@Article{CiCP-36-71,
author = {Jiao , YulingLu , XiliangWu , Peiying and Yang , Jerry Zhijian},
title = {Convergence Analysis for Over-Parameterized Deep Learning},
journal = {Communications in Computational Physics},
year = {2024},
volume = {36},
number = {1},
pages = {71--103},
abstract = {<p style="text-align: justify;">The success of deep learning in various applications has generated a growing interest in understanding its theoretical foundations. This paper presents a theoretical framework that explains why over-parameterized neural networks can perform
well. Our analysis begins from the perspective of approximation theory and argues
that over-parameterized deep neural networks with bounded norms can effectively
approximate the target. Additionally, we demonstrate that the metric entropy of such
networks is independent of the number of network parameters. We utilize these findings to derive consistency results for over-parameterized deep regression and the deep
Ritz method, respectively. Furthermore, we prove convergence rates when the target
has higher regularity, which, to our knowledge, represents the first convergence rate
for over-parameterized deep learning.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2023-0264},
url = {http://global-sci.org/intro/article_detail/cicp/23297.html}
}