Gradient Descent on Infinitely Wide Neural Networks: Global Convergence and Generalization
Machine Learning
2021-10-18 v1 Optimization and Control
Statistics Theory
Statistics Theory
Abstract
Many supervised machine learning methods are naturally cast as optimization problems. For prediction models which are linear in their parameters, this often leads to convex problems for which many mathematical guarantees exist. Models which are non-linear in their parameters such as neural networks lead to non-convex optimization problems for which guarantees are harder to obtain. In this review paper, we consider two-layer neural networks with homogeneous activation functions where the number of hidden neurons tends to infinity, and show how qualitative convergence guarantees may be derived.
Cite
@article{arxiv.2110.08084,
title = {Gradient Descent on Infinitely Wide Neural Networks: Global Convergence and Generalization},
author = {Francis Bach and Lenaïc Chizat},
journal= {arXiv preprint arXiv:2110.08084},
year = {2021}
}