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

2026-05-11

AI Summary

This work addresses a fundamental limitation of traditional Sharpness-Aware Minimization (SAM), which employs a fixed perturbation radius in parameter space that fails to align with the second-order curvature characteristics inherent to flat minima. To overcome this mismatch, the authors propose Loss-Equated SAM (LE-SAM), which reformulates the perturbation constraint from a fixed radius to a fixed loss-space budget. This shift enables optimization to prioritize curvature-dominated terms over gradient norm magnitudes. LE-SAM achieves this through loss-constrained adversarial perturbations, a curvature-aware generalization mechanism, and a decoupling of first- and second-order optimization signals—collectively offering a more theoretically grounded approach to seeking flat minima. Empirical evaluations demonstrate that LE-SAM consistently outperforms SAM and its variants across multiple benchmark tasks, achieving state-of-the-art generalization performance.

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.

Problem

• Sharpness-Aware Minimization
• flat minima
• adversarial perturbation
• curvature
• generalization

Innovation

• Sharpness-Aware Minimization
• loss-space budget
• curvature-aware optimization
• flat minima
• adversarial perturbation