# An Information-Theoretic Analysis of Compute-Optimal Neural Scaling Laws

arXiv: https://arxiv.org/abs/2212.01365 · HTML: https://mlsanity.com/paper/2212.01365/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 13 references that are in the map.
- First posted on arXiv 2 Dec 2022.

## Builds on (most cited first, 9 of 9)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Scaling Language Models: Methods, Analysis & Insights from Training Gopher](https://mlsanity.com/paper/2112.11446/) (2021)
- [A Priori Estimates of the Population Risk for Two-layer Neural Networks](https://mlsanity.com/paper/1810.06397/) (2018)
- [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)

We study the compute-optimal trade-off between model and training data set sizes for large neural networks. Our result suggests a linear relation similar to that supported by the empirical analysis of chinchilla. While that work studies transformer-based large language models trained on the MassiveText corpus gopher, as a starting point for development of a mathematical theory, we focus on a simpler learning model and data generating process, each based on a neural network with a sigmoidal output unit and single hidden layer of ReLU activation units. We introduce general error upper bounds for a class of algorithms which incrementally update a statistic (for example gradient descent). For a particular learning model inspired by barron 1993, we establish an upper bound on the minimal information-theoretically achievable expected error as a function of model and data set sizes. We then derive allocations of computation that minimize this bound. We present empirical results which suggest that this approximation correctly identifies an asymptotic linear compute-optimal scaling. This approximation also generates new insights. Among other things, it suggests that, as the input dimension or latent space complexity grows, as might be the case for example if a longer history of tokens is taken as input to a language model, a larger fraction of the compute budget should be allocated to growing the learning model rather than training data.