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We study empirical scaling laws for language model performance on the cross-entropy loss. The loss scales as a power-law with model size, dataset size, and the amount of compute used for training, with some trends spanning more than seven…

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

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…

Large language models with a huge number of parameters, when trained on near internet-sized number of tokens, have been empirically shown to obey neural scaling laws: specifically, their performance behaves predictably as a power law in…

Machine Learning · Computer Science 2022-11-01 Alexander Maloney , Daniel A. Roberts , James Sully

Kaplan et al. [2020] (`Kaplan') and Hoffmann et al. [2022] (`Chinchilla') studied the scaling behavior of transformers trained on next-token language prediction. These studies produced different estimates for how the number of parameters…

Machine Learning · Computer Science 2024-11-22 Tim Pearce , Jinyeop Song

Neural scaling laws predict how language model performance improves with increased training inputs. While aggregate metrics like validation loss can follow smooth power-law curves, individual downstream tasks exhibit diverse scaling…

Machine Learning · Computer Science 2026-05-11 Michael Y. Hu , Jane Pan , Ayush Rajesh Jhaveri , Nicholas Lourie , Kyunghyun Cho

Recent works have highlighted optimization difficulties faced by gradient descent in training the first and last layers of transformer-based language models, which are overcome by optimizers such as Adam. These works suggest that the…

Machine Learning · Computer Science 2025-05-27 Frederik Kunstner , Francis Bach

Neural scaling laws define a predictable relationship between a model's parameter count and its performance after training in the form of a power law. However, most research to date has not explicitly investigated whether scaling laws can…

Computation and Language · Computer Science 2022-10-19 Maor Ivgi , Yair Carmon , Jonathan Berant

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

The remarkable progress in deep learning in recent years is largely driven by improvements in scale, where bigger models are trained on larger datasets for longer schedules. To predict the benefit of scale empirically, we argue for a more…

Machine Learning · Computer Science 2022-11-02 Ibrahim Alabdulmohsin , Behnam Neyshabur , Xiaohua Zhai

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

Training compute is increasingly outpacing the availability of high-quality data. This shifts the central challenge from optimal compute allocation to extracting maximum value from limited data. The widely adopted Chinchilla scaling law…

Machine Learning · Computer Science 2026-05-05 Justin Lovelace , Christian Belardi , Srivatsa Kundurthy , Shriya Sudhakar , Kilian Q. Weinberger

When training deep neural networks, a model's generalization error is often observed to follow a power scaling law dependent both on the model size and the data size. Perhaps the best known example of such scaling laws are for…

Machine Learning · Computer Science 2024-11-12 Alex Havrilla , Wenjing Liao

Deep neural networks exhibit empirical neural scaling laws, with error decreasing as a power law with increasing model or data size, across a wide variety of architectures, tasks, and datasets. This universality suggests that scaling laws…

Machine Learning · Computer Science 2024-12-12 Ari Brill

The quality of Large Language Model (LLM) pretraining depends on multiple factors, including the compute budget and the choice of optimization algorithm. Empirical scaling laws are widely used to predict loss as model size and training data…

Machine Learning · Computer Science 2026-02-25 Alexandra Volkova , Mher Safaryan , Christoph H. Lampert , Dan Alistarh

While scaling laws for Large Language Models (LLMs) traditionally focus on proxy metrics like pretraining loss, predicting downstream task performance has been considered unreliable. This paper challenges that view by proposing a direct…

Machine Learning · Computer Science 2025-12-10 Jakub Krajewski , Amitis Shidani , Dan Busbridge , Sam Wiseman , Jason Ramapuram

Scaling laws in language modeling traditionally quantify training loss as a function of dataset size and model parameters, providing compute-optimal estimates but often neglecting the impact of data quality on model generalization. In this…

Computation and Language · Computer Science 2024-10-07 Ernie Chang , Matteo Paltenghi , Yang Li , Pin-Jie Lin , Changsheng Zhao , Patrick Huber , Zechun Liu , Rastislav Rabatin , Yangyang Shi , Vikas Chandra

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…

Neural scaling laws--power-law relationships between generalization errors and characteristics of deep learning models--are vital tools for developing reliable models while managing limited resources. Although the success of large language…

Machine Learning · Computer Science 2026-03-27 Tilen Cadez , Kyoung-Min Kim

Empirically, large-scale deep learning models often satisfy a neural scaling law: the test error of the trained model improves polynomially as the model size and data size grow. However, conventional wisdom suggests the test error consists…

Machine Learning · Computer Science 2025-06-11 Licong Lin , Jingfeng Wu , Sham M. Kakade , Peter L. Bartlett , Jason D. Lee
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