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Explaining f-Divergence-Based Regularization via Local Curvature and Sharpness-Aware Minimization

arXiv · AI, language, vision and robotics · article · Sep 8, 2026 · UTC

Divergence-based regularization and Sharpness-Aware Minimization (SAM) are two prominent approaches for improving generalization in deep learning, both motivated by robustness to perturbations. However, their relationship has remained largely unexplored. Building on classical second-order expansions of $f$-divergences, we show that the two methods are locally consistent under parameter-space perturbations: both induce curvature-sensitive penalties, with divergence regularization yielding a Fisher-weighted quadratic form and SAM penalizing sharpness through the dominant Hessian eigenvalue. For

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