Daily Papers

Large Language Models (LLMs) have recently demonstrated strong potential in generating 'believable human-like' behavior in web environments. Prior work has explored augmenting training data with LLM-synthesized rationales and applying supervised fine-tuning (SFT) to enhance reasoning ability, which in turn can improve downstream action prediction. However, the performance of such approaches remains inherently bounded by the reasoning capabilities of the model used to generate the rationales. In this paper, we introduce Shop-R1, a novel reinforcement learning (RL) framework aimed at enhancing the reasoning ability of LLMs for simulation of real human behavior in online shopping environments Specifically, Shop-R1 decomposes the human behavior simulation task into two stages: rationale generation and action prediction, each guided by distinct reward signals. For rationale generation, we leverage internal model signals (e.g., logit distributions) to guide the reasoning process in a self-supervised manner. For action prediction, we propose a hierarchical reward structure with difficulty-aware scaling to prevent reward hacking and enable fine-grained reward assignment. This design evaluates both high-level action types and the correctness of fine-grained sub-action details (attributes and values), rewarding outputs proportionally to their difficulty. Experimental results show that our method achieves a relative improvement of over 65% compared to the baseline.

Recent Graphical User Interface (GUI) agents replicate the R1-Zero paradigm, coupling online Reinforcement Learning (RL) with explicit chain-of-thought reasoning prior to object grounding and thereby achieving substantial performance gains. In this paper, we first conduct extensive analysis experiments of three key components of that training pipeline: input design, output evaluation, and policy update-each revealing distinct challenges arising from blindly applying general-purpose RL without adapting to GUI grounding tasks. Input design: Current templates encourage the model to generate chain-of-thought reasoning, but longer chains unexpectedly lead to worse grounding performance. Output evaluation: Reward functions based on hit signals or box area allow models to exploit box size, leading to reward hacking and poor localization quality. Policy update: Online RL tends to overfit easy examples due to biases in length and sample difficulty, leading to under-optimization on harder cases. To address these issues, we propose three targeted solutions. First, we adopt a Fast Thinking Template that encourages direct answer generation, reducing excessive reasoning during training. Second, we incorporate a box size constraint into the reward function to mitigate reward hacking. Third, we revise the RL objective by adjusting length normalization and adding a difficulty-aware scaling factor, enabling better optimization on hard samples. Our GUI-G1-3B, trained on 17K public samples with Qwen2.5-VL-3B-Instruct, achieves 90.3% accuracy on ScreenSpot and 37.1% on ScreenSpot-Pro. This surpasses all prior models of similar size and even outperforms the larger UI-TARS-7B, establishing a new state-of-the-art in GUI agent grounding. The project repository is available at https://github.com/Yuqi-Zhou/GUI-G1.

On-device training enables the model to adapt to new data collected from the sensors by fine-tuning a pre-trained model. Users can benefit from customized AI models without having to transfer the data to the cloud, protecting the privacy. However, the training memory consumption is prohibitive for IoT devices that have tiny memory resources. We propose an algorithm-system co-design framework to make on-device training possible with only 256KB of memory. On-device training faces two unique challenges: (1) the quantized graphs of neural networks are hard to optimize due to low bit-precision and the lack of normalization; (2) the limited hardware resource does not allow full back-propagation. To cope with the optimization difficulty, we propose Quantization-Aware Scaling to calibrate the gradient scales and stabilize 8-bit quantized training. To reduce the memory footprint, we propose Sparse Update to skip the gradient computation of less important layers and sub-tensors. The algorithm innovation is implemented by a lightweight training system, Tiny Training Engine, which prunes the backward computation graph to support sparse updates and offload the runtime auto-differentiation to compile time. Our framework is the first solution to enable tiny on-device training of convolutional neural networks under 256KB SRAM and 1MB Flash without auxiliary memory, using less than 1/1000 of the memory of PyTorch and TensorFlow while matching the accuracy on tinyML application VWW. Our study enables IoT devices not only to perform inference but also to continuously adapt to new data for on-device lifelong learning. A video demo can be found here: https://youtu.be/XaDCO8YtmBw.

Large language models exhibit a puzzling inconsistency: they solve complex problems yet frequently fail on seemingly simpler ones. We investigate whether LLMs internally encode problem difficulty in a way that aligns with human judgment, and whether this representation tracks generalization during reinforcement learning post-training. We train linear probes across layers and token positions on 60 models, evaluating on mathematical and coding subsets of Easy2HardBench. We find that human-labeled difficulty is strongly linearly decodable (AMC: rho approx 0.88) and exhibits clear model-size scaling, whereas LLM-derived difficulty is substantially weaker and scales poorly. Steering along the difficulty direction reveals that pushing models toward "easier" representations reduces hallucination and improves accuracy. During GRPO training on Qwen2.5-Math-1.5B, the human-difficulty probe strengthens and positively correlates with test accuracy across training steps, while the LLM-difficulty probe degrades and negatively correlates with performance. These results suggest that human annotations provide a stable difficulty signal that RL amplifies, while automated difficulty estimates derived from model performance become misaligned precisely as models improve. We release probe code and evaluation scripts to facilitate replication.

Widely observed neural scaling laws, in which error falls off as a power of the training set size, model size, or both, have driven substantial performance improvements in deep learning. However, these improvements through scaling alone require considerable costs in compute and energy. Here we focus on the scaling of error with dataset size and show how in theory we can break beyond power law scaling and potentially even reduce it to exponential scaling instead if we have access to a high-quality data pruning metric that ranks the order in which training examples should be discarded to achieve any pruned dataset size. We then test this improved scaling prediction with pruned dataset size empirically, and indeed observe better than power law scaling in practice on ResNets trained on CIFAR-10, SVHN, and ImageNet. Next, given the importance of finding high-quality pruning metrics, we perform the first large-scale benchmarking study of ten different data pruning metrics on ImageNet. We find most existing high performing metrics scale poorly to ImageNet, while the best are computationally intensive and require labels for every image. We therefore developed a new simple, cheap and scalable self-supervised pruning metric that demonstrates comparable performance to the best supervised metrics. Overall, our work suggests that the discovery of good data-pruning metrics may provide a viable path forward to substantially improved neural scaling laws, thereby reducing the resource costs of modern deep learning.

The current trend of scaling language models involves increasing both parameter count and training dataset size. Extrapolating this trend suggests that training dataset size may soon be limited by the amount of text data available on the internet. Motivated by this limit, we investigate scaling language models in data-constrained regimes. Specifically, we run a large set of experiments varying the extent of data repetition and compute budget, ranging up to 900 billion training tokens and 9 billion parameter models. We find that with constrained data for a fixed compute budget, training with up to 4 epochs of repeated data yields negligible changes to loss compared to having unique data. However, with more repetition, the value of adding compute eventually decays to zero. We propose and empirically validate a scaling law for compute optimality that accounts for the decreasing value of repeated tokens and excess parameters. Finally, we experiment with approaches mitigating data scarcity, including augmenting the training dataset with code data or removing commonly used filters. Models and datasets from our 400 training runs are publicly available at https://github.com/huggingface/datablations.

Large Reasoning Models (LRMs) have shown impressive capabilities in complex problem-solving, often benefiting from training on difficult mathematical problems that stimulate intricate reasoning. Recent efforts have explored automated synthesis of mathematical problems by prompting proprietary models or large-scale open-source models from seed data or inherent mathematical concepts. However, scaling up these methods remains challenging due to their high computational/API cost, complexity of prompting, and limited difficulty level of the generated problems. To overcome these limitations, we propose ScaleDiff, a simple yet effective pipeline designed to scale the creation of difficult problems. We efficiently identify difficult problems from existing datasets with only a single forward pass using an adaptive thinking model, which can perceive problem difficulty and automatically switch between "Thinking" and "NoThinking" modes. We then train a specialized difficult problem generator (DiffGen-8B) on this filtered difficult data, which can produce new difficult problems in large scale, eliminating the need for complex, per-instance prompting and its associated high API costs. Fine-tuning Qwen2.5-Math-7B-Instruct on the ScaleDiff-Math dataset yields a substantial performance increase of 11.3% compared to the original dataset and achieves a 65.9% average accuracy on AIME'24, AIME'25, HMMT-Feb'25, BRUMO'25, and MATH500, outperforming recent strong LRMs like OpenThinker3. Notably, this performance is achieved using the cost-efficient Qwen3-8B model as a teacher, demonstrating that our pipeline can effectively transfer advanced reasoning capabilities without relying on larger, more expensive teacher models. Furthermore, we observe a clear scaling phenomenon in model performance on difficult benchmarks as the quantity of difficult problems increases. Code: https://github.com/QizhiPei/ScaleDiff.

Scaling up language models has been empirically shown to improve performance on a wide range of downstream tasks. However, if we were to observe worse performance as a function of scale ("inverse scaling") on certain tasks, this would indicate that scaling can also encourage behaviors that are misaligned with human preferences. The Inverse Scaling Prize (McKenzie et al. 2022) identified eleven such inverse scaling tasks, evaluated on models of up to 280B parameters and up to 500 zettaFLOPs of training compute. This paper takes a closer look at these inverse scaling tasks. We evaluate models of up to 540B parameters, trained on five times more compute than those evaluated in the Inverse Scaling Prize. With this increased range of model sizes and training compute, only four out of the eleven tasks remain inverse scaling. Six out of the eleven tasks exhibit "U-shaped scaling", where performance decreases up to a certain size, and then increases again up to the largest model evaluated (the one remaining task displays positive scaling). In addition, we find that 1-shot examples and chain-of-thought can help mitigate undesirable scaling patterns even further. U-shaped scaling suggests that the inverse scaling trend observed in McKenzie et al. (2022) may not continue to hold for larger models, which we attribute to the presence of distractor tasks that only sufficiently large models can avoid.

While generalization over tasks from easy to hard is crucial to profile language models (LLMs), the datasets with fine-grained difficulty annotations for each problem across a broad range of complexity are still blank. Aiming to address this limitation, we present Easy2Hard-Bench, a consistently formatted collection of 6 benchmark datasets spanning various domains, such as mathematics and programming problems, chess puzzles, and reasoning questions. Each problem within these datasets is annotated with numerical difficulty scores. To systematically estimate problem difficulties, we collect abundant performance data on attempts to each problem by humans in the real world or LLMs on the prominent leaderboard. Leveraging the rich performance data, we apply well-established difficulty ranking systems, such as Item Response Theory (IRT) and Glicko-2 models, to uniformly assign numerical difficulty scores to problems. Moreover, datasets in Easy2Hard-Bench distinguish themselves from previous collections by a higher proportion of challenging problems. Through extensive experiments with six state-of-the-art LLMs, we provide a comprehensive analysis of their performance and generalization capabilities across varying levels of difficulty, with the aim of inspiring future research in LLM generalization. The datasets are available at https://huggingface.co/datasets/furonghuang-lab/Easy2Hard-Bench.

Recent work has identified simple empirical scaling laws for language models, linking compute budget, dataset size, model size, and autoregressive modeling loss. The validity of these simple power laws across orders of magnitude in model scale provides compelling evidence that larger models are also more capable models. However, scaling up models under the constraints of hardware and infrastructure is no easy feat, and rapidly becomes a hard and expensive engineering problem. We investigate ways to tentatively cheat scaling laws, and train larger models for cheaper. We emulate an increase in effective parameters, using efficient approximations: either by doping the models with frozen random parameters, or by using fast structured transforms in place of dense linear layers. We find that the scaling relationship between test loss and compute depends only on the actual number of trainable parameters; scaling laws cannot be deceived by spurious parameters.

Language models have been shown to exhibit positive scaling, where performance improves as models are scaled up in terms of size, compute, or data. In this work, we introduce NeQA, a dataset consisting of questions with negation in which language models do not exhibit straightforward positive scaling. We show that this task can exhibit inverse scaling, U-shaped scaling, or positive scaling, and the three scaling trends shift in this order as we use more powerful prompting methods or model families. We hypothesize that solving NeQA depends on two subtasks: question answering (task 1) and negation understanding (task 2). We find that task 1 has linear scaling, while task 2 has sigmoid-shaped scaling with an emergent transition point, and composing these two scaling trends yields the final scaling trend of NeQA. Our work reveals and provides a way to analyze the complex scaling trends of language models.

Work on scaling laws has found that large language models (LMs) show predictable improvements to overall loss with increased scale (model size, training data, and compute). Here, we present evidence for the claim that LMs may show inverse scaling, or worse task performance with increased scale, e.g., due to flaws in the training objective and data. We present empirical evidence of inverse scaling on 11 datasets collected by running a public contest, the Inverse Scaling Prize, with a substantial prize pool. Through analysis of the datasets, along with other examples found in the literature, we identify four potential causes of inverse scaling: (i) preference to repeat memorized sequences over following in-context instructions, (ii) imitation of undesirable patterns in the training data, (iii) tasks containing an easy distractor task which LMs could focus on, rather than the harder real task, and (iv) correct but misleading few-shot demonstrations of the task. We release the winning datasets at https://inversescaling.com/data to allow for further investigation of inverse scaling. Our tasks have helped drive the discovery of U-shaped and inverted-U scaling trends, where an initial trend reverses, suggesting that scaling trends are less reliable at predicting the behavior of larger-scale models than previously understood. Overall, our results suggest that there are tasks for which increased model scale alone may not lead to progress, and that more careful thought needs to go into the data and objectives for training language models.

Estimating the difficulty of input questions as perceived by large language models (LLMs) is essential for accurate performance evaluation and adaptive inference. Existing methods typically rely on repeated response sampling, auxiliary models, or fine-tuning the target model itself, which may incur substantial computational costs or compromise generality. In this paper, we propose a novel approach for difficulty estimation that leverages only the hidden representations produced by the target LLM. We model the token-level generation process as a Markov chain and define a value function to estimate the expected output quality given any hidden state. This allows for efficient and accurate difficulty estimation based solely on the initial hidden state, without generating any output tokens. Extensive experiments across both textual and multimodal tasks demonstrate that our method consistently outperforms existing baselines in difficulty estimation. Moreover, we apply our difficulty estimates to guide adaptive reasoning strategies, including Self-Consistency, Best-of-N, and Self-Refine, achieving higher inference efficiency with fewer generated tokens.

Chain-of-thought reasoning, while powerful, can produce unnecessarily verbose output for simpler problems. We present a framework for difficulty-aware reasoning that teaches models to dynamically adjust reasoning depth based on problem complexity. Remarkably, we show that models can be endowed with such dynamic inference pathways without any architectural modifications; we simply post-train on data that is carefully curated to include chain-of-thought traces that are proportional in length to problem difficulty. Our analysis reveals that post-training via supervised fine-tuning (SFT) primarily captures patterns like reasoning length and format, while direct preference optimization (DPO) preserves reasoning accuracy, with their combination reducing length and maintaining or improving performance. Both quantitative metrics and qualitative assessments confirm that models can learn to "think proportionally", reasoning minimally on simple problems while maintaining depth for complex ones.

The measure of a machine learning algorithm is the difficulty of the tasks it can perform, and sufficiently difficult tasks are critical drivers of strong machine learning models. However, quantifying the generalization difficulty of machine learning benchmarks has remained challenging. We propose what is to our knowledge the first model-agnostic measure of the inherent generalization difficulty of tasks. Our inductive bias complexity measure quantifies the total information required to generalize well on a task minus the information provided by the data. It does so by measuring the fractional volume occupied by hypotheses that generalize on a task given that they fit the training data. It scales exponentially with the intrinsic dimensionality of the space over which the model must generalize but only polynomially in resolution per dimension, showing that tasks which require generalizing over many dimensions are drastically more difficult than tasks involving more detail in fewer dimensions. Our measure can be applied to compute and compare supervised learning, reinforcement learning and meta-learning generalization difficulties against each other. We show that applied empirically, it formally quantifies intuitively expected trends, e.g. that in terms of required inductive bias, MNIST < CIFAR10 < Imagenet and fully observable Markov decision processes (MDPs) < partially observable MDPs. Further, we show that classification of complex images < few-shot meta-learning with simple images. Our measure provides a quantitative metric to guide the construction of more complex tasks requiring greater inductive bias, and thereby encourages the development of more sophisticated architectures and learning algorithms with more powerful generalization capabilities.

The scientific scale-up of large language models (LLMs) necessitates a comprehensive understanding of their scaling properties. However, the existing literature on the scaling properties only yields an incomplete answer: optimization loss decreases predictably as the model size increases, in line with established scaling law; yet no scaling law for task has been established and the task performances are far from predictable during scaling. Task performances typically show minor gains on small models until they improve dramatically once models exceed a size threshold, exemplifying the ``emergent abilities''. In this study, we discover that small models, although they exhibit minor performance, demonstrate critical and consistent task performance improvements that are not captured by conventional evaluation strategies due to insufficient measurement resolution. To measure such improvements, we introduce PassUntil, an evaluation strategy through massive sampling in the decoding phase. We conduct quantitative investigations into the scaling law of task performance. Firstly, a strict task scaling law is identified, enhancing the predictability of task performances. Remarkably, we are able to predict the performance of the 2.4B model on code generation with merely 0.05\% deviation before training starts. Secondly, underpinned by PassUntil, we observe concrete evidence of emergent abilities and ascertain that they are not in conflict with the continuity of performance improvement. Their semblance to break-through is that their scaling curve cannot be fitted by standard scaling law function. We then introduce a mathematical definition for the emergent abilities. Through the definition, we refute a prevalent ``multi-step reasoning hypothesis'' regarding the genesis of emergent abilities and propose a new hypothesis with a satisfying fit to the observed scaling curve.

The ever-growing ecosystem of LLMs has posed a challenge in selecting the most appropriate pre-trained model to fine-tune amidst a sea of options. Given constrained resources, fine-tuning all models and making selections afterward is unrealistic. In this work, we formulate this resource-constrained selection task into predicting fine-tuning performance and illustrate its natural connection with scaling laws. Unlike pre-training, We find that the fine-tuning scaling curve includes not just the well-known "power phase" but also the previously unobserved "pre-power phase". We also explain why existing scaling laws fail to capture this phase transition phenomenon both theoretically and empirically. To address this, we introduce the concept of "pre-learned data size" into our rectified scaling law, which overcomes theoretical limitations and fits experimental results much better. By leveraging our law, we propose a novel LLM selection algorithm that selects the near-optimal model with hundreds of times less resource consumption, while other methods may provide negatively correlated selection.

Understanding how language model performance varies with scale is critical to benchmark and algorithm development. Scaling laws are one approach to building this understanding, but the requirement of training models across many different scales has limited their use. We propose an alternative, observational approach that bypasses model training and instead builds scaling laws from ~80 publically available models. Building a single scaling law from multiple model families is challenging due to large variations in their training compute efficiencies and capabilities. However, we show that these variations are consistent with a simple, generalized scaling law where language model performance is a function of a low-dimensional capability space, and model families only vary in their efficiency in converting training compute to capabilities. Using this approach, we show the surprising predictability of complex scaling phenomena: we show that several emergent phenomena follow a smooth, sigmoidal behavior and are predictable from small models; we show that the agent performance of models such as GPT-4 can be precisely predicted from simpler non-agentic benchmarks; and we show how to predict the impact of post-training interventions like Chain-of-Thought and Self-Consistency as language model capabilities continue to improve.

The interest in linear complexity models for large language models is on the rise, although their scaling capacity remains uncertain. In this study, we present the scaling laws for linear complexity language models to establish a foundation for their scalability. Specifically, we examine the scaling behaviors of three efficient linear architectures. These include TNL, a linear attention model with data-independent decay; HGRN2, a linear RNN with data-dependent decay; and cosFormer2, a linear attention model without decay. We also include LLaMA as a baseline architecture for softmax attention for comparison. These models were trained with six variants, ranging from 70M to 7B parameters on a 300B-token corpus, and evaluated with a total of 1,376 intermediate checkpoints on various downstream tasks. These tasks include validation loss, commonsense reasoning, and information retrieval and generation. The study reveals that existing linear complexity language models exhibit similar scaling capabilities as conventional transformer-based models while also demonstrating superior linguistic proficiency and knowledge retention.

As language models scale up, it becomes increasingly expensive to verify research ideas because conclusions on small models do not trivially transfer to large ones. A possible solution is to establish a generic system that directly predicts some metrics for large models solely based on the results and hyperparameters from small models. Existing methods based on scaling laws require hyperparameter search on the largest models, which is impractical with limited resources. We address this issue by presenting our discoveries indicating that Maximal Update parametrization (Mup) enables accurate fitting of scaling laws for hyperparameters close to common loss basins, without any search. Thus, different models can be directly compared on large scales with loss prediction even before the training starts. We propose a new paradigm as a first step towards reliable academic research for any model scale without heavy computation. Code is publicly available at https://github.com/cofe-ai/Mu-scaling.

Over the past few years, the size of language models has grown exponentially, as has the computational cost to train these large models. This rapid growth has motivated researchers to develop new techniques aimed at enhancing the efficiency of the training process. Despite these advancements, optimally predicting the model size or allocating optimal resources remains a challenge. Several efforts have addressed the challenge by proposing different scaling laws, but almost all of them are architecture-specific (dense or sparse). In this work we revisit existing scaling laws and propose a generalized scaling law to provide a unified framework that is applicable to both dense and sparse large language models. We evaluate and compare our proposed scaling law with existing scaling laws to demonstrate its effectiveness.

The rapid advancements in computing dramatically increase the scale and cost of training Large Language Models (LLMs). Accurately predicting downstream task performance prior to model training is crucial for efficient resource allocation, yet remains challenging due to two primary constraints: (1) the "emergence phenomenon", wherein downstream performance metrics become meaningful only after extensive training, which limits the ability to use smaller models for prediction; (2) Uneven task difficulty distributions and the absence of consistent scaling laws, resulting in substantial metric variability. Existing performance prediction methods suffer from limited accuracy and reliability, thereby impeding the assessment of potential LLM capabilities. To address these challenges, we propose a Clustering-On-Difficulty (COD) downstream performance prediction framework. COD first constructs a predictable support subset by clustering tasks based on difficulty features, strategically excluding non-emergent and non-scalable clusters. The scores on the selected subset serve as effective intermediate predictors of downstream performance on the full evaluation set. With theoretical support, we derive a mapping function that transforms performance metrics from the predictable subset to the full evaluation set, thereby ensuring accurate extrapolation of LLM downstream performance. The proposed method has been applied to predict performance scaling for a 70B LLM, providing actionable insights for training resource allocation and assisting in monitoring the training process. Notably, COD achieves remarkable predictive accuracy on the 70B LLM by leveraging an ensemble of small models, demonstrating an absolute mean deviation of 1.36% across eight important LLM evaluation benchmarks.

The performance of a language model has been shown to be effectively modeled as a power-law in its parameter count. Here we study the scaling behaviors of Routing Networks: architectures that conditionally use only a subset of their parameters while processing an input. For these models, parameter count and computational requirement form two independent axes along which an increase leads to better performance. In this work we derive and justify scaling laws defined on these two variables which generalize those known for standard language models and describe the performance of a wide range of routing architectures trained via three different techniques. Afterwards we provide two applications of these laws: first deriving an Effective Parameter Count along which all models scale at the same rate, and then using the scaling coefficients to give a quantitative comparison of the three routing techniques considered. Our analysis derives from an extensive evaluation of Routing Networks across five orders of magnitude of size, including models with hundreds of experts and hundreds of billions of parameters.

Reinforcement learning (RL) has become central to training large language models (LLMs), yet the field lacks predictive scaling methodologies comparable to those established for pre-training. Despite rapidly rising compute budgets, there is no principled understanding of how to evaluate algorithmic improvements for scaling RL compute. We present the first large-scale systematic study, amounting to more than 400,000 GPU-hours, that defines a principled framework for analyzing and predicting RL scaling in LLMs. We fit sigmoidal compute-performance curves for RL training and ablate a wide range of common design choices to analyze their effects on asymptotic performance and compute efficiency. We observe: (1) Not all recipes yield similar asymptotic performance, (2) Details such as loss aggregation, normalization, curriculum, and off-policy algorithm primarily modulate compute efficiency without materially shifting the asymptote, and (3) Stable, scalable recipes follow predictable scaling trajectories, enabling extrapolation from smaller-scale runs. Combining these insights, we propose a best-practice recipe, ScaleRL, and demonstrate its effectiveness by successfully scaling and predicting validation performance on a single RL run scaled up to 100,000 GPU-hours. Our work provides both a scientific framework for analyzing scaling in RL and a practical recipe that brings RL training closer to the predictability long achieved in pre-training.

A major challenge for scaling machine learning is training models to perform tasks that are very difficult or time-consuming for humans to evaluate. We present progress on this problem on the task of abstractive summarization of entire fiction novels. Our method combines learning from human feedback with recursive task decomposition: we use models trained on smaller parts of the task to assist humans in giving feedback on the broader task. We collect a large volume of demonstrations and comparisons from human labelers, and fine-tune GPT-3 using behavioral cloning and reward modeling to do summarization recursively. At inference time, the model first summarizes small sections of the book and then recursively summarizes these summaries to produce a summary of the entire book. Our human labelers are able to supervise and evaluate the models quickly, despite not having read the entire books themselves. Our resulting model generates sensible summaries of entire books, even matching the quality of human-written summaries in a few cases (sim5% of books). We achieve state-of-the-art results on the recent BookSum dataset for book-length summarization. A zero-shot question-answering model using these summaries achieves state-of-the-art results on the challenging NarrativeQA benchmark for answering questions about books and movie scripts. We release datasets of samples from our model.

As the field progresses toward Artificial General Intelligence (AGI), there is a pressing need for more comprehensive and insightful evaluation frameworks that go beyond aggregate performance metrics. This paper introduces a unified rating system that jointly models the difficulty of individual test cases and the competency of AI models (or humans) across vision, language, and action domains. Unlike existing metrics that focus solely on models, our approach allows for fine-grained, difficulty-aware evaluations through competitive interactions between models and tasks, capturing both the long-tail distribution of real-world challenges and the competency gap between current models and full task mastery. We validate the generalizability and robustness of our system through extensive experiments on multiple established datasets and models across distinct AGI domains. The resulting rating distributions offer novel perspectives and interpretable insights into task difficulty, model progression, and the outstanding challenges that remain on the path to achieving full AGI task mastery.

