这个研究把SAM的内扰动改成矩阵谱范数，再用Muon做外更新，在ImageNet的ViT和ResNet上准确率都最高。
Sharpness-Aware Minimization（SAM）通过鼓励对参数扰动不敏感来提升泛化，但扰动几何依赖尚未清晰。本文借鉴Muon优化器的矩阵感知思路，为矩阵权重引入逐层谱内扰动，并与AdamW/SGDW或Muon外更新组合。在ImageNet-1K上对ViT-Small/16和ResNet-50的实验表明，谱内步+Muon外步在两类模型上均取得最高验证准确率。该工作揭示了谱范数几何在SAM中的有效性。
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 matrix-valued hidden-layer parameters and combine it with either AdamW/SGDW or Muon in the outer update. Across ImageNet-1K experiments on ViT-Small/16 and ResNet-50, we find that the combination of a spectral inner step with a Muon outer step performs consistently strongly, achieving the best validation accuracy on both models among the evaluated methods.