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October 3, 2025Open Access

Unveiling m-Sharpness Through the Structure of Stochastic Gradient Noise

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The performance of sharpness-aware minimization improves as micro-batch size decreases, showing a direct correlation.
By characterizing m-sharpness using an extended stochastic differential equation framework, key dynamics of SAM are revealed.
The stochastic gradient noise during perturbations leads to a variance-based sharpness regularization effect that enhances model generalization.
Reweighted SAM introduces sharpness-weighted sampling to achieve m-SAM-like benefits while ensuring parallelizability.

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This research demonstrates that reducing micro-batch size enhances performance in SAM, suggesting a new regularization approach.

Luo et al. (2025) studied this question.

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