ICML 2025 Papers

Scaling laws guide the development of large language models (LLMs) by offering estimates for the optimal balance of model size, tokens, and compute. More recently, loss-to-loss scaling laws that relate losses across pretraining datasets and downstream tasks have emerged as a powerful tool for understanding and improving LLM performance and generalization. In this work, we investigate which factors most strongly influence loss-to-loss scaling. Our experiments reveal that the pretraining data determines the scaling trend. In contrast, model size, optimization hyperparameters, tokenizer and even significant architectural differences, such as between transformer-based models like Llama and state-space models like Mamba, generally have limited impact. Consequently, practitioners should carefully curate pretraining datasets for optimal downstream performance, while architectures and other settings can be freely optimized for training efficiency.

Predictable behavior from scaling advanced AI systems is an extremely desirable property for engineers, companies, economists and governments alike, and while a well-established literature exists on how pretraining performance scales, predictable scaling behavior on downstream capabilities remains elusive. While many factors are certainly responsible, this paper shines a light on a significant factor that makes predicting scaling behavior on widely used multiple-choice question answering benchmarks challenging and illuminates a path towards making such downstream evaluations predictable with scale. Using five model families and twelve well-established multiple-choice benchmarks, we show that downstream performance is computed from negative log likelihoods via a sequence of transformations that progressively degrades the statistical relationship between performance and scale. We then reveal the mechanism causing this degradation: downstream metrics require comparing the correct choice against a small number of specific incorrect choices, meaning accurately predicting downstream capabilities requires predicting not just how probability mass concentrates on the correct choice with scale, but also how probability mass fluctuates on specific incorrect choices with scale. We empirically study how probability mass on the correct choice co-varies with probability mass on incorrect choices with increasing compute, suggesting that scaling laws for \textit{incorrect} choices might be achievable. Our work also explains why pretraining scaling laws are commonly regarded as more predictable than downstream capabilities and contributes towards establishing scaling-predictable evaluations of frontier AI models.

The performance of embodied agents has been shown to improve by increasing model parameters, dataset size, and compute. This has been demonstrated in domains from robotics to video games, when generative learning objectives on offline datasets (pre-training) are used to model an agent's behavior (imitation learning) or their environment (world modeling). This paper characterizes the role of scale in these tasks more precisely. Going beyond the simple intuition that `bigger is better', we show that the same types of power laws found in language modeling also arise in world modeling and imitation learning (e.g. between loss and optimal model size). However, the coefficients of these laws are heavily influenced by the tokenizer, task \& architecture -- this has important implications on the optimal sizing of models and data.

Understanding neural network training dynamics at scale is an important open problem. Although realistic model architectures, optimizers, and data interact in complex ways that make predictive theory challenging, we show that compute-optimally trained models exhibit remarkably precise collective regularities. Specifically, loss curves from models of varying sizes collapse onto a single universal curve when training compute and loss are normalized to unity at the end of training. With learning rate decay, discrepancies between normalized curves fall below the noise floor of individual models' loss curves across random seeds, yielding an exceptionally tight collapse we term "supercollapse." We observe supercollapse across learning rate schedules, datasets, and architectures, including transformers trained on next-token prediction. This collapse breaks down when hyperparameters are scaled suboptimally, providing a practical indicator of proper scaling. We explain these phenomena by connecting collapse to the power-law structure in typical neural scaling laws, and analyzing a simple but effective model of SGD noise dynamics that accurately captures how learning rate schedules deform loss curves away from power laws while preserving universality, and why learning rate decay suppresses variance to enable supercollapse.

Reinforcement learning with offline data suffers from Q-value extrapolation errors. To address this issue, we first demonstrate that linear extrapolation of the Q-function beyond the data range is particularly problematic. To mitigate this, we propose guiding the gradual decrease of Q-values outside the data range, which is achieved through reward scaling with layer normalization (RS-LN) and a penalization mechanism for infeasible actions (PA). By combining RS-LN and PA, we develop a new algorithm called PARS. We evaluate PARS across a range of tasks, demonstrating superior performance compared to state-of-the-art algorithms in both offline training and online fine-tuning on the D4RL benchmark, with notable success in the challenging AntMaze Ultra task.

Scaling data and compute is critical in modern machine learning. However, scaling also demands _predictability_: we want methods to not only perform well with more compute or data, but also have their performance be predictable from low compute or low data runs, without ever running the large-scale experiment. In this paper, we show predictability of value-based off-policy deep RL. First, we show that data and compute requirements to reach a given performance level lie on a _Pareto frontier_, controlled by the updates-to-data (UTD) ratio. By estimating this frontier, we can extrapolate data requirements into a higher compute regime, and compute requirements into a higher data regime. Second, we determine the optimal allocation of total _budget_ across data and compute to obtain given performance and use it to determine hyperparameters that maximize performance for a given budget. Third, this scaling behavior is enabled by first estimating predictable relationships between different _hyperparameters_, which is used to counteract effects of overfitting and plasticity loss unique to RL. We validate our approach using three algorithms: SAC, BRO, and PQL on DeepMind Control, OpenAI gym, and IsaacGym, when extrapolating to higher levels of data, compute, budget, or performance.

Scaling laws have emerged as important components of large language model (LLM) training as they can predict performance gains through scale, and provide guidance on important hyper-parameter choices that would otherwise be expensive. LLMs also rely on large, high-quality training datasets, like those sourced from (sometimes sensitive) user data. Training models on this sensitive user data requires careful privacy protections like differential privacy (DP). However, the dynamics of DP training are significantly different, and consequently their scaling laws are not yet fully understood. In this work, we establish scaling laws that accurately model the intricacies of DP LLM training, providing a complete picture of the compute-privacy-utility and the optimal training configurations in many settings.

