# Information-Theoretic Foundations for Neural Scaling Laws

arXiv: https://arxiv.org/abs/2407.01456 · HTML: https://mlsanity.com/paper/2407.01456/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 7 references that are in the map.
- First posted on arXiv 28 Jun 2024.

## Builds on (most cited first, 5 of 5)

- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Reinforcement Learning, Bit by Bit](https://mlsanity.com/paper/2103.04047/) (2021)
- [An Information-Theoretic Framework for Supervised Learning](https://mlsanity.com/paper/2203.00246/) (2022)
- [Is Stochastic Gradient Descent Near Optimal?](https://mlsanity.com/paper/2209.08627/) (2022)

## Abstract (arXiv)

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. However, existing theoretical support for neural scaling laws lacks rigor and clarity, entangling the roles of information and optimization. In this work, we develop rigorous information-theoretic foundations for neural scaling laws. This allows us to characterize scaling laws for data generated by a two-layer neural network of infinite width. We observe that the optimal relation between data and model size is linear, up to logarithmic factors, corroborating large-scale empirical investigations. Concise yet general results of the kind we establish may bring clarity to this topic and inform future investigations.