arXiv:2607. 23012v1 Announce Type: new Abstract: During SGD training, the gradients often align strongly with the dominant subspace spanned by the top-$k$ eigenvectors of the Hessian of the loss.
arXiv:2503. 11891v2 Announce Type: replace Abstract: We analyze the landscape and training dynamics of diagonal linear networks in a linear regression task, with the network parameters being perturbed by isotropic normal noise during training.
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:2602. 11557v2 Announce Type: replace Abstract: A variety of widely used optimization methods like SignSGD and Muon can be interpreted as instances of steepest descent under different norm-induced geometries.
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.
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:2607. 12360v1 Announce Type: new Abstract: The cooldown phase of a warmup-stable-decay (WSD) learning-rate schedule, now a default in large-model pretraining, lowers the final training loss in some settings and does nothing in others.
arXiv:2601. 22652v2 Announce Type: replace-cross Abstract: Spectral gradient methods, such as the Muon optimizer, modify gradient updates by preserving directional information while discarding scale, and have shown strong empirical performance in deep learning.
arXiv:2607. 08104v1 Announce Type: new Abstract: Stochastic gradient descent (SGD) is a cornerstone of modern optimization.
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:2608. 01032v1 Announce Type: new Abstract: Training error is what we can observe on a training set; test error is the quantity we actually care about.
arXiv:2602. 03001v2 Announce Type: replace-cross Abstract: To maximize hardware utilization, modern machine learning systems typically employ large constant or manually tuned batch size schedules, relying on heuristics that are brittle and costly to tune.
arXiv:2602. 14789v2 Announce Type: replace Abstract: The dynamical stability of the iterates during training plays a key role in determining the minima obtained by optimization algorithms.