Sharpness-Aware Minimization and Muon: Robustness under the Spectral Norm
Sharpness-Aware Minimization (SAM) aims to improve generalization by encouraging insensitivity to small, worst-case parameter perturbations. However, the notion of a "small" perturbation is inherently geometry-dependent: while existing SAM variants have explored a wide range of choices, a clear perspective on which geometries are most effective in practice remains elusive. Recent work on matrix-aware optimization, particularly the Muon optimizer, suggests that respecting the matrix structure of hidden-layer weights can lead to strong empirical performance. Motivated by this, we study matrix-aware geometry in both stages of SAM: we introduce a layerwise spectral inner perturbation for matr...
| Authors | Wenzhi Zhong, Edward Milsom, Michael Murray |
|---|---|
| Primary category | cs.LG |
| Published | 28 July 2026 |
| Last updated at source | 28 July 2026 |
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