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Related papers: A Dynamical Model of Neural Scaling Laws

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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

This work studies the general principles of improving the learning of language models (LMs), which aims at reducing the necessary training steps for achieving superior performance. Specifically, we present a theory for the optimal learning…

Computation and Language · Computer Science 2024-03-05 Yuxian Gu , Li Dong , Yaru Hao , Qingxiu Dong , Minlie Huang , Furu Wei

We consider shallow (single hidden layer) neural networks and characterize their performance when trained with stochastic gradient descent as the number of hidden units $N$ and gradient descent steps grow to infinity. In particular, we…

Machine Learning · Statistics 2022-06-02 Jiahui Yu , Konstantinos Spiliopoulos

We propose a simple mechanism by which scaling laws emerge from feature learning in multi-layer networks. We study a high-dimensional hierarchical target that is a globally high-degree function, but that can be represented by a combination…

Machine Learning · Statistics 2026-05-15 Arie Wortsman-Zurich , Hugo Tabanelli , Yatin Dandi , Florent Krzakala , Bruno Loureiro

Recent empirical studies show three phenomena with increasing size of language models: compute-optimal size scaling, emergent capabilities, and performance plateauing. We present a simple unified mathematical framework to explain all of…

Information Theory · Computer Science 2024-10-17 Anuj K. Nayak , Lav R. Varshney

The choice of initial learning rate can have a profound effect on the performance of deep networks. We present a class of neural networks with solvable training dynamics, and confirm their predictions empirically in practical deep learning…

Machine Learning · Statistics 2020-03-05 Aitor Lewkowycz , Yasaman Bahri , Ethan Dyer , Jascha Sohl-Dickstein , Guy Gur-Ari

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…

We present a smoothly broken power law functional form (that we refer to as a Broken Neural Scaling Law (BNSL)) that accurately models & extrapolates the scaling behaviors of deep neural networks (i.e. how the evaluation metric of interest…

Machine Learning · Computer Science 2023-07-25 Ethan Caballero , Kshitij Gupta , Irina Rish , David Krueger

Recent theories suggest that Neural Scaling Laws arise whenever the task is linearly decomposed into power-law distributed units. Alternatively, scaling laws also emerge when data exhibit a hierarchically compositional structure, as is…

Machine Learning · Statistics 2025-05-13 Francesco Cagnetta , Hyunmo Kang , Matthieu Wyart

Within the scaling laws paradigm, which underpins the training of large neural networks like ChatGPT and Llama, we consider a supervised regression setting and establish the existance of a strong form of the model collapse phenomenon, a…

Machine Learning · Computer Science 2024-10-10 Elvis Dohmatob , Yunzhen Feng , Arjun Subramonian , Julia Kempe

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

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

Large genomic and imaging datasets can be used to train models that learn meaningful representations of cellular systems. Across domains, model performance improves predictably with dataset size and compute budget, providing a basis for…

Quantitative Methods · Quantitative Biology 2026-02-23 Gokul Gowri , Igor Sadalski , Dan Raviv , Peng Yin , Jonathan Rosenfeld , Allon M. Klein

Machine learning, and in particular neural network models, have revolutionized fields such as image, text, and speech recognition. Today, many important real-world applications in these areas are driven by neural networks. There are also…

Probability · Mathematics 2019-11-12 Justin Sirignano , Konstantinos Spiliopoulos

Recently observed empirical scaling laws describe the performance of foundation-type models as three independent key quantities -- dataset size, compute, and model parameters -- are modified. Extracting these scaling laws informs the…

High Energy Physics - Phenomenology · Physics 2026-05-29 Oz Amram , Darius A. Faroughy , Tjarko Gerdes , Anna Hallin , Gregor Kasieczka , Michael Krämer , Humberto Reyes-Gonzalez , David Shih

Scaling laws for large language models (LLMs) have provided useful guidance in training ever larger models for predictable performance gains. Time series forecasting shares a similar sequential structure to language, and is amenable to…

Machine Learning · Computer Science 2025-01-09 Thomas D. P. Edwards , James Alvey , Justin Alsing , Nam H. Nguyen , Benjamin D. Wandelt

The process of training an artificial neural network involves iteratively adapting its parameters so as to minimize the error of the network's prediction, when confronted with a learning task. This iterative change can be naturally…

Machine Learning · Computer Science 2024-04-10 Kaloyan Danovski , Miguel C. Soriano , Lucas Lacasa

Effective LLM training depends on predictable scaling of key quantities -- such as final loss and optimal hyperparameters -- with model and dataset size. Qiu et al. (2025) recently showed that this predictability can extend beyond scalars:…

Machine Learning · Computer Science 2026-03-03 Shane Bergsma , Bin Claire Zhang , Nolan Dey , Shaheer Muhammad , Gurpreet Gosal , Joel Hestness

Scaling laws are a critical component of the LLM development pipeline, most famously as a way to forecast training decisions such as 'compute-optimally' trading-off parameter count and dataset size, alongside a more recent growing list of…

Machine Learning · Computer Science 2025-06-17 Nicholas Roberts , Niladri Chatterji , Sharan Narang , Mike Lewis , Dieuwke Hupkes

An important characteristic of neural networks is their ability to learn representations of the input data with effective features for prediction, which is believed to be a key factor to their superior empirical performance. To better…

Machine Learning · Computer Science 2022-06-06 Zhenmei Shi , Junyi Wei , Yingyu Liang