arXiv:2606. 04327v1 Announce Type: cross Abstract: We investigate the geometric structure of stationary plateaus that arise in the loss landscape of two-layer neural networks with smooth activation functions.
arXiv:2607. 10869v1 Announce Type: new Abstract: We study the population gradient flow of an infinitely wide two-layer neural network learning a misspecified single-index model in high dimension.
arXiv:2606. 30226v1 Announce Type: new Abstract: Hessian spectral properties are a standard tool in analysing neural-network training, with eigenvalues linked to sharpness, generalization, and optimization dynamics.
arXiv:2505. 22578v2 Announce Type: replace Abstract: The optimization of neural networks under weight decay remains poorly understood from a theoretical standpoint.
arXiv:2607. 03613v1 Announce Type: new Abstract: We study the implicit bias of noisy stochastic gradient descent in training wide two-layer ReLU networks for multivariate regression.
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:2606. 28662v1 Announce Type: cross Abstract: The flatness hypothesis suggests that flatness of the loss landscape, as measured by the eigenvalues of the loss Hessian, correlates with better neural network generalization.
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:2606. 15551v1 Announce Type: new Abstract: The Edge of Stability (EoS) phenomenon, where gradient descent operates with sharpness exceeding the classical convergence threshold yet the loss decreases over long timescales, is ubiquitous in modern deep learning but remains poorly understood in realistic settings.
arXiv:2509. 12154v2 Announce Type: replace Abstract: The first part of this paper studies the evolution of gradient flow for homogeneous neural networks near a class of saddle points exhibiting a sparsity structure.
arXiv:2502. 11152v4 Announce Type: replace-cross Abstract: The optimization foundations of deep linear networks have recently received significant attention.
arXiv:2502. 15952v3 Announce Type: replace Abstract: Recent works exploring the training dynamics of homogeneous neural network weights under gradient flow with small initialization have established that in the early stages of training, the weights remain small and near the origin, but converge in direction.
arXiv:2607. 16720v1 Announce Type: new Abstract: Understanding deep neural networks remains a central challenge in machine learning.