Systematic Investigation of Sparse Perturbed Sharpness-Aware Minimization Optimizer

Deep neural networks often suffer from poor generalization due to complex and non-convex loss landscapes. Sharpness-Aware Minimization (SAM) is a popular solution that smooths the loss landscape by minimizing the maximized change of training loss when adding a perturbation to the weight. However, indiscriminate perturbation of SAM on all parameters is suboptimal and results in excessive computation, double the overhead of common optimizers like Stochastic Gradient Descent (SGD). In this paper, we propose Sparse SAM (SSAM), an efficient and effective training scheme that achieves sparse perturbation by a binary mask. To obtain the sparse mask, we provide two solutions based on Fisher information and dynamic sparse training, respectively. We investigate the impact of different masks, including unstructured, structured, and $N$:$M$ structured patterns, as well as explicit and implicit forms of implementing sparse perturbation. We theoretically prove that SSAM can converge at the same rate as SAM, i.e., $O(\log T/\sqrt{T})$ . Sparse SAM has the potential to accelerate training and smooth the loss landscape effectively. Extensive experimental results on CIFAR and ImageNet-1K confirm that our method is superior to SAM in terms of efficiency, and the performance is preserved or even improved with a perturbation of merely 50% sparsity.