Fix the Loss, Not the Radius: Rethinking the Adversarial Perturbation of Sharpness-Aware Minimization
For deep learning practitioners, LE-SAM provides a principled fix to SAM's theoretical mismatch, yielding consistent improvements over SAM and its variants.
Sharpness-Aware Minimization (SAM) uses a fixed perturbation radius but relies on a first-order surrogate, mismatching the second-order nature of flat minima. Loss-Equated SAM (LE-SAM) inverts this by fixing a loss-space budget, removing gradient-norm signals and focusing on curvature, achieving state-of-the-art generalization across benchmarks.
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.