NeurIPS 2025 论文列表

Neural scaling laws are observed in a range of domains, to date with no universal understanding of why they occur. Recent theories suggest that loss power laws arise from Zipf's law, a power law observed in domains like natural language. One theory suggests that language scaling laws emerge when Zipf-distributed task quanta are learned in descending order of frequency. In this paper we examine power-law scaling in AlphaZero, a reinforcement learning algorithm, using a model of language-model scaling. We find that game states in training and inference data scale with Zipf's law, which is known to arise from the tree structure of the environment, and examine the correlation between scaling-law and Zipf's-law exponents. In agreement with the quanta scaling model, we find that agents optimize state loss in descending order of frequency, even though this order scales inversely with modelling complexity. We also find that inverse scaling, the failure of models to improve with size, is correlated with unusual Zipf curves where end-game states are among the most frequent states. We show evidence that larger models shift their focus to these less-important states, sacrificing their understanding of important early-game states.

Part of the success of diffusion models stems from their ability to perform iterative refinement, i.e., repeatedly correcting outputs during generation. However, modern masked discrete diffusion lacks this capability: when a token is generated, it cannot be updated again, even when it introduces an error. Here, we address this limitation by introducing the remasking diffusion model (ReMDM) sampler, a method that can be applied to pretrained masked diffusion models in a principled way and that is derived from a discrete diffusion model with a custom remasking backward process. Most interestingly, ReMDM endows discrete diffusion with a form of inference-time compute scaling. By increasing the number of sampling steps, ReMDM generates natural language outputs that approach the quality of autoregressive models, whereas when the computation budget is limited, ReMDM better maintains quality. ReMDM also improves sample quality of masked diffusion models for discretized images, and in scientific domains such as molecule design, ReMDM facilitates diffusion guidance and pushes the Pareto frontier of controllability relative to classical masking and uniform noise diffusion. When applied to large pretrained diffusion language models, ReMDM boosts the model’s performance on downstream tasks requiring factual knowledge grasp and reasoning ability.

We propose two simple, principled and practical algorithms that enjoy provable scaling laws for the test-time compute of large language models (LLMs). The first one is a two-stage knockout-style algorithm: given an input problem, it first generates multiple candidate solutions, and then aggregate them via a knockout tournament for the final output. Assuming that the LLM can generate a correct solution with non-zero probability and do better than a random guess in comparing a pair of correct and incorrect solutions, we prove theoretically that the failure probability of this algorithm decays to zero exponentially or by a power law (depending on the specific way of scaling) as its test-time compute grows. The second one is a two-stage league-style algorithm, where each candidate is evaluated by its average win rate against multiple opponents, rather than eliminated upon loss to a single opponent. Under analogous but more robust assumptions, we prove that its failure probability also decays to zero exponentially with more test-time compute. Both algorithms require a black-box LLM and nothing else (e.g., no verifier or reward model) for a minimalistic implementation, which makes them appealing for practical applications and easy to adapt for different tasks. Through extensive experiments with diverse models and datasets, we validate the proposed theories and demonstrate the outstanding scaling properties of both algorithms.

Reinforcement learning has achieved significant milestones, but sample efficiency remains a bottleneck for real-world applications. Recently, CrossQ has demonstrated state-of-the-art sample efficiency with a low update-to-data (UTD) ratio of 1. In this work, we explore CrossQ's scaling behavior with higher UTD ratios. We identify challenges in the training dynamics, which are emphasized by higher UTD ratios. To address these, we integrate weight normalization into the CrossQ framework, a solution that stabilizes training, has been shown to prevent potential loss of plasticity, and keeps the effective learning rate constant. Our proposed approach reliably scales with increasing UTD ratios, achieving competitive performance across 25 challenging continuous control tasks on the DeepMind Control Suite and Myosuite benchmarks, notably the complex dog and humanoid environments. This work eliminates the need for drastic interventions, such as network resets, and offers a simple yet robust pathway for improving sample efficiency and scalability in model-free reinforcement learning.

