On the Importance of Gradient Norm in PAC-Bayesian BoundsDownload PDF

Published: 31 Oct 2022, Last Modified: 15 Jan 2023NeurIPS 2022 AcceptReaders: Everyone
Keywords: generalization bound, pac-bayes
Abstract: Generalization bounds which assess the difference between the true risk and the empirical risk have been studied extensively. However, to obtain bounds, current techniques use strict assumptions such as a uniformly bounded or a Lipschitz loss function. To avoid these assumptions, in this paper, we follow an alternative approach: we relax uniform bounds assumptions by using on-average bounded loss and on-average bounded gradient norm assumptions. Following this relaxation, we propose a new generalization bound that exploits the contractivity of the log-Sobolev inequalities. These inequalities add an additional loss-gradient norm term to the generalization bound, which is intuitively a surrogate of the model complexity. We apply the proposed bound on Bayesian deep nets and empirically analyze the effect of this new loss-gradient norm term on different neural architectures.
TL;DR: A new generalization bound that exploits the contractivity of the log-Sobolev inequalities.
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