Fix the Loss, Not the Radius: Rethinking the Adversarial Perturbation of Sharpness-Aware Minimization
Jinping Wang, Qinhan Liu, Zhiwu Xie, Zhiqiang Gao
Abstract
Sharpness-Aware Minimization (SAM) improves generalization by minimizing the worst-case loss within a fixed parameter-space radius neighborhood. SAM and its variants mainly rely on a first-order linearized surrogate, while flat minima are inherently a second-order (curvature) notion. We revisit this mismatch and propose Loss-Equated SAM (LE-SAM), which inverts the traditional SAM mechanism that fixed perturbation radius with a fixed loss-space budget, effectively removing gradient-norm–dominated learning signals and shifting optimization toward curvature-dominated terms. Extensive experiments across diverse benchmarks and tasks demonstrate the strong generalization ability of LESAM that consistently outperforms SAM and even its variants, achieving the state-of-the-art performance.
BibTeX
@inproceedings{
wang2026fix,
title={Fix the Loss, Not the Radius: Rethinking the Adversarial Perturbation of Sharpness-Aware Minimization},
author={Jinping Wang and Qinhan Liu and Zhiwu Xie and Zhiqiang Gao},
booktitle={Forty-third International Conference on Machine Learning},
year={2026},
url={https://openreview.net/forum?id=3XGJpH7Y1r}
}