With the growing size of data and models in Large Recommendation Models, the time required for debugging has become increasingly prohibitive, underscoring the urgent need for effective guidance in parameter configuration. The Scaling Law (SL) offers analogous guidance in the Sequential Language domain, having achieved significant success by predicting model loss when scaling model size. However, the existing guidance from SL for Sequential Recommendation (SR) remains qualitative, which is because quantitative analysis of SL on SR encounters challenges with quality measurement on redundant sequences along with loss-performance discrepancy. In response, we introduce the Performance Law (P-Law) for SR models, which predicts model performance across various settings, intending to provide a quantitative framework for guiding the parameter optimization of future models. Initially, Performance Law utilizes Real Entropy to measure data quality, aiming to remove the low-quality influence of low-entropy redundant sequences. Subsequently, Performance Law investigates a fitting decay term, which facilitated the prediction of the major loss-performance discrepancy phenomena of overfitting, ultimately achieving quantitative performance prediction. Extensive experiment on various datasets demonstrates the effectiveness of Performance Law by displaying exceptional quantitative prediction ability against the original and modified qualitative SL. Additional application experiments on optimal parameter prediction and model expansion potential prediction also demonstrated the broad applicability of the Performance Law. Our code is available at https://github.com/USTC-StarTeam/P-Law.

Several recently introduced deep learning optimizers inspired by second-order methods have shown promising speedups relative to the current dominant optimizer AdamW, particularly in relatively small-scale experiments. However, efforts to validate and replicate their successes have reported mixed results, with some finding quickly diminishing advantage over AdamW with scale. In this work, we investigate \emph{how to scale} second-order optimizers to achieve optimal performance at scale. Through theoretical and empirical analysis, we derive scaling rules for hyperparameters such as learning rate and weight decay as we scale up model width and depth for a wide range of optimizers, including Shampoo, SOAP, and Muon, accounting for the impact of commonly used techniques such as blocking and grafting. For compute-optimal scaling, we find scaling independent weight decay as $1/\mathrm{width}$ is nearly optimal across optimizers, and that second-order optimizers have a substantially larger optimal model size compared to AdamW for a fixed compute budget. Applying these scaling rules, we show Muon achieves close to $1.4\times$ or higher speedup over AdamW in training transformer language models, while incorrect scaling can decrease the speedup from $1.4\times$ to below $1.1\times$ from $190$M to $640$M parameter models.

Recent work on neural scaling laws demonstrates that model performance scales predictably with compute budget, model size, and dataset size. In this work, we develop scaling laws based on problem complexity. We analyze two fundamental complexity measures: solution space size and representation space size. Using the Traveling Salesman Problem (TSP) as a case study, we show that combinatorial optimization promotes smooth cost trends, and therefore meaningful scaling laws can be obtained even in the absence of an interpretable loss. We then show that suboptimality grows predictably for fixed-size models when scaling the number of TSP nodes or spatial dimensions, independent of whether the model was trained with reinforcement learning or supervised fine-tuning on a static dataset. We conclude with an analogy to problem complexity scaling in local search, showing that a much simpler gradient descent of the cost landscape produces similar trends.

We study the problem of entropy calibration, which asks whether a language model's entropy over generations matches its log loss on human text. Past work found that models are miscalibrated, with entropy per step increasing (and text quality decreasing) as generations grow longer. This error accumulation is a fundamental problem in autoregressive models, and the standard solution is to truncate the distribution, which improves text quality at the cost of diversity. In this paper, we ask: is miscalibration likely to improve with scale, and is it theoretically possible to calibrate without tradeoffs? To build intuition, we first study a simplified theoretical setting to characterize the scaling behavior of miscalibration with respect to dataset size. We find that the scaling behavior depends on the power law exponent of the data distribution --- in particular, for a power law exponent close to 1, the scaling exponent is close to 0, meaning that miscalibration improves very slowly with scale. Next, we measure miscalibration empirically in language models ranging from 0.5B to 70B parameters. We find that the observed scaling behavior is similar to what is predicted by the simplified setting: our fitted scaling exponents for text are close to 0, meaning that larger models accumulate error at a similar rate as smaller ones. This scaling (or, lack thereof) provides one explanation for why we sample from larger models with similar amounts of truncation as smaller models, even though the larger models are of higher quality. However, truncation is not a satisfying solution because it comes at the cost of increased log loss. In theory, is it even possible to reduce entropy while preserving log loss? We prove that it is possible, if we assume access to a black box which can fit models to predict the future entropy of text.

