arXiv:2607. 10589v1 Announce Type: cross Abstract: In contrast to most studies on neural network approximation theory that characterize results through a single parameter, such as the total number of network parameters, \cite{shen2020deep} pioneered the characterization of approximation rates as a joint function of the width parameter $N$ and the depth parameter $L$, thereby granting greater architectural flexibility.
By Yanming Lai, Defeng Sun, Yang Wang
arXