Year: 2023
Type: preprint
Abstract: We propose a novel framework for exploring weak and $L_2$ generalization errors of algorithms through the lens of differential calculus on the space of probability measures. Specifically, we consider the KL-regularized empirical risk minimization problem and establish generic conditions under which the generalization error convergence rate, when training on a sample of size $n$, is $\mathcal{O}(1/n)$. In the context of supervised learning with a one-hidden layer neural network in the mean-field regime, these conditions are reflected in suitable integrability and regularity assumptions on the loss and activation functions.
Source: arXiv (Cornell University)
Institutions: The Alan Turing Institute, University of Oxford
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4381586713