +8% improvement over the prior state-of-the-art on unsupervised classification on ImageNet-1K. We also demonstrate that I-Con can be used to derive principled debiasing methods which improve contrastive representation learners.

A central challenge in training classification models in the real-world federated system is learning with non-IID data. To cope with this, most of the existing works involve enforcing regularization in local optimization or improving the model aggregation scheme at the server. Other works also share public datasets or synthesized samples to supplement the training of under-represented classes or introduce a certain level of personalization. Though effective, they lack a deep understanding of how the data heterogeneity affects each layer of a deep classification model. In this paper, we bridge this gap by performing an experimental analysis of the representations learned by different layers. Our observations are surprising: (1) there exists a greater bias in the classifier than other layers, and (2) the classification performance can be significantly improved by post-calibrating the classifier after federated training. Motivated by the above findings, we propose a novel and simple algorithm called Classifier Calibration with Virtual Representations (CCVR), which adjusts the classifier using virtual representations sampled from an approximated gaussian mixture model. Experimental results demonstrate that CCVR achieves state-of-the-art performance on popular federated learning benchmarks including CIFAR-10, CIFAR-100, and CINIC-10. We hope that our simple yet effective method can shed some light on the future research of federated learning with non-IID data.

In "Backprop as functor", the authors show that the fundamental elements of deep learning -- gradient descent and backpropagation -- can be conceptualized as a strong monoidal functor Para(Euc)toLearn from the category of parameterized Euclidean spaces to that of learners, a category developed explicitly to capture parameter update and backpropagation. It was soon realized that there is an isomorphism LearncongPara(Slens), where Slens is the symmetric monoidal category of simple lenses as used in functional programming. In this note, we observe that Slens is a full subcategory of Poly, the category of polynomial functors in one variable, via the functor Amapsto Ay^A. Using the fact that (Poly,otimes) is monoidal closed, we show that a map Ato B in Para(Slens) has a natural interpretation in terms of dynamical systems (more precisely, generalized Moore machines) whose interface is the internal-hom type [Ay^A,By^B]. Finally, we review the fact that the category p-Coalg of dynamical systems on any p in Poly forms a topos, and consider the logical propositions that can be stated in its internal language. We give gradient descent as an example, and we conclude by discussing some directions for future work.

Generalized Category Discovery (GCD) is a pragmatic and challenging open-world task, which endeavors to cluster unlabeled samples from both novel and old classes, leveraging some labeled data of old classes. Given that knowledge learned from old classes is not fully transferable to new classes, and that novel categories are fully unlabeled, GCD inherently faces intractable problems, including imbalanced classification performance and inconsistent confidence between old and new classes, especially in the low-labeling regime. Hence, some annotations of new classes are deemed necessary. However, labeling new classes is extremely costly. To address this issue, we take the spirit of active learning and propose a new setting called Active Generalized Category Discovery (AGCD). The goal is to improve the performance of GCD by actively selecting a limited amount of valuable samples for labeling from the oracle. To solve this problem, we devise an adaptive sampling strategy, which jointly considers novelty, informativeness and diversity to adaptively select novel samples with proper uncertainty. However, owing to the varied orderings of label indices caused by the clustering of novel classes, the queried labels are not directly applicable to subsequent training. To overcome this issue, we further propose a stable label mapping algorithm that transforms ground truth labels to the label space of the classifier, thereby ensuring consistent training across different active selection stages. Our method achieves state-of-the-art performance on both generic and fine-grained datasets. Our code is available at https://github.com/mashijie1028/ActiveGCD