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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

We propose an approach to estimate the number of samples required for a model to reach a target performance. We find that the power law, the de facto principle to estimate model performance, leads to large error when using a small dataset…

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

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

Recently, Large Language Models (LLMs) have achieved remarkable success. A key factor behind this success is the scaling law observed by OpenAI. Specifically, for models with Transformer architecture, the test loss exhibits a power-law…

Machine Learning · Computer Science 2025-03-04 Yifang Chen , Xuyang Guo , Xiaoyu Li , Yingyu Liang , Zhenmei Shi , Zhao Song

We study empirical scaling laws for transfer learning between distributions in an unsupervised, fine-tuning setting. When we train increasingly large neural networks from-scratch on a fixed-size dataset, they eventually become data-limited…

Machine Learning · Computer Science 2021-02-03 Danny Hernandez , Jared Kaplan , Tom Henighan , Sam McCandlish

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

There is a recent trend in machine learning to increase model quality by growing models to sizes previously thought to be unreasonable. Recent work has shown that autoregressive generative models with cross-entropy objective functions…

Audio and Speech Processing · Electrical Eng. & Systems 2021-06-18 Jasha Droppo , Oguz Elibol

Training large language models (LLMs) is computationally expensive, partly because the loss exhibits slow power-law convergence whose origin remains debatable. Through systematic analysis of toy models and empirical evaluation of LLMs, we…

Machine Learning · Computer Science 2026-02-04 Yizhou Liu , Ziming Liu , Cengiz Pehlevan , Jeff Gore

While scaling laws for large language models (LLMs) during pre-training have been extensively studied, their behavior under reinforcement learning (RL) post-training remains largely unexplored. This paper presents a systematic empirical…

In machine learning, a bias occurs whenever training sets are not representative for the test data, which results in unreliable models. The most common biases in data are arguably class imbalance and covariate shift. In this work, we aim to…

Machine Learning · Computer Science 2018-04-04 Patrick Glauner , Radu State , Petko Valtchev , Diogo Duarte

Scaling laws, a defining feature of deep learning, reveal a striking power-law improvement in model performance with increasing dataset and model size. Yet, their mathematical origins, especially the scaling exponent, have remained elusive.…

Machine Learning · Computer Science 2026-03-24 Yuda Bi , Vince D Calhoun

Large language models (LLMs) can internally distinguish between evaluation and deployment contexts, a behaviour known as \emph{evaluation awareness}. This undermines AI safety evaluations, as models may conceal dangerous capabilities during…

Artificial Intelligence · Computer Science 2025-11-11 Maheep Chaudhary , Ian Su , Nikhil Hooda , Nishith Shankar , Julia Tan , Kevin Zhu , Ryan Lagasse , Vasu Sharma , Ashwinee Panda

Empirically-determined scaling laws have been broadly successful in predicting the evolution of large machine learning models with training data and number of parameters. As a consequence, they have been useful for optimizing the allocation…

Computer Vision and Pattern Recognition · Computer Science 2024-07-26 Katherine L. Mentzer , Andrea Montanari

Ensembles of deep neural networks are known to achieve state-of-the-art performance in uncertainty estimation and lead to accuracy improvement. In this work, we focus on a classification problem and investigate the behavior of both…

Machine Learning · Computer Science 2021-06-29 Ekaterina Lobacheva , Nadezhda Chirkova , Maxim Kodryan , Dmitry Vetrov

In recent years, the state-of-the-art in deep learning has been dominated by very large models that have been pre-trained on vast amounts of data. The paradigm is very simple: investing more computational resources (optimally) leads to…

Machine Learning · Computer Science 2024-05-24 Sotiris Anagnostidis , Gregor Bachmann , Imanol Schlag , Thomas Hofmann

Neural scaling laws describe how model performance improves as a power law with size, but existing work focuses on models above 100M parameters. The sub-20M regime -- where TinyML and edge AI operate -- remains unexamined. We train 90…

Machine Learning · Computer Science 2026-03-10 Mohammed Alnemari , Rizwan Qureshi , Nader Begrazadah

As neural networks continue to grow in size but datasets might not, it is vital to understand how much performance improvement can be expected: is it more important to scale network size or data volume? Thus, neural network scaling laws,…

Machine Learning · Computer Science 2024-09-10 Akhilan Boopathy , Ila Fiete

Power-law distributions are typical macroscopic features occurring in almost all complex systems observable in nature. As a result, researchers in quantitative analyses must often generate random synthetic variates obeying power-law…

Physics and Society · Physics 2014-11-11 Filippo Radicchi

For a given distribution, learning algorithm, and performance metric, the rate of convergence (or data-scaling law) is the asymptotic behavior of the algorithm's test performance as a function of number of train samples. Many learning…

Machine Learning · Computer Science 2021-11-10 Preetum Nakkiran