Fisher-Geometric Sharpness and the Implicit Bias of SGD toward Flat Minima
A widely held intuition in deep learning is that stochastic gradient descent (SGD) implicitly favors flat minima and that flat minima generalize better, but standard Euclidean measures of flatness such as the trace or maximum eigenvalue of the loss Hessian are not invariant under reparametrizations that preserve the network function, which undermines the theoretical foundations of this narrative. In this study we resolve this issue by grounding flatness in the Riemannian geometry of the statistical manifold induced by the Fisher Information Matrix (FIM). We define Riemannian sharpness mathematically and prove that it is invariant under smooth, function-preserving reparametrizations, which...
| Authors | Md Sakir Ahmed, Kumaresh Sarmah, Hemen Dutta |
|---|---|
| Primary category | cs.LG |
| Published | 18 June 2026 |
| Last updated at source | 18 June 2026 |
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