On the Implicit Flatness Bias of Sharpness-Aware Minimization: A Linear Stability Analysis with Quantitative Hyperparameter Bounds
Sharpness-Aware Minimization (SAM) improves generalization by seeking parameters whose loss is robust to local adversarial perturbations, but the quantitative mechanism underlying its implicit bias toward flat minima remains unclear. In particular, the perturbation radius $ρ$ is typically treated as an isolated tuning parameter, despite defining the neighborhood in which SAM measures sharpness. We analyze mini-batch SAM near an interpolating minimum through linear stability. Under local linearization and gradient-noise alignment assumptions, we prove that every linearly stable minimum satisfies $λ_{\max}\leq\sqrt[3]{bΓ/(2ρη^2)}$, where $λ_{\max}$ is the largest Hessian eigenvalue, $b$ is ...
| Authors | Jiaxin Deng, Junbiao Pang |
|---|---|
| Primary category | cs.LG |
| Published | 4 August 2026 |
| Last updated at source | 4 August 2026 |
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