Symmetry-quotient Flatness and Generalization
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 typically defined in the raw parameter space and are therefore not invariant under function-preserving symmetries such as positive rescaling. We develop a symmetry-aware theory of quotient flatness, quotient linear stability, input smoothness, and genera...
| Authors | Taiki Miyagawa |
|---|---|
| Primary category | cs.LG |
| Published | 10 September 2026 |
| Last updated at source | 10 September 2026 |
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