CRIK: Convolutional Reshaping on Perturbation Intervals Partitioned by Key Points to Enhance Generalization

Generalization is a primary criterion for evaluating deep neural networks. Research shows that sharp minima in the loss landscape often lead to poor generalization. Sharpness-aware minimization (SAM) employs worst-case perturbations around minima to enhance generalization. However, SAM overlooks important geometric information about the loss landscape within the perturbation interval, which can be reflected by the key points we proposed. To address this limitation, we partition the perturbation interval using the key points and employ convolutional operations to adaptively adjust each interval's contribution to generalization performance. Furthermore, our analysis shows the impact of interval numbers on generalization. Based on this analysis, we propose convolutional reshaping on perturbation intervals partitioned by key points (CRIK). We theoretically examine CRIK's convergence, derive its escape time from sharp minima, and demonstrate that it implicitly combines gradient and Hessian information adaptively. Simulations and experiments demonstrate that CRIK improves generalization performance.