arXiv:2607. 07884v1 Announce Type: new Abstract: In this short note we consider the gradient descent dynamics of deep scalar linear networks, $f(x) = \prod_{l=1}^L w_l x$, which enjoy exact time-course solutions for any integer depth.
Summary generated by The Flow from the publisher's feed. The full article lives at arXiv Machine Learning.
arXiv:2502. 11152v4 Announce Type: replace-cross Abstract: The optimization foundations of deep linear networks have recently received significant attention.
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.
arXiv:2604. 20219v2 Announce Type: replace Abstract: Depth is widely viewed as a central contributor to the success of deep neural networks, whereas standard neural network approximation theory typically provides guarantees only for the final output and leaves the role of intermediate layers largely unclear.
arXiv:2510. 02779v4 Announce Type: replace Abstract: Recent advances have significantly improved our understanding of the generalization performance of gradient descent (GD) methods in deep neural networks.
arXiv:2606. 06772v2 Announce Type: replace-cross Abstract: Characterizing the optimization dynamics and statistical performance of over-parameterized deep neural networks (DNNs) remains a central challenge in understanding the remarkable success of deep learning.
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.