对称商平坦性与泛化：商几何下的平坦性到泛化理论

AI 摘要

该论文在对称商（symmetry-quotient）几何下重新构建了平坦性与泛化之间的理论链条。作者将平坦性定义在去除函数保持对称性后的商流形上，证明商平坦性控制输入光滑性，并进一步在局部覆盖假设下导出泛化界。研究还证明SGD的一步均方商线性稳定性可推出显式的商平坦性上界，从而把优化侧稳定性与函数侧泛化联系起来。

正文节选

Symmetry-quotient Flatness and Generalization Abstract This paper develops a theorem-level pipeline in symmetry-quotient settings: quotient linear stability implies quotient flatness, quotient flatness implies input smoothness, and input smoothness yields generalization under local covering assumptions. Flatness is often associated with generalization, and Stochastic Gradient Descent (SGD) is frequently viewed as implicitly biased toward flat solutions. However, standard flatness measures are ty

发布时间：2026-09-30 12:00

抓取时间：2026-09-29 13:27

来源机构：arXiv