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SAM as an Optimal Relaxation of Bayes

Thomas Möllenhoff · Mohammad Emtiyaz Khan

MH1-2-3-4 #113

Keywords: [ Probabilistic Methods ] [ convex duality ] [ bayesian deep learning ] [ Sharpness-aware minimization ] [ variational bayes ]


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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