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Related papers: Neural Scaling Laws for Deep Regression

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Representation learning that leverages large-scale labelled datasets, is central to recent progress in machine learning. Access to task relevant labels at scale is often scarce or expensive, motivating the need to learn from unlabelled…

Machine Learning · Computer Science 2022-02-14 Arna Ghosh , Arnab Kumar Mondal , Kumar Krishna Agrawal , Blake Richards

Recent works have shown that machine learning models improve at a predictable rate with the total amount of training data, leading to scaling laws that describe the relationship between error and dataset size. These scaling laws can help…

Machine Learning · Computer Science 2024-06-03 Ian Covert , Wenlong Ji , Tatsunori Hashimoto , James Zou

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…

Training large neural networks exposes neural scaling laws for the generalization error, which points to a universal behavior across network architectures of learning in high dimensions. It was also shown that this effect persists in the…

Disordered Systems and Neural Networks · Physics 2026-02-27 Jakob Kramp , Javed Lindner , Moritz Helias

Neural scaling laws, which in some domains can predict the performance of large neural networks as a function of model, data, and compute scale, are the cornerstone of building foundation models in Natural Language Processing and Computer…

Machine Learning · Computer Science 2026-03-27 Shashank Subramanian , Alexander Kiefer , Arnur Nigmetov , Amir Gholami , Dmitriy Morozov , Michael W. Mahoney

The guidance of scaling laws has increased the resource demands of modern large language models (LLMs), yet it remains questionable whether these models utilize resources effectively under a fixed budget. Previous research has proved…

Machine Learning · Computer Science 2026-05-28 Wenjie Sun , Jinning Yang , Shuai Zhang , Mengnan Du

Neural scaling laws -- power-law relationships between loss, model size, and data -- have been extensively documented for language and vision transformers, yet their existence in single-cell genomics remains largely unexplored. We present…

Machine Learning · Computer Science 2026-02-18 Ihor Kendiukhov

In materials science, data are scarce and expensive to generate, whether computationally or experimentally. Therefore, it is crucial to identify how model performance scales with dataset size and model capacity to distinguish between data-…

Materials Science · Physics 2026-02-06 Max Großmann , Malte Grunert , Erich Runge

In many applications, one works with neural network models trained by someone else. For such pretrained models, one may not have access to training data or test data. Moreover, one may not know details about the model, e.g., the specifics…

Machine Learning · Computer Science 2021-09-15 Charles H. Martin , Tongsu , Peng , Michael W. Mahoney

Neural scaling laws relate loss to model size in large language models (LLMs), yet depth and width may contribute to performance differently, requiring more detailed studies. Here, we quantify how depth affects loss via analysis of LLMs and…

Machine Learning · Computer Science 2026-02-06 Yizhou Liu , Sara Kangaslahti , Ziming Liu , Jeff Gore

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

Scaling laws are useful guides for derisking expensive training runs, as they predict performance of large models using cheaper, small-scale experiments. However, there remain gaps between current scaling studies and how language models are…

Scaling laws have been used to describe how large language model (LLM) performance scales with model size, training data size, or amount of computational resources. Motivated by the fact that neural quantum states (NQS) has increasingly…

Machine Learning · Computer Science 2025-09-17 Oliver Knitter , Dan Zhao , Stefan Leichenauer , Shravan Veerapaneni

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…

We propose the Quantization Model of neural scaling laws, explaining both the observed power law dropoff of loss with model and data size, and also the sudden emergence of new capabilities with scale. We derive this model from what we call…

Machine Learning · Computer Science 2024-01-17 Eric J. Michaud , Ziming Liu , Uzay Girit , Max Tegmark

We present an empirical study in the geometric task of learning interatomic potentials, which shows equivariance matters even more at larger scales; we show a clear power-law scaling behaviour with respect to data, parameters and compute…

Machine Learning · Computer Science 2026-05-06 Khang Ngo , Siamak Ravanbakhsh

Modern foundation models rely heavily on using scaling laws to guide crucial training decisions. Researchers often extrapolate the optimal architecture and hyper parameters settings from smaller training runs by describing the relationship…

Machine Learning · Computer Science 2025-02-27 Margaret Li , Sneha Kudugunta , Luke Zettlemoyer

We propose a novel scaling law for general-purpose decoder-only language models (LMs) trained on multilingual data, tackling the problem of balancing languages during multilingual pretraining. A primary challenge in studying multilingual…

Computation and Language · Computer Science 2024-12-05 Yifei He , Alon Benhaim , Barun Patra , Praneetha Vaddamanu , Sanchit Ahuja , Parul Chopra , Vishrav Chaudhary , Han Zhao , Xia Song

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…

Machine Learning · Computer Science 2026-05-05 Yizhou Liu , Ziming Liu , Jeff Gore

Scaling laws aim to accurately predict model performance across different scales. Existing scaling-law studies almost exclusively rely on cross-entropy as the evaluation metric. However, cross-entropy provides only a partial view of…

Machine Learning · Computer Science 2025-10-24 Baoqing Yue , Jinyuan Zhou , Zixi Wei , Jingtao Zhan , Qingyao Ai , Yiqun Liu