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.
@article{arxiv.2210.01620,
title = {SAM as an Optimal Relaxation of Bayes},
author = {Thomas Möllenhoff and Mohammad Emtiyaz Khan},
journal= {arXiv preprint arXiv:2210.01620},
year = {2023}
}
Comments
Accepted at ICLR 2023. Changes: Link to source code (https://github.com/team-approx-bayes/bayesian-sam), fix a typo in Appendix D