Scaling laws play an instrumental role in the sustainable improvement in model quality. Unfortunately, recommendation models to date do not exhibit such laws similar to those observed in the domain of large language models, due to the inefficiencies of their upscaling mechanisms. This limitation poses significant challenges in adapting these models to increasingly more complex real-world datasets. In this paper, we propose an effective network architecture based purely on stacked factorization machines, and a synergistic upscaling strategy, collectively dubbed Wukong, to establish a scaling law in the domain of recommendation. Wukong's unique design makes it possible to capture diverse, any-order of interactions simply through taller and wider layers. We conducted extensive evaluations on six public datasets, and our results demonstrate that Wukong consistently outperforms state-of-the-art models quality-wise. Further, we assessed Wukong's scalability on an internal, large-scale dataset. The results show that Wukong retains its superiority in quality over state-of-the-art models, while holding the scaling law across two orders of magnitude in model complexity, extending beyond 100 Gflop or equivalently up to GPT-3/LLaMa-2 scale of total training compute, where prior arts fall short.

We rethink test-time scaling laws from a practical efficiency perspective, revealing that the effectiveness of smaller models is significantly overestimated. Prior work, grounded in compute-optimality, overlooks critical memory access bottlenecks introduced by inference-time strategies (e.g., Best-of-N, long CoTs). Our holistic analysis, spanning models from 0.6B to 32B parameters, reveals a new Kinetics Scaling Law that better guides resource allocation by incorporating both computation and memory access costs. Kinetics Scaling Law suggests that test-time compute is more effective when used on models above a threshold than smaller ones. A key reason is that in TTS, attention, rather than parameter count, emerges as the dominant cost factor. Motivated by this, we propose a new scaling paradigm centered on sparse attention, which lowers per-token cost and enables longer generations and more parallel samples within the same resource budget. Empirically, we show that sparse attention models consistently outperform dense counterparts, achieving over 60 points gains in low-cost regimes and over 5 points gains in high-cost regimes for problem-solving accuracy on AIME, encompassing evaluations on state-of-the-art MoEs. These results suggest that sparse attention is essential for realizing the full potential of test-time scaling because, unlike training, where parameter scaling saturates, test-time accuracy continues to improve through increased generation. The code is available at https://github.com/Infini-AI-Lab/Kinetics.

Pretraining large language models (LLMs) is resource-intensive, often requiring months of training time even with high-end GPU clusters. There are two approaches of mitigating such computational demands: reusing smaller models to train larger ones (upcycling), and training computationally efficient models like mixture-of-experts (MoE). In this paper, we study the upcycling of LLMs to MoE models, of which the scaling behavior remains underexplored. Through extensive experiments, we identify empirical scaling laws that describe how performance depends on dataset size and model configuration. Particularly, we show that, while scaling these factors improves performance, there is a novel interaction term between the dense and upcycled training dataset that limits the efficiency of upcycling at large computational budgets. Based on these findings, we provide guidance to scale upcycling, and establish conditions under which upcycling outperforms from-scratch trainings within budget constraints.

The impressive capabilities of Large Language Models (LLMs) across diverse tasks are now well-established, yet their effective deployment necessitates careful hyperparameter optimization. Through extensive empirical studies involving grid searches across diverse configurations, we discover universal scaling laws governing these hyperparameters: optimal learning rate follows a power-law relationship with both model parameters and data sizes, while optimal batch size scales primarily with data sizes. Our analysis reveals a convex optimization landscape for hyperparameters under fixed models and data size conditions. This convexity implies an optimal hyperparameter plateau. We contribute a universal, plug-and-play optimal hyperparameter tool for the community. Its estimated values on the test set are merely 0.07\% away from the globally optimal LLM performance found via an exhaustive search. These laws demonstrate remarkable robustness across variations in model sparsity, training data distribution, and model shape. To our best known, this is the first work that unifies different model shapes and structures, such as Mixture-of-Experts models and dense transformers, as well as establishes optimal hyperparameter scaling laws across diverse data distributions. This exhaustive optimization process demands substantial computational resources, utilizing nearly one million NVIDIA H800 GPU hours to train 3,700 LLMs of varying sizes and hyperparameters from scratch and consuming approximately 100 trillion tokens in total. To facilitate reproducibility and further research, we will progressively release all loss measurements and model checkpoints through our designated repository https://step-law.github.io/

In-context learning (ICL) is a new learning paradigm that has gained popularity along with the development of large language models. In this work, we adapt a recently proposed hardness metric, pointwise V-usable information (PVI), to an in-context version (in-context PVI). Compared to the original PVI, in-context PVI is more efficient in that it requires only a few exemplars and does not require fine-tuning. We conducted a comprehensive empirical analysis to evaluate the reliability of in-context PVI. Our findings indicate that in-context PVI estimates exhibit similar characteristics to the original PVI. Specific to the in-context setting, we show that in-context PVI estimates remain consistent across different exemplar selections and numbers of shots. The variance of in-context PVI estimates across different exemplar selections is insignificant, which suggests that in-context PVI are stable. Furthermore, we demonstrate how in-context PVI can be employed to identify challenging instances. Our work highlights the potential of in-context PVI and provides new insights into the capabilities of ICL.

In the realm of deep learning-based recommendation systems, the increasing computational demands, driven by the growing number of users and items, pose a significant challenge to practical deployment. This challenge is primarily twofold: reducing the model size while effectively learning user and item representations for efficient recommendations. Despite considerable advancements in model compression and architecture search, prevalent approaches face notable constraints. These include substantial additional computational costs from pre-training/re-training in model compression and an extensive search space in architecture design. Additionally, managing complexity and adhering to memory constraints is problematic, especially in scenarios with strict time or space limitations. Addressing these issues, this paper introduces a novel learning paradigm, Dynamic Sparse Learning (DSL), tailored for recommendation models. DSL innovatively trains a lightweight sparse model from scratch, periodically evaluating and dynamically adjusting each weight's significance and the model's sparsity distribution during the training. This approach ensures a consistent and minimal parameter budget throughout the full learning lifecycle, paving the way for "end-to-end" efficiency from training to inference. Our extensive experimental results underline DSL's effectiveness, significantly reducing training and inference costs while delivering comparable recommendation performance.

Estimating the difficulty of a dataset typically involves comparing state-of-the-art models to humans; the bigger the performance gap, the harder the dataset is said to be. However, this comparison provides little understanding of how difficult each instance in a given distribution is, or what attributes make the dataset difficult for a given model. To address these questions, we frame dataset difficulty -- w.r.t. a model V -- as the lack of V-usable information (Xu et al., 2019), where a lower value indicates a more difficult dataset for V. We further introduce pointwise \mathcal{V-information} (PVI) for measuring the difficulty of individual instances w.r.t. a given distribution. While standard evaluation metrics typically only compare different models for the same dataset, V-usable information and PVI also permit the converse: for a given model V, we can compare different datasets, as well as different instances/slices of the same dataset. Furthermore, our framework allows for the interpretability of different input attributes via transformations of the input, which we use to discover annotation artefacts in widely-used NLP benchmarks.

Reasoning models have demonstrated impressive performance on difficult tasks that traditional language models struggle at. However, many are plagued with the problem of overthinking--generating large amounts of unnecessary tokens which don't improve accuracy on a question. We introduce approximate measures of problem-level difficulty and demonstrate that a clear relationship between problem difficulty and optimal token spend exists, and evaluate how well calibrated a variety of reasoning models are in terms of efficiently allocating the optimal token count. We find that in general, reasoning models are poorly calibrated, particularly on easy problems. To evaluate calibration on easy questions we introduce DUMB500, a dataset of extremely easy math, reasoning, code, and task problems, and jointly evaluate reasoning model on these simple examples and extremely difficult examples from existing frontier benchmarks on the same task domain. Finally, we introduce THOUGHTTERMINATOR, a training-free black box decoding technique that significantly improves reasoning model calibration.

Attention layers, as commonly used in transformers, form the backbone of modern deep learning, yet there is no mathematical description of their benefits and deficiencies as compared with other architectures. In this work we establish both positive and negative results on the representation power of attention layers, with a focus on intrinsic complexity parameters such as width, depth, and embedding dimension. On the positive side, we present a sparse averaging task, where recurrent networks and feedforward networks all have complexity scaling polynomially in the input size, whereas transformers scale merely logarithmically in the input size; furthermore, we use the same construction to show the necessity and role of a large embedding dimension in a transformer. On the negative side, we present a triple detection task, where attention layers in turn have complexity scaling linearly in the input size; as this scenario seems rare in practice, we also present natural variants that can be efficiently solved by attention layers. The proof techniques emphasize the value of communication complexity in the analysis of transformers and related models, and the role of sparse averaging as a prototypical attention task, which even finds use in the analysis of triple detection.

Neural network scaling has been critical for improving the model quality in many real-world machine learning applications with vast amounts of training data and compute. Although this trend of scaling is affirmed to be a sure-fire approach for better model quality, there are challenges on the path such as the computation cost, ease of programming, and efficient implementation on parallel devices. GShard is a module composed of a set of lightweight annotation APIs and an extension to the XLA compiler. It provides an elegant way to express a wide range of parallel computation patterns with minimal changes to the existing model code. GShard enabled us to scale up multilingual neural machine translation Transformer model with Sparsely-Gated Mixture-of-Experts beyond 600 billion parameters using automatic sharding. We demonstrate that such a giant model can efficiently be trained on 2048 TPU v3 accelerators in 4 days to achieve far superior quality for translation from 100 languages to English compared to the prior art.

We revisit test-time scaling for language model reasoning and ask a fundamental question: at equal token budget and compute, is it better to run multiple independent chains in parallel, or to run fewer chains that iteratively refine through sequential steps? Through comprehensive evaluation across 5 state-of-the-art open source models and 3 challenging reasoning benchmarks, we find that sequential scaling where chains explicitly build upon previous attempts consistently outperforms the dominant parallel self-consistency paradigm in 95.6% of configurations with gains in accuracy upto 46.7%. Further, we introduce inverse-entropy weighted voting, a novel training-free method to further boost the accuracy of sequential scaling. By weighing answers in proportion to the inverse entropy of their reasoning chains, we increase our success rate over parallel majority and establish it as the optimal test-time scaling strategy. Our findings fundamentally challenge the parallel reasoning orthodoxy that has dominated test-time scaling since Wang et al.'s self-consistency decoding (Wang et al., 2022), positioning sequential refinement as the robust default for modern LLM reasoning and necessitating a paradigm shift in how we approach inference-time optimization.

We present a new approach for the approximate K-nearest neighbor search based on navigable small world graphs with controllable hierarchy (Hierarchical NSW, HNSW). The proposed solution is fully graph-based, without any need for additional search structures, which are typically used at the coarse search stage of the most proximity graph techniques. Hierarchical NSW incrementally builds a multi-layer structure consisting from hierarchical set of proximity graphs (layers) for nested subsets of the stored elements. The maximum layer in which an element is present is selected randomly with an exponentially decaying probability distribution. This allows producing graphs similar to the previously studied Navigable Small World (NSW) structures while additionally having the links separated by their characteristic distance scales. Starting search from the upper layer together with utilizing the scale separation boosts the performance compared to NSW and allows a logarithmic complexity scaling. Additional employment of a heuristic for selecting proximity graph neighbors significantly increases performance at high recall and in case of highly clustered data. Performance evaluation has demonstrated that the proposed general metric space search index is able to strongly outperform previous opensource state-of-the-art vector-only approaches. Similarity of the algorithm to the skip list structure allows straightforward balanced distributed implementation.

We propose a multitask pretraining approach ZeroPrompt for zero-shot generalization, focusing on task scaling and zero-shot prompting. While previous models are trained on only a few dozen tasks, we scale to 1,000 tasks for the first time using real-world data. This leads to a crucial discovery that task scaling can be an efficient alternative to model scaling; i.e., the model size has little impact on performance with an extremely large number of tasks. Our results show that task scaling can substantially improve training efficiency by 30 times in FLOPs. Moreover, we present a prompting method that incorporates a genetic algorithm to automatically search for the best prompt for unseen tasks, along with a few other improvements. Empirically, ZeroPrompt substantially improves both the efficiency and the performance of zero-shot learning across a variety of academic and production datasets.

Traditionally, data selection has been studied in settings where all samples from prospective sources are fully revealed to a machine learning developer. However, in practical data exchange scenarios, data providers often reveal only a limited subset of samples before an acquisition decision is made. Recently, there have been efforts to fit scaling laws that predict model performance at any size and data source composition using the limited available samples. However, these scaling functions are black-box, computationally expensive to fit, highly susceptible to overfitting, or/and difficult to optimize for data selection. This paper proposes a framework called <projektor>, which predicts model performance and supports data selection decisions based on partial samples of prospective data sources. Our approach distinguishes itself from existing work by introducing a novel *two-stage* performance inference process. In the first stage, we leverage the Optimal Transport distance to predict the model's performance for any data mixture ratio within the range of disclosed data sizes. In the second stage, we extrapolate the performance to larger undisclosed data sizes based on a novel parameter-free mapping technique inspired by neural scaling laws. We further derive an efficient gradient-based method to select data sources based on the projected model performance. Evaluation over a diverse range of applications demonstrates that <projektor> significantly improves existing performance scaling approaches in terms of both the accuracy of performance inference and the computation costs associated with constructing the performance predictor. Also, <projektor> outperforms by a wide margin in data selection effectiveness compared to a range of other off-the-shelf solutions.

Contrastive learning (CL) continuously achieves significant breakthroughs across multiple domains. However, the most common InfoNCE-based methods suffer from some dilemmas, such as uniformity-tolerance dilemma (UTD) and gradient reduction, both of which are related to a P_{ij} term. It has been identified that UTD can lead to unexpected performance degradation. We argue that the fixity of temperature is to blame for UTD. To tackle this challenge, we enrich the CL loss family by presenting a Model-Aware Contrastive Learning (MACL) strategy, whose temperature is adaptive to the magnitude of alignment that reflects the basic confidence of the instance discrimination task, then enables CL loss to adjust the penalty strength for hard negatives adaptively. Regarding another dilemma, the gradient reduction issue, we derive the limits of an involved gradient scaling factor, which allows us to explain from a unified perspective why some recent approaches are effective with fewer negative samples, and summarily present a gradient reweighting to escape this dilemma. Extensive remarkable empirical results in vision, sentence, and graph modality validate our approach's general improvement for representation learning and downstream tasks.

Self-supervised learning aims to learn representations from the data itself without explicit manual supervision. Existing efforts ignore a crucial aspect of self-supervised learning - the ability to scale to large amount of data because self-supervision requires no manual labels. In this work, we revisit this principle and scale two popular self-supervised approaches to 100 million images. We show that by scaling on various axes (including data size and problem 'hardness'), one can largely match or even exceed the performance of supervised pre-training on a variety of tasks such as object detection, surface normal estimation (3D) and visual navigation using reinforcement learning. Scaling these methods also provides many interesting insights into the limitations of current self-supervised techniques and evaluations. We conclude that current self-supervised methods are not 'hard' enough to take full advantage of large scale data and do not seem to learn effective high level semantic representations. We also introduce an extensive benchmark across 9 different datasets and tasks. We believe that such a benchmark along with comparable evaluation settings is necessary to make meaningful progress. Code is at: https://github.com/facebookresearch/fair_self_supervision_benchmark.

We investigate the rate at which algorithms for pre-training language models have improved since the advent of deep learning. Using a dataset of over 200 language model evaluations on Wikitext and Penn Treebank spanning 2012-2023, we find that the compute required to reach a set performance threshold has halved approximately every 8 months, with a 95% confidence interval of around 5 to 14 months, substantially faster than hardware gains per Moore's Law. We estimate augmented scaling laws, which enable us to quantify algorithmic progress and determine the relative contributions of scaling models versus innovations in training algorithms. Despite the rapid pace of algorithmic progress and the development of new architectures such as the transformer, our analysis reveals that the increase in compute made an even larger contribution to overall performance improvements over this time period. Though limited by noisy benchmark data, our analysis quantifies the rapid progress in language modeling, shedding light on the relative contributions from compute and algorithms.

In this work we analyze strategies for convolutional neural network scaling; that is, the process of scaling a base convolutional network to endow it with greater computational complexity and consequently representational power. Example scaling strategies may include increasing model width, depth, resolution, etc. While various scaling strategies exist, their tradeoffs are not fully understood. Existing analysis typically focuses on the interplay of accuracy and flops (floating point operations). Yet, as we demonstrate, various scaling strategies affect model parameters, activations, and consequently actual runtime quite differently. In our experiments we show the surprising result that numerous scaling strategies yield networks with similar accuracy but with widely varying properties. This leads us to propose a simple fast compound scaling strategy that encourages primarily scaling model width, while scaling depth and resolution to a lesser extent. Unlike currently popular scaling strategies, which result in about O(s) increase in model activation w.r.t. scaling flops by a factor of s, the proposed fast compound scaling results in close to O(s) increase in activations, while achieving excellent accuracy. This leads to comparable speedups on modern memory-limited hardware (e.g., GPU, TPU). More generally, we hope this work provides a framework for analyzing and selecting scaling strategies under various computational constraints.

Multi-task learning (MTL) has shown considerable practical benefits, particularly when using pre-trained language models (PLMs). While this is commonly achieved by simultaneously learning n tasks under a joint optimization procedure, recent methods such as AdapterFusion structure the problem into two distinct stages: (i) task learning, where knowledge specific to a task is encapsulated within sets of parameters (\eg adapters), and (ii) transfer, where this already learned knowledge is leveraged for a target task. This separation of concerns provides numerous benefits, such as promoting reusability, and addressing cases involving data privacy and societal concerns; on the flip side, current two-stage MTL methods come with the cost of introducing a substantial number of additional parameters. In this work, we address this issue by leveraging the usefulness of linearly scaling the output representations of source adapters for transfer learning. We introduce ScaLearn, a simple and highly parameter-efficient two-stage MTL method that capitalizes on the knowledge of the source tasks by learning a minimal set of scaling parameters that enable effective knowledge transfer to a target task. Our experiments on three benchmarks (GLUE, SuperGLUE, and HumSet) show that our ScaLearn, in addition to facilitating the benefits of two-stage MTL, consistently outperforms strong baselines with only a small number of transfer parameters - roughly 0.35% of those of AdapterFusion. Remarkably, we observe that ScaLearn maintains its strong abilities even when further reducing parameters through uniform scaling and layer-sharing, achieving similarly competitive results with only 8 transfer parameters for each target task. Our proposed approach thus demonstrates the power of simple scaling as a promise for more efficient task transfer.

Dense retrieval in most industries employs dual-tower architectures to retrieve query-relevant documents. Due to online deployment requirements, existing real-world dense retrieval systems mainly enhance performance by designing negative sampling strategies, overlooking the advantages of scaling up. Recently, Large Language Models (LLMs) have exhibited superior performance that can be leveraged for scaling up dense retrieval. However, scaling up retrieval models significantly increases online query latency. To address this challenge, we propose ScalingNote, a two-stage method to exploit the scaling potential of LLMs for retrieval while maintaining online query latency. The first stage is training dual towers, both initialized from the same LLM, to unlock the potential of LLMs for dense retrieval. Then, we distill only the query tower using mean squared error loss and cosine similarity to reduce online costs. Through theoretical analysis and comprehensive offline and online experiments, we show the effectiveness and efficiency of ScalingNote. Our two-stage scaling method outperforms end-to-end models and verifies the scaling law of dense retrieval with LLMs in industrial scenarios, enabling cost-effective scaling of dense retrieval systems. Our online method incorporating ScalingNote significantly enhances the relevance between retrieved documents and queries.

Scaling laws have transformed our understanding of large language models by linking upstream metrics like cross-entropy loss to design factors such as model size, training data, and compute. However, these conventional laws fail to capture downstream task performance, where context plays a critical role. In this work, we propose a straightforward, interpretable framework that jointly models downstream performance as a function of the training compute and the provided context. We empirically validate our framework by fitting it on the observed downstream performance of extended-context variants of Llama-2-7B and Llama-2-13B across 65,500 unique instances spanning three tasks: arithmetic reasoning, common sense reasoning, and machine translation. Our results demonstrate that our framework accurately models in-distribution downstream performance, generalizes across three orders of magnitude in training compute, and reliably extrapolates performance as the amount of context increases. These findings offer valuable insights into the interplay between training compute and context utilization, providing guidance for designing more efficient long-context LLMs for diverse downstream tasks. Our code is available at https://github.com/wang-research-lab/context-scaling.

Scaling visual generation models is essential for real-world content creation, yet requires substantial training and computational expenses. Alternatively, test-time scaling has garnered growing attention due to resource efficiency and promising performance. In this work, we present TTS-VAR, the first general test-time scaling framework for visual auto-regressive (VAR) models, modeling the generation process as a path searching problem. To dynamically balance computational efficiency with exploration capacity, we first introduce an adaptive descending batch size schedule throughout the causal generation process. Besides, inspired by VAR's hierarchical coarse-to-fine multi-scale generation, our framework integrates two key components: (i) At coarse scales, we observe that generated tokens are hard for evaluation, possibly leading to erroneous acceptance of inferior samples or rejection of superior samples. Noticing that the coarse scales contain sufficient structural information, we propose clustering-based diversity search. It preserves structural variety through semantic feature clustering, enabling later selection on samples with higher potential. (ii) In fine scales, resampling-based potential selection prioritizes promising candidates using potential scores, which are defined as reward functions incorporating multi-scale generation history. Experiments on the powerful VAR model Infinity show a notable 8.7% GenEval score improvement (from 0.69 to 0.75). Key insights reveal that early-stage structural features effectively influence final quality, and resampling efficacy varies across generation scales. Code is available at https://github.com/ali-vilab/TTS-VAR.

The rapid advancements in large Language models (LLMs) have significantly enhanced their reasoning capabilities, driven by various strategies such as multi-agent collaboration. However, unlike the well-established performance improvements achieved through scaling data and model size, the scaling of reasoning in LLMs is more complex and can even negatively impact reasoning performance, introducing new challenges in model alignment and robustness. In this survey, we provide a comprehensive examination of scaling in LLM reasoning, categorizing it into multiple dimensions and analyzing how and to what extent different scaling strategies contribute to improving reasoning capabilities. We begin by exploring scaling in input size, which enables LLMs to process and utilize more extensive context for improved reasoning. Next, we analyze scaling in reasoning steps that improves multi-step inference and logical consistency. We then examine scaling in reasoning rounds, where iterative interactions refine reasoning outcomes. Furthermore, we discuss scaling in training-enabled reasoning, focusing on optimization through iterative model improvement. Finally, we review applications of scaling across domains and outline future directions for further advancing LLM reasoning. By synthesizing these diverse perspectives, this survey aims to provide insights into how scaling strategies fundamentally enhance the reasoning capabilities of LLMs and further guide the development of next-generation AI systems.

Improvements in language models' capabilities have pushed their applications towards longer contexts, making long-context evaluation and development an active research area. However, many disparate use-cases are grouped together under the umbrella term of "long-context", defined simply by the total length of the model's input, including - for example - Needle-in-a-Haystack tasks, book summarization, and information aggregation. Given their varied difficulty, in this position paper we argue that conflating different tasks by their context length is unproductive. As a community, we require a more precise vocabulary to understand what makes long-context tasks similar or different. We propose to unpack the taxonomy of long-context based on the properties that make them more difficult with longer contexts. We propose two orthogonal axes of difficulty: (I) Diffusion: How hard is it to find the necessary information in the context? (II) Scope: How much necessary information is there to find? We survey the literature on long-context, provide justification for this taxonomy as an informative descriptor, and situate the literature with respect to it. We conclude that the most difficult and interesting settings, whose necessary information is very long and highly diffused within the input, is severely under-explored. By using a descriptive vocabulary and discussing the relevant properties of difficulty in long-context, we can implement more informed research in this area. We call for a careful design of tasks and benchmarks with distinctly long context, taking into account the characteristics that make it qualitatively different from shorter context.

Large language models (LLMs) have achieved significant performance gains via scaling up model sizes and/or data. However, recent evidence suggests diminishing returns from such approaches, motivating scaling the computation spent at inference time. Existing inference-time scaling methods, usually with reward models, cast the task as a search problem, which tends to be vulnerable to reward hacking as a consequence of approximation errors in reward models. In this paper, we instead cast inference-time scaling as a probabilistic inference task and leverage sampling-based techniques to explore the typical set of the state distribution of a state-space model with an approximate likelihood, rather than optimize for its mode directly. We propose a novel inference-time scaling approach by adapting particle-based Monte Carlo methods to this task. Our empirical evaluation demonstrates that our methods have a 4-16x better scaling rate over our deterministic search counterparts on various challenging mathematical reasoning tasks. Using our approach, we show that Qwen2.5-Math-1.5B-Instruct can surpass GPT-4o accuracy in only 4 rollouts, while Qwen2.5-Math-7B-Instruct scales to o1 level accuracy in only 32 rollouts. Our work not only presents an effective method to inference-time scaling, but also connects the rich literature in probabilistic inference with inference-time scaling of LLMs to develop more robust algorithms in future work. Code and further information is available at https://probabilistic-inference-scaling.github.io.

We consider the solvable neural scaling model with three parameters: data complexity, target complexity, and model-parameter-count. We use this neural scaling model to derive new predictions about the compute-limited, infinite-data scaling law regime. To train the neural scaling model, we run one-pass stochastic gradient descent on a mean-squared loss. We derive a representation of the loss curves which holds over all iteration counts and improves in accuracy as the model parameter count grows. We then analyze the compute-optimal model-parameter-count, and identify 4 phases (+3 subphases) in the data-complexity/target-complexity phase-plane. The phase boundaries are determined by the relative importance of model capacity, optimizer noise, and embedding of the features. We furthermore derive, with mathematical proof and extensive numerical evidence, the scaling-law exponents in all of these phases, in particular computing the optimal model-parameter-count as a function of floating point operation budget.

