---
title: "谱范数下的鲁棒性：锐度感知最小化与Muon优化器的几何统一"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2607.26001v1"
permalink: "https://feed.astralor.com/items/itm_0ada9936f1daee42f8a1526d"
published: "2026-07-28T17:18:11.000Z"
score: 73
channel: "ai"
tags: ["Muon优化器","SAM","泛化鲁棒性","矩阵感知优化","谱扰动"]
---

# 谱范数下的鲁棒性：锐度感知最小化与Muon优化器的几何统一

## AI 点评

> 这篇论文最值得关注的点在于它没有简单堆砌改进，而是从几何本质出发统一了SAM和Muon的设计哲学，对于研究优化器与泛化理论的人很有启发。如果你是工程向的AI从业者，这个谱扰动+Muon的组合很可能成为你训练ViT等模型的实用技巧。

## 速览

这篇论文从几何角度重新审视锐度感知最小化（SAM），提出在矩阵值隐藏层参数上应用逐层谱内扰动，并分别搭配AdamW/SGDW或Muon作为外更新优化器。在ImageNet-1K上使用ViT-Small/16和ResNet-50的实验表明，谱内步骤与Muon外步骤的组合在验证准确率上一致最优，揭示了矩阵感知几何在SAM两个阶段中的关键作用。该工作为理解优化器与泛化机制提供了新视角，并推动了高效训练方法的实用化。

## 关键点

- 提出逐层谱内扰动，利用矩阵结构替换传统向量扰动，增强SAM对参数几何的适应性。
- 将Muon优化器引入SAM外更新阶段，与谱内步骤形成协同，在ViT和ResNet上均取得最佳验证准确率。
- 通过在ImageNet-1K上的系统实验，揭示了矩阵感知几何相比于标量或向量几何在SAM中的优势。

## 全文

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.

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引用前请核对原文;本文由星际流动整理:https://feed.astralor.com/items/itm_0ada9936f1daee42f8a1526d