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.
arXiv:2606. 02078v1 Announce Type: new Abstract: The existing optimizers for deep neural networks (DNNs) typically rely on either the $\ell_2$ norm or the $\ell_\infty$ norm, resulting in optimizers that do not adapt well to substantial changes in curvature across parameter dimensions.
arXiv:2505.20817v3 Announce Type: replace-cross Abstract: Gradient clipping is widely used in language-model training to control heavy-tailed gradient noise and can improve convergence guarantees ove...
Sharpness-Aware Minimization (SAM) improves generalization by seeking parameters whose loss is robust to local adversarial perturbations, but the quantitative mechanism underlying its implicit bias toward flat minima remains unclear. In particular, the perturbation radius $ρ$ is typically treated as an isolated tuning parameter, despite defining the neighborhood in which SAM measures sharpness.
arXiv:2610.20415v1 Announce Type: new Abstract: Poor generalisation in deep neural networks is frequently associated with convergence to sharp minima. Sharpness-Aware Minimisation (SAM) improves gene...
arXiv:2607. 22906v1 Announce Type: new Abstract: We study adaptive gradient descent for continuously differentiable, possibly nonconvex objectives under one-sided H\"older regularity.
arXiv:2608. 03197v1 Announce Type: new Abstract: Sharpness-Aware Minimization (SAM) improves generalization by seeking parameters whose loss is robust to local adversarial perturbations, but the quantitative mechanism underlying its implicit bias toward flat minima remains unclear.
arXiv:2607. 18306v1 Announce Type: cross Abstract: Sharpness-Aware Minimization (SAM) improves generalization by minimizing the worst-case loss in a local parameter neighborhood.
arXiv:2607. 14731v1 Announce Type: new Abstract: Local SGD, also known as Federated Averaging, is a widely used distributed optimization algorithm.
arXiv:2301. 06308v2 Announce Type: replace-cross Abstract: Sharpness-aware minimization (SAM) is a training method that seeks to find flat minima in deep learning, resulting in state-of-the-art performance across various domains.
arXiv:2608. 15105v1 Announce Type: new Abstract: Recent progress in optimization research has highlighted the sharpness of the loss landscape as a key factor in narrowing the generalization gap.
arXiv:2608.30382v1 Announce Type: new Abstract: Popular adaptive stochastic gradient descent (SGD) methods to train artificial intelligence (AI) systems include the RMSprop, the Adam, and the AdamW o...
arXiv:2608.09523v2 Announce Type: replace Abstract: Stochastic gradient descent (SGD) and its variants train deep neural networks (DNNs) effectively in practice, yet classical optimization theory doe...