Mean-field Analysis of Generalization Errors
This work provides theoretical insights into generalization bounds for mean-field neural networks, which is incremental but addresses a core challenge in understanding algorithm performance for researchers in statistical learning theory.
The paper tackles the problem of analyzing generalization errors in machine learning by proposing a framework using differential calculus on probability measures, establishing conditions for a convergence rate of O(1/n) in KL-regularized empirical risk minimization.
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.