Year: 2023
Type: conference-paper
Abstract: Recently, flat minima are proven to be effective for improving generalization and sharpness-aware minimization (SAM) achieves state-of-the-art performance. Yet the current definition of flatness discussed in SAM and its follow-ups are limited to the zeroth-order flatness (i.e., the worst-case loss within a perturbation radius). We show that the zeroth-order flatness can be insufficient to discriminate minima with low generalization error from those with high generalization error both when there is a single minimum or multiple minima within the given perturbation radius. Thus we present first-order flatness, a stronger measure of flatness focusing on the maximal gradient norm within a perturbation radius which bounds both the maximal eigenvalue of Hessian at local minima and the regularization function of SAM. We also present a novel training procedure named Gradient norm Aware Minimization (GAM) to seek minima with uniformly small curvature across all directions. Experimental results show that GAM improves the generalization of models trained with current optimizers such as SGD and Adam W on various datasets and networks. Furthermore, we show that GAM can help SAM find flatter minima and achieve better generalization. The code is available at https://github.com/xxgege/GAM.
Authors: Xingxuan Zhang, Renzhe Xu, Han Yu, Hao Zou, Peng Cui
Institution: Tsinghua University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G4427191711, G5050118973, G7972761409
OpenAlex ID: W4386047779