Scaling laws are typically fit using a family of models with a narrow range of frozen hyper-parameter choices. In this work we study scaling laws using a wide range of architecture and hyper-parameter choices, and highlight their impact on resulting prescriptions. As a primary artifact of our research, we release the Gemstones: the most comprehensive open-source scaling law dataset to date, consisting of over 4000 checkpoints from transformers with up to 2 billion parameters; these models have been trained with different learning rates, cooldown schedules, and architectural shapes. Our checkpoints enable more complex studies of scaling, such as a law that predicts language modeling performance as a function of model width and depth. By examining the various facets of our model suite, we find that the prescriptions of scaling laws can be highly sensitive to the experimental design process and the specific model checkpoints used during fitting. Code: https://github.com/mcleish7/gemstone-scaling-laws

Large language models trained with reinforcement learning with verifiable rewards tend to trade accuracy for length--inflating response lengths to achieve gains in accuracy. While longer answers may be warranted for harder problems, many tokens are merely "filler": repetitive, verbose text that makes no real progress. We introduce GFPO (Group Filtered Policy Optimization), which curbs this length explosion by sampling larger groups per problem during training and filtering responses to train on based on two key metrics: (1) response length and (2) token efficiency: reward per token ratio. By sampling more at training time, we teach models to think less at inference time. On the Phi-4-reasoning model, GFPO cuts GRPO's length inflation by 46-71% across challenging STEM and coding benchmarks (AIME 24/25, GPQA, Omni-MATH, LiveCodeBench) while maintaining accuracy. Optimizing for reward per token further increases reductions in length inflation to 71-85%. We also propose Adaptive Difficulty GFPO, which dynamically allocates more training resources to harder problems based on real-time difficulty estimates, improving the balance between computational efficiency and accuracy especially on difficult questions. GFPO demonstrates that increased training-time compute directly translates to reduced test-time compute--a simple yet effective trade-off for efficient reasoning.

Deep learning (DL) creates impactful advances following a virtuous recipe: model architecture search, creating large training data sets, and scaling computation. It is widely believed that growing training sets and models should improve accuracy and result in better products. As DL application domains grow, we would like a deeper understanding of the relationships between training set size, computational scale, and model accuracy improvements to advance the state-of-the-art. This paper presents a large scale empirical characterization of generalization error and model size growth as training sets grow. We introduce a methodology for this measurement and test four machine learning domains: machine translation, language modeling, image processing, and speech recognition. Our empirical results show power-law generalization error scaling across a breadth of factors, resulting in power-law exponents---the "steepness" of the learning curve---yet to be explained by theoretical work. Further, model improvements only shift the error but do not appear to affect the power-law exponent. We also show that model size scales sublinearly with data size. These scaling relationships have significant implications on deep learning research, practice, and systems. They can assist model debugging, setting accuracy targets, and decisions about data set growth. They can also guide computing system design and underscore the importance of continued computational scaling.

One of the main challenges in optimal scaling of large language models (LLMs) is the prohibitive cost of hyperparameter tuning, particularly learning rate eta and batch size B. While techniques like muP (Yang et al., 2022) provide scaling rules for optimal eta transfer in the infinite model size limit, the optimal scaling behavior in the infinite data size limit remains unknown. We fill in this gap by observing for the first time an intricate dependence of optimal eta scaling on the pretraining token budget T, B and its relation to the critical batch size B_crit, which we measure to evolve as B_crit propto T. Furthermore, we show that the optimal batch size is positively correlated with B_crit: keeping it fixed becomes suboptimal over time even if learning rate is scaled optimally. Surprisingly, our results demonstrate that the observed optimal eta and B dynamics are preserved with muP model scaling, challenging the conventional view of B_crit dependence solely on loss value. Complementing optimality, we examine the sensitivity of loss to changes in learning rate, where we find the sensitivity to decrease with increase of T and to remain constant with muP model scaling. We hope our results make the first step towards a unified picture of the joint optimal data and model scaling.

Large Language Models have achieved strong performance on reasoning tasks, solving competition-level coding and math problems. However, their scalability is limited by human-labeled datasets and the lack of large-scale, challenging coding problem training data. Existing competitive coding datasets contain only thousands to tens of thousands of problems. Previous synthetic data generation methods rely on either augmenting existing instruction datasets or selecting challenging problems from human-labeled data. In this paper, we propose QueST, a novel framework which combines difficulty-aware graph sampling and difficulty-aware rejection fine-tuning that directly optimizes specialized generators to create challenging coding problems. Our trained generators demonstrate superior capability compared to even GPT-4o at creating challenging problems that benefit downstream performance. We leverage QueST to generate large-scale synthetic coding problems, which we then use to distill from strong teacher models with long chain-of-thought or to conduct reinforcement learning for smaller models, proving effective in both scenarios. Our distillation experiments demonstrate significant performance gains. Specifically, after fine-tuning Qwen3-8B-base on 100K difficult problems generated by QueST, we surpass the performance of the original Qwen3-8B on LiveCodeBench. With an additional 112K examples (i.e., 28K human-written problems paired with multiple synthetic solutions), our 8B model matches the performance of the much larger DeepSeek-R1-671B. These findings indicate that generating complex problems via QueST offers an effective and scalable approach to advancing the frontiers of competitive coding and reasoning for large language models.

Scaling architectures have been proven effective for improving Scene Text Recognition (STR), but the individual contribution of vision encoder and text decoder scaling remain under-explored. In this work, we present an in-depth empirical analysis and demonstrate that, contrary to previous observations, scaling the decoder yields significant performance gains, always exceeding those achieved by encoder scaling alone. We also identify label noise as a key challenge in STR, particularly in real-world data, which can limit the effectiveness of STR models. To address this, we propose Cloze Self-Distillation (CSD), a method that mitigates label noise by distilling a student model from context-aware soft predictions and pseudolabels generated by a teacher model. Additionally, we enhance the decoder architecture by introducing differential cross-attention for STR. Our methodology achieves state-of-the-art performance on 10 out of 11 benchmarks using only real data, while significantly reducing the parameter size and computational costs.

We introduce a framework for automatically defining and learning deep generative models with problem-specific structure. We tackle problem domains that are more traditionally solved by algorithms such as sorting, constraint satisfaction for Sudoku, and matrix factorization. Concretely, we train diffusion models with an architecture tailored to the problem specification. This problem specification should contain a graphical model describing relationships between variables, and often benefits from explicit representation of subcomputations. Permutation invariances can also be exploited. Across a diverse set of experiments we improve the scaling relationship between problem dimension and our model's performance, in terms of both training time and final accuracy. Our code can be found at https://github.com/plai-group/gsdm.

Hyperparameter tuning of deep learning models can lead to order-of-magnitude performance gains for the same amount of compute. Despite this, systematic tuning is uncommon, particularly for large models, which are expensive to evaluate and tend to have many hyperparameters, necessitating difficult judgment calls about tradeoffs, budgets, and search bounds. To address these issues and propose a practical method for robustly tuning large models, we present Cost-Aware Pareto Region Bayesian Search (CARBS), a Bayesian optimization algorithm that performs local search around the performance-cost Pareto frontier. CARBS does well even in unbounded search spaces with many hyperparameters, learns scaling relationships so that it can tune models even as they are scaled up, and automates much of the "black magic" of tuning. Among our results, we effectively solve the entire ProcGen benchmark just by tuning a simple baseline (PPO, as provided in the original ProcGen paper). We also reproduce the model size vs. training tokens scaling result from the Chinchilla project (Hoffmann et al. 2022), while simultaneously discovering scaling laws for every other hyperparameter, via an easy automated process that uses significantly less compute and is applicable to any deep learning problem (not just language models).

Training large-scale models under given resources requires careful design of parallelism strategies. In particular, the efficiency notion of critical batch size (CBS), concerning the compromise between time and compute, marks the threshold beyond which greater data parallelism leads to diminishing returns. To operationalize it, we propose a measure of CBS and pre-train a series of auto-regressive language models, ranging from 85 million to 1.2 billion parameters, on the C4 dataset. Through extensive hyper-parameter sweeps and careful control of factors such as batch size, momentum, and learning rate along with its scheduling, we systematically investigate the impact of scale on CBS. Then we fit scaling laws with respect to model and data sizes to decouple their effects. Overall, our results demonstrate that CBS scales primarily with data size rather than model size, a finding we justify theoretically through the analysis of infinite-width limits of neural networks and infinite-dimensional least squares regression. Of independent interest, we highlight the importance of common hyper-parameter choices and strategies for studying large-scale pre-training beyond fixed training durations.

Model pruning is a popular approach to enable the deployment of large deep learning models on edge devices with restricted computational or storage capacities. Although sparse models achieve performance comparable to that of their dense counterparts at the level of the entire dataset, they exhibit high accuracy drops for some data sub-groups. Existing methods to mitigate this disparate impact induced by pruning (i) rely on surrogate metrics that address the problem indirectly and have limited interpretability; or (ii) scale poorly with the number of protected sub-groups in terms of computational cost. We propose a constrained optimization approach that directly addresses the disparate impact of pruning: our formulation bounds the accuracy change between the dense and sparse models, for each sub-group. This choice of constraints provides an interpretable success criterion to determine if a pruned model achieves acceptable disparity levels. Experimental results demonstrate that our technique scales reliably to problems involving large models and hundreds of protected sub-groups.

We present unit scaling, a paradigm for designing deep learning models that simplifies the use of low-precision number formats. Training in FP16 or the recently proposed FP8 formats offers substantial efficiency gains, but can lack sufficient range for out-of-the-box training. Unit scaling addresses this by introducing a principled approach to model numerics: seeking unit variance of all weights, activations and gradients at initialisation. Unlike alternative methods, this approach neither requires multiple training runs to find a suitable scale nor has significant computational overhead. We demonstrate the efficacy of unit scaling across a range of models and optimisers. We further show that existing models can be adapted to be unit-scaled, training BERT-Large in FP16 and then FP8 with no degradation in accuracy.

In the complex domain of large language models (LLMs), striking a balance between computational efficiency and maintaining model quality is a formidable challenge. Navigating the inherent limitations of uniform quantization, particularly when dealing with outliers, and motivated by the launch of NVIDIA's H100 hardware, this study delves into the viability of floating-point (FP) quantization, particularly focusing on FP8 and FP4, as a potential solution. Our comprehensive investigation reveals that for LLMs, FP8 activation consistently outshines its integer (INT8) equivalent, with the performance edge becoming more noticeable in models possessing parameters beyond one billion. For weight quantization, our findings indicate that FP4 exhibits comparable, if not superior, performance to INT4, simplifying deployment on FP-supported hardware like H100. To mitigate the overhead from precision alignment caused by the disparity between weights and activations, we propose two scaling constraints for weight quantization that negligibly impact the performance compared to the standard W4A8 model. We additionally enhance our quantization methods by integrating the Low Rank Compensation (LoRC) strategy, yielding improvements especially in smaller models. The results of our investigation emphasize the immense potential of FP quantization for LLMs, paving the way for high-efficiency deployment in resource-limited settings.

Scaling laws research has focused overwhelmingly on English -- yet the most prominent AI models explicitly serve billions of international users. In this work, we undertake the largest multilingual scaling laws study to date, totaling 774 multilingual training experiments, spanning 10M-8B model parameters, 400+ training languages and 48 evaluation languages. We introduce the Adaptive Transfer Scaling Law (ATLAS) for both monolingual and multilingual pretraining, which outperforms existing scaling laws' out-of-sample generalization often by more than 0.3 R^2. Our analyses of the experiments shed light on multilingual learning dynamics, transfer properties between languages, and the curse of multilinguality. First, we derive a cross-lingual transfer matrix, empirically measuring mutual benefit scores between 38 x 38=1444 language pairs. Second, we derive a language-agnostic scaling law that reveals how to optimally scale model size and data when adding languages without sacrificing performance. Third, we identify the computational crossover points for when to pretrain from scratch versus finetune from multilingual checkpoints. We hope these findings provide the scientific foundation for democratizing scaling laws across languages, and enable practitioners to efficiently scale models -- beyond English-first AI.

Large language models (LLMs) process entire input contexts indiscriminately, which is inefficient in cases where the information required to answer a query is localized within the context. We present dynamic context cutoff, a human-inspired method enabling LLMs to self-terminate processing upon acquiring sufficient task-relevant information. Through analysis of model internals, we discover that specific attention heads inherently encode "sufficiency signals" - detectable through lightweight classifiers - that predict when critical information has been processed. This reveals a new efficiency paradigm: models' internal understanding naturally dictates processing needs rather than external compression heuristics. Comprehensive experiments across six QA datasets (up to 40K tokens) with three model families (LLaMA/Qwen/Mistral, 1B0-70B) demonstrate 1.33x average token reduction while improving accuracy by 1.3%. Furthermore, our method demonstrates better performance with the same rate of token reduction compared to other context efficiency methods. Additionally, we observe an emergent scaling phenomenon: while smaller models require require probing for sufficiency detection, larger models exhibit intrinsic self-assessment capabilities through prompting.

The alignment of large language models (LLMs) often assumes that using more clean data yields better outcomes, overlooking the match between model capacity and example difficulty. Challenging this, we propose a new principle: Preference data vary in difficulty, and overly difficult examples hinder alignment, by exceeding the model's capacity. Through systematic experimentation, we validate this principle with three key findings: (1) preference examples vary in difficulty, as evidenced by consistent learning orders across alignment runs; (2) overly difficult examples significantly degrade performance across four LLMs and two datasets; and (3) the capacity of a model dictates its threshold for handling difficult examples, underscoring a critical relationship between data selection and model capacity. Building on this principle, we introduce Selective DPO, which filters out overly difficult examples. This simple adjustment improves alignment performance by 9-16% in win rates on the AlpacaEval 2 benchmark compared to the DPO baseline, suppressing a series of DPO variants with different algorithmic adjustments. Together, these results illuminate the importance of aligning data difficulty with model capacity, offering a transformative perspective for improving alignment strategies in LLMs. Code is available at https://github.com/glorgao/SelectiveDPO.

In recent years, the state-of-the-art in deep learning has been dominated by very large models that have been pre-trained on vast amounts of data. The paradigm is very simple: Investing more computational resources (optimally) leads to better performance, and even predictably so; neural scaling laws have been derived that accurately forecast the performance of a network for a desired level of compute. This leads to the notion of a "compute-optimal" model, i.e. a model that allocates a given level of compute during training optimally to maximise performance. In this work, we extend the concept of optimality by allowing for an "adaptive" model, i.e. a model that can change its shape during the course of training. By allowing the shape to adapt, we can optimally traverse between the underlying scaling laws, leading to a significant reduction in the required compute to reach a given target performance. We focus on vision tasks and the family of Vision Transformers, where the patch size as well as the width naturally serve as adaptive shape parameters. We demonstrate that, guided by scaling laws, we can design compute-optimal adaptive models that beat their "static" counterparts.

In this paper, we investigate which questions are challenging for retrieval-based Question Answering (QA). We (i) propose retrieval complexity (RC), a novel metric conditioned on the completeness of retrieved documents, which measures the difficulty of answering questions, and (ii) propose an unsupervised pipeline to measure RC given an arbitrary retrieval system. Our proposed pipeline measures RC more accurately than alternative estimators, including LLMs, on six challenging QA benchmarks. Further investigation reveals that RC scores strongly correlate with both QA performance and expert judgment across five of the six studied benchmarks, indicating that RC is an effective measure of question difficulty. Subsequent categorization of high-RC questions shows that they span a broad set of question shapes, including multi-hop, compositional, and temporal QA, indicating that RC scores can categorize a new subset of complex questions. Our system can also have a major impact on retrieval-based systems by helping to identify more challenging questions on existing datasets.

According to Algorithmic Information Theory (AIT) -- Intelligent representations compress data into the shortest possible program that can reconstruct its content, exhibiting low Kolmogorov Complexity (KC). In contrast, most visual representation learning systems use fixed-length representations for all inputs, ignoring variations in complexity or familiarity. Recent adaptive tokenization methods address this by allocating variable-length representations but typically require test-time search over multiple encodings to find the most predictive one. Inspired by Kolmogorov Complexity principles, we propose a single-pass adaptive tokenizer, KARL, which predicts the appropriate number of tokens for an image in a single forward pass, halting once its approximate KC is reached. The token count serves as a proxy for the minimum description length. KARL's training procedure closely resembles the Upside-Down Reinforcement Learning paradigm, as it learns to conditionally predict token halting based on a desired reconstruction quality. KARL matches the performance of recent adaptive tokenizers while operating in a single pass. We present scaling laws for KARL, analyzing the role of encoder/decoder size, continuous vs. discrete tokenization and more. Additionally, we offer a conceptual study drawing an analogy between Adaptive Image Tokenization and Algorithmic Information Theory, examining the predicted image complexity (KC) across axes such as structure vs. noise and in- vs. out-of-distribution familiarity -- revealing alignment with human intuition.

Mixture of Experts (MoE) architectures have significantly increased computational efficiency in both research and real-world applications of large-scale machine learning models. However, their scalability and efficiency under memory constraints remain relatively underexplored. In this work, we present joint scaling laws for dense and MoE models, incorporating key factors such as the number of active parameters, dataset size, and the number of experts. Our findings provide a principled framework for selecting the optimal MoE configuration under fixed memory and compute budgets. Surprisingly, we show that MoE models can be more memory-efficient than dense models, contradicting conventional wisdom. To derive and validate the theoretical predictions of our scaling laws, we conduct over 280 experiments with up to 2.7B active parameters and up to 5B total parameters. These results offer actionable insights for designing and deploying MoE models in practical large-scale training scenarios.

Despite the promise of Multi-Task Learning in leveraging complementary knowledge across tasks, existing multi-task optimization (MTO) techniques remain fixated on resolving conflicts via optimizer-centric loss scaling and gradient manipulation strategies, yet fail to deliver consistent gains. In this paper, we argue that the shared representation space, where task interactions naturally occur, offers rich information and potential for operations complementary to existing optimizers, especially for facilitating the inter-task complementarity, which is rarely explored in MTO. This intuition leads to Rep-MTL, which exploits the representation-level task saliency to quantify interactions between task-specific optimization and shared representation learning. By steering these saliencies through entropy-based penalization and sample-wise cross-task alignment, Rep-MTL aims to mitigate negative transfer by maintaining the effective training of individual tasks instead pure conflict-solving, while explicitly promoting complementary information sharing. Experiments are conducted on four challenging MTL benchmarks covering both task-shift and domain-shift scenarios. The results show that Rep-MTL, even paired with the basic equal weighting policy, achieves competitive performance gains with favorable efficiency. Beyond standard performance metrics, Power Law exponent analysis demonstrates Rep-MTL's efficacy in balancing task-specific learning and cross-task sharing. The project page is available at HERE.

Scaling language models improves performance but comes with significant computational costs. This paper proposes UL2R, a method that substantially improves existing language models and their scaling curves with a relatively tiny amount of extra compute. The key idea is to continue training a state-of-the-art large language model (e.g., PaLM) on a few more steps with UL2's mixture-of-denoiser objective. We show that, with almost negligible extra computational costs and no new sources of data, we are able to substantially improve the scaling properties of large language models on downstream metrics. In this paper, we continue training PaLM with UL2R, introducing a new set of models at 8B, 62B, and 540B scale which we call U-PaLM. Impressively, at 540B scale, we show an approximately 2x computational savings rate where U-PaLM achieves the same performance as the final PaLM 540B model at around half its computational budget (i.e., saving sim4.4 million TPUv4 hours). We further show that this improved scaling curve leads to 'emergent abilities' on challenging BIG-Bench tasks -- for instance, U-PaLM does much better than PaLM on some tasks or demonstrates better quality at much smaller scale (62B as opposed to 540B). Overall, we show that U-PaLM outperforms PaLM on many few-shot setups, i.e., English NLP tasks (e.g., commonsense reasoning, question answering), reasoning tasks with chain-of-thought (e.g., GSM8K), multilingual tasks (MGSM, TydiQA), MMLU and challenging BIG-Bench tasks. Finally, we provide qualitative examples showing the new capabilities of U-PaLM for single and multi-span infilling.

In this paper, we introduce SCALE, a collaborative framework that connects compact Specialized Translation Models (STMs) and general-purpose Large Language Models (LLMs) as one unified translation engine. By introducing translation from STM into the triplet in-context demonstrations, SCALE unlocks refinement and pivoting ability of LLM, thus mitigating language bias of LLM and parallel data bias of STM, enhancing LLM speciality without sacrificing generality, and facilitating continual learning without expensive LLM fine-tuning. Our comprehensive experiments show that SCALE significantly outperforms both few-shot LLMs (GPT-4) and specialized models (NLLB) in challenging low-resource settings. Moreover, in Xhosa to English translation, SCALE experiences consistent improvement by a 4 BLEURT score without tuning LLM and surpasses few-shot GPT-4 by 2.5 COMET score and 3.8 BLEURT score when equipped with a compact model consisting of merely 600M parameters. SCALE could also effectively exploit the existing language bias of LLMs by using an English-centric STM as a pivot for translation between any language pairs, outperforming few-shot GPT-4 by an average of 6 COMET points across eight translation directions. Furthermore we provide an in-depth analysis of SCALE's robustness, translation characteristics, and latency costs, providing solid foundation for future studies exploring the potential synergy between LLMs and more specialized, task-specific models.

We investigate large language model performance across five orders of magnitude of compute scaling in eleven recent model architectures. We show that average benchmark performance, aggregating over many individual tasks and evaluations as in the commonly-used BIG-Bench dataset, is decently predictable as a function of training compute scale. Specifically, when extrapolating BIG-Bench Hard performance across one order of magnitude in compute, we observe average absolute errors of 6 percentage points (pp). By contrast, extrapolation for individual BIG-Bench tasks across an order of magnitude in compute yields higher average errors of 18pp. Nonetheless, individual task performance remains significantly more predictable than chance. Overall, our work suggests compute scaling provides a promising basis to forecast AI capabilities in diverse benchmarks, though predicting performance in specific tasks poses challenges.

We consider the problem of ranking n experts based on their performances on d tasks. We make a monotonicity assumption stating that for each pair of experts, one outperforms the other on all tasks. We consider the sequential setting where in each round, the learner has access to noisy evaluations of actively chosen pair of expert-task, given the information available up to the actual round. Given a confidence parameter delta in (0, 1), we provide strategies allowing to recover the correct ranking of experts and develop a bound on the total number of queries made by our algorithm that hold with probability at least 1 -- delta. We show that our strategy is adaptive to the complexity of the problem (our bounds are instance dependent), and develop matching lower bounds up to a poly-logarithmic factor. Finally, we adapt our strategy to the relaxed problem of best expert identification and provide numerical simulation consistent with our theoretical results.

Scale has become a main ingredient in obtaining strong machine learning models. As a result, understanding a model's scaling properties is key to effectively designing both the right training setup as well as future generations of architectures. In this work, we argue that scale and training research has been needlessly complex due to reliance on the cosine schedule, which prevents training across different lengths for the same model size. We investigate the training behavior of a direct alternative - constant learning rate and cooldowns - and find that it scales predictably and reliably similar to cosine. Additionally, we show that stochastic weight averaging yields improved performance along the training trajectory, without additional training costs, across different scales. Importantly, with these findings we demonstrate that scaling experiments can be performed with significantly reduced compute and GPU hours by utilizing fewer but reusable training runs.

Motivated by scaling laws in language modeling that demonstrate how test loss scales as a power law with model and dataset sizes, we find that similar laws exist in preference modeling. We propose World Preference Modeling$ (WorldPM) to emphasize this scaling potential, where World Preference embodies a unified representation of human preferences. In this paper, we collect preference data from public forums covering diverse user communities, and conduct extensive training using 15M-scale data across models ranging from 1.5B to 72B parameters. We observe distinct patterns across different evaluation metrics: (1) Adversarial metrics (ability to identify deceptive features) consistently scale up with increased training data and base model size; (2) Objective metrics (objective knowledge with well-defined answers) show emergent behavior in larger language models, highlighting WorldPM's scalability potential; (3) Subjective metrics (subjective preferences from a limited number of humans or AI) do not demonstrate scaling trends. Further experiments validate the effectiveness of WorldPM as a foundation for preference fine-tuning. Through evaluations on 7 benchmarks with 20 subtasks, we find that WorldPM broadly improves the generalization performance across human preference datasets of varying sizes (7K, 100K and 800K samples), with performance gains exceeding 5% on many key subtasks. Integrating WorldPM into our internal RLHF pipeline, we observe significant improvements on both in-house and public evaluation sets, with notable gains of 4% to 8% in our in-house evaluations.

Recent trends in language modeling have focused on increasing performance through scaling, and have resulted in an environment where training language models is out of reach for most researchers and practitioners. While most in the community are asking how to push the limits of extreme computation, we ask the opposite question: How far can we get with a single GPU in just one day? We investigate the downstream performance achievable with a transformer-based language model trained completely from scratch with masked language modeling for a single day on a single consumer GPU. Aside from re-analyzing nearly all components of the pretraining pipeline for this scenario and providing a modified pipeline with performance close to BERT, we investigate why scaling down is hard, and which modifications actually improve performance in this scenario. We provide evidence that even in this constrained setting, performance closely follows scaling laws observed in large-compute settings. Through the lens of scaling laws, we categorize a range of recent improvements to training and architecture and discuss their merit and practical applicability (or lack thereof) for the limited compute setting.

Large language models (LLMs) have recently garnered significant interest. With in-context learning, LLMs achieve impressive results in various natural language tasks. However, the application of LLMs to sentence embeddings remains an area of ongoing research. In this work, we propose an in-context learning-based method aimed at improving sentence embeddings performance. Our approach involves adapting the previous prompt-based representation method for autoregressive models, constructing a demonstration set that enables LLMs to perform in-context learning, and scaling up the LLMs to different model sizes. Through extensive experiments, in-context learning enables LLMs to generate high-quality sentence embeddings without any fine-tuning. It helps LLMs achieve performance comparable to current contrastive learning methods. By scaling model size, we find scaling to more than tens of billion parameters harms the performance on semantic textual similarity (STS) tasks. However, the largest model outperforms other counterparts and achieves the new state-of-the-art result on transfer tasks. We also fine-tune LLMs with current contrastive learning approach, and the 2.7B OPT model, incorporating our prompt-based method, surpasses the performance of 4.8B ST5, achieving the new state-of-the-art results on STS tasks. Our code is available at https://github.com/kongds/scaling_sentemb.

While Large Language Models require more and more data to train and scale, rather than looking for any data to acquire, we should consider what types of tasks are more likely to benefit from data scaling. We should be intentional in our data acquisition. We argue that the topology of data itself informs which tasks to prioritize in data scaling, and shapes the development of the next generation of compute paradigms for tasks where data scaling is inefficient, or even insufficient.

