Stability and Generalization Analysis of Gradient Methods for Shallow Neural NetworksDownload PDF

Published: 31 Oct 2022, Last Modified: 13 Jan 2023NeurIPS 2022 AcceptReaders: Everyone
Keywords: Statistical Learning Theory, Algorithmic Stability, Shallow Neural Networks, Generalization Error
TL;DR: We develop stability and generalization bounds for gradient methods on shallow neural networks.
Abstract: While significant theoretical progress has been achieved, unveiling the generalization mystery of overparameterized neural networks still remains largely elusive. In this paper, we study the generalization behavior of shallow neural networks (SNNs) by leveraging the concept of algorithmic stability. We consider gradient descent (GD) and stochastic gradient descent (SGD) to train SNNs, for both of which we develop consistent excess risk bounds by balancing the optimization and generalization via early-stopping. As compared to existing analysis on GD, our new analysis requires a relaxed overparameterization assumption and also applies to SGD. The key for the improvement is a better estimation of the smallest eigenvalues of the Hessian matrices of the empirical risks and the loss function along the trajectories of GD and SGD by providing a refined estimation of their iterates.
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