SAM as an Optimal Relaxation of Bayes
This work bridges adversarial and Bayesian deep learning, offering a new approach to robustness for practitioners.
The paper connects sharpness-aware minimization (SAM) to Bayesian methods by showing SAM is a relaxation of the Bayes objective using the Fenchel biconjugate, enabling an Adam-like extension that provides uncertainty estimates and sometimes improves accuracy.
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.