Compositional training has been the de-facto paradigm in existing Multimodal Large Language Models (MLLMs), where pre-trained vision encoders are connected with pre-trained LLMs through continuous multimodal pre-training. However, the multimodal scaling property of this paradigm remains difficult to explore due to the separated training. In this paper, we focus on the native training of MLLMs in an end-to-end manner and systematically study its design space and scaling property under a practical setting, i.e., data constraint. Through careful study of various choices in MLLM, we obtain the optimal meta-architecture that best balances performance and training cost. After that, we further explore the scaling properties of the native MLLM and indicate the positively correlated scaling relationship between visual encoders and LLMs. Based on these findings, we propose a native MLLM called NaViL, combined with a simple and cost-effective recipe. Experimental results on 14 multimodal benchmarks confirm the competitive performance of NaViL against existing MLLMs. Besides that, our findings and results provide in-depth insights for the future study of native MLLMs.

As models grow larger and training them becomes expensive, it becomes increasingly important to scale training recipes not just to larger models and more data, but to do so in a compute-optimal manner that extracts maximal performance per unit of compute. While such scaling has been well studied for language modeling, reinforcement learning (RL) has received less attention in this regard. In this paper, we investigate compute scaling for online, value-based deep RL. These methods present two primary axes for compute allocation: model capacity and the update-to-data (UTD) ratio. Given a fixed compute budget, we ask: how should resources be partitioned across these axes to maximize data efficiency? Our analysis reveals a nuanced interplay between model size, batch size, and UTD. In particular, we identify a phenomenon we call TD-overfitting: increasing the batch quickly harms Q-function accuracy for small models, but this effect is absent in large models, enabling effective use of large batch size at scale. We provide a mental model for understanding this phenomenon and build guidelines for choosing batch size and UTD to optimize compute usage. Our findings provide a grounded starting point for compute-optimal scaling in deep RL, mirroring studies in supervised learning but adapted to TD learning. Project page: https://value-scaling.github.io/.

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 accurately and offers insights into scaling behaviors for complex downstream tasks, increased test-time compute, and compute-optimal scaling of skills.

Inference-time scaling trades efficiency for increased reasoning accuracy by generating longer or more parallel sequences. However, in Transformer LLMs, generation cost is bottlenecked by the size of the key–value (KV) cache, rather than the number of generated tokens. Hence, we explore inference-time hyper-scaling: by compressing the KV cache, we can generate more tokens within the same compute budget and further improve the accuracy of scaled inference. The success of this approach, however, hinges on the ability of compression methods to preserve accuracy even at high compression ratios. To make hyper-scaling practical, we introduce Dynamic Memory Sparsification (DMS), a novel method for sparsifying KV caches that only requires 1K training steps to achieve 8× compression, while maintaining better accuracy than training-free sparse attention. Instead of prematurely discarding cached tokens, DMS delays token eviction, implicitly merging representations and preserving critical information. We demonstrate the effectiveness of inference-time hyper-scaling with DMS on multiple families of LLMs, showing that it boosts accuracy for comparable inference latency and memory load. For instance, we enhance Qwen-R1 32B by 9.1 points on AIME 24, 7.6 on GPQA, and 9.6 on LiveCodeBench on average for an equivalent number of memory reads.

Large Language Models (LLMs) have demonstrated remarkable capabilities across numerous tasks, yet principled explanations for their underlying mechanisms and several phenomena, such as scaling laws, hallucinations, and related behaviors, remain elusive. In this work, we revisit the classical relationship between compression and prediction, grounded in Kolmogorov complexity and Shannon information theory, to provide deeper insights into LLM behaviors. By leveraging the Kolmogorov Structure Function and interpreting LLM compression as a two-part coding process, we offer a detailed view of how LLMs acquire and store information across increasing model and data scales -- from pervasive syntactic patterns to progressively rarer knowledge elements. Motivated by this theoretical perspective and natural assumptions inspired by Heap’s and Zipf’s laws, we introduce a simplified yet representative hierarchical data-generation framework called the Syntax-Knowledge model. Under the Bayesian setting, we show that prediction and compression within this model naturally lead to diverse learning and scaling behaviors of LLMs. In particular, our theoretical analysis offers intuitive and principled explanations for both data and model scaling laws, the dynamics of knowledge acquisition during training and fine-tuning, factual knowledge hallucinations in LLMs. The experimental results validate our theoretical predictions.

