Minor First, Major Last: A Depth-Induced Implicit Bias of Sharpness-Aware Minimization
We study the implicit bias of Sharpness-Aware Minimization (SAM) when training $L$-layer linear diagonal networks on linearly separable binary classification. For linear models ($L=1$), both $\ell_\infty$- and $\ell_2$-SAM recover the $\ell_2$ max-margin classifier, matching gradient descent (GD). However, for depth $L = 2$, the behavior changes drastically -- even on a single-example dataset. For $\ell_\infty$-SAM, the limit direction depends critically on initialization and can converge to $\mathbf{0}$ or to any standard basis vector, in stark contrast to GD, whose limit aligns with the basis vector of the dominant data coordinate. For $\ell_2$-SAM, we show that although its limit direc...
| Authors | Chaewon Moon, Dongkuk Si, Chulhee Yun |
|---|---|
| Primary category | cs.LG |
| Published | 9 March 2026 |
| Last updated at source | 18 May 2026 |
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