Reward Models (RMs) are critical for improving generation models via Reinforcement Learning (RL), yet the RM scaling paradigm in visual generation remains largely unexplored. It primarily due to fundamental limitations in existing approaches: CLIP-based RMs suffer from architectural and input modality constraints, while prevalent Bradley-Terry losses are fundamentally misaligned with the next-token prediction mechanism of Vision-Language Models (VLMs), hindering effective scaling. More critically, the RLHF optimization process is plagued by Reward Hacking issue, where models exploit flaws in the reward signal without improving true quality. To address these challenges, we introduce RewardDance, a scalable reward modeling framework that overcomes these barriers through a novel generative reward paradigm. By reformulating the reward score as the model's probability of predicting a "yes" token, indicating that the generated image outperforms a reference image according to specific criteria, RewardDance intrinsically aligns reward objectives with VLM architectures. This alignment unlocks scaling across two dimensions: (1) Model Scaling: Systematic scaling of RMs up to 26 billion parameters; (2) Context Scaling: Integration of task-specific instructions, reference examples, and chain-of-thought (CoT) reasoning. Extensive experiments demonstrate that RewardDance significantly surpasses state-of-the-art methods in text-to-image, text-to-video, and image-to-video generation. Crucially, we resolve the persistent challenge of "reward hacking": Our large-scale RMs exhibit and maintain high reward variance during RL fine-tuning, proving their resistance to hacking and ability to produce diverse, high-quality outputs. It greatly relieves the mode collapse problem that plagues smaller models.

Large language models with a huge number of parameters, when trained on near internet-sized number of tokens, have been empirically shown to obey neural scaling laws: specifically, their performance behaves predictably as a power law in either parameters or dataset size until bottlenecked by the other resource. To understand this better, we first identify the necessary properties allowing such scaling laws to arise and then propose a statistical model -- a joint generative data model and random feature model -- that captures this neural scaling phenomenology. By solving this model in the dual limit of large training set size and large number of parameters, we gain insight into (i) the statistical structure of datasets and tasks that lead to scaling laws, (ii) the way nonlinear feature maps, such as those provided by neural networks, enable scaling laws when trained on these datasets, (iii) the optimality of the equiparameterization scaling of training sets and parameters, and (iv) whether such scaling laws can break down and how they behave when they do. Key findings are the manner in which the power laws that occur in the statistics of natural datasets are extended by nonlinear random feature maps and then translated into power-law scalings of the test loss and how the finite extent of the data's spectral power law causes the model's performance to plateau.

Comprehensively understanding and accurately predicting the performance of large language models across diverse downstream tasks has emerged as a pivotal challenge in NLP research. The pioneering scaling law on downstream works demonstrated intrinsic similarities within model families and utilized such similarities for performance prediction. However, they tend to overlook the similarities between model families and only consider design factors listed in the original scaling law. To overcome these limitations, we introduce a novel framework, Collaborative Performance Prediction (CPP), which significantly enhances prediction accuracy by leveraging the historical performance of various models on downstream tasks and other design factors for both model and task. We also collect a collaborative data sourced from online platforms containing both historical performance and additional design factors. With the support of the collaborative data, CPP not only surpasses traditional scaling laws in predicting the performance of scaled LLMs but also facilitates a detailed analysis of factor importance, an area previously overlooked.

Among the most important properties of algorithms investigated in computer science are soundness, completeness, and complexity. These properties, however, are rarely analyzed for the vast collection of recently proposed methods for planning with large language models. In this work, we alleviate this gap. We analyse these properties of using LLMs for planning and highlight that recent trends abandon both soundness and completeness for the sake of inefficiency. We propose a significantly more efficient approach that can, at the same time, maintain both soundness and completeness. We exemplify on four representative search problems, comparing to the LLM-based solutions from the literature that attempt to solve these problems. We show that by using LLMs to produce the code for the search components we can solve the entire datasets with 100\% accuracy with only a few calls to the LLM. We argue for a responsible use of compute resources; urging research community to investigate sound and complete LLM-based approaches that uphold efficiency.

The prohibitive cost of evaluating large language models (LLMs) on comprehensive benchmarks necessitates the creation of small yet representative data subsets (i.e., tiny benchmarks) that enable efficient assessment while retaining predictive fidelity. Current methods for this task operate under a model-centric paradigm, selecting benchmarking items based on the collective performance of existing models. Such approaches are limited by large upfront costs, an inability to immediately handle new benchmarks (`cold-start'), and the fragile assumption that future models will share the failure patterns of their predecessors. In this work, we challenge this paradigm and propose a item-centric approach to benchmark subset selection, arguing that selection should be based on the intrinsic properties of the task items themselves, rather than on model-specific failure patterns. We instantiate this item-centric efficient benchmarking approach via a novel method, Scales++, where data selection is based on the cognitive demands of the benchmark samples. Empirically, we show Scales++ reduces the upfront selection cost by over 18x while achieving competitive predictive fidelity. On the Open LLM Leaderboard, using just a 0.5\% data subset, we predict full benchmark scores with a 2.9% mean absolute error. We demonstrate that this item-centric approach enables more efficient model evaluation without significant fidelity degradation, while also providing better cold-start performance and more interpretable benchmarking.

Inference-time scaling can enhance the reasoning capabilities of large language models (LLMs) on complex problems that benefit from step-by-step problem solving. Although lengthening generated scratchpads has proven effective for mathematical tasks, the broader impact of this approach on other tasks remains less clear. In this work, we investigate the benefits and limitations of scaling methods across nine state-of-the-art models and eight challenging tasks, including math and STEM reasoning, calendar planning, NP-hard problems, navigation, and spatial reasoning. We compare conventional models (e.g., GPT-4o) with models fine-tuned for inference-time scaling (e.g., o1) through evaluation protocols that involve repeated model calls, either independently or sequentially with feedback. These evaluations approximate lower and upper performance bounds and potential for future performance improvements for each model, whether through enhanced training or multi-model inference systems. Our extensive empirical analysis reveals that the advantages of inference-time scaling vary across tasks and diminish as problem complexity increases. In addition, simply using more tokens does not necessarily translate to higher accuracy in these challenging regimes. Results from multiple independent runs with conventional models using perfect verifiers show that, for some tasks, these models can achieve performance close to the average performance of today's most advanced reasoning models. However, for other tasks, a significant performance gap remains, even in very high scaling regimes. Encouragingly, all models demonstrate significant gains when inference is further scaled with perfect verifiers or strong feedback, suggesting ample potential for future improvements.

In the realm of large language models (LLMs), enhancing instruction-following capability often involves curating expansive training data. This is achieved through two primary schemes: i) Scaling-Inputs: Amplifying (input, output) pairs per task instruction, aiming for better instruction adherence. ii) Scaling Input-Free Tasks: Enlarging tasks, each composed of an (instruction, output) pair (without requiring a separate input anymore). However, LLMs under Scaling-Inputs tend to be overly sensitive to inputs, leading to misinterpretation or non-compliance with instructions. Conversely, Scaling Input-Free Tasks demands a substantial number of tasks but is less effective in instruction following when dealing with instances in Scaling-Inputs. This work introduces MUFFIN, a new scheme of instruction-following dataset curation. Specifically, we automatically Scale Tasks per Input by diversifying these tasks with various input facets. Experimental results across four zero-shot benchmarks, spanning both Scaling-Inputs and Scaling Input-Free Tasks schemes, reveal that LLMs, at various scales, trained on MUFFIN generally demonstrate superior instruction-following capabilities compared to those trained on the two aforementioned schemes.

Large foundation models are typically trained on data from multiple domains, with the data mixture--the proportion of each domain used--playing a critical role in model performance. The standard approach to selecting this mixture relies on trial and error, which becomes impractical for large-scale pretraining. We propose a systematic method to determine the optimal data mixture for any target domain using scaling laws. Our approach accurately predicts the loss of a model of size N trained with D tokens and a specific domain weight vector h. We validate the universality of these scaling laws by demonstrating their predictive power in three distinct and large-scale settings: large language model (LLM), native multimodal model (NMM), and large vision models (LVM) pretraining. We further show that these scaling laws can extrapolate to new data mixtures and across scales: their parameters can be accurately estimated using a few small-scale training runs, and used to estimate the performance at larger scales and unseen domain weights. The scaling laws allow to derive the optimal domain weights for any target domain under a given training budget (N,D), providing a principled alternative to costly trial-and-error methods.

Large language models have exhibited intriguing in-context learning capability, achieving promising zero- and few-shot performance without updating the parameters. However, conventional in-context learning is usually restricted by length constraints, rendering it ineffective to absorb supervision from a large number of examples. In order to go beyond few shots, we introduce structured prompting that breaks the length limit and scales in-context learning to thousands of examples. Specifically, demonstration examples are separately encoded with well-designed position embeddings, and then they are jointly attended by the test example using a rescaled attention mechanism. So we can scale the number of exemplars with linear complexity instead of quadratic complexity with respect to length. Experimental results on a diverse set of tasks show that our approach improves end-task performance and reduces evaluation variance over conventional in-context learning as the number of demonstration examples increases. Code has been released at https://aka.ms/structured-prompting.

Experts advising decision-makers are likely to display expertise which varies as a function of the problem instance. In practice, this may lead to sub-optimal or discriminatory decisions against minority cases. In this work we model such changes in depth and breadth of knowledge as a partitioning of the problem space into regions of differing expertise. We provide here new algorithms that explicitly consider and adapt to the relationship between problem instances and experts' knowledge. We first propose and highlight the drawbacks of a naive approach based on nearest neighbor queries. To address these drawbacks we then introduce a novel algorithm - expertise trees - that constructs decision trees enabling the learner to select appropriate models. We provide theoretical insights and empirically validate the improved performance of our novel approach on a range of problems for which existing methods proved to be inadequate.

Many NLP researchers are experiencing an existential crisis triggered by the astonishing success of ChatGPT and other systems based on large language models (LLMs). After such a disruptive change to our understanding of the field, what is left to do? Taking a historical lens, we look for guidance from the first era of LLMs, which began in 2005 with large n-gram models for machine translation. We identify durable lessons from the first era, and more importantly, we identify evergreen problems where NLP researchers can continue to make meaningful contributions in areas where LLMs are ascendant. Among these lessons, we discuss the primacy of hardware advancement in shaping the availability and importance of scale, as well as the urgent challenge of quality evaluation, both automated and human. We argue that disparities in scale are transient and that researchers can work to reduce them; that data, rather than hardware, is still a bottleneck for many meaningful applications; that meaningful evaluation informed by actual use is still an open problem; and that there is still room for speculative approaches.

Solving mathematical problems requires advanced reasoning abilities and presents notable challenges for large language models. Previous works usually synthesize data from proprietary models to augment existing datasets, followed by instruction tuning to achieve top-tier results. However, our analysis of these datasets reveals severe biases towards easy queries, with frequent failures to generate any correct response for the most challenging queries. Hypothesizing that difficult queries are crucial to learn complex reasoning, we propose Difficulty-Aware Rejection Tuning (DART), a method that allocates difficult queries more trials during the synthesis phase, enabling more extensive training on difficult samples. Utilizing DART, we have created new datasets for mathematical problem-solving that focus more on difficult queries and are substantially smaller than previous ones. Remarkably, our synthesis process solely relies on a 7B-sized open-weight model, without reliance on the commonly used proprietary GPT-4. We fine-tune various base models on our datasets ranging from 7B to 70B in size, resulting in a series of strong models called DART-MATH. In comprehensive in-domain and out-of-domain evaluation on 6 mathematical benchmarks, DART-MATH outperforms vanilla rejection tuning significantly, being superior or comparable to previous arts, despite using much smaller datasets and no proprietary models. Furthermore, our results position our synthetic datasets as the most effective and cost-efficient publicly available resources for advancing mathematical problem-solving.

Despite recent progress in optimal hyperparameter transfer under model and dataset scaling, no unifying explanatory principle has been established. Using the Scion optimizer, we discover that joint optimal scaling across model and dataset sizes is governed by a single invariant: the operator norm of the output layer. Across models with up to 1.3B parameters trained on up to 138B tokens, the optimal learning rate/batch size pair (eta^{ast}, B^{ast}) consistently has the same operator norm value - a phenomenon we term norm transfer. This constant norm condition is necessary but not sufficient: while for each dataset size, multiple (eta, B) reach the optimal norm, only a unique (eta^{ast}, B^{ast}) achieves the best loss. As a sufficient condition, we provide the first measurement of (eta^{ast}, B^{ast}) scaling with dataset size for Scion, and find that the scaling rules are consistent with those of the Adam optimizer. Tuning per-layer-group learning rates also improves model performance, with the output layer being the most sensitive and hidden layers benefiting from lower learning rates. We provide practical insights on norm-guided optimal scaling and release our Distributed Scion (Disco) implementation with logs from over two thousand runs to support research on LLM training dynamics at scale.

We propose a novel approach to scaling LLM inference for code generation. We frame code generation as a black box optimization problem within the code space, and employ optimization-inspired techniques to enhance exploration. Specifically, we introduce Scattered Forest Search to enhance solution diversity while searching for solutions. Our theoretical analysis illustrates how these methods avoid local optima during optimization. Extensive experiments on HumanEval, MBPP, APPS, CodeContests, and Leetcode reveal significant performance improvements. For instance, our method achieves a pass@1 rate of 67.1% on HumanEval+ and 87.2% on HumanEval with GPT-3.5, marking improvements of 8.6% and 4.3% over the state-of-the-art, while also halving the iterations needed to find the correct solution. Furthermore, our method scales more efficiently than existing search techniques, including tree search, line search, and repeated sampling.

Hyperbolic embeddings offer excellent quality with few dimensions when embedding hierarchical data structures like synonym or type hierarchies. Given a tree, we give a combinatorial construction that embeds the tree in hyperbolic space with arbitrarily low distortion without using optimization. On WordNet, our combinatorial embedding obtains a mean-average-precision of 0.989 with only two dimensions, while Nickel et al.'s recent construction obtains 0.87 using 200 dimensions. We provide upper and lower bounds that allow us to characterize the precision-dimensionality tradeoff inherent in any hyperbolic embedding. To embed general metric spaces, we propose a hyperbolic generalization of multidimensional scaling (h-MDS). We show how to perform exact recovery of hyperbolic points from distances, provide a perturbation analysis, and give a recovery result that allows us to reduce dimensionality. The h-MDS approach offers consistently low distortion even with few dimensions across several datasets. Finally, we extract lessons from the algorithms and theory above to design a PyTorch-based implementation that can handle incomplete information and is scalable.

Inverse reinforcement learning (IRL) offers a powerful and general framework for learning humans' latent preferences in route recommendation, yet no approach has successfully addressed planetary-scale problems with hundreds of millions of states and demonstration trajectories. In this paper, we introduce scaling techniques based on graph compression, spatial parallelization, and improved initialization conditions inspired by a connection to eigenvector algorithms. We revisit classic IRL methods in the routing context, and make the key observation that there exists a trade-off between the use of cheap, deterministic planners and expensive yet robust stochastic policies. This insight is leveraged in Receding Horizon Inverse Planning (RHIP), a new generalization of classic IRL algorithms that provides fine-grained control over performance trade-offs via its planning horizon. Our contributions culminate in a policy that achieves a 16-24% improvement in route quality at a global scale, and to the best of our knowledge, represents the largest published study of IRL algorithms in a real-world setting to date. We conclude by conducting an ablation study of key components, presenting negative results from alternative eigenvalue solvers, and identifying opportunities to further improve scalability via IRL-specific batching strategies.

We rigorously establish a bipartite mutual information scaling law in natural language that governs long-range dependencies. This scaling law, which we show is distinct from and scales independently of the conventional two-point mutual information, is the key to understanding long-context language modeling. Using this scaling law, we formulate the Long-context Language Modeling (L^2M) condition, which relates a model's capacity for effective long context length modeling to the scaling of its latent state size for storing past information. Our results are validated through experiments on both transformers and state space models. This work establishes a theoretical foundation that guides the development of large language models toward longer context lengths.

Training Large Language Models (LLMs) is prohibitively expensive, creating a critical scaling gap where insights from small-scale experiments often fail to transfer to resource-intensive production systems, thereby hindering efficient innovation. To bridge this, we introduce Farseer, a novel and refined scaling law offering enhanced predictive accuracy across scales. By systematically constructing a model loss surface L(N,D), Farseer achieves a significantly better fit to empirical data than prior laws (e.g., Chinchilla's law). Our methodology yields accurate, robust, and highly generalizable predictions, demonstrating excellent extrapolation capabilities, improving upon Chinchilla's law by reducing extrapolation error by 433\%. This allows for the reliable evaluation of competing training strategies across all (N,D) settings, enabling conclusions from small-scale ablation studies to be confidently extrapolated to predict large-scale performance. Furthermore, Farseer provides new insights into optimal compute allocation, better reflecting the nuanced demands of modern LLM training. To validate our approach, we trained an extensive suite of approximately 1,000 LLMs across diverse scales and configurations, consuming roughly 3 million NVIDIA H100 GPU hours. We are comprehensively open-sourcing all models, data, results, and logs at https://github.com/Farseer-Scaling-Law/Farseer to foster further research.

Neural scaling laws define a predictable relationship between a model's parameter count and its performance after training in the form of a power law. However, most research to date has not explicitly investigated whether scaling laws can be used to accelerate model development. In this work, we perform such an empirical investigation across a wide range of language understanding tasks, starting from models with as few as 10K parameters, and evaluate downstream performance across 9 language understanding tasks. We find that scaling laws emerge at finetuning time in some NLP tasks, and that they can also be exploited for debugging convergence when training large models. Moreover, for tasks where scaling laws exist, they can be used to predict the performance of larger models, which enables effective model selection. However, revealing scaling laws requires careful hyperparameter tuning and multiple runs for the purpose of uncertainty estimation, which incurs additional overhead, partially offsetting the computational benefits.

The population loss of trained deep neural networks often follows precise power-law scaling relations with either the size of the training dataset or the number of parameters in the network. We propose a theory that explains the origins of and connects these scaling laws. We identify variance-limited and resolution-limited scaling behavior for both dataset and model size, for a total of four scaling regimes. The variance-limited scaling follows simply from the existence of a well-behaved infinite data or infinite width limit, while the resolution-limited regime can be explained by positing that models are effectively resolving a smooth data manifold. In the large width limit, this can be equivalently obtained from the spectrum of certain kernels, and we present evidence that large width and large dataset resolution-limited scaling exponents are related by a duality. We exhibit all four scaling regimes in the controlled setting of large random feature and pretrained models and test the predictions empirically on a range of standard architectures and datasets. We also observe several empirical relationships between datasets and scaling exponents under modifications of task and architecture aspect ratio. Our work provides a taxonomy for classifying different scaling regimes, underscores that there can be different mechanisms driving improvements in loss, and lends insight into the microscopic origins of and relationships between scaling exponents.

Difficult problems, which often result in long reasoning traces, are widely recognized as key factors for enhancing the performance of reasoning models. However, such high-challenge problems are scarce, limiting the size of available datasets. In this paper, we propose a simple method to decouple the reliance on problem difficulty. First, we empirically demonstrate that reasoning length, rather than problem difficulty, primarily influences the performance of trained models. Second, we identify a scaling law on reasoning length, showing that model performance increases in a log-linear fashion as the reasoning data length grows. Finally, we introduce a straightforward technique to generate reasoning data of arbitrary length, and show that synthesized data is effective for training reasoning models. After fine-tuning the Qwen2.5-32B-Instruct language model on our Long1K dataset, we present our model, Long1K-32B, which achieves remarkable performance with only 1,000 training samples, achieving 95.6\% accuracy on MATH, and 71.1\% on GPQA outperforming DeepSeek-R1-Distill-Qwen-32B. The model, code, and dataset are all open-sourced, available at https://huggingface.co/ZTss/LONG1.

Building effective and efficient Transformer-based large language models (LLMs) has recently become a research focus, requiring maximizing model language capabilities and minimizing training and deployment costs. Existing efforts have primarily described complex relationships among model performance, parameter size, and data size, as well as searched for the optimal compute allocation to train LLMs. However, they overlook the impacts of context length and attention head configuration (the number of query and key-value heads in grouped-query attention) on training and inference. In this paper, we systematically compare models with different parameter sizes, context lengths, and attention head configurations in terms of model performance, computational cost, and memory cost. Then, we extend the existing scaling methods, which are based solely on parameter size and training compute, to guide the construction of cost-optimal LLMs during both training and inference. Our quantitative scaling studies show that, when processing sufficiently long sequences, a larger model with fewer attention heads can achieve a lower loss while incurring lower computational and memory costs. Our findings provide valuable insights for developing practical LLMs, especially in long-context processing scenarios. We will publicly release our code and data.

Vision-language models (VLMs) are trained for thousands of GPU hours on carefully curated web datasets. In recent times, data curation has gained prominence with several works developing strategies to retain 'high-quality' subsets of 'raw' scraped data. For instance, the LAION public dataset retained only 10% of the total crawled data. However, these strategies are typically developed agnostic of the available compute for training. In this paper, we first demonstrate that making filtering decisions independent of training compute is often suboptimal: the limited high-quality data rapidly loses its utility when repeated, eventually requiring the inclusion of 'unseen' but 'lower-quality' data. To address this quality-quantity tradeoff (QQT), we introduce neural scaling laws that account for the non-homogeneous nature of web data, an angle ignored in existing literature. Our scaling laws (i) characterize the differing 'utility' of various quality subsets of web data; (ii) account for how utility diminishes for a data point at its 'nth' repetition; and (iii) formulate the mutual interaction of various data pools when combined, enabling the estimation of model performance on a combination of multiple data pools without ever jointly training on them. Our key message is that data curation cannot be agnostic of the total compute that a model will be trained for. Our scaling laws allow us to curate the best possible pool for achieving top performance on Datacomp at various compute budgets, carving out a pareto-frontier for data curation. Code is available at https://github.com/locuslab/scaling_laws_data_filtering.

Foundation models have revolutionized general-purpose problem-solving, offering rapid task adaptation through pretraining, meta-training, and finetuning. Recent crucial advances in these paradigms reveal the importance of challenging task prioritized sampling to enhance adaptation robustness under distribution shifts. However, ranking task difficulties over iteration as a preliminary step typically requires exhaustive task evaluation, which is practically unaffordable in computation and data-annotation. This study provides a novel perspective to illuminate the possibility of leveraging the dual importance of adaptation robustness and learning efficiency, particularly in scenarios where task evaluation is risky or costly, such as iterative agent-environment interactions for robotic policy evaluation or computationally intensive inference steps for finetuning foundation models. Firstly, we introduce Model Predictive Task Sampling (MPTS), a framework that bridges the task space and adaptation risk landscape, providing a theoretical foundation for robust active task sampling. MPTS employs a generative model to characterize the episodic optimization process and predicts task-specific adaptation risk via posterior inference. The resulting risk learner amortizes the costly evaluation of task adaptation performance and provably approximates task difficulty rankings. MPTS seamlessly integrates into zero-shot, few-shot, and supervised finetuning settings. Empirically, we conduct extensive experiments in pattern recognition using foundation models and sequential decision-making. Our results demonstrate that MPTS significantly enhances adaptation robustness for tail or out-of-distribution (OOD) tasks and improves learning efficiency compared to state-of-the-art (SOTA) methods. The code is available at the project site https://github.com/thu-rllab/MPTS.

We address the long-standing problem of how to learn effective pixel-based image diffusion models at scale, introducing a remarkably simple greedy growing method for stable training of large-scale, high-resolution models. without the needs for cascaded super-resolution components. The key insight stems from careful pre-training of core components, namely, those responsible for text-to-image alignment {\it vs.} high-resolution rendering. We first demonstrate the benefits of scaling a {\it Shallow UNet}, with no down(up)-sampling enc(dec)oder. Scaling its deep core layers is shown to improve alignment, object structure, and composition. Building on this core model, we propose a greedy algorithm that grows the architecture into high-resolution end-to-end models, while preserving the integrity of the pre-trained representation, stabilizing training, and reducing the need for large high-resolution datasets. This enables a single stage model capable of generating high-resolution images without the need of a super-resolution cascade. Our key results rely on public datasets and show that we are able to train non-cascaded models up to 8B parameters with no further regularization schemes. Vermeer, our full pipeline model trained with internal datasets to produce 1024x1024 images, without cascades, is preferred by 44.0% vs. 21.4% human evaluators over SDXL.

Recent studies in using deep reinforcement learning (DRL) to solve Job-shop scheduling problems (JSSP) focus on construction heuristics. However, their performance is still far from optimality, mainly because the underlying graph representation scheme is unsuitable for modelling partial solutions at each construction step. This paper proposes a novel DRL-guided improvement heuristic for solving JSSP, where graph representation is employed to encode complete solutions. We design a Graph Neural-Network-based representation scheme, consisting of two modules to effectively capture the information of dynamic topology and different types of nodes in graphs encountered during the improvement process. To speed up solution evaluation during improvement, we present a novel message-passing mechanism that can evaluate multiple solutions simultaneously. We prove that the computational complexity of our method scales linearly with problem size. Experiments on classic benchmarks show that the improvement policy learned by our method outperforms state-of-the-art DRL-based methods by a large margin.

In recent years, language models have drastically grown in size, and the abilities of these models have been shown to improve with scale. The majority of recent scaling laws studies focused on high-compute high-parameter count settings, leaving the question of when these abilities begin to emerge largely unanswered. In this paper, we investigate whether the effects of pre-training can be observed when the problem size is reduced, modeling a smaller, reduced-vocabulary language. We show the benefits of pre-training with masked language modeling (MLM) objective in models as small as 1.25M parameters, and establish a strong correlation between pre-training perplexity and downstream performance (GLUE benchmark). We examine downscaling effects, extending scaling laws to models as small as ~1M parameters. At this scale, we observe a break of the power law for compute-optimal models and show that the MLM loss does not scale smoothly with compute-cost (FLOPs) below 2.2 times 10^{15} FLOPs. We also find that adding layers does not always benefit downstream performance.

State-of-the-art LLMs often rely on scale with high computational costs, which has sparked a research agenda to reduce parameter counts and costs without significantly impacting performance. Our study focuses on Transformer-based LLMs, specifically applying low-rank parametrization to the computationally intensive feedforward networks (FFNs), which are less studied than attention blocks. In contrast to previous works, (i) we explore low-rank parametrization at scale, up to 1.3B parameters; (ii) within Transformer language models rather than convolutional architectures; and (iii) starting from training from scratch. Experiments on the large RefinedWeb dataset show that low-rank parametrization is both efficient (e.g., 2.6times FFN speed-up with 32\% parameters) and effective during training. Interestingly, these structured FFNs exhibit steeper scaling curves than the original models. Motivated by this finding, we develop the wide and structured networks surpassing the current medium-sized and large-sized Transformer in perplexity and throughput performance. Our code is available at https://github.com/CLAIRE-Labo/StructuredFFN/tree/main.

