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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

Predicting material properties is crucial for designing better batteries, semiconductors, and medical devices. Deep learning helps scientists quickly find promising materials by predicting their energy, forces, and stresses. Companies scale…

Machine Learning · Computer Science 2025-09-29 Akshay Trikha , Kyle Chu , Advait Gosai , Parker Szachta , Eric Weiner

While scaling laws provide a reliable methodology for predicting train loss across compute scales for a single data distribution, less is known about how these predictions should change as we change the distribution. In this paper, we…

Machine Learning · Computer Science 2024-11-21 David Brandfonbrener , Nikhil Anand , Nikhil Vyas , Eran Malach , Sham Kakade

Increasing the size of a Transformer does not always lead to enhanced performance. This phenomenon cannot be explained by the empirical scaling laws. Furthermore, the model's enhanced performance is closely associated with its memorization…

Machine Learning · Computer Science 2024-12-02 Xueyan Niu , Bo Bai , Lei Deng , Wei Han

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

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…

Machine Learning · Statistics 2021-09-27 Amélie Chatelain , Amine Djeghri , Daniel Hesslow , Julien Launay , Iacopo Poli

Low-precision training is critical for optimizing the trade-off between model quality and training costs, necessitating the joint allocation of model size, dataset size, and numerical precision. While empirical scaling laws suggest that…

Machine Learning · Statistics 2026-02-27 Dechen Zhang , Xuan Tang , Yingyu Liang , Difan Zou

What scaling limits govern neural network training dynamics when model size and training time grow in tandem? We show that despite the complex interactions between architecture, training algorithms, and data, compute-optimally trained…

Machine Learning · Computer Science 2025-07-08 Shikai Qiu , Lechao Xiao , Andrew Gordon Wilson , Jeffrey Pennington , Atish Agarwala

This paper investigates the scaling properties of autoregressive next-pixel prediction, a simple, end-to-end yet under-explored framework for unified vision models. Starting with images at resolutions of 32x32, we train a family of…

Computer Vision and Pattern Recognition · Computer Science 2026-05-19 Xinchen Yan , Chen Liang , Lijun Yu , Adams Wei Yu , Yifeng Lu , Quoc V. Le

Supervised learning has become a cornerstone of modern machine learning, yet a comprehensive theory explaining its effectiveness remains elusive. Empirical phenomena, such as neural analogy-making and the linear representation hypothesis,…

Machine Learning · Computer Science 2025-02-26 Patrik Reizinger , Alice Bizeul , Attila Juhos , Julia E. Vogt , Randall Balestriero , Wieland Brendel , David Klindt

Continual Pre-training (CPT) serves as a fundamental approach for adapting foundation models to domain-specific applications. Scaling laws for pre-training define a power-law relationship between dataset size and the test loss of an LLM.…

Machine Learning · Computer Science 2025-12-29 Lei Liu , Hao Zhu , Yue Shen , Zhixuan Chu , Jian Wang , Jinjie Gu , Kui Ren

Neural network-based emulators for the inference of stellar parameters and elemental abundances represent an increasingly popular methodology in modern spectroscopic surveys. However, these approaches are often constrained by their…

Instrumentation and Methods for Astrophysics · Physics 2025-06-10 Tomasz Różański , Yuan-Sen Ting

Scaling laws describe how language models improve with additional data, parameters, and compute. While widely used, they are typically measured on aggregate test sets. Aggregate evaluations yield clean trends but average over heterogeneous…

Computation and Language · Computer Science 2026-01-16 William Held , David Hall , Percy Liang , Diyi Yang

Large language models (LLMs) achieve strong performance across diverse tasks, largely driven by high-quality web data used in pre-training. However, recent studies indicate this data source is rapidly depleting. Synthetic data emerges as a…

Learned image compression methods have attracted great research interest and exhibited superior rate-distortion performance to the best classical image compression standards of the present. The entropy model plays a key role in learned…

Computer Vision and Pattern Recognition · Computer Science 2025-05-16 Jingbo Lu , Leheng Zhang , Xingyu Zhou , Mu Li , Wen Li , Shuhang Gu

Nearly all practical neural models for classification are trained using cross-entropy loss. Yet this ubiquitous choice is supported by little theoretical or empirical evidence. Recent work (Hui & Belkin, 2020) suggests that training using…

Machine Learning · Computer Science 2023-02-09 Like Hui , Mikhail Belkin , Stephen Wright

Recent advances in large language models (LLMs) highlight a strong connection between intelligence and compression. Learned image compression, a fundamental task in modern data compression, has made significant progress in recent years.…

Computer Vision and Pattern Recognition · Computer Science 2025-08-13 Yuqi Li , Haotian Zhang , Li Li , Dong Liu , Feng Wu

Generative language models define distributions over sequences of tokens that can represent essentially any combination of data modalities (e.g., any permutation of image tokens from VQ-VAEs, speech tokens from HuBERT, BPE tokens for…

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

Deep learning has recently revealed the existence of scaling laws, demonstrating that model performance follows predictable trends based on dataset and model sizes. Inspired by these findings and fascinating phenomena emerging in the…

Machine Learning · Statistics 2026-02-10 Mattia Rosso , Simone Rossi , Giulio Franzese , Markus Heinonen , Maurizio Filippone