arXiv:2210. 16286v2 Announce Type: replace Abstract: To understand the training dynamics of neural networks, prior studies have considered the mean-field limit of two-layer neural networks as the width tends to infinity, establishing theoretical guarantees for its convergence under gradient flow training as well as approximation and generalization capabilities.
By Zhengdao Chen, Eric Vanden-Eijnden, Joan Bruna
arXiv:2608. 11479v1 Announce Type: new Abstract: We establish convergence guarantees of gradient descent for general feedforward neural networks of arbitrary width or depth, with no special requirements on the initialization or dataset.
By Siqiao Mu, Diego Klabjan
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
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:2607. 08843v1 Announce Type: new Abstract: In artificial and biological neural networks, concepts are often encoded as consistent linear directions in representation space.
By William W. Yang, Andrew M. Saxe, Peter E. Latham
arXiv:2609.07755v1 Announce Type: new
Abstract: Understanding generalization remains a central challenge in machine learning because it requires jointly considering data, architecture, and training d...
By Yuqing Wang, Ioannis G. Kevrekidis, Mikhail Belkin