A key puzzle in search, ads, and recommendation is that the ranking model can only utilize a small portion of the vastly available user interaction data. As a result, increasing data volume, model size, or computation FLOPs will quickly suffer from diminishing returns. We examined this problem and found that one of the root causes may lie in the so-called ``item-centric'' formulation, which has an unbounded vocabulary and thus uncontrolled model complexity. To mitigate quality saturation, we introduce an alternative formulation named ``user-centric ranking'', which is based on a transposed view of the dyadic user-item interaction data. We show that this formulation has a promising scaling property, enabling us to train better-converged models on substantially larger data sets.

Scaling up neural networks has led to remarkable performance across a wide range of tasks. Moreover, performance often follows reliable scaling laws as a function of training set size, model size, and compute, which offers valuable guidance as large-scale experiments are becoming increasingly expensive. However, previous work on scaling laws has primarily used private data \& models or focused on uni-modal language or vision learning. To address these limitations, we investigate scaling laws for contrastive language-image pre-training (CLIP) with the public LAION dataset and the open-source OpenCLIP repository. Our large-scale experiments involve models trained on up to two billion image-text pairs and identify power law scaling for multiple downstream tasks including zero-shot classification, retrieval, linear probing, and end-to-end fine-tuning. We find that the training distribution plays a key role in scaling laws as the OpenAI and OpenCLIP models exhibit different scaling behavior despite identical model architectures and similar training recipes. We open-source our evaluation workflow and all models, including the largest public CLIP models, to ensure reproducibility and make scaling laws research more accessible. Source code and instructions to reproduce this study will be available at https://github.com/LAION-AI/scaling-laws-openclip

Low precision training and inference affect both the quality and cost of language models, but current scaling laws do not account for this. In this work, we devise "precision-aware" scaling laws for both training and inference. We propose that training in lower precision reduces the model's "effective parameter count," allowing us to predict the additional loss incurred from training in low precision and post-train quantization. For inference, we find that the degradation introduced by post-training quantization increases as models are trained on more data, eventually making additional pretraining data actively harmful. For training, our scaling laws allow us to predict the loss of a model with different parts in different precisions, and suggest that training larger models in lower precision may be compute optimal. We unify the scaling laws for post and pretraining quantization to arrive at a single functional form that predicts degradation from training and inference in varied precisions. We fit on over 465 pretraining runs and validate our predictions on model sizes up to 1.7B parameters trained on up to 26B tokens.

Scaling laws with respect to the amount of training data and the number of parameters allow us to predict the cost-benefit trade-offs of pretraining language models (LMs) in different configurations. In this paper, we consider another dimension of scaling: the amount of data available at inference time. Specifically, we find that increasing the size of the datastore used by a retrieval-based LM monotonically improves language modeling and several downstream tasks without obvious saturation, such that a smaller model augmented with a large datastore outperforms a larger LM-only model on knowledge-intensive tasks. By plotting compute-optimal scaling curves with varied datastore, model, and pretraining data sizes, we show that using larger datastores can significantly improve model performance for the same training compute budget. We carry out our study by constructing a 1.4 trillion-token datastore named MassiveDS, which is the largest and the most diverse open-sourced datastore for retrieval-based LMs to date, and designing an efficient pipeline for studying datastore scaling in a computationally accessible manner. Finally, we analyze the effect of improving the retriever, datastore quality filtering, and other design choices on our observed scaling trends. Overall, our results show that datastore size should be considered as an integral part of LM efficiency and performance trade-offs. To facilitate future research, we open-source our datastore and code at https://github.com/RulinShao/retrieval-scaling.

Recent progress has pushed AI frontiers from pattern recognition tasks toward problems that require step by step, System2 style reasoning, especially with large language models. Yet, unlike learning, where generalization and out of distribution (OoD) evaluation concepts are well formalized, there is no clear, consistent definition or metric for reasoning ability. We propose Complexity Out of Distribution (Complexity OoD) generalization as a framework and problem setting to define and measure reasoning. A model exhibits Complexity OoD generalization when it maintains performance on test instances whose minimal required solution complexity, either representational (richer solution structure) or computational (more reasoning steps/program length), exceeds that of all training examples. We formalize complexity via solution description Kolmogorov complexity and operational proxies (e.g., object/relation counts; reasoning step counts), clarifying how Complexity OoD differs from length and compositional OoD. This lens unifies learning and reasoning: many cases solvable with System1 like processing at low complexity become System2 like under complexity pressure, while System2 can be viewed as generalization over solution structures. We translate this perspective into practice with recommendations for operationalizing Complexity OoD across the stack: incorporating complexity into benchmark and evaluation metric design, rethinking supervision to target solution traces, seeking and designing inductive biases for Complexity OoD generalization, addressing learning to reason spillovers such as spurious shortcuts, semantic robustness, catastrophic forgetting, and step wise calibration. Because Complexity OoD cannot be solved by scaling data alone, progress toward robust reasoning will require architectures and training regimes that explicitly model and allocate computation with respect to complexity.

Pre-trained language models (PLM), for example BERT or RoBERTa, mark the state-of-the-art for natural language understanding task when fine-tuned on labeled data. However, their large size poses challenges in deploying them for inference in real-world applications, due to significant GPU memory requirements and high inference latency. This paper explores neural architecture search (NAS) for structural pruning to find sub-parts of the fine-tuned network that optimally trade-off efficiency, for example in terms of model size or latency, and generalization performance. We also show how we can utilize more recently developed two-stage weight-sharing NAS approaches in this setting to accelerate the search process. Unlike traditional pruning methods with fixed thresholds, we propose to adopt a multi-objective approach that identifies the Pareto optimal set of sub-networks, allowing for a more flexible and automated compression process.

Large language models (LLMs) have shown significant progress in reasoning tasks. However, recent studies show that transformers and LLMs fail catastrophically once reasoning problems exceed modest complexity. We revisit these findings through the lens of large reasoning models (LRMs) -- LLMs fine-tuned with incentives for step-by-step argumentation and self-verification. LRM performance on graph and reasoning benchmarks such as NLGraph seem extraordinary, with some even claiming they are capable of generalized reasoning and innovation in reasoning-intensive fields such as mathematics, physics, medicine, and law. However, by more carefully scaling the complexity of reasoning problems, we show existing benchmarks actually have limited complexity. We develop a new dataset, the Deep Reasoning Dataset (DeepRD), along with a generative process for producing unlimited examples of scalable complexity. We use this dataset to evaluate model performance on graph connectivity and natural language proof planning. We find that the performance of LRMs drop abruptly at sufficient complexity and do not generalize. We also relate our LRM results to the distributions of the complexities of large, real-world knowledge graphs, interaction graphs, and proof datasets. We find the majority of real-world examples fall inside the LRMs' success regime, yet the long tails expose substantial failure potential. Our analysis highlights the near-term utility of LRMs while underscoring the need for new methods that generalize beyond the complexity of examples in the training distribution.

State-of-the-art results in large language models (LLMs) often rely on scale, which becomes computationally expensive. This has sparked a research agenda to reduce these models' parameter counts and computational costs without significantly impacting their performance. Our study focuses on transformer-based LLMs, specifically targeting the computationally intensive feedforward networks (FFNs), which are less studied than attention blocks. We consider three structured linear parameterizations of the FFN using efficient low-rank and block-diagonal matrices. In contrast to many previous works that examined these approximations, our study i) explores these structures from a training-from-scratch perspective, ii) scales up to 1.3B parameters, and iii) is conducted within recent Transformer-based LLMs rather than convolutional architectures. We demonstrate that these structures can lead to actual computational gains in various scenarios, including online decoding when using a pre-merge technique. Additionally, we propose a novel training regime, called self-guided training, aimed at improving the poor training dynamics that these approximations exhibit when used from initialization. Interestingly, the scaling performance of structured matrices is explored, revealing steeper curves in scaling training FLOPs, along with a favorable scaling trend in the overtraining regime. Specifically, we show that wide and structured networks can utilize training FLOPs more efficiently, with fewer parameters and lower loss than dense models at their optimal trade-off. Our code is available at https://github.com/CLAIRE-Labo/StructuredFFN/tree/main.

Recent advances in Large Language Models (LLMs) have been driven by test-time compute scaling - a strategy that improves reasoning by generating longer, sequential thought processes. While effective, this approach encounters a significant bottleneck as computation increases, where further computation offers only marginal performance gains. We argue this ceiling is not an inherent limit of the model's capability but a flaw in the scaling strategy itself, a phenomenon we term "Tunnel Vision", where a model's imperfect initial steps lock it into a suboptimal reasoning path. To overcome this, we introduce a new scaling paradigm: native thought parallelism. We present ParaThinker, an end-to-end framework that trains an LLM to generate multiple, diverse reasoning paths in parallel and synthesize them into a superior final answer. By exploring different lines of thoughts simultaneously, ParaThinker effectively sidesteps the Tunnel Vision issue and unlocks the model's latent reasoning potential. Our approach demonstrates that scaling compute in parallel (width) is a more effective and efficient way to superior reasoning than simply scaling sequentially (depth). On challenging reasoning benchmarks, ParaThinker achieves substantial accuracy improvements over sequential LLMs (12.3% for 1.5B and 7.5% for 7B models on average with 8 parallel paths), while adding only negligible latency overhead (7.1%). This enables smaller models to surpass much larger counterparts and establishes parallel thinking as a critical, efficient dimension for scaling future LLMs.

Novel computer vision architectures monopolize the spotlight, but the impact of the model architecture is often conflated with simultaneous changes to training methodology and scaling strategies. Our work revisits the canonical ResNet (He et al., 2015) and studies these three aspects in an effort to disentangle them. Perhaps surprisingly, we find that training and scaling strategies may matter more than architectural changes, and further, that the resulting ResNets match recent state-of-the-art models. We show that the best performing scaling strategy depends on the training regime and offer two new scaling strategies: (1) scale model depth in regimes where overfitting can occur (width scaling is preferable otherwise); (2) increase image resolution more slowly than previously recommended (Tan & Le, 2019). Using improved training and scaling strategies, we design a family of ResNet architectures, ResNet-RS, which are 1.7x - 2.7x faster than EfficientNets on TPUs, while achieving similar accuracies on ImageNet. In a large-scale semi-supervised learning setup, ResNet-RS achieves 86.2% top-1 ImageNet accuracy, while being 4.7x faster than EfficientNet NoisyStudent. The training techniques improve transfer performance on a suite of downstream tasks (rivaling state-of-the-art self-supervised algorithms) and extend to video classification on Kinetics-400. We recommend practitioners use these simple revised ResNets as baselines for future research.

Recent diagnostic datasets on compositional generalization, such as SCAN (Lake and Baroni, 2018) and COGS (Kim and Linzen, 2020), expose severe problems in models trained from scratch on these datasets. However, in contrast to this poor performance, state-of-the-art models trained on larger and more general datasets show better generalization ability. In this work, to reconcile this inconsistency, we conduct an empirical analysis by training Transformer models on a variety of training sets with different data factors, including dataset scale, pattern complexity, example difficulty, etc. First, we show that increased dataset complexity can lead to better generalization behavior on multiple different generalization challenges. To further understand this improvement, we show two axes of the benefit from more complex datasets: they provide more diverse examples so compositional understanding becomes more effective, and they also prevent ungeneralizable memorization of the examples due to reduced example repetition frequency. Finally, we explore how training examples of different difficulty levels influence generalization differently. On synthetic datasets, simple examples invoke stronger compositionality than hard examples do. On larger-scale real language datasets, while hard examples become more important potentially to ensure decent data coverage, a balanced mixture of simple and hard examples manages to induce the strongest generalizability. The code and data for this work are available at https://github.com/owenzx/data4comp

How can we train models to perform well on hard test data when hard training data is by definition difficult to label correctly? This question has been termed the scalable oversight problem and has drawn increasing attention as language models have continually improved. In this paper, we present the surprising conclusion that current language models often generalize relatively well from easy to hard data, even performing as well as "oracle" models trained on hard data. We demonstrate this kind of easy-to-hard generalization using simple training methods like in-context learning, linear classifier heads, and QLoRA for seven different measures of datapoint hardness, including six empirically diverse human hardness measures (like grade level) and one model-based measure (loss-based). Furthermore, we show that even if one cares most about model performance on hard data, it can be better to collect and train on easy data rather than hard data, since hard data is generally noisier and costlier to collect. Our experiments use open models up to 70b in size and four publicly available question-answering datasets with questions ranging in difficulty from 3rd grade science questions to college level STEM questions and general-knowledge trivia. We conclude that easy-to-hard generalization in LMs is surprisingly strong for the tasks studied, suggesting the scalable oversight problem may be easier than previously thought. Our code is available at https://github.com/allenai/easy-to-hard-generalization

Low-precision formats such as float8 have been introduced in machine learning accelerated hardware to improve computational efficiency for large language models training and inference. Nevertheless, adoption by the ML community has been slowed down by the complex, and sometimes brittle, techniques required to match higher precision training accuracy. In this work, we present Scalify, a end-to-end scale propagation paradigm for computational graphs, generalizing and formalizing existing tensor scaling methods. Experiment results show that Scalify supports out-of-the-box float8 matrix multiplication and gradients representation, as well as float16 optimizer state storage. Our JAX implementation of Scalify is open-sourced at https://github.com/graphcore-research/jax-scalify

Scaling recommendation models into large recommendation models has become one of the most widely discussed topics. Recent efforts focus on components beyond the scaling embedding dimension, as it is believed that scaling embedding may lead to performance degradation. Although there have been some initial observations on embedding, the root cause of their non-scalability remains unclear. Moreover, whether performance degradation occurs across different types of models and datasets is still an unexplored area. Regarding the effect of embedding dimensions on performance, we conduct large-scale experiments across 10 datasets with varying sparsity levels and scales, using 4 representative classical architectures. We surprisingly observe two novel phenomenon: double-peak and logarithmic. For the former, as the embedding dimension increases, performance first improves, then declines, rises again, and eventually drops. For the latter, it exhibits a perfect logarithmic curve. Our contributions are threefold. First, we discover two novel phenomena when scaling collaborative filtering models. Second, we gain an understanding of the underlying causes of the double-peak phenomenon. Lastly, we theoretically analyze the noise robustness of collaborative filtering models, with results matching empirical observations.

Weight sharing promises to make neural architecture search (NAS) tractable even on commodity hardware. Existing methods in this space rely on a diverse set of heuristics to design and train the shared-weight backbone network, a.k.a. the super-net. Since heuristics and hyperparameters substantially vary across different methods, a fair comparison between them can only be achieved by systematically analyzing the influence of these factors. In this paper, we therefore provide a systematic evaluation of the heuristics and hyperparameters that are frequently employed by weight-sharing NAS algorithms. Our analysis uncovers that some commonly-used heuristics for super-net training negatively impact the correlation between super-net and stand-alone performance, and evidences the strong influence of certain hyperparameters and architectural choices. Our code and experiments set a strong and reproducible baseline that future works can build on.

Kaplan et al. and Hoffmann et al. developed influential scaling laws for the optimal model size as a function of the compute budget, but these laws yield substantially different predictions. We explain the discrepancy by reproducing the Kaplan scaling law on two datasets (OpenWebText2 and RefinedWeb) and identifying three factors causing the difference: last layer computational cost, warmup duration, and scale-dependent optimizer tuning. With these factors corrected, we obtain excellent agreement with the Hoffmann et al. (i.e., "Chinchilla") scaling law. Counter to a hypothesis of Hoffmann et al., we find that careful learning rate decay is not essential for the validity of their scaling law. As a secondary result, we derive scaling laws for the optimal learning rate and batch size, finding that tuning the AdamW beta_2 parameter is essential at lower batch sizes.

The rapid growth of dataset scales has been a key driver in advancing deep learning research. However, as dataset scale increases, the training process becomes increasingly inefficient due to the presence of low-value samples, including excessive redundant samples, overly challenging samples, and inefficient easy samples that contribute little to model improvement.To address this challenge, we propose Scale Efficient Training (SeTa) for large datasets, a dynamic sample pruning approach that losslessly reduces training time. To remove low-value samples, SeTa first performs random pruning to eliminate redundant samples, then clusters the remaining samples according to their learning difficulty measured by loss. Building upon this clustering, a sliding window strategy is employed to progressively remove both overly challenging and inefficient easy clusters following an easy-to-hard curriculum.We conduct extensive experiments on large-scale synthetic datasets, including ToCa, SS1M, and ST+MJ, each containing over 3 million samples.SeTa reduces training costs by up to 50\% while maintaining or improving performance, with minimal degradation even at 70\% cost reduction. Furthermore, experiments on various scale real datasets across various backbones (CNNs, Transformers, and Mambas) and diverse tasks (instruction tuning, multi-view stereo, geo-localization, composed image retrieval, referring image segmentation) demonstrate the powerful effectiveness and universality of our approach. Code is available at https://github.com/mrazhou/SeTa.

The problem of designing NLP solvers for math word problems (MWP) has seen sustained research activity and steady gains in the test accuracy. Since existing solvers achieve high performance on the benchmark datasets for elementary level MWPs containing one-unknown arithmetic word problems, such problems are often considered "solved" with the bulk of research attention moving to more complex MWPs. In this paper, we restrict our attention to English MWPs taught in grades four and lower. We provide strong evidence that the existing MWP solvers rely on shallow heuristics to achieve high performance on the benchmark datasets. To this end, we show that MWP solvers that do not have access to the question asked in the MWP can still solve a large fraction of MWPs. Similarly, models that treat MWPs as bag-of-words can also achieve surprisingly high accuracy. Further, we introduce a challenge dataset, SVAMP, created by applying carefully chosen variations over examples sampled from existing datasets. The best accuracy achieved by state-of-the-art models is substantially lower on SVAMP, thus showing that much remains to be done even for the simplest of the MWPs.

Large language models encode impressively broad world knowledge in their parameters. However, the knowledge in static language models falls out of date, limiting the model's effective "shelf life." While online fine-tuning can reduce this degradation, we find that naively fine-tuning on a stream of documents leads to a low level of information uptake. We hypothesize that online fine-tuning does not sufficiently attend to important information. That is, the gradient signal from important tokens representing factual information is drowned out by the gradient from inherently noisy tokens, suggesting that a dynamic, context-aware learning rate may be beneficial. We therefore propose learning which tokens to upweight. We meta-train a small, autoregressive model to reweight the language modeling loss for each token during online fine-tuning, with the objective of maximizing the out-of-date base question-answering model's ability to answer questions about a document after a single weighted gradient step. We call this approach Context-aware Meta-learned Loss Scaling (CaMeLS). Across three different distributions of documents, our experiments find that CaMeLS provides substantially improved information uptake on streams of thousands of documents compared with standard fine-tuning and baseline heuristics for reweighting token losses.

Robust and effective scaling of models from small to large width typically requires the precise adjustment of many algorithmic and architectural details, such as parameterization and optimizer choices. In this work, we propose a new perspective on parameterization by investigating a key assumption in prior work about the alignment between parameters and data and derive new theoretical results under weaker assumptions and a broader set of optimizers. Our extensive empirical investigation includes tens of thousands of models trained with all combinations of three optimizers, four parameterizations, several alignment assumptions, more than a dozen learning rates, and fourteen model sizes up to 26.8B parameters. We find that the best learning rate scaling prescription would often have been excluded by the assumptions in prior work. Our results show that all parameterizations, not just maximal update parameterization (muP), can achieve hyperparameter transfer; moreover, our novel per-layer learning rate prescription for standard parameterization outperforms muP. Finally, we demonstrate that an overlooked aspect of parameterization, the epsilon parameter in Adam, must be scaled correctly to avoid gradient underflow and propose Adam-atan2, a new numerically stable, scale-invariant version of Adam that eliminates the epsilon hyperparameter entirely.

Learning arguably involves the discovery and memorization of abstract rules. The aim of this paper is to study associative memory mechanisms. Our model is based on high-dimensional matrices consisting of outer products of embeddings, which relates to the inner layers of transformer language models. We derive precise scaling laws with respect to sample size and parameter size, and discuss the statistical efficiency of different estimators, including optimization-based algorithms. We provide extensive numerical experiments to validate and interpret theoretical results, including fine-grained visualizations of the stored memory associations.

Scaling the capacity of language models has consistently proven to be a reliable approach for improving performance and unlocking new capabilities. Capacity can be primarily defined by two dimensions: the number of model parameters and the compute per example. While scaling typically involves increasing both, the precise interplay between these factors and their combined contribution to overall capacity remains not fully understood. We explore this relationship in the context of sparse Mixture-of-Experts (MoEs), which allow scaling the number of parameters without proportionally increasing the FLOPs per example. We investigate how varying the sparsity level, i.e., the fraction of inactive parameters, impacts model's performance during pretraining and downstream few-shot evaluation. We find that under different constraints (e.g., parameter size and total training compute), there is an optimal level of sparsity that improves both training efficiency and model performance. These results provide a better understanding of the impact of sparsity in scaling laws for MoEs and complement existing works in this area, offering insights for designing more efficient architectures.

As language models (LMs) scale, they develop many novel behaviors, good and bad, exacerbating the need to evaluate how they behave. Prior work creates evaluations with crowdwork (which is time-consuming and expensive) or existing data sources (which are not always available). Here, we automatically generate evaluations with LMs. We explore approaches with varying amounts of human effort, from instructing LMs to write yes/no questions to making complex Winogender schemas with multiple stages of LM-based generation and filtering. Crowdworkers rate the examples as highly relevant and agree with 90-100% of labels, sometimes more so than corresponding human-written datasets. We generate 154 datasets and discover new cases of inverse scaling where LMs get worse with size. Larger LMs repeat back a dialog user's preferred answer ("sycophancy") and express greater desire to pursue concerning goals like resource acquisition and goal preservation. We also find some of the first examples of inverse scaling in RL from Human Feedback (RLHF), where more RLHF makes LMs worse. For example, RLHF makes LMs express stronger political views (on gun rights and immigration) and a greater desire to avoid shut down. Overall, LM-written evaluations are high-quality and let us quickly discover many novel LM behaviors.

Recent neural network-based language models have benefited greatly from scaling up the size of training datasets and the number of parameters in the models themselves. Scaling can be complicated due to various factors including the need to distribute computation on supercomputer clusters (e.g., TPUs), prevent bottlenecks when infeeding data, and ensure reproducible results. In this work, we present two software libraries that ease these issues: t5x simplifies the process of building and training large language models at scale while maintaining ease of use, and seqio provides a task-based API for simple creation of fast and reproducible training data and evaluation pipelines. These open-source libraries have been used to train models with hundreds of billions of parameters on datasets with multiple terabytes of training data. Along with the libraries, we release configurations and instructions for T5-like encoder-decoder models as well as GPT-like decoder-only architectures. t5x and seqio are open source and available at https://github.com/google-research/t5x and https://github.com/google/seqio, respectively.

Test-time scaling (TTS) enhances the performance of large language models (LLMs) by allocating additional compute resources during inference. However, existing research primarily investigates TTS in single-stage tasks; while many real-world problems are multi-stage complex tasks, composed of a sequence of heterogeneous subtasks with each subtask requires LLM of specific capability. Therefore, we study a novel problem: the test-time compute-optimal scaling in multi-stage complex tasks, aiming to select suitable models and allocate budgets per subtask to maximize overall performance. TTS in multi-stage tasks introduces two fundamental challenges: (i) The combinatorial search space of model and budget allocations, combined with the high cost of inference, makes brute-force search impractical. (ii) The optimal model and budget allocations across subtasks are interdependent, increasing the complexity of the compute-optimal search. To address this gap, we conduct extensive pilot experiments on four tasks across six datasets, deriving three empirical insights characterizing the behavior of LLMs in multi-stage complex tasks. Informed by these insights, we propose AgentTTS, an LLM-agent-based framework that autonomously searches for compute-optimal allocations through iterative feedback-driven interactions with the execution environment. Experimental results demonstrate that AgentTTS significantly outperforms traditional and other LLM-based baselines in search efficiency, and shows improved robustness to varying training set sizes and enhanced interpretability.

Autonomous agents have recently achieved remarkable progress across diverse domains, yet most evaluations focus on short-horizon, fully observable tasks. In contrast, many critical real-world tasks, such as large-scale software development, commercial investment, and scientific discovery, unfold in long-horizon and partially observable scenarios where success hinges on sustained reasoning, planning, memory management, and tool use. Existing benchmarks rarely capture these long-horizon challenges, leaving a gap in systematic evaluation. To bridge this gap, we introduce UltraHorizon a novel benchmark that measures the foundational capabilities essential for complex real-world challenges. We use exploration as a unifying task across three distinct environments to validate these core competencies. Agents are designed in long-horizon discovery tasks where they must iteratively uncover hidden rules through sustained reasoning, planning, memory and tools management, and interaction with environments. Under the heaviest scale setting, trajectories average 200k+ tokens and 400+ tool calls, whereas in standard configurations they still exceed 35k tokens and involve more than 60 tool calls on average. Our extensive experiments reveal that LLM-agents consistently underperform in these settings, whereas human participants achieve higher scores, underscoring a persistent gap in agents' long-horizon abilities. We also observe that simple scaling fails in our task. To better illustrate the failure of agents, we conduct an in-depth analysis of collected trajectories. We identify eight types of errors and attribute them to two primary causes: in-context locking and functional fundamental capability gaps. https://github.com/StarDewXXX/UltraHorizon{Our code will be available here.}

There remain many open questions pertaining to the scaling behaviour of Transformer architectures. These scaling decisions and findings can be critical, as training runs often come with an associated computational cost which have both financial and/or environmental impact. The goal of this paper is to present scaling insights from pretraining and finetuning Transformers. While Kaplan et al. presents a comprehensive study of the scaling behaviour of Transformer language models, the scope is only on the upstream (pretraining) loss. Therefore, it is still unclear if these set of findings transfer to downstream task within the context of the pretrain-finetune paradigm. The key findings of this paper are as follows: (1) we show that aside from only the model size, model shape matters for downstream fine-tuning, (2) scaling protocols operate differently at different compute regions, (3) widely adopted T5-base and T5-large sizes are Pareto-inefficient. To this end, we present improved scaling protocols whereby our redesigned models achieve similar downstream fine-tuning quality while having 50\% fewer parameters and training 40\% faster compared to the widely adopted T5-base model. We publicly release over 100 pretrained checkpoints of different T5 configurations to facilitate future research and analysis.

