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:2505. 21423v3 Announce Type: replace Abstract: The remarkable generalization properties of overparameterized networks are often attributed to implicit biases, such as norm minimization at small learning rates and low sharpness in the Edge-of-Stability regime.
arXiv:2607. 21005v1 Announce Type: new Abstract: Most explanations of training instability focus on \emph{learning-rate criticality}, typically characterized by the Edge of Stability, beyond which optimization becomes unstable.
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:2505. 22578v2 Announce Type: replace Abstract: The optimization of neural networks under weight decay remains poorly understood from a theoretical standpoint.
The Hessian matrix is an important quantity of interest when it comes to studying the loss landscape and optimization dynamics in deep learning, as well as designing measures of generalization, second-order learning algorithms, etc. Prior works have focused on empirical results or pursued a theoretical treatment under overly simplified settings.
arXiv:2607. 13631v1 Announce Type: new Abstract: The Hessian matrix is an important quantity of interest when it comes to studying the loss landscape and optimization dynamics in deep learning, as well as designing measures of generalization, second-order learning algorithms, etc.
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.
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.
The paper investigates how stochastic gradient descent (SGD) selects specific functional decompositions when training a deep linear residual network to learn the identity function. Although many weight configurations minimize the population loss, SGD consistently prefers particular solutions, especially under anisotropic label noise or different parametrizations. The authors explain this bias using an entropic loss term that penalizes the expected squared norm of the minibatch gradient, analytically characterizing its minimizers and showing that trained networks align with these predictions.
arXiv:2609.06064v1 Announce Type: cross Abstract: Stochastic min-max optimization has attracted increasing attention due to its applications in modern machine learning, while existing theoretical stu...
arXiv:2606. 00340v1 Announce Type: new Abstract: We study optimal learning-rate selection in two-layer and three-layer linear neural networks trained to learn linear target functions.
arXiv:2509. 24882v2 Announce Type: replace Abstract: Neural scaling laws underlie many of the recent advances in deep learning, yet their theoretical understanding remains largely confined to linear models.