Paper Detail
Nour Jamoussi, Marios Kountouris
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 negative log-likelihood objectives with exponential-family output distributions, this correspondence becomes especially transparent, since the Fisher and Gauss-Newton matrices coincide. We further show that the same local geometric perspective extends to input-space perturbations, where divergence-based regularization is defined through transformations of the input. In this setting, the regularizer induces a pullback quadratic form on the input space, providing a more general perturbation framework than standard SAM while preserving the same local sensitivity interpretation. To validate the analysis empirically, we use the asymmetric $α$-skew Jensen-Shannon divergence (JSD) family as a controlled testbed. Its local curvature coefficient scales as $α(1-α)$ and is maximized at the symmetric point $α=\tfrac12$, which recovers the standard JSD. Loss-landscape visualizations in the input-perturbation regime show that stronger induced curvature penalization is associated with flatter local minima. Experiments on four benchmark datasets further demonstrate that both accuracy and negative log-likelihood are consistently best near this regime of maximal curvature penalization.
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@article{jamoussi2026explaining,
title = {Explaining f-Divergence-Based Regularization via Local Curvature and Sharpness-Aware Minimization},
author = {Nour Jamoussi and Marios Kountouris},
year = {2026},
abstract = {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 Fishe},
url = {https://arxiv.org/abs/2609.09367},
keywords = {cs.LG, cs.IT},
eprint = {2609.09367},
archiveprefix = {arXiv},
}
{}