Process reward models (PRMs) play a central role in guiding inference-time scaling algorithms for large language models (LLMs). However, we observe that even state-of-the-art PRMs can be poorly calibrated and often overestimate success probabilities. To address this, we present a calibration approach, performed via quantile regression, that adjusts PRM outputs to better align with true success probabilities. Leveraging these calibrated success estimates and their associated confidence bounds, we introduce an instance-adaptive scaling (IAS) framework that dynamically adjusts the inference budget based on the estimated likelihood that a partial reasoning trajectory will yield a correct final answer. Unlike conventional methods that allocate a fixed number of reasoning trajectories per query, this approach successfully adapts to each instance and reasoning step when using our calibrated PRMs. Experiments on mathematical reasoning benchmarks show that (i) our PRM calibration method successfully achieves small calibration error, outperforming the baseline methods, (ii) calibration is crucial for enabling effective adaptive scaling, and (iii) the proposed IAS strategy reduces inference costs while maintaining final answer accuracy, utilizing less compute on more confident problems as desired.

Inference-time scaling has emerged as a powerful alternative to parameter scaling for improving language model performance on complex reasoning tasks. While existing methods have shown strong performance gains under fixed compute budgets, there has been little focus on optimally utilizing that budget during inference. In this work, we introduce A*-decoding, a search-based inference-time strategy that builds on the A* search algorithm to optimally utilize a fixed compute budget by prioritizing high-quality reasoning paths during generation. We frame language model decoding as a structured search in a state space of partial solutions, applying the A* transition model to identify promising continuations guided by an external process supervision signal. In our experiments, A*-decoding reaches the performance levels of strong inference scaling baselines like best-of-N and particle filtering while using up to 3x fewer tokens and 30% fewer PRM passes under equivalent compute budgets. On the MATH500 and AIME 2024 benchmarks, A*-decoding enables Llama-3.2-1B-Instruct to match the performance of the 70x larger Llama-3.1-70B-Instruct, and allows Qwen3-1.7B to reach o1-like reasoning accuracy. These results highlight the power of structured search in decoding, offering an alternative to brute-force sampling or scale-driven gains. Our work demonstrates how thoughtful inference-time strategies can enhance reasoning in SLMs, pointing toward future advances in more efficient and scalable language model deployment.

Test-Time Scaling (TTS) improves large language models (LLMs) by allocating additional computation during inference, typically through parallel, sequential, or hybrid scaling. However, prior studies often assume fixed collaboration architectures (e.g., topologies) and single-model usage, overlooking that optimal architectures and model combinations can vary across tasks. Therefore, we study the novel problem of searching for compute-optimal model combinations and architectures in TTS under a fixed budget. We formalize it as a multi-LLM collaboration graph, where nodes encode roles and LLM model assignments, and edges capture information flow. This problem is challenging because (i) the combinatorial search space is prohibitively large, and (ii) task-specific requirements demand tailored designs. To address these, we reformulate the problem as probabilistic graph optimization and, through pilot experiments, derive three empirical insights into TTS collaboration graphs. Guided by these insights, we propose Agent-REINFORCE, an LLM-agent-augmented framework that mirrors the REINFORCE pipeline by mapping sampling-gradient-update to sampling-feedback-update, where feedback serves as a textual gradient to update the probabilistic graph and efficiently search for optimal multi-LLM collaboration graphs. Experiments show that Agent-REINFORCE outperforms both traditional and LLM-based baselines in sample efficiency and search performance, and effectively identifies optimal graphs under joint objectives of accuracy and inference latency.

Large models represent a groundbreaking advancement in multiple application fields, enabling remarkable achievements across various tasks. However, their unprecedented scale comes with significant computational costs. These models, often consisting of billions of parameters, require vast amounts of computational resources for execution. Especially, the expansive scale and computational demands pose considerable challenges when customizing them for particular downstream tasks, particularly over the hardware platforms constrained by computational capabilities. Parameter Efficient Fine-Tuning (PEFT) provides a practical solution by efficiently adapt the large models over the various downstream tasks. In particular, PEFT refers to the process of adjusting the parameters of a pre-trained large models to adapt it to a specific task while minimizing the number of additional parameters introduced or computational resources required. This approach is particularly important when dealing with large language models with high parameter counts, as fine-tuning these models from scratch can be computationally expensive and resource-intensive, posing considerable challenges in the supporting system platform design. In this survey, we present comprehensive studies of various PEFT algorithms, examining their performance and computational overhead. Moreover, we provide an overview of applications developed using different PEFT algorithms and discuss common techniques employed to mitigate computation costs for PEFT. In addition to the algorithmic perspective, we overview various real-world system designs to investigate the implementation costs associated with different PEFT algorithms. This survey serves as an indispensable resource for researchers aiming to understand both the PEFT algorithm and its system implementation, offering detailed insights into recent advancements and practical applications.

We study empirical scaling laws for language model performance on the cross-entropy loss. The loss scales as a power-law with model size, dataset size, and the amount of compute used for training, with some trends spanning more than seven orders of magnitude. Other architectural details such as network width or depth have minimal effects within a wide range. Simple equations govern the dependence of overfitting on model/dataset size and the dependence of training speed on model size. These relationships allow us to determine the optimal allocation of a fixed compute budget. Larger models are significantly more sample-efficient, such that optimally compute-efficient training involves training very large models on a relatively modest amount of data and stopping significantly before convergence.

Large language models (LLMs) have surged in popularity and are extensively used in commercial applications, where the efficiency of model serving is crucial for the user experience. Most current research focuses on optimizing individual sub-procedures, e.g. local inference and communication, however, there is no comprehensive framework that provides a holistic system view for optimizing LLM serving in an end-to-end manner. In this work, we conduct a detailed analysis to identify major bottlenecks that impact end-to-end latency in LLM serving systems. Our analysis reveals that a comprehensive LLM serving endpoint must address a series of efficiency bottlenecks that extend beyond LLM inference. We then propose ScaleLLM, an optimized system for resource-efficient LLM serving. Our extensive experiments reveal that with 64 concurrent requests, ScaleLLM achieves a 4.3x speed up over vLLM and outperforms state-of-the-arts with 1.5x higher throughput.

Recently, Visual Autoregressive (VAR) Models introduced a groundbreaking advancement in the field of image generation, offering a scalable approach through a coarse-to-fine "next-scale prediction" paradigm. However, the state-of-the-art algorithm of VAR models in [Tian, Jiang, Yuan, Peng and Wang, NeurIPS 2024] takes O(n^4) time, which is computationally inefficient. In this work, we analyze the computational limits and efficiency criteria of VAR Models through a fine-grained complexity lens. Our key contribution is identifying the conditions under which VAR computations can achieve sub-quadratic time complexity. Specifically, we establish a critical threshold for the norm of input matrices used in VAR attention mechanisms. Above this threshold, assuming the Strong Exponential Time Hypothesis (SETH) from fine-grained complexity theory, a sub-quartic time algorithm for VAR models is impossible. To substantiate our theoretical findings, we present efficient constructions leveraging low-rank approximations that align with the derived criteria. This work initiates the study of the computational efficiency of the VAR model from a theoretical perspective. Our technique will shed light on advancing scalable and efficient image generation in VAR frameworks.

Cascade Ranking is a prevalent architecture in large-scale top-k selection systems like recommendation and advertising platforms. Traditional training methods focus on single-stage optimization, neglecting interactions between stages. Recent advances have introduced interaction-aware training paradigms, but still struggle to 1) align training objectives with the goal of the entire cascade ranking (i.e., end-to-end recall of ground-truth items) and 2) learn effective collaboration patterns for different stages. To address these challenges, we propose LCRON, which introduces a novel surrogate loss function derived from the lower bound probability that ground truth items are selected by cascade ranking, ensuring alignment with the overall objective of the system. According to the properties of the derived bound, we further design an auxiliary loss for each stage to drive the reduction of this bound, leading to a more robust and effective top-k selection. LCRON enables end-to-end training of the entire cascade ranking system as a unified network. Experimental results demonstrate that LCRON achieves significant improvement over existing methods on public benchmarks and industrial applications, addressing key limitations in cascade ranking training and significantly enhancing system performance.

This paper investigates scaling laws for local SGD in LLM training, a distributed optimization algorithm that facilitates training on loosely connected devices. Through extensive experiments, we show that local SGD achieves competitive results compared to conventional methods, given equivalent model parameters, datasets, and computational resources. Furthermore, we explore the application of local SGD in various practical scenarios, including multi-cluster setups and edge computing environments. Our findings elucidate the necessary conditions for effective multi-cluster LLM training and examine the potential and limitations of leveraging edge computing resources in the LLM training process. This demonstrates its viability as an alternative to single large-cluster training.

This paper addresses the scalability challenge of architecture search by formulating the task in a differentiable manner. Unlike conventional approaches of applying evolution or reinforcement learning over a discrete and non-differentiable search space, our method is based on the continuous relaxation of the architecture representation, allowing efficient search of the architecture using gradient descent. Extensive experiments on CIFAR-10, ImageNet, Penn Treebank and WikiText-2 show that our algorithm excels in discovering high-performance convolutional architectures for image classification and recurrent architectures for language modeling, while being orders of magnitude faster than state-of-the-art non-differentiable techniques. Our implementation has been made publicly available to facilitate further research on efficient architecture search algorithms.

It is often advantageous to train models on a subset of the available train examples, because the examples are of variable quality or because one would like to train with fewer examples, without sacrificing performance. We present Gradient Information Optimization (GIO), a scalable, task-agnostic approach to this data selection problem that requires only a small set of (unlabeled) examples representing a target distribution. GIO begins from a natural, information-theoretic objective that is intractable in practice. Our contribution is in showing that it can be made highly scalable through a simple relaxation of the objective and a highly efficient implementation. In experiments with machine translation, spelling correction, and image recognition, we show that GIO delivers outstanding results with very small train sets. These findings are robust to different representation models and hyperparameters for GIO itself. GIO is task- and domain-agnostic and can be applied out-of-the-box to new datasets and domains.

Large Language Models have shown remarkable capabilities in the NLP domain. Their effectiveness can mainly be attributed to their ability to adapt to an array of downstream tasks. However, generally, full fine-tuning is a computationally expensive job. To mitigate this, many techniques have been developed that prime efficiency, a prominent one being Low-Rank Adaptation (LoRA). However, LoRA and its variants employ re-parametrized additive updates. In this paper, we propose Low-Rank Multiplicative Adaptation (LoRMA), which shifts the paradigm of additive updates to a richer space of matrix multiplicative transformations. We tackle challenges such as computational complexity and rank bottleneck of matrix multiplication by effectively re-ordering operations and introducing rank inflation strategies. We conduct extensive experiments to demonstrate the effectiveness of our approach in terms of various evaluation metrics.

The remarkable success of large language pretraining and the discovery of scaling laws signify a paradigm shift in machine learning. Notably, the primary objective has evolved from minimizing generalization error to reducing approximation error, and the most effective strategy has transitioned from regularization (in a broad sense) to scaling up models. This raises a critical question: Do the established principles that proved successful in the generalization-centric era remain valid in this new era of scaling? This paper examines several influential regularization-based principles that may no longer hold true in the scaling-centric, large language model (LLM) era. These principles include explicit L2 regularization and implicit regularization through small batch sizes and large learning rates. Additionally, we identify a new phenomenon termed ``scaling law crossover,'' where two scaling curves intersect at a certain scale, implying that methods effective at smaller scales may not generalize to larger ones. Together, these observations highlight two fundamental questions within this new paradigm: bullet Guiding Principles for Scaling: If regularization is no longer the primary guiding principle for model design, what new principles are emerging to guide scaling? bullet Model Comparison at Scale: How to reliably and effectively compare models at the scale where only a single experiment is feasible?

While scaling training compute has led to remarkable improvements in large language models (LLMs), scaling inference compute has not yet yielded analogous gains. We hypothesize that a core missing component is a lack of diverse LLM outputs, leading to inefficient search due to models repeatedly sampling highly similar, yet incorrect generations. We empirically demonstrate that this lack of diversity can be mitigated by searching over candidate plans for solving a problem in natural language. Based on this insight, we propose PLANSEARCH, a novel search algorithm which shows strong results across HumanEval+, MBPP+, and LiveCodeBench (a contamination-free benchmark for competitive coding). PLANSEARCH generates a diverse set of observations about the problem and then uses these observations to construct plans for solving the problem. By searching over plans in natural language rather than directly over code solutions, PLANSEARCH explores a significantly more diverse range of potential solutions compared to baseline search methods. Using PLANSEARCH on top of Claude 3.5 Sonnet achieves a state-of-the-art pass@200 of 77.0% on LiveCodeBench, outperforming both the best score achieved without search (pass@1 = 41.4%) and using standard repeated sampling (pass@200 = 60.6%). Finally, we show that, across all models, search algorithms, and benchmarks analyzed, we can accurately predict performance gains due to search as a direct function of the diversity over generated ideas.

Large, pre-trained models are problematic to use in resource constrained applications. Fortunately, task-aware structured pruning methods offer a solution. These approaches reduce model size by dropping structural units like layers and attention heads in a manner that takes into account the end-task. However, these pruning algorithms require more task-specific data than is typically available. We propose a framework which combines structured pruning with transfer learning to reduce the need for task-specific data. Our empirical results answer questions such as: How should the two tasks be coupled? What parameters should be transferred? And, when during training should transfer learning be introduced? Leveraging these insights, we demonstrate that our framework results in pruned models with improved generalization over strong baselines.

Large language models (LLMs) have shown excellent performance on various tasks, but the astronomical model size raises the hardware barrier for serving (memory size) and slows down token generation (memory bandwidth). In this paper, we propose Activation-aware Weight Quantization (AWQ), a hardware-friendly approach for LLM low-bit weight-only quantization. Our method is based on the observation that weights are not equally important: protecting only 1% of salient weights can greatly reduce quantization error. We then propose to search for the optimal per-channel scaling that protects the salient weights by observing the activation, not weights. AWQ does not rely on any backpropagation or reconstruction, so it can well preserve LLMs' generalization ability on different domains and modalities, without overfitting to the calibration set; it also does not rely on any data layout reordering, maintaining the hardware efficiency. AWQ outperforms existing work on various language modeling, common sense QA, and domain-specific benchmarks. Thanks to better generalization, it achieves excellent quantization performance for instruction-tuned LMs and, for the first time, multi-modal LMs. We also implement efficient tensor core kernels with reorder-free online dequantization to accelerate AWQ, achieving a 1.45x speedup over GPTQ and is 1.85x faster than the cuBLAS FP16 implementation. Our method provides a turn-key solution to compress LLMs to 3/4 bits for efficient deployment.

Pre-trained models produce strong generic representations that can be adapted via fine-tuning. The learned weight difference relative to the pre-trained model, known as a task vector, characterises the direction and stride of fine-tuning. The significance of task vectors is such that simple arithmetic operations on them can be used to combine diverse representations from different domains. This paper builds on these properties of task vectors and aims to answer (1) whether components of task vectors, particularly parameter blocks, exhibit similar characteristics, and (2) how such blocks can be used to enhance knowledge composition and transfer. To this end, we introduce aTLAS, an algorithm that linearly combines parameter blocks with different learned coefficients, resulting in anisotropic scaling at the task vector level. We show that such linear combinations explicitly exploit the low intrinsic dimensionality of pre-trained models, with only a few coefficients being the learnable parameters. Furthermore, composition of parameter blocks leverages the already learned representations, thereby reducing the dependency on large amounts of data. We demonstrate the effectiveness of our method in task arithmetic, few-shot recognition and test-time adaptation, with supervised or unsupervised objectives. In particular, we show that (1) learned anisotropic scaling allows task vectors to be more disentangled, causing less interference in composition; (2) task vector composition excels with scarce or no labeled data and is less prone to domain shift, thus leading to better generalisability; (3) mixing the most informative parameter blocks across different task vectors prior to training can reduce the memory footprint and improve the flexibility of knowledge transfer. Moreover, we show the potential of aTLAS as a PEFT method, particularly with less data, and demonstrate that its scalibility.

Large language models display remarkable capabilities in logical and mathematical reasoning, allowing them to solve complex tasks. Interestingly, these abilities emerge in networks trained on the simple task of next-token prediction. In this work, we present a theoretical framework for studying auto-regressive next-token predictors. We demonstrate that even simple models such as linear next-token predictors, trained on Chain-of-Thought (CoT) data, can approximate any function efficiently computed by a Turing machine. We introduce a new complexity measure -- length complexity -- which measures the number of intermediate tokens in a CoT sequence required to approximate some target function, and analyze the interplay between length complexity and other notions of complexity. Finally, we show experimentally that simple next-token predictors, such as linear networks and shallow Multi-Layer Perceptrons (MLPs), display non-trivial performance on text generation and arithmetic tasks. Our results demonstrate that the power of language models can be attributed, to a great extent, to the auto-regressive next-token training scheme, and not necessarily to a particular choice of architecture.

While machine learning has advanced through massive parallelization, we identify a critical blind spot: some problems are fundamentally sequential. These "inherently serial" problems-from mathematical reasoning to physical simulations to sequential decision-making-require dependent computational steps that cannot be parallelized. Drawing from complexity theory, we formalize this distinction and demonstrate that current parallel-centric architectures face fundamental limitations on such tasks. We argue that recognizing the serial nature of computation holds profound implications on machine learning, model design, hardware development. As AI tackles increasingly complex reasoning, deliberately scaling serial computation-not just parallel computation-is essential for continued progress.

Recently similarity graphs became the leading paradigm for efficient nearest neighbor search, outperforming traditional tree-based and LSH-based methods. Similarity graphs perform the search via greedy routing: a query traverses the graph and in each vertex moves to the adjacent vertex that is the closest to this query. In practice, similarity graphs are often susceptible to local minima, when queries do not reach its nearest neighbors, getting stuck in suboptimal vertices. In this paper we propose to learn the routing function that overcomes local minima via incorporating information about the graph global structure. In particular, we augment the vertices of a given graph with additional representations that are learned to provide the optimal routing from the start vertex to the query nearest neighbor. By thorough experiments, we demonstrate that the proposed learnable routing successfully diminishes the local minima problem and significantly improves the overall search performance.

Test-time compute scaling has emerged as a new axis along which to improve model accuracy, where additional computation is used at inference time to allow the model to think longer for more challenging problems. One promising approach for test-time compute scaling is search against a process reward model, where a model generates multiple potential candidates at each step of the search, and these partial trajectories are then scored by a separate reward model in order to guide the search process. The diversity of trajectories in the tree search process affects the accuracy of the search, since increasing diversity promotes more exploration. However, this diversity comes at a cost, as divergent trajectories have less KV sharing, which means they consume more memory and slow down the search process. Previous search methods either do not perform sufficient exploration, or else explore diverse trajectories but have high latency. We address this challenge by proposing Efficient Tree Search (ETS), which promotes KV sharing by pruning redundant trajectories while maintaining necessary diverse trajectories. ETS incorporates a linear programming cost model to promote KV cache sharing by penalizing the number of nodes retained, while incorporating a semantic coverage term into the cost model to ensure that we retain trajectories which are semantically different. We demonstrate how ETS can achieve 1.8times reduction in average KV cache size during the search process, leading to 1.4times increased throughput relative to prior state-of-the-art methods, with minimal accuracy degradation and without requiring any custom kernel implementation. Code is available at: https://github.com/SqueezeAILab/ETS.

Which transformer scaling regimes are able to perfectly solve different classes of algorithmic problems? While tremendous empirical advances have been attained by transformer-based neural networks, a theoretical understanding of their algorithmic reasoning capabilities in realistic parameter regimes is lacking. We investigate this question in terms of the network's depth, width, and number of extra tokens for algorithm execution. Our novel representational hierarchy separates 9 algorithmic reasoning problems into classes solvable by transformers in different realistic parameter scaling regimes. We prove that logarithmic depth is necessary and sufficient for tasks like graph connectivity, while single-layer transformers with small embedding dimensions can solve contextual retrieval tasks. We also support our theoretical analysis with ample empirical evidence using the GraphQA benchmark. These results show that transformers excel at many graph reasoning tasks, even outperforming specialized graph neural networks.

We study a novel language model architecture that is capable of scaling test-time computation by implicitly reasoning in latent space. Our model works by iterating a recurrent block, thereby unrolling to arbitrary depth at test-time. This stands in contrast to mainstream reasoning models that scale up compute by producing more tokens. Unlike approaches based on chain-of-thought, our approach does not require any specialized training data, can work with small context windows, and can capture types of reasoning that are not easily represented in words. We scale a proof-of-concept model to 3.5 billion parameters and 800 billion tokens. We show that the resulting model can improve its performance on reasoning benchmarks, sometimes dramatically, up to a computation load equivalent to 50 billion parameters.

We develop task scaling laws and model ladders to predict the individual task performance of pretrained language models (LMs) in the overtrained setting. Standard power laws for language modeling loss cannot accurately model task performance. Therefore, we leverage a two-step prediction approach: first use model and data size to predict a task-specific loss, and then use this task loss to predict task performance. We train a set of small-scale "ladder" models, collect data points to fit the parameterized functions of the two prediction steps, and make predictions for two target models: a 7B model trained to 4T tokens and a 13B model trained to 5T tokens. Training the ladder models only costs 1% of the compute used for the target models. On four multiple-choice tasks written in ranked classification format, we can predict the accuracy of both target models within 2 points of absolute error. We have higher prediction error on four other tasks (average absolute error 6.9) and find that these are often tasks with higher variance in task metrics. We also find that using less compute to train fewer ladder models tends to deteriorate predictions. Finally, we empirically show that our design choices and the two-step approach lead to superior performance in establishing scaling laws.

We present an online post-hoc calibration method, called Online Platt Scaling (OPS), which combines the Platt scaling technique with online logistic regression. We demonstrate that OPS smoothly adapts between i.i.d. and non-i.i.d. settings with distribution drift. Further, in scenarios where the best Platt scaling model is itself miscalibrated, we enhance OPS by incorporating a recently developed technique called calibeating to make it more robust. Theoretically, our resulting OPS+calibeating method is guaranteed to be calibrated for adversarial outcome sequences. Empirically, it is effective on a range of synthetic and real-world datasets, with and without distribution drifts, achieving superior performance without hyperparameter tuning. Finally, we extend all OPS ideas to the beta scaling method.

Language model pretraining with next token prediction has proved effective for scaling compute but is limited to the amount of available training data. Scaling reinforcement learning (RL) unlocks a new axis for the continued improvement of artificial intelligence, with the promise that large language models (LLMs) can scale their training data by learning to explore with rewards. However, prior published work has not produced competitive results. In light of this, we report on the training practice of Kimi k1.5, our latest multi-modal LLM trained with RL, including its RL training techniques, multi-modal data recipes, and infrastructure optimization. Long context scaling and improved policy optimization methods are key ingredients of our approach, which establishes a simplistic, effective RL framework without relying on more complex techniques such as Monte Carlo tree search, value functions, and process reward models. Notably, our system achieves state-of-the-art reasoning performance across multiple benchmarks and modalities -- e.g., 77.5 on AIME, 96.2 on MATH 500, 94-th percentile on Codeforces, 74.9 on MathVista -- matching OpenAI's o1. Moreover, we present effective long2short methods that use long-CoT techniques to improve short-CoT models, yielding state-of-the-art short-CoT reasoning results -- e.g., 60.8 on AIME, 94.6 on MATH500, 47.3 on LiveCodeBench -- outperforming existing short-CoT models such as GPT-4o and Claude Sonnet 3.5 by a large margin (up to +550%).

Weight oscillation is an undesirable side effect of quantization-aware training, in which quantized weights frequently jump between two quantized levels, resulting in training instability and a sub-optimal final model. We discover that the learnable scaling factor, a widely-used de facto setting in quantization aggravates weight oscillation. In this study, we investigate the connection between the learnable scaling factor and quantized weight oscillation and use ViT as a case driver to illustrate the findings and remedies. In addition, we also found that the interdependence between quantized weights in query and key of a self-attention layer makes ViT vulnerable to oscillation. We, therefore, propose three techniques accordingly: statistical weight quantization (rm StatsQ) to improve quantization robustness compared to the prevalent learnable-scale-based method; confidence-guided annealing (rm CGA) that freezes the weights with high confidence and calms the oscillating weights; and query-key reparameterization (rm QKR) to resolve the query-key intertwined oscillation and mitigate the resulting gradient misestimation. Extensive experiments demonstrate that these proposed techniques successfully abate weight oscillation and consistently achieve substantial accuracy improvement on ImageNet. Specifically, our 2-bit DeiT-T/DeiT-S algorithms outperform the previous state-of-the-art by 9.8% and 7.7%, respectively. Code and models are available at: https://github.com/nbasyl/OFQ.

Given a set of dissimilarity measurements amongst data points, determining what metric representation is most "consistent" with the input measurements or the metric that best captures the relevant geometric features of the data is a key step in many machine learning algorithms. Existing methods are restricted to specific kinds of metrics or small problem sizes because of the large number of metric constraints in such problems. In this paper, we provide an active set algorithm, Project and Forget, that uses Bregman projections, to solve metric constrained problems with many (possibly exponentially) inequality constraints. We provide a theoretical analysis of Project and Forget and prove that our algorithm converges to the global optimal solution and that the L_2 distance of the current iterate to the optimal solution decays asymptotically at an exponential rate. We demonstrate that using our method we can solve large problem instances of three types of metric constrained problems: general weight correlation clustering, metric nearness, and metric learning; in each case, out-performing the state of the art methods with respect to CPU times and problem sizes.

The increasing interest in Large Language Models (LLMs) within the telecommunications sector underscores their potential to revolutionize operational efficiency. However, the deployment of these sophisticated models is often hampered by their substantial size and computational demands, raising concerns about their viability in resource-constrained environments. Addressing this challenge, recent advancements have seen the emergence of small language models that surprisingly exhibit performance comparable to their larger counterparts in many tasks, such as coding and common-sense reasoning. Phi-2, a compact yet powerful model, exemplifies this new wave of efficient small language models. This paper conducts a comprehensive evaluation of Phi-2's intrinsic understanding of the telecommunications domain. Recognizing the scale-related limitations, we enhance Phi-2's capabilities through a Retrieval-Augmented Generation approach, meticulously integrating an extensive knowledge base specifically curated with telecom standard specifications. The enhanced Phi-2 model demonstrates a profound improvement in accuracy, answering questions about telecom standards with a precision that closely rivals the more resource-intensive GPT-3.5. The paper further explores the refined capabilities of Phi-2 in addressing problem-solving scenarios within the telecom sector, highlighting its potential and limitations.

