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arXiv Machine Learning By Dimitris Oikonomou, Nicolas Loizou

Curvature-Scaled Sharpness-Aware Minimization: Convergence Beyond Smoothness

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The paper introduces Curvature-Scaled Sharpness-Aware Minimization (CS‑SAM), a variant of SAM that scales both the perturbation and descent step by curvature bounds to uniformly control gradient distortion under generalized smoothness conditions. It proves deterministic ≥1/T convergence rates for nonconvex objectives, last‑iterate ≥1/T rates for convex objectives, and linear convergence under the Polyak‑Łojasiewicz condition, while recovering standard gradient descent rates when the perturbation is zero. Experiments on computer vision tasks show that CS‑SAM, particularly the (H0,H1) variant, achieves the highest mean best‑test accuracy across four settings compared to tuned SAM and USAM.

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