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.

翻译：锐度感知最小化（Sharpness-Aware Minimization，SAM）及相关的对抗性深度学习方法能显著提升泛化性能，但其底层机制尚未完全明晰。本文证明，SAM可视为贝叶斯目标函数的一种松弛形式——其中期望负损失被替换为通过Fenchel双共轭方法得到的最优凸下界。该关联催生了SAM的类Adam扩展方法，可自动获取合理的置信度估计，同时有时能提升模型精度。通过联结对抗性与贝叶斯方法，本研究为鲁棒性开辟了新路径。