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（SAM）及相关对抗性深度学习方法可显著提升泛化性能，但其内在机制尚未完全明晰。本文证明SAM是贝叶斯目标函数的松弛形式——该目标函数通过Fenchel双共轭方法将期望负损失替换为最优凸下界。这一联系使得我们能够将SAM扩展为新型类Adam算法，在自动获得合理不确定性估计的同时，有时还能提升其准确性。通过建立对抗方法与贝叶斯方法之间的关联，本研究为提升模型鲁棒性开辟了新路径。