arXiv:2606. 04476v1 Announce Type: new Abstract: In this paper, we study the gradient descent dynamics for jointly training both layers of a one-hidden-layer ReLU network to fit a linear target function.
By Berk Tinaz, Changzhi Xie, Mahdi Soltanolkotabi
arXiv:2501. 07400v2 Announce Type: replace-cross Abstract: We derive explicit equations governing the cumulative biases and weights in Deep Learning with ReLU activation function, based on gradient descent for the Euclidean loss in the input layer, and under the assumption that the weights are, in a precise sense, adapted to the coordinate system distinguished by the activations.
By Thomas Chen
arXiv:2607. 16720v1 Announce Type: new Abstract: Understanding deep neural networks remains a central challenge in machine learning.
By Haruka Eshima, Makoto Yamada
The paper presents a near-complete, nonasymptotic generalization theory for multilayer neural networks using path regularization, applicable to broad Lipschitz loss functions without requiring bounded loss or extreme network hyperparameters. It provides an explicit upper bound that addresses approximation rates in generalized Barron spaces and demonstrates the double descent phenomenon for ReLU networks. The authors claim near-minimax optimality for regression problems and plan to establish matching lower bounds in future work.
By Hao Yu
arXiv:2505. 22578v2 Announce Type: replace Abstract: The optimization of neural networks under weight decay remains poorly understood from a theoretical standpoint.
By Etienne Boursier, Matthew Bowditch, Matthias Englert, Ranko Lazic
arXiv:2603. 04895v2 Announce Type: replace-cross Abstract: Overparameterized ML models, including neural networks, typically induce underdetermined training objectives with multiple global minima.
By Kuo-Wei Lai, Guanghui Wang, Molei Tao, Vidya Muthukumar