Sharpness-Aware Minimization (SAM) enhances generalization by reducing a Max-Sharpness (MaxS). Despite the practical success, we empirically found that the MAxS behind SAM's generalization enhancements face the "Flatness Indicator Problem" (FIP), where SAM only considers the flatness in the direction of gradient ascent, resulting in a next minimization region that is not sufficiently flat. A better Flatness Indicator (FI) would bring a better generalization of neural networks. Because SAM is a greedy search method in nature. In this paper, we propose to utilize the difference between the training loss and the minimum loss over the neighborhood surrounding the current weight, which we denote as Min-Sharpness (MinS). By merging MaxS and MinS, we created a better FI that indicates a flatter direction during the optimization. Specially, we combine this FI with SAM into the proposed Bilateral SAM (BSAM) which finds a more flatter minimum than that of SAM. The theoretical analysis proves that BSAM converges to local minima. Extensive experiments demonstrate that BSAM offers superior generalization performance and robustness compared to vanilla SAM across various tasks, i.e., classification, transfer learning, human pose estimation, and network quantization. Code is publicly available at: https://github.com/ajiaaa/BSAM.

本研究针对锐度感知最小化（SAM）在提升泛化能力过程中存在的“平坦指示器问题”进行了探讨，提出了双边SAM（BSAM）方法。通过引入当前权重周围邻域内训练损失与最小损失之间的差异，BSAM能够指导优化过程朝向更平坦的最小值，实验证明其在多项任务中的泛化性能和鲁棒性优于传统SAM。

双边锐度感知最小化以获取更平坦的极小值