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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…

Machine Learning · Computer Science 2023-04-25 Ben Sorscher , Robert Geirhos , Shashank Shekhar , Surya Ganguli , Ari S. Morcos

Reasoning is an integral part of many tasks performed by language models (LMs). However, the effects of scaling model sizes and data on reasoning abilities at pretraining time remain understudied. To rigorously investigate this problem, we…

Artificial Intelligence · Computer Science 2025-09-30 Xinyi Wang , Shawn Tan , Shenbo Xu , Mingyu Jin , William Yang Wang , Rameswar Panda , Yikang Shen

While the scaling laws of large language models (LLMs) training have been extensively studied, optimal inference configurations of LLMs remain underexplored. We study inference scaling laws (aka test-time scaling laws) and compute-optimal…

Artificial Intelligence · Computer Science 2025-03-04 Yangzhen Wu , Zhiqing Sun , Shanda Li , Sean Welleck , Yiming Yang

Learning to generalise from limited data is a fundamental challenge for both artificial and biological systems. A common strategy is to extract reusable structure from abundant unlabelled data, enabling efficient adaptation to new tasks…

Machine Learning · Computer Science 2026-05-20 Valentina Njaradi , Clémentine Dominé , Rachel Swanson , Marco Mondelli , Andrew Saxe

Training data plays a crucial role in Large Language Models (LLM) scaling, yet high quality data is of limited supply. Synthetic data techniques offer a potential path toward sidestepping these limitations. We conduct a large-scale…

Neural scaling laws suggest that the test error of large language models trained online decreases polynomially as the model size and data size increase. However, such scaling can be unsustainable when running out of new data. In this work,…

Machine Learning · Computer Science 2025-09-26 Licong Lin , Jingfeng Wu , Peter L. Bartlett

Deep learning has non-convex loss landscape and its optimization dynamics is hard to analyze or control. Nevertheless, the dynamics can be empirically convex-like across various tasks, models, optimizers, hyperparameters, etc. In this work,…

Machine Learning · Computer Science 2026-02-10 Zhiqi Bu , Shiyun Xu , Jialin Mao

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…

Machine Learning · Statistics 2024-12-10 Noam Levi

In this work, we provide a sharp theory of scaling laws for two-layer neural networks trained on a class of hierarchical multi-index targets, in a genuinely representation-limited regime. We derive exact information-theoretic scaling laws…

Machine Learning · Statistics 2026-02-06 Leonardo Defilippis , Florent Krzakala , Bruno Loureiro , Antoine Maillard

Data duplication during pretraining can degrade generalization and lead to memorization, motivating aggressive deduplication pipelines. However, at web scale, it is unclear what constitutes a ``duplicate'': beyond surface-form matches,…

Machine Learning · Computer Science 2026-03-10 Joshua Kazdan , Noam Levi , Rylan Schaeffer , Jessica Chudnovsky , Abhay Puri , Bo He , Mehmet Donmez , Sanmi Koyejo , David Donoho

Scaling laws play a central role in the success of Large Language Models (LLMs), enabling the prediction of model performance relative to compute budgets prior to training. While Transformers have been the dominant architecture, recent…

Machine Learning · Computer Science 2026-02-23 Maximilian Beck , Kajetan Schweighofer , Sebastian Böck , Sebastian Lehner , Sepp Hochreiter

Recent large language models have been trained on vast datasets, but also often on repeated data, either intentionally for the purpose of upweighting higher quality data, or unintentionally because data deduplication is not perfect and the…

Scaling laws in deep learning -- empirical power-law relationships linking model performance to resource growth -- have emerged as simple yet striking regularities across architectures, datasets, and tasks. These laws are particularly…

Machine Learning · Computer Science 2026-05-01 Francesco D'Amico , Dario Bocchi , Matteo Negri

Hyperparameter transfer has become an important component of modern large-scale training recipes. Existing methods, such as muP, primarily focus on transfer between model sizes, with transfer across batch sizes and training horizons often…

Machine Learning · Computer Science 2026-03-18 Egor Shulgin , Dimitri von Rütte , Tianyue H. Zhang , Niccolò Ajroldi , Bernhard Schölkopf , Antonio Orvieto

Neural scaling laws aim to characterize how out-of-sample error behaves as a function of model and training dataset size. Such scaling laws guide allocation of a computational resources between model and data processing to minimize error.…

Machine Learning · Computer Science 2024-07-02 Hong Jun Jeon , Benjamin Van Roy

When data is plentiful, the loss achieved by well-trained neural networks scales as a power-law $L \propto N^{-\alpha}$ in the number of network parameters $N$. This empirical scaling law holds for a wide variety of data modalities, and may…

Machine Learning · Computer Science 2020-04-24 Utkarsh Sharma , Jared Kaplan

The prevailing paradigm in large language model (LLM) development is to pretrain a base model, then perform further training to improve performance and model behavior. However, hyperparameter optimization and scaling laws have been studied…

Machine Learning · Computer Science 2026-02-12 Tessa Han , Sebastian Bordt , Hanlin Zhang , Sham Kakade

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…

Empirical scaling laws prescribe how to allocate parameters, data, and compute, while maximal-update parameterization ($\mu$P) enables learning-rate transfer across widths by equalizing early-time update magnitudes. However, in modern…

Machine Learning · Computer Science 2025-10-20 Zhiyuan Fan , Yifeng Liu , Qingyue Zhao , Angela Yuan , Quanquan Gu

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…

Machine Learning · Computer Science 2025-08-26 Preston Fu , Oleh Rybkin , Zhiyuan Zhou , Michal Nauman , Pieter Abbeel , Sergey Levine , Aviral Kumar