Mean-field Analysis of Generalization Errors

Gholamali Aminian; Samuel N. Cohen; Łukasz Szpruch

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arXiv · 2306.11623

Mean-field Analysis of Generalization Errors

Gholamali Aminian·Samuel N. Cohen·Łukasz Szpruch

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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.

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Gholamali Aminian, Samuel N. Cohen, Łukasz Szpruch. 2023-06-20. Mean-field Analysis of Generalization Errors. https://arxiv.org/abs/2306.11623

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