Abstract for the talk on 04.03.2021 (17:00 h)Math Machine Learning seminar MPI MIS + UCLA
Marcus Hutter (DeepMind and Australian National University)
Learning Curve Theory
04.03.2021, 17:00 h, only video broadcast
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.