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arXiv · 2605.10183

Fix the Loss, Not the Radius: Rethinking the Adversarial Perturbation of Sharpness-Aware Minimization

Jinping Wang·Qinhan Liu·Zhiwu Xie·Zhiqiang Gao
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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.

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Jinping Wang, Qinhan Liu, Zhiwu Xie, Zhiqiang Gao. 2026-05-11. Fix the Loss, Not the Radius: Rethinking the Adversarial Perturbation of Sharpness-Aware Minimization. https://arxiv.org/abs/2605.10183

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