SSE-SAM: Balancing Head and Tail Classes Gradually Through Stage-Wise SAM

Real-world datasets often exhibit a long-tailed distribution, where vast majority of classes known as tail classes have only few samples. Traditional methods tend to overfit on these tail classes. Recently, a new approach called Imbalanced SAM (ImbSAM) is proposed to leverage the generalization benefits of Sharpness-Aware Minimization (SAM) for long-tailed distributions. The main strategy is to merely enhance the smoothness of the loss function for tail classes. However, we argue that improving generalization in long-tail scenarios requires a careful balance between head and tail classes. We show that neither SAM nor ImbSAM alone can fully achieve this balance. For SAM, we prove that although it enhances the model's generalization ability by  escaping saddle point in the overall loss landscape, it does not effectively address this for tail-class losses. Conversely, while ImbSAM is more effective at avoiding saddle points in tail classes, the head classes are trained insufficiently, resulting in significant performance drops. Based on these insights, we propose Stage-wise Saddle Escaping SAM (SSE-SAM), which uses complementary strengths of ImbSAM and SAM in a phased approach. Initially, SSE-SAM follows the majority sample to avoid saddle points of the head-class loss. During the later phase, it focuses on tail-classes to help them escape saddle points. Our experiments confirm that SSE-SAM has better ability in escaping saddles both on head and tail classes, and shows performance improvements.