We challenge the dominant focus on neural scaling laws and advocate for a paradigm shift toward downscaling in the development of large language models (LLMs). While scaling laws have provided critical insights into performance improvements through increasing model and dataset size, we emphasize the significant limitations of this approach, particularly in terms of computational inefficiency, environmental impact, and deployment constraints. To address these challenges, we propose a holistic framework for downscaling LLMs that seeks to maintain performance while drastically reducing resource demands. This paper outlines practical strategies for transitioning away from traditional scaling paradigms, advocating for a more sustainable, efficient, and accessible approach to LLM development.

Memory layers use a trainable key-value lookup mechanism to add extra parameters to a model without increasing FLOPs. Conceptually, sparsely activated memory layers complement compute-heavy dense feed-forward layers, providing dedicated capacity to store and retrieve information cheaply. This work takes memory layers beyond proof-of-concept, proving their utility at contemporary scale. On downstream tasks, language models augmented with our improved memory layer outperform dense models with more than twice the computation budget, as well as mixture-of-expert models when matched for both compute and parameters. We find gains are especially pronounced for factual tasks. We provide a fully parallelizable memory layer implementation, demonstrating scaling laws with up to 128B memory parameters, pretrained to 1 trillion tokens, comparing to base models with up to 8B parameters.

Low-precision training is considered an effective strategy for reducing both training and downstream inference costs. Previous scaling laws for precision mainly focus on integer quantization, which pay less attention to the constituents in floating-point (FP) quantization, and thus cannot well fit the LLM losses in this scenario. In contrast, while FP quantization training is more commonly implemented in production, it's research has been relatively superficial. In this paper, we thoroughly explore the effects of FP quantization targets, exponent bits, mantissa bits, and the calculation granularity of the scaling factor in FP quantization training performance of LLM models. In addition to an accurate FP quantization unified scaling law, we also provide valuable suggestions for the community: (1) Exponent bits contribute slightly more to the model performance than mantissa bits. We provide the optimal exponent-mantissa bit ratio for different bit numbers, which is available for future reference by hardware manufacturers; (2) We discover the formation of the critical data size in low-precision LLM training. Too much training data exceeding the critical data size will inversely bring in degradation of LLM performance; (3) The optimal FP quantization precision is directly proportional to the computational power, but within a wide computational power range. We estimate that the best cost-performance precision should lie between 4-8 bits.

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. Extensive empirical validation confirms the theoretical predictions of our scaling laws. These results offer actionable insights for designing and deploying MoE models in practical large-scale training scenarios.

Neural scaling laws have garnered significant interest due to their ability to predict model performance as a function of increasing parameters, data, and compute. In this work, we propose a simple statistical ansatz based on memorization to study scaling laws in the context of inference. Specifically, how performance improves with multiple inference attempts. We explore the coverage, or pass@k metric, which measures the chance of success over repeated attempts and provide a motivation for the observed functional form of the inference scaling behavior of the coverage in large language models (LLMs) on reasoning tasks. We then define an "inference loss", which exhibits a power law decay as the number of trials increases, and connect this result with prompting costs. We further test the universality of our construction by conducting experiments on a simple generative model, and find that our predictions are in agreement with the empirical coverage curves in a controlled setting. Our simple framework sets the ground for incorporating inference scaling with other known scaling laws.

Despite the empirical success of foundation models, we do not have a systematic characterization of the representations that these models learn. In this paper, we establish the contexture theory. It shows that a large class of representation learning methods can be characterized as learning from the association between the input and a context variable. Specifically, we show that many popular methods aim to approximate the top-d singular functions of the expectation operator induced by the context, in which case we say that the representation learns the contexture. We demonstrate the generality of the contexture theory by proving that representation learning within various learning paradigms -- supervised, self-supervised, and manifold learning -- can all be studied from such a perspective. We prove that representations that learn the contexture are optimal on those tasks that are compatible with the context. One important implication of our theory is that once the model is large enough to approximate the top singular functions, scaling up the model size yields diminishing returns, so further improvement requires better contexts. To this end, we study how to evaluate a context without knowing the downstream tasks. We propose a metric and show by experiments that it correlates well with the actual performance of the encoder on many real datasets.

We propose a distillation scaling law that estimates distilled model performance based on a compute budget and its allocation between the student and teacher. Our findings mitigate the risks associated with large-scale distillation by enabling compute-optimal allocation for both the teacher and student to maximize student performance. We provide compute-optimal distillation recipes for two key scenarios: when a teacher already exists, and when a teacher needs training. In settings involving many students or an existing teacher, distillation outperforms supervised learning up to a compute level that scales predictably with student size. Conversely, if only one student is to be distilled and a teacher also requires training, supervised learning is generally preferable. Additionally, our large-scale study of distillation increases our understanding of the process and helps inform experimental design.

Inspired by the principle of deliberate practice in human learning, we propose Deliberate Practice for Synthetic Data Generation (DP), a novel framework that improves sample efficiency through dynamic synthetic data generation. Prior work has shown that scaling synthetic data is inherently challenging, as naively adding new data leads to diminishing returns. To address this, pruning has been identified as a key mechanism for improving scaling, enabling models to focus on the most informative synthetic samples. Rather than generating a large dataset and pruning it afterward, DP efficiently approximates the direct generation of informative samples. We theoretically show how training on challenging, informative examples improves scaling laws and empirically validate that DP achieves better scaling performance with significantly fewer training samples and iterations. On ImageNet-100, DP generates 3.4x fewer samples and requires six times fewer iterations, while on ImageNet-1k, it generates 8x fewer samples with a 30% reduction in iterations, all while achieving superior performance compared to prior work.