Long-context capabilities are essential for a wide range of applications, including document and video understanding, in-context learning, and inference-time scaling, all of which require models to process and reason over long sequences of text and multimodal data. In this work, we introduce a efficient training recipe for building ultra-long context LLMs from aligned instruct model, pushing the boundaries of context lengths from 128K to 1M, 2M, and 4M tokens. Our approach leverages efficient continued pretraining strategies to extend the context window and employs effective instruction tuning to maintain the instruction-following and reasoning abilities. Our UltraLong-8B, built on Llama3.1-Instruct with our recipe, achieves state-of-the-art performance across a diverse set of long-context benchmarks. Importantly, models trained with our approach maintain competitive performance on standard benchmarks, demonstrating balanced improvements for both long and short context tasks. We further provide an in-depth analysis of key design choices, highlighting the impacts of scaling strategies and data composition. Our findings establish a robust framework for efficiently scaling context lengths while preserving general model capabilities. We release all model weights at: https://ultralong.github.io/.

ML-augmented algorithms utilize predictions to achieve performance beyond their worst-case bounds. Producing these predictions might be a costly operation -- this motivated Im et al. '22 to introduce the study of algorithms which use predictions parsimoniously. We design parsimonious algorithms for caching and MTS with action predictions, proposed by Antoniadis et al. '20, focusing on the parameters of consistency (performance with perfect predictions) and smoothness (dependence of their performance on the prediction error). Our algorithm for caching is 1-consistent, robust, and its smoothness deteriorates with the decreasing number of available predictions. We propose an algorithm for general MTS whose consistency and smoothness both scale linearly with the decreasing number of predictions. Without the restriction on the number of available predictions, both algorithms match the earlier guarantees achieved by Antoniadis et al. '20.

Scaling laws for large language models (LLMs) predict model performance based on parameters like size and training data. However, differences in training configurations and data processing across model families lead to significant variations in benchmark performance, making it difficult for a single scaling law to generalize across all LLMs. On the other hand, training family-specific scaling laws requires training models of varying sizes for every family. In this work, we propose Skills Scaling Laws (SSLaws, pronounced as Sloth), a novel scaling law that leverages publicly available benchmark data and assumes LLM performance is driven by low-dimensional latent skills, such as reasoning and instruction following. These latent skills are influenced by computational resources like model size and training tokens but with varying efficiencies across model families. Sloth exploits correlations across benchmarks to provide more accurate and interpretable predictions while alleviating the need to train multiple LLMs per family. We present both theoretical results on parameter identification and empirical evaluations on 12 prominent benchmarks, from Open LLM Leaderboard v1/v2, demonstrating that Sloth predicts LLM performance efficiently and offers insights into scaling behaviors for complex downstream tasks and increased test-time compute.

The scaling of inference computation has unlocked the potential of long-context large language models (LLMs) across diverse settings. For knowledge-intensive tasks, the increased compute is often allocated to incorporate more external knowledge. However, without effectively utilizing such knowledge, solely expanding context does not always enhance performance. In this work, we investigate inference scaling for retrieval augmented generation (RAG), exploring strategies beyond simply increasing the quantity of knowledge. We focus on two inference scaling strategies: in-context learning and iterative prompting. These strategies provide additional flexibility to scale test-time computation (e.g., by increasing retrieved documents or generation steps), thereby enhancing LLMs' ability to effectively acquire and utilize contextual information. We address two key questions: (1) How does RAG performance benefit from the scaling of inference computation when optimally configured? (2) Can we predict the optimal test-time compute allocation for a given budget by modeling the relationship between RAG performance and inference parameters? Our observations reveal that increasing inference computation leads to nearly linear gains in RAG performance when optimally allocated, a relationship we describe as the inference scaling laws for RAG. Building on this, we further develop the computation allocation model to estimate RAG performance across different inference configurations. The model predicts optimal inference parameters under various computation constraints, which align closely with the experimental results. By applying these optimal configurations, we demonstrate that scaling inference compute on long-context LLMs achieves up to 58.9% gains on benchmark datasets compared to standard RAG.

We classify and re-examine some of the current approaches to improve the performance-computes trade-off of language models, including (1) non-causal models (such as masked language models), (2) extension of batch length with efficient attention, (3) recurrence, (4) conditional computation and (5) retrieval. We identify some limitations (1) - (4) suffer from. For example, (1) currently struggles with open-ended text generation with the output loosely constrained by the input as well as performing general textual tasks like GPT-2/3 due to its need for a specific fine-tuning dataset. (2) and (3) do not improve the prediction of the first sim 10^3 tokens. Scaling up a model size (e.g. efficiently with (4)) still results in poor performance scaling for some tasks. We argue (5) would resolve many of these limitations, and it can (a) reduce the amount of supervision and (b) efficiently extend the context over the entire training dataset and the entire past of the current sample. We speculate how to modify MARGE to perform unsupervised causal modeling that achieves (b) with the retriever jointly trained.

Scaling law principles indicate a power-law correlation between loss and variables such as model size, dataset size, and computational resources utilized during training. These principles play a vital role in optimizing various aspects of model pre-training, ultimately contributing to the success of large language models such as GPT-4, Llama and Gemini. However, the original scaling law paper by OpenAI did not disclose the complete details necessary to derive the precise scaling law formulas, and their conclusions are only based on models containing up to 1.5 billion parameters. Though some subsequent works attempt to unveil these details and scale to larger models, they often neglect the training dependency of important factors such as the learning rate, context length and batch size, leading to their failure to establish a reliable formula for predicting the test loss trajectory. In this technical report, we confirm that the scaling law formulations proposed in the original OpenAI paper remain valid when scaling the model size up to 33 billion, but the constant coefficients in these formulas vary significantly with the experiment setup. We meticulously identify influential factors and provide transparent, step-by-step instructions to estimate all constant terms in scaling-law formulas by training on models with only 1M~60M parameters. Using these estimated formulas, we showcase the capability to accurately predict various attributes for models with up to 33B parameters before their training, including (1) the minimum possible test loss; (2) the minimum required training steps and processed tokens to achieve a specific loss; (3) the critical batch size with an optimal time/computation trade-off at any loss value; and (4) the complete test loss trajectory with arbitrary batch size.

We introduce a novel large language model (LLM)-driven agent framework, which iteratively refines queries and filters contextual evidence by leveraging dynamically evolving knowledge. A defining feature of the system is its decoupling of external sources from an internal knowledge cache that is progressively updated to guide both query generation and evidence selection. This design mitigates bias-reinforcement loops and enables dynamic, trackable search exploration paths, thereby optimizing the trade-off between exploring diverse information and maintaining accuracy through autonomous agent decision-making. Our approach is evaluated on a broad range of open-domain question answering benchmarks, including multi-step tasks that mirror real-world scenarios where integrating information from multiple sources is critical, especially given the vulnerabilities of LLMs that lack explicit reasoning or planning capabilities. The results show that the proposed system not only outperforms single-step baselines regardless of task difficulty but also, compared to conventional iterative retrieval methods, demonstrates pronounced advantages in complex tasks through precise evidence-based reasoning and enhanced efficiency. The proposed system supports both competitive and collaborative sharing of updated context, enabling multi-agent extension. The benefits of multi-agent configurations become especially prominent as task difficulty increases. The number of convergence steps scales with task difficulty, suggesting cost-effective scalability.

It is commonly believed that scaling language models should commit a significant space or time cost, by increasing the parameters (parameter scaling) or output tokens (inference-time scaling). We introduce the third and more inference-efficient scaling paradigm: increasing the model's parallel computation during both training and inference time. We apply P diverse and learnable transformations to the input, execute forward passes of the model in parallel, and dynamically aggregate the P outputs. This method, namely parallel scaling (ParScale), scales parallel computation by reusing existing parameters and can be applied to any model structure, optimization procedure, data, or task. We theoretically propose a new scaling law and validate it through large-scale pre-training, which shows that a model with P parallel streams is similar to scaling the parameters by O(log P) while showing superior inference efficiency. For example, ParScale can use up to 22times less memory increase and 6times less latency increase compared to parameter scaling that achieves the same performance improvement. It can also recycle an off-the-shelf pre-trained model into a parallelly scaled one by post-training on a small amount of tokens, further reducing the training budget. The new scaling law we discovered potentially facilitates the deployment of more powerful models in low-resource scenarios, and provides an alternative perspective for the role of computation in machine learning.

We propose Chain-of-Experts (CoE), a new Mixture-of-Experts (MoE) architecture that introduces sequential expert communication within each layer. Unlike traditional MoE models, where experts operate independently in parallel, CoE processes tokens iteratively across a chain of experts inside a layer. To support dynamic expert selection across iterations, CoE employs a dedicated router at each iteration step within a layer. This design allows tokens to re-evaluate and select different experts during each iteration, rather than being statically assigned. As a result, CoE introduces a flexible routing mechanism that increases the diversity of expert combinations and enriches the model's representational capacity. CoE demonstrates improved performance under fixed compute: on math reasoning tasks, it reduces validation loss from 1.20 to 1.12 compared to a standard MoE. Beyond performance, CoE offers a new scaling axis: depth through expert iteration, which complements conventional width/depth scaling. For example, using 2x iterations matches the performance of 3x expert selections (in width), while reducing memory usage by 17.6-42% relative to other scaling strategies. Our analysis reveals that CoE's benefits stem from its iterative residual structure and enhanced expert specialization empowered by iterative routing, which together unlock more expressive representations. Code is available at https://github.com/ZihanWang314/coe.

The advent of the transformer has sparked a quick growth in the size of language models, far outpacing hardware improvements. (Dense) transformers are expected to reach the trillion-parameter scale in the near future, for which training requires thousands or even tens of thousands of GPUs. We investigate the challenges of training at this scale and beyond on commercially available hardware. In particular, we analyse the shortest possible training time for different configurations of distributed training, leveraging empirical scaling laws for language models to estimate the optimal (critical) batch size. Contrary to popular belief, we find no evidence for a memory wall, and instead argue that the real limitation -- other than the cost -- lies in the training duration. In addition to this analysis, we introduce two new methods, layered gradient accumulation and modular pipeline parallelism, which together cut the shortest training time by half. The methods also reduce data movement, lowering the network requirement to a point where a fast InfiniBand connection is not necessary. This increased network efficiency also improve on the methods introduced with the ZeRO optimizer, reducing the memory usage to a tiny fraction of the available GPU memory.

Long-context large language models (LC LLMs) promise to increase reliability of LLMs in real-world tasks requiring processing and understanding of long input documents. However, this ability of LC LLMs to reliably utilize their growing context windows remains under investigation. In this work, we evaluate the performance of state-of-the-art GPT-4 suite of LC LLMs in solving a series of progressively challenging tasks, as a function of factors such as context length, task difficulty, and position of key information by creating a real world financial news dataset. Our findings indicate that LC LLMs exhibit brittleness at longer context lengths even for simple tasks, with performance deteriorating sharply as task complexity increases. At longer context lengths, these state-of-the-art models experience catastrophic failures in instruction following resulting in degenerate outputs. Our prompt ablations also reveal unfortunate continued sensitivity to both the placement of the task instruction in the context window as well as minor markdown formatting. Finally, we advocate for more rigorous evaluation of LC LLMs by employing holistic metrics such as F1 (rather than recall) and reporting confidence intervals, thereby ensuring robust and conclusive findings.

Discovering scaling laws for predicting model performance at scale is a fundamental and open-ended challenge, mostly reliant on slow, case specific human experimentation. To investigate the potential for LLMs to automate this process, we collect over 5,000 experiments from existing literature and curate seven diverse scaling law discovery tasks. While existing agents struggle to produce accurate law formulas, this paper introduces SLDAgent, an evolution-based agent that co-optimize the scaling law model and the parameters, enabling it to autonomously explore complex relationships between variables. For the first time, we demonstrates that SLDAgent can automatically discover laws that exhibit consistently more accurate extrapolation than their established, human-derived counterparts across all tasks. Through comprehensive analysis, we elucidate why these discovered laws are superior and verify their practical utility in both pretraining and finetuning applications. This work establishes a new paradigm for agentic scientific discovery, showing that AI systems can understand their own scaling behavior, and can contribute novel and practical knowledge back to the research community.

Scaling of deep neural networks, especially Transformers, is pivotal for their surging performance and has further led to the emergence of sophisticated reasoning capabilities in foundation models. Such scaling generally requires training large models from scratch with random initialization, failing to leverage the knowledge acquired by their smaller counterparts, which are already resource-intensive to obtain. To tackle this inefficiency, we present LosslEss MOdel ExpansioN (LEMON), a recipe to initialize scaled models using the weights of their smaller but pre-trained counterparts. This is followed by model training with an optimized learning rate scheduler tailored explicitly for the scaled models, substantially reducing the training time compared to training from scratch. Notably, LEMON is versatile, ensuring compatibility with various network structures, including models like Vision Transformers and BERT. Our empirical results demonstrate that LEMON reduces computational costs by 56.7% for Vision Transformers and 33.2% for BERT when compared to training from scratch.

Contrastive loss is a powerful approach for representation learning, where larger batch sizes enhance performance by providing more negative samples to better distinguish between similar and dissimilar data. However, scaling batch sizes is constrained by the quadratic growth in GPU memory consumption, primarily due to the full instantiation of the similarity matrix. To address this, we propose a tile-based computation strategy that partitions the contrastive loss calculation into arbitrary small blocks, avoiding full materialization of the similarity matrix. Furthermore, we introduce a multi-level tiling strategy to leverage the hierarchical structure of distributed systems, employing ring-based communication at the GPU level to optimize synchronization and fused kernels at the CUDA core level to reduce I/O overhead. Experimental results show that the proposed method scales batch sizes to unprecedented levels. For instance, it enables contrastive training of a CLIP-ViT-L/14 model with a batch size of 4M or 12M using 8 or 32 A800 80GB without sacrificing any accuracy. Compared to SOTA memory-efficient solutions, it achieves a two-order-of-magnitude reduction in memory while maintaining comparable speed. The code will be made publicly available.

The rapid development of open-source large language models (LLMs) has been truly remarkable. However, the scaling law described in previous literature presents varying conclusions, which casts a dark cloud over scaling LLMs. We delve into the study of scaling laws and present our distinctive findings that facilitate scaling of large scale models in two commonly used open-source configurations, 7B and 67B. Guided by the scaling laws, we introduce DeepSeek LLM, a project dedicated to advancing open-source language models with a long-term perspective. To support the pre-training phase, we have developed a dataset that currently consists of 2 trillion tokens and is continuously expanding. We further conduct supervised fine-tuning (SFT) and Direct Preference Optimization (DPO) on DeepSeek LLM Base models, resulting in the creation of DeepSeek Chat models. Our evaluation results demonstrate that DeepSeek LLM 67B surpasses LLaMA-2 70B on various benchmarks, particularly in the domains of code, mathematics, and reasoning. Furthermore, open-ended evaluations reveal that DeepSeek LLM 67B Chat exhibits superior performance compared to GPT-3.5.

Enhancing the reasoning capabilities of Large Language Models (LLMs) with efficiency and scalability remains a fundamental challenge in artificial intelligence research. This paper presents a rigorous experimental investigation into how difficulty-aware staged reinforcement learning (RL) strategies can substantially improve LLM reasoning performance. Through systematic analysis, we demonstrate that strategically selecting training data according to well-defined difficulty levels markedly enhances RL optimization. Moreover, we introduce a staged training methodology, progressively exposing models to increasingly challenging tasks, further amplifying reasoning capabilities. Our findings reveal significant cross-domain benefits when simultaneously training models on mathematical reasoning and code generation tasks. Notably, our proposed approach enables a 1.5B parameter model to achieve an accuracy of 42.3\% on the AIME-2024 benchmark, 89.5\% on the MATH-500 benchmark. These results underscore the efficacy of our method in advancing the reasoning proficiency of LLMs. We will open-source our datasets on GitHub and Hugging Face.

We introduce Virtual Width Networks (VWN), a framework that delivers the benefits of wider representations without incurring the quadratic cost of increasing the hidden size. VWN decouples representational width from backbone width, expanding the embedding space while keeping backbone compute nearly constant. In our large-scale experiment, an 8-times expansion accelerates optimization by over 2 times for next-token and 3 times for next-2-token prediction. The advantage amplifies over training as both the loss gap grows and the convergence-speedup ratio increases, showing that VWN is not only token-efficient but also increasingly effective with scale. Moreover, we identify an approximately log-linear scaling relation between virtual width and loss reduction, offering an initial empirical basis and motivation for exploring virtual-width scaling as a new dimension of large-model efficiency.

Large language models (LLMs) have made remarkable advances in recent years, with scaling laws playing a critical role in this rapid progress. In this paper, we empirically investigate how a critical hyper-parameter, i.e., the global batch size, influences the LLM training prdocess. We begin by training language models ranging from 125 million to 2.6 billion parameters, using up to 300 billion high-quality tokens. Through these experiments, we establish a basic scaling law on model size and training data amount. We then examine how varying batch sizes and learning rates affect the convergence and generalization of these models. Our analysis yields batch size scaling laws under two different cases: with a fixed compute budget, and with a fixed amount of training data. Extrapolation experiments on models of increasing sizes validate our predicted laws, which provides guidance for optimizing LLM training strategies under specific resource constraints.

When using Large Language Models (LLMs) to support Knowledge Graph Engineering (KGE), one of the first indications when searching for an appropriate model is its size. According to the scaling laws, larger models typically show higher capabilities. However, in practice, resource costs are also an important factor and thus it makes sense to consider the ratio between model performance and costs. The LLM-KG-Bench framework enables the comparison of LLMs in the context of KGE tasks and assesses their capabilities of understanding and producing KGs and KG queries. Based on a dataset created in an LLM-KG-Bench run covering 26 open state-of-the-art LLMs, we explore the model size scaling laws specific to KGE tasks. In our analyses, we assess how benchmark scores evolve between different model size categories. Additionally, we inspect how the general score development of single models and families of models correlates to their size. Our analyses revealed that, with a few exceptions, the model size scaling laws generally also apply to the selected KGE tasks. However, in some cases, plateau or ceiling effects occurred, i.e., the task performance did not change much between a model and the next larger model. In these cases, smaller models could be considered to achieve high cost-effectiveness. Regarding models of the same family, sometimes larger models performed worse than smaller models of the same family. These effects occurred only locally. Hence it is advisable to additionally test the next smallest and largest model of the same family.

Structured data sources, such as tables, graphs, and databases, are ubiquitous knowledge sources. Despite the demonstrated capabilities of large language models (LLMs) on plain text, their proficiency in interpreting and utilizing structured data remains limited. Our investigation reveals a notable deficiency in LLMs' ability to process structured data, e.g., ChatGPT lags behind state-of-the-art (SoTA) model by an average of 35%. To augment the Structured Knowledge Grounding (SKG) capabilities in LLMs, we have developed a comprehensive instruction tuning dataset comprising 1.1 million examples. Utilizing this dataset, we train a series of models, referred to as StructLM, based on the Code-LLaMA architecture, ranging from 7B to 34B parameters. Our StructLM series surpasses task-specific models on 14 out of 18 evaluated datasets and establishes new SoTA achievements on 7 SKG tasks. Furthermore, StructLM demonstrates exceptional generalization across 6 novel SKG tasks. Contrary to expectations, we observe that scaling model size offers marginal benefits, with StructLM-34B showing only slight improvements over StructLM-7B. This suggests that structured knowledge grounding is still a challenging task and requires more innovative design to push to a new level.

Vector embeddings have been tasked with an ever-increasing set of retrieval tasks over the years, with a nascent rise in using them for reasoning, instruction-following, coding, and more. These new benchmarks push embeddings to work for any query and any notion of relevance that could be given. While prior works have pointed out theoretical limitations of vector embeddings, there is a common assumption that these difficulties are exclusively due to unrealistic queries, and those that are not can be overcome with better training data and larger models. In this work, we demonstrate that we may encounter these theoretical limitations in realistic settings with extremely simple queries. We connect known results in learning theory, showing that the number of top-k subsets of documents capable of being returned as the result of some query is limited by the dimension of the embedding. We empirically show that this holds true even if we restrict to k=2, and directly optimize on the test set with free parameterized embeddings. We then create a realistic dataset called LIMIT that stress tests models based on these theoretical results, and observe that even state-of-the-art models fail on this dataset despite the simple nature of the task. Our work shows the limits of embedding models under the existing single vector paradigm and calls for future research to develop methods that can resolve this fundamental limitation.

Language models typically tokenize raw text into sequences of subword identifiers from a predefined vocabulary, a process inherently sensitive to typographical errors, length variations, and largely oblivious to the internal structure of tokens-issues we term the curse of tokenization. In this study, we delve into these drawbacks and demonstrate that large language models (LLMs) remain susceptible to these problems. This study systematically investigates these challenges and their impact on LLMs through three critical research questions: (1) complex problem solving, (2) token structure probing, and (3) resilience to typographical variation. Our findings reveal that scaling model parameters can mitigate the issue of tokenization; however, LLMs still suffer from biases induced by typos and other text format variations. Our experiments show that subword regularization such as BPE-dropout can mitigate this issue. We will release our code and data to facilitate further research.

Compute scaling for language model (LM) pretraining has outpaced the growth of human-written texts, leading to concerns that data will become the bottleneck to LM scaling. To continue scaling pretraining in this data-constrained regime, we propose that explicitly modeling and inferring the latent thoughts that underlie the text generation process can significantly improve pretraining data efficiency. Intuitively, our approach views web text as the compressed final outcome of a verbose human thought process and that the latent thoughts contain important contextual knowledge and reasoning steps that are critical to data-efficient learning. We empirically demonstrate the effectiveness of our approach through data-constrained continued pretraining for math. We first show that synthetic data approaches to inferring latent thoughts significantly improve data efficiency, outperforming training on the same amount of raw data (5.7\% rightarrow 25.4\% on MATH). Furthermore, we demonstrate latent thought inference without a strong teacher, where an LM bootstraps its own performance by using an EM algorithm to iteratively improve the capability of the trained LM and the quality of thought-augmented pretraining data. We show that a 1B LM can bootstrap its performance across at least three iterations and significantly outperform baselines trained on raw data, with increasing gains from additional inference compute when performing the E-step. The gains from inference scaling and EM iterations suggest new opportunities for scaling data-constrained pretraining.

Recent reasoning-first models (e.g., OpenAI o1, DeepSeek R1) have spurred a resurgence of interest in RLVR. Nevertheless, advances are dominated by mathematics (e.g., AIME), with competitive-programming code generation underexplored and data curation receiving less attention than RL algorithm design. We investigate how to construct RLVR datasets (i.e., RL prompts) and present practical training techniques that yield strong performance on competitive-programming code generation. Our pipeline begins with supervised fine-tuning (SFT) distilled from strong open-source models, augmented with general-purpose and reasoning-intensive data. RL then follows a two-stage process with executable, testcase-driven rewards: first, training on a large, uniformly distributed set of competitive-programming problems using Group Relative Policy Optimization (GRPO) with 8 rollouts per prompt and a relatively short response-generation window (e.g., 32k during SFT and 24k in this stage) to expand entropy and mitigate repetition and truncation; second, we perform Pre-GRPO: updating on a small, high-quality set of challenging problems with a large rollout budget (64 rollouts per prompt) under a hard-focus curriculum that continuously retains the most difficult instances throughout training. We implement our method on Qwen2.5-32B and evaluate on LeetCode and Codeforces weekly contests to avoid data leakage. The resulting model achieves state-of-the-art performance among models of similar scale and is comparable to leading systems such as DeepSeek v3.1 and Doubao-1.5-Thinking. We also examine scaling trends and observe strong RL scaling on an internal large-scale MoE model. Our study distills concise best practices for data curation, entropy expansion, and curriculum design in RLVR for competitive-programming code generation.

Scaling laws are useful guides for developing language models, but there are still gaps between current scaling studies and how language models are ultimately trained and evaluated. For instance, scaling is usually studied in the compute-optimal training regime (i.e., "Chinchilla optimal" regime); however, in practice, models are often over-trained to reduce inference costs. Moreover, scaling laws mostly predict loss on next-token prediction, but ultimately models are compared based on downstream task performance. In this paper, we address both shortcomings. To do so, we create a testbed of 104 models with 0.011B to 6.9B parameters trained with various numbers of tokens on three data distributions. First, we investigate scaling in the over-trained regime. We fit scaling laws that extrapolate in both the number of model parameters and the ratio of training tokens to parameters. This enables us to predict the validation loss of a 1.4B parameter, 900B token run (i.e., 32times over-trained) and a 6.9B parameter, 138B token runx2014each from experiments that take 300times less compute. Second, we relate the perplexity of a language model to its downstream task performance via a power law. We use this law to predict top-1 error averaged over downstream tasks for the two aforementioned models using experiments that take 20times less compute. Our experiments are available at https://github.com/mlfoundations/scaling.

Low-resource language translation is a challenging but socially valuable NLP task. Building on recent work adapting the Transformer's normalization to this setting, we propose QKNorm, a normalization technique that modifies the attention mechanism to make the softmax function less prone to arbitrary saturation without sacrificing expressivity. Specifically, we apply ell_2 normalization along the head dimension of each query and key matrix prior to multiplying them and then scale up by a learnable parameter instead of dividing by the square root of the embedding dimension. We show improvements averaging 0.928 BLEU over state-of-the-art bilingual benchmarks for 5 low-resource translation pairs from the TED Talks corpus and IWSLT'15.

Large Language Models (LLMs) typically generate outputs token by token using a fixed compute budget, leading to inefficient resource utilization. To address this shortcoming, recent advancements in mixture of expert (MoE) models, speculative decoding, and early exit strategies leverage the insight that computational demands can vary significantly based on the complexity and nature of the input. However, identifying optimal routing patterns for dynamic execution remains an open challenge, limiting the full potential of these adaptive methods. To address this need, we study adaptive computation in LLMs more systematically. We propose a novel framework that integrates smaller auxiliary modules within each Feed-Forward Network layer of the LLM. This design enables dynamic routing of tokens based on task complexity: tokens can be processed by either the small or big modules at each layer, or even bypass certain layers entirely. This allows us to introduce a novel notion of a token's difficulty, defined by its potential to benefit from additional computational resources. Importantly, by employing oracles to identify optimal patterns of adaptive computations, we gain valuable insights into the internal workings of LLMs and the routing processes in a simplified heterogeneous MoE setup. We show that trained routers operate differently from oracles and often yield suboptimal solutions. Notably, activating a large module in just one layer outperforms models that use large modules across all layers, underscoring the gap between practical implementations of routing in MoE models and theoretical optima for adaptive computation.

