SAM as an Optimal Relaxation of BayesDownload PDF

Published: 01 Feb 2023, Last Modified: 02 Mar 2023ICLR 2023 notable top 5%Readers: Everyone
Keywords: bayesian deep learning, sharpness-aware minimization, variational bayes, convex duality
TL;DR: We show that SAM can be seen as a relaxation of Bayes, by using Fenchel conjugates.
Abstract: Sharpness-aware minimization (SAM) and related adversarial deep-learning methods can drastically improve generalization, but their underlying mechanisms are not yet fully understood. Here, we establish SAM as a relaxation of the Bayes objective where the expected negative-loss is replaced by the optimal convex lower bound, obtained by using the so-called Fenchel biconjugate. The connection enables a new Adam-like extension of SAM to automatically obtain reasonable uncertainty estimates, while sometimes also improving its accuracy. By connecting adversarial and Bayesian methods, our work opens a new path to robustness.
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