“Learning Curve Theory”, Marcus Hutter2021-02-08 (AI scaling; similar)⁠:

Recently a number of empirical “universal” scaling law papers have been published, most notably by OpenAI. ‘Scaling laws’ refers to power-law decreases of training or test error w.r.t. more data, larger neural networks, and/or more compute. In this work we focus on scaling w.r.t. data size n.

Theoretical understanding of this phenomenon is largely lacking, except in finite-dimensional models for which error typically decreases with n^−1⁄2 or n⁻¹, where n is the sample size.

We develop and theoretically analyse the simplest possible (toy) model that can exhibit n^−β learning curves for arbitrary power β > 0, and determine whether power laws are universal or depend on the data distribution.

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