The growing disparity between the exponential scaling of computational resources and the finite growth of high-quality text data now constrains conventional scaling approaches for large language models (LLMs). To address this challenge, we introduce Reinforcement Learning on Pre-Training data (RLPT), a new training-time scaling paradigm for optimizing LLMs. In contrast to prior approaches that scale training primarily through supervised learning, RLPT enables the policy to autonomously explore meaningful trajectories to learn from pre-training data and improve its capability through reinforcement learning (RL). While existing RL strategies such as reinforcement learning from human feedback (RLHF) and reinforcement learning with verifiable rewards (RLVR) rely on human annotation for reward construction, RLPT eliminates this dependency by deriving reward signals directly from pre-training data. Specifically, it adopts a next-segment reasoning objective, rewarding the policy for accurately predicting subsequent text segments conditioned on the preceding context. This formulation allows RL to be scaled on pre-training data, encouraging the exploration of richer trajectories across broader contexts and thereby fostering more generalizable reasoning skills. Extensive experiments on both general-domain and mathematical reasoning benchmarks across multiple models validate the effectiveness of RLPT. For example, when applied to Qwen3-4B-Base, RLPT yields absolute improvements of 3.0, 5.1, 8.1, 6.0, 6.6, and 5.3 on MMLU, MMLU-Pro, GPQA-Diamond, KOR-Bench, AIME24, and AIME25, respectively. The results further demonstrate favorable scaling behavior, suggesting strong potential for continued gains with more compute. In addition, RLPT provides a solid foundation, extending the reasoning boundaries of LLMs and enhancing RLVR performance.

We consider concept generalization at a large scale in the diverse and natural visual spectrum. Established computational modes (i.e., rule-based or similarity-based) are primarily studied isolated and focus on confined and abstract problem spaces. In this work, we study these two modes when the problem space scales up, and the complexity of concepts becomes diverse. Specifically, at the representational level, we seek to answer how the complexity varies when a visual concept is mapped to the representation space. Prior psychology literature has shown that two types of complexities (i.e., subjective complexity and visual complexity) (Griffiths and Tenenbaum, 2003) build an inverted-U relation (Donderi, 2006; Sun and Firestone, 2021). Leveraging Representativeness of Attribute (RoA), we computationally confirm the following observation: Models use attributes with high RoA to describe visual concepts, and the description length falls in an inverted-U relation with the increment in visual complexity. At the computational level, we aim to answer how the complexity of representation affects the shift between the rule- and similarity-based generalization. We hypothesize that category-conditioned visual modeling estimates the co-occurrence frequency between visual and categorical attributes, thus potentially serving as the prior for the natural visual world. Experimental results show that representations with relatively high subjective complexity outperform those with relatively low subjective complexity in the rule-based generalization, while the trend is the opposite in the similarity-based generalization.

We study the effect of mini-batching on the loss landscape of deep neural networks using spiked, field-dependent random matrix theory. We demonstrate that the magnitude of the extremal values of the batch Hessian are larger than those of the empirical Hessian. We also derive similar results for the Generalised Gauss-Newton matrix approximation of the Hessian. As a consequence of our theorems we derive an analytical expressions for the maximal learning rates as a function of batch size, informing practical training regimens for both stochastic gradient descent (linear scaling) and adaptive algorithms, such as Adam (square root scaling), for smooth, non-convex deep neural networks. Whilst the linear scaling for stochastic gradient descent has been derived under more restrictive conditions, which we generalise, the square root scaling rule for adaptive optimisers is, to our knowledge, completely novel. %For stochastic second-order methods and adaptive methods, we derive that the minimal damping coefficient is proportional to the ratio of the learning rate to batch size. We validate our claims on the VGG/WideResNet architectures on the CIFAR-100 and ImageNet datasets. Based on our investigations of the sub-sampled Hessian we develop a stochastic Lanczos quadrature based on the fly learning rate and momentum learner, which avoids the need for expensive multiple evaluations for these key hyper-parameters and shows good preliminary results on the Pre-Residual Architecure for CIFAR-100.

Learned sparse representations form an attractive class of contextual embeddings for text retrieval. That is so because they are effective models of relevance and are interpretable by design. Despite their apparent compatibility with inverted indexes, however, retrieval over sparse embeddings remains challenging. That is due to the distributional differences between learned embeddings and term frequency-based lexical models of relevance such as BM25. Recognizing this challenge, a great deal of research has gone into, among other things, designing retrieval algorithms tailored to the properties of learned sparse representations, including approximate retrieval systems. In fact, this task featured prominently in the latest BigANN Challenge at NeurIPS 2023, where approximate algorithms were evaluated on a large benchmark dataset by throughput and recall. In this work, we propose a novel organization of the inverted index that enables fast yet effective approximate retrieval over learned sparse embeddings. Our approach organizes inverted lists into geometrically-cohesive blocks, each equipped with a summary vector. During query processing, we quickly determine if a block must be evaluated using the summaries. As we show experimentally, single-threaded query processing using our method, Seismic, reaches sub-millisecond per-query latency on various sparse embeddings of the MS MARCO dataset while maintaining high recall. Our results indicate that Seismic is one to two orders of magnitude faster than state-of-the-art inverted index-based solutions and further outperforms the winning (graph-based) submissions to the BigANN Challenge by a significant margin.

We introduce the Autoregressive Block-Based Iterative Encoder (AbbIE), a novel recursive generalization of the encoder-only Transformer architecture, which achieves better perplexity than a standard Transformer and allows for the dynamic scaling of compute resources at test time. This simple, recursive approach is a complement to scaling large language model (LLM) performance through parameter and token counts. AbbIE performs its iterations in latent space, but unlike latent reasoning models, does not require a specialized dataset or training protocol. We show that AbbIE upward generalizes (ability to generalize to arbitrary iteration lengths) at test time by only using 2 iterations during train time, far outperforming alternative iterative methods. AbbIE's ability to scale its computational expenditure based on the complexity of the task gives it an up to 12\% improvement in zero-shot in-context learning tasks versus other iterative and standard methods and up to 5\% improvement in language perplexity. The results from this study open a new avenue to Transformer performance scaling. We perform all of our evaluations on model sizes up to 350M parameters.

In studies of transferable learning, scaling laws are obtained for various important foundation models to predict their properties and performance at larger scales. We show here how scaling law derivation can also be used for model and dataset comparison, allowing to decide which procedure is to be preferred for pre-training. For the first time, full scaling laws based on dense measurements across a wide span of model and samples seen scales are derived for two important language-vision learning procedures, CLIP and MaMMUT, that use either contrastive only or contrastive and captioning text generative loss. Ensuring sufficient prediction accuracy for held out points, we use derived scaling laws to compare both models, obtaining evidence for MaMMUT's stronger improvement with scale and better sample efficiency than standard CLIP. To strengthen validity of the comparison, we show scaling laws for various downstream tasks, classification, retrieval, and segmentation, and for different open datasets, DataComp, DFN and Re-LAION, observing consistently the same trends. We show that comparison can also be performed when deriving scaling laws with a constant learning rate schedule, reducing compute cost. Accurate derivation of scaling laws provides thus means to perform model and dataset comparison across scale spans, avoiding misleading conclusions based on measurements from single reference scales only, paving the road for systematic comparison and improvement of open foundation models and datasets for their creation. We release all the pre-trained models with their intermediate checkpoints, including openMaMMUT-L/14, which achieves 80.3% zero-shot ImageNet-1k accuracy, trained on 12.8B samples from DataComp-1.4B. Code for reproducing experiments in the paper and raw experiments data can be found at https://github.com/LAION-AI/scaling-laws-for-comparison.

A fundamental open challenge in modern LLM scaling is the lack of understanding around emergent capabilities. In particular, language model pretraining loss is known to be highly predictable as a function of compute. However, downstream capabilities are far less predictable -- sometimes even exhibiting emergent jumps -- which makes it challenging to anticipate the capabilities of future models. In this work, we first pose the task of emergence prediction: given access to current LLMs that have random few-shot accuracy on a task, can we predict whether future models (GPT-N+1) will have non-trivial accuracy on that task? We then discover a simple insight for this problem: finetuning LLMs on a given task can shift the point in scaling at which emergence occurs towards less capable models. To operationalize this insight, we can finetune LLMs with varying amounts of data and fit a parametric function that predicts when emergence will occur (i.e., "emergence laws"). We validate this approach using four standard NLP benchmarks where large-scale open-source LLMs already demonstrate emergence (MMLU, GSM8K, CommonsenseQA, and CoLA). Using only small-scale LLMs, we find that, in some cases, we can accurately predict whether models trained with up to 4x more compute have emerged. Finally, we present a case study of two realistic uses for emergence prediction.

Mixture-of-Experts (MoE) models promise efficient scaling of large language models (LLMs) by activating only a small subset of experts per token, but their parallelized inference pipelines make elastic serving challenging. Existing strategies fall short: horizontal scaling provisions entire replicas of the current configuration, often tens to hundreds of accelerators, leading to coarse granularity, long provisioning delays, and costly overprovisioning. Vertical scaling offers finer adjustments but typically requires instance restarts, incurring downtime. These limitations make current approaches ill-suited for the bursty, short-lived traffic patterns common in cloud deployments. We present ElasticMoE, an elastic scaling framework for MoE LLMs that achieves fine-grained, low-latency, and zero-downtime scaling. ElasticMoE decouples inference execution from memory operations, enabling scaling steps to proceed concurrently with serving. An HBM Management Module (HMM) reuses weights and KV caches via zero-copy remapping, while high-bandwidth peer-to-peer transfers bring newly added accelerators online without interrupting service. A virtual memory based expert redistribution mechanism migrates MoE experts without costly buffer reallocations, reducing peak memory usage during expert parallelism reconfiguration. Our evaluation on Ascend NPUs with three popular MoE LLMs shows that ElasticMoE achieves up to 9x lower scale-up latency, up to 2x better throughput during scaling, and significantly improves SLO attainment compared to baselines. By enabling fine-grained, concurrent scaling with minimal disruption, ElasticMoE advances the practicality of deploying massive MoE LLMs in dynamic cloud environments.

Integrating Large Language Models (LLMs) with Knowledge Graphs (KGs) results in complex systems with numerous hyperparameters that directly affect performance. While such systems are increasingly common in retrieval-augmented generation, the role of systematic hyperparameter optimization remains underexplored. In this paper, we study this problem in the context of Cognee, a modular framework for end-to-end KG construction and retrieval. Using three multi-hop QA benchmarks (HotPotQA, TwoWikiMultiHop, and MuSiQue) we optimize parameters related to chunking, graph construction, retrieval, and prompting. Each configuration is scored using established metrics (exact match, F1, and DeepEval's LLM-based correctness metric). Our results demonstrate that meaningful gains can be achieved through targeted tuning. While the gains are consistent, they are not uniform, with performance varying across datasets and metrics. This variability highlights both the value of tuning and the limitations of standard evaluation measures. While demonstrating the immediate potential of hyperparameter tuning, we argue that future progress will depend not only on architectural advances but also on clearer frameworks for optimization and evaluation in complex, modular systems.

Understanding how humans perceive visual complexity is a key area of study in visual cognition. Previous approaches to modeling visual complexity assessments have often resulted in intricate, difficult-to-interpret algorithms that employ numerous features or sophisticated deep learning architectures. While these complex models achieve high performance on specific datasets, they often sacrifice interpretability, making it challenging to understand the factors driving human perception of complexity. Recently (Shen, et al. 2024) proposed an interpretable segmentation-based model that accurately predicted complexity across various datasets, supporting the idea that complexity can be explained simply. In this work, we investigate the failure of their model to capture structural, color and surprisal contributions to complexity. To this end, we propose Multi-Scale Sobel Gradient (MSG) which measures spatial intensity variations, Multi-Scale Unique Color (MUC) which quantifies colorfulness across multiple scales, and surprise scores generated using a Large Language Model. We test our features on existing benchmarks and a novel dataset (Surprising Visual Genome) containing surprising images from Visual Genome. Our experiments demonstrate that modeling complexity accurately is not as simple as previously thought, requiring additional perceptual and semantic factors to address dataset biases. Our model improves predictive performance while maintaining interpretability, offering deeper insights into how visual complexity is perceived and assessed. Our code, analysis and data are available at https://github.com/Complexity-Project/Complexity-in-Complexity.

No free lunch theorems for supervised learning state that no learner can solve all problems or that all learners achieve exactly the same accuracy on average over a uniform distribution on learning problems. Accordingly, these theorems are often referenced in support of the notion that individual problems require specially tailored inductive biases. While virtually all uniformly sampled datasets have high complexity, real-world problems disproportionately generate low-complexity data, and we argue that neural network models share this same preference, formalized using Kolmogorov complexity. Notably, we show that architectures designed for a particular domain, such as computer vision, can compress datasets on a variety of seemingly unrelated domains. Our experiments show that pre-trained and even randomly initialized language models prefer to generate low-complexity sequences. Whereas no free lunch theorems seemingly indicate that individual problems require specialized learners, we explain how tasks that often require human intervention such as picking an appropriately sized model when labeled data is scarce or plentiful can be automated into a single learning algorithm. These observations justify the trend in deep learning of unifying seemingly disparate problems with an increasingly small set of machine learning models.

Large reasoning models (LRMs) have exhibited the capacity of enhancing reasoning performance via internal test-time scaling. Building upon this, a promising direction is to further scale test-time compute to unlock even greater reasoning capabilities. However, as we push these scaling boundaries, systematically understanding the practical limits and achieving optimal resource allocation becomes a critical challenge. In this paper, we investigate the scaling Pareto of test-time scaling and introduce the Test-Time Scaling Performance Model (TTSPM). We theoretically analyze two fundamental paradigms for such extended scaling, parallel scaling and sequential scaling, from a probabilistic modeling perspective. Our primary contribution is the derivation of the saturation point on the scaling budget for both strategies, identifying thresholds beyond which additional computation yields diminishing returns. Remarkably, despite their distinct mechanisms, both paradigms converge to a unified mathematical structure in their upper bounds. We empirically validate our theoretical findings on challenging reasoning benchmarks, including AIME, MATH-500, and GPQA, demonstrating the practical utility of these bounds for test-time resource allocation. We hope that this work provides insights into the cost-benefit trade-offs of test-time scaling, guiding the development of more resource-efficient inference strategies for large reasoning models.

Enterprise search systems often struggle to retrieve accurate, domain-specific information due to semantic mismatches and overlapping terminologies. These issues can degrade the performance of downstream applications such as knowledge management, customer support, and retrieval-augmented generation agents. To address this challenge, we propose a scalable hard-negative mining framework tailored specifically for domain-specific enterprise data. Our approach dynamically selects semantically challenging but contextually irrelevant documents to enhance deployed re-ranking models. Our method integrates diverse embedding models, performs dimensionality reduction, and uniquely selects hard negatives, ensuring computational efficiency and semantic precision. Evaluation on our proprietary enterprise corpus (cloud services domain) demonstrates substantial improvements of 15\% in MRR@3 and 19\% in MRR@10 compared to state-of-the-art baselines and other negative sampling techniques. Further validation on public domain-specific datasets (FiQA, Climate Fever, TechQA) confirms our method's generalizability and readiness for real-world applications.

We introduce a novel framework for analyzing sorting algorithms in pairwise ranking prompting (PRP), re-centering the cost model around LLM inferences rather than traditional pairwise comparisons. While classical metrics based on comparison counts have traditionally been used to gauge efficiency, our analysis reveals that expensive LLM inferences overturn these predictions; accordingly, our framework encourages strategies such as batching and caching to mitigate inference costs. We show that algorithms optimal in the classical setting can lose efficiency when LLM inferences dominate the cost under certain optimizations.

The recent breakthrough successes in machine learning are mainly attributed to scale: namely large-scale attention-based architectures and datasets of unprecedented scale. This paper investigates the impact of training at scale for chess. Unlike traditional chess engines that rely on complex heuristics, explicit search, or a combination of both, we train a 270M parameter transformer model with supervised learning on a dataset of 10 million chess games. We annotate each board in the dataset with action-values provided by the powerful Stockfish 16 engine, leading to roughly 15 billion data points. Our largest model reaches a Lichess blitz Elo of 2895 against humans, and successfully solves a series of challenging chess puzzles, without any domain-specific tweaks or explicit search algorithms. We also show that our model outperforms AlphaZero's policy and value networks (without MCTS) and GPT-3.5-turbo-instruct. A systematic investigation of model and dataset size shows that strong chess performance only arises at sufficient scale. To validate our results, we perform an extensive series of ablations of design choices and hyperparameters.

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.

Scaling laws have shaped recent advances in machine learning by enabling predictable scaling of model performance based on model size, computation, and data volume. Concurrently, the rise in computational cost for AI has motivated model compression techniques, notably quantization and sparsification, which have emerged to mitigate the steep computational demands associated with large-scale training and inference. This paper investigates the interplay between scaling laws and compression formats, exploring whether a unified scaling framework can accurately predict model performance when training occurs over various compressed representations, such as sparse, scalar-quantized, sparse-quantized or even vector-quantized formats. Our key contributions include validating a general scaling law formulation and showing that it is applicable both individually but also composably across compression types. Based on this, our main finding is demonstrating both theoretically and empirically that there exists a simple "capacity" metric -- based on the representation's ability to fit random Gaussian data -- which can robustly predict parameter efficiency across multiple compressed representations. On the practical side, we extend our formulation to directly compare the accuracy potential of different compressed formats, and to derive better algorithms for training over sparse-quantized formats.

State-of-the-art LLMs are powered by scaling -- scaling model size, dataset size and cluster size. It is economically infeasible to extensively tune hyperparameter for the largest runs. Instead, approximately optimal hyperparameters must be inferred or transferred from smaller experiments. Hyperparameter transfer across model sizes has been studied in Yang et al. However, hyperparameter transfer across dataset size -- or token horizon -- has not been studied yet. To remedy this we conduct a large scale empirical study on how optimal learning rate (LR) depends on token horizon in LLM training. We first demonstrate that the optimal LR changes significantly with token horizon -- longer training necessitates smaller LR. Secondly we demonstrate the the optimal LR follows a scaling law, and that the optimal LR for longer horizons can be accurately estimated from shorter horizons via such scaling laws. We also provide a rule-of-thumb for transferring LR across token horizons with zero overhead over current practices. Lastly we provide evidence that LLama-1 used too high LR, and estimate the performance hit from this. We thus argue that hyperparameter transfer across data size is an important and overlooked component of LLM training.

Efficient LLM pre-training requires well-tuned hyperparameters (HPs), including learning rate {\eta} and weight decay {\lambda}. We study scaling laws for HPs: formulas for how to scale HPs as we scale model size N, dataset size D, and batch size B. Recent work suggests the AdamW timescale, B/({\eta}{\lambda}D), should remain constant across training settings, and we verify the implication that optimal {\lambda} scales linearly with B, for a fixed N,D. However, as N,D scale, we show the optimal timescale obeys a precise power law in the tokens-per-parameter ratio, D/N. This law thus provides a method to accurately predict {\lambda}opt in advance of large-scale training. We also study scaling laws for optimal batch size Bopt (the B enabling lowest loss at a given N,D) and critical batch size Bcrit (the B beyond which further data parallelism becomes ineffective). In contrast with prior work, we find both Bopt and Bcrit scale as power laws in D, independent of model size, N. Finally, we analyze how these findings inform the real-world selection of Pareto-optimal N and D under dual training time and compute objectives.

Recurrent large language models that compete with Transformers in language modeling perplexity are emerging at a rapid rate (e.g., Mamba, RWKV). Excitingly, these architectures use a constant amount of memory during inference. However, due to the limited memory, recurrent LMs cannot recall and use all the information in long contexts leading to brittle in-context learning (ICL) quality. A key challenge for efficient LMs is selecting what information to store versus discard. In this work, we observe the order in which information is shown to the LM impacts the selection difficulty. To formalize this, we show that the hardness of information recall reduces to the hardness of a problem called set disjointness (SD), a quintessential problem in communication complexity that requires a streaming algorithm (e.g., recurrent model) to decide whether inputted sets are disjoint. We empirically and theoretically show that the recurrent memory required to solve SD changes with set order, i.e., whether the smaller set appears first in-context. Our analysis suggests, to mitigate the reliance on data order, we can put information in the right order in-context or process prompts non-causally. Towards that end, we propose: (1) JRT-Prompt, where context gets repeated multiple times in the prompt, effectively showing the model all data orders. This gives 11.0 pm 1.3 points of improvement, averaged across 16 recurrent LMs and the 6 ICL tasks, with 11.9times higher throughput than FlashAttention-2 for generation prefill (length 32k, batch size 16, NVidia H100). We then propose (2) JRT-RNN, which uses non-causal prefix-linear-attention to process prompts and provides 99% of Transformer quality at 360M params., 30B tokens and 96% at 1.3B params., 50B tokens on average across the tasks, with 19.2times higher throughput for prefill than FA2.

Large language models (LLMs) can improve reasoning at inference time through test-time scaling (TTS), where multiple reasoning traces are generated and the best one is selected. Prior work shows that increasing the number of samples K steadily improves accuracy. In this paper, we demonstrate that this trend does not hold indefinitely: at large K, further scaling yields no gains, and certain hard questions remain unsolved regardless of the number of traces. Interestingly, we find that different sampling temperatures solve different subsets of problems, implying that single-temperature scaling explores only part of a model's potential. We therefore propose scaling along the temperature dimension, which enlarges the reasoning boundary of LLMs. Averaged over Qwen3 (0.6B, 1.7B, 4B, 8B) and five representative reasoning benchmarks (AIME 2024/2025, MATH500, LiveCodeBench, Hi-ToM), temperature scaling yields an additional 7.3 points over single-temperature TTS. Temperature scaling also enables base models to reach performance comparable to reinforcement learning (RL)-trained counterparts, without additional post-training. We further provide a comprehensive analysis of this phenomenon and design a multi-temperature voting method that reduces the overhead of temperature scaling. Overall, our findings suggest that TTS is more powerful than previously thought, and that temperature scaling offers a simple and effective way to unlock the latent potential of base models.

The time complexity of the standard attention mechanism in a transformer scales quadratically with the length of the sequence. We introduce a method to reduce this to linear scaling with time, based on defining attention via latent vectors. The method is readily usable as a drop-in replacement for the standard attention mechanism. Our "Latte Transformer" model can be implemented for both bidirectional and unidirectional tasks, with the causal version allowing a recurrent implementation which is memory and time-efficient during inference of language generation tasks. Whilst next token prediction scales linearly with the sequence length for a standard transformer, a Latte Transformer requires constant time to compute the next token. The empirical performance of our method is comparable to standard attention, yet allows scaling to context windows much larger than practical in standard attention.

While large language models (LLMs) have shown exceptional capabilities in understanding complex queries and performing sophisticated tasks, their generalization abilities are often deeply entangled with memorization, necessitating more precise evaluation. To address this challenge, we introduce Scylla, a dynamic evaluation framework that quantitatively measures the generalization abilities of LLMs. Scylla disentangles generalization from memorization via assessing model performance on both in-distribution (ID) and out-of-distribution (OOD) data through 20 tasks across 5 levels of complexity. Through extensive experiments, we uncover a non-monotonic relationship between task complexity and the performance gap between ID and OOD data, which we term the generalization valley. Specifically, this phenomenon reveals a critical threshold - referred to as critical complexity - where reliance on non-generalizable behavior peaks, indicating the upper bound of LLMs' generalization capabilities. As model size increases, the critical complexity shifts toward higher levels of task complexity, suggesting that larger models can handle more complex reasoning tasks before over-relying on memorization. Leveraging Scylla and the concept of critical complexity, we benchmark 28LLMs including both open-sourced models such as LLaMA and Qwen families, and close-sourced models like Claude and GPT, providing a more robust evaluation and establishing a clearer understanding of LLMs' generalization capabilities.

The recent rapid progress in (self) supervised learning models is in large part predicted by empirical scaling laws: a model's performance scales proportionally to its size. Analogous scaling laws remain elusive for reinforcement learning domains, however, where increasing the parameter count of a model often hurts its final performance. In this paper, we demonstrate that incorporating Mixture-of-Expert (MoE) modules, and in particular Soft MoEs (Puigcerver et al., 2023), into value-based networks results in more parameter-scalable models, evidenced by substantial performance increases across a variety of training regimes and model sizes. This work thus provides strong empirical evidence towards developing scaling laws for reinforcement learning.

Numerous deep learning algorithms have been inspired by and understood via the notion of information bottleneck, where unnecessary information is (often implicitly) minimized while task-relevant information is maximized. However, a rigorous argument for justifying why it is desirable to control information bottlenecks has been elusive. In this paper, we provide the first rigorous learning theory for justifying the benefit of information bottleneck in deep learning by mathematically relating information bottleneck to generalization errors. Our theory proves that controlling information bottleneck is one way to control generalization errors in deep learning, although it is not the only or necessary way. We investigate the merit of our new mathematical findings with experiments across a range of architectures and learning settings. In many cases, generalization errors are shown to correlate with the degree of information bottleneck: i.e., the amount of the unnecessary information at hidden layers. This paper provides a theoretical foundation for current and future methods through the lens of information bottleneck. Our new generalization bounds scale with the degree of information bottleneck, unlike the previous bounds that scale with the number of parameters, VC dimension, Rademacher complexity, stability or robustness. Our code is publicly available at: https://github.com/xu-ji/information-bottleneck

Standardized benchmarks drive progress in machine learning. However, with repeated testing, the risk of overfitting grows as algorithms over-exploit benchmark idiosyncrasies. In our work, we seek to mitigate this challenge by compiling ever-expanding large-scale benchmarks called Lifelong Benchmarks. As exemplars of our approach, we create Lifelong-CIFAR10 and Lifelong-ImageNet, containing (for now) 1.69M and 1.98M test samples, respectively. While reducing overfitting, lifelong benchmarks introduce a key challenge: the high cost of evaluating a growing number of models across an ever-expanding sample set. To address this challenge, we also introduce an efficient evaluation framework: Sort \& Search (S&S), which reuses previously evaluated models by leveraging dynamic programming algorithms to selectively rank and sub-select test samples, enabling cost-effective lifelong benchmarking. Extensive empirical evaluations across 31,000 models demonstrate that S&S achieves highly-efficient approximate accuracy measurement, reducing compute cost from 180 GPU days to 5 GPU hours (1000x reduction) on a single A100 GPU, with low approximation error. As such, lifelong benchmarks offer a robust, practical solution to the "benchmark exhaustion" problem.