Despite recent progress in Language Models (LMs) for software engineering, collecting training data remains a significant pain point. Existing datasets are small, with at most 1,000s of training instances from 11 or fewer GitHub repositories. The procedures to curate such datasets are often complex, necessitating hundreds of hours of human labor; companion execution environments also take up several terabytes of storage, severely limiting their scalability and usability. To address this pain point, we introduce SWE-smith, a novel pipeline for generating software engineering training data at scale. Given any Python codebase, SWE-smith constructs a corresponding execution environment, then automatically synthesizes 100s to 1,000s of task instances that break existing test(s) in the codebase. Using SWE-smith, we create a dataset of 50k instances sourced from 128 GitHub repositories, an order of magnitude larger than all previous works. We train SWE-agent-LM-32B, achieving 40.2% Pass@1 resolve rate on the SWE-bench Verified benchmark, state of the art among open source models. We open source SWE-smith (collection procedure, task instances, trajectories, models) to lower the barrier of entry for research in LM systems for automated software engineering. All assets available at \url{https://swesmith.com}.

AI audits play a critical role in AI accountability and safety. They are particularly salient in anti-discrimination law. Several areas of anti-discrimination law implicate what is known as the "less discriminatory alternative" (LDA) requirement, under which a protocol is defensible if no less discriminatory model that achieves comparable performance can be found with reasonable effort. Notably, the burden of proving an LDA exists typically falls on the claimant (the party alleging discrimination). This creates a significant hurdle in AI cases, as the claimant would seemingly need to train a less discriminatory yet high-performing model, a task requiring resources and expertise beyond most litigants. Moreover, developers often restrict access to their models and data as trade secrets, hindering replicability. In this work, we present a procedure enabling claimants to determine if an LDA exists, even when they have limited compute, data, and model access. To illustrate our approach, we focus on the setting in which fairness is given by demographic parity and performance by binary cross-entropy loss. As our main result, we provide a novel closed-form upper bound for the loss-fairness Pareto frontier (PF). This expression is powerful because the claimant can use it to fit the PF in the ''low-resource regime," then extrapolate the PF that applies to the (large) model being contested, all without training a single large model. The expression thus serves as a scaling law for loss-fairness PFs. To use this scaling law, the claimant would require a small subsample of the train/test data. Then, for a given compute budget, the claimant can fit the context-specific PF by training as few as 7 (small) models. We stress test our main result in simulations, finding that our scaling law applies even when the exact conditions of our theory do not hold.

Recent studies suggest that the representations learned by large language models (LLMs) are partially aligned to those of the human brain. However, whether this representational alignment arises from a similar sequence of computations remains elusive. In this study, we explore this question by examining temporally-resolved brain signals of participants listening to 10 hours of an audiobook. We study these neural dynamics jointly with a benchmark encompassing 17 LLMs varying in size and architecture type. Our analyses reveal that LLMs and the brain generate representations in a similar order: specifically, activations in the initial layers of LLMs tend to best align with early brain responses, while the deeper layers of LLMs tend to best align with later brain responses. This brain-LLM alignment is consistent across transformers and recurrent architectures. However, its emergence depends on both model size and context length. Overall, the alignment between LLMs and the brain provides novel elements supporting a partial convergence between biological and artificial neural networks.

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, outperforming Chinchilla's law, whose extrapolation error is 433\% higher. 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. To foster further research, we are comprehensively open-sourcing all code, data, results (https://github.com/Farseer-Scaling-Law/Farseer), all training logs (https://wandb.ai/billzid/Farseer?nw=nwuserbillzid), all models used in scaling law fitting (https://huggingface.co/Farseer-Scaling-Law).

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 strategies, 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 proposing and validating a general scaling law formulation applicable both individually but also composably across compression types. We demonstrate both theoretically and empirically that a simple metric based on Gaussian mean squared error fitting can robustly predict parameter efficiency across compressed models. Additionally, 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. Finally, we identify conditions under which these unified scaling laws fail.

The success of today's large language models (LLMs) depends on the observation that larger models perform better. However, the origin of this neural scaling law, that loss decreases as a power law with model size, remains unclear. We propose that representation superposition, meaning that LLMs represent more features than they have dimensions, can be a key contributor to loss and cause neural scaling. Based on Anthropic's toy model, we use weight decay to control the degree of superposition, allowing us to systematically study how loss scales with model size. When superposition is weak, the loss follows a power law only if data feature frequencies are power-law distributed. In contrast, under strong superposition, the loss generically scales inversely with model dimension across a broad class of frequency distributions, due to geometric overlaps between representation vectors. We confirmed that open-sourced LLMs operate in the strong superposition regime and have loss scaling inversely with model dimension, and that the Chinchilla scaling laws are also consistent with this behavior. Our results identify representation superposition as a central driver of neural scaling laws, providing insights into questions like when neural scaling laws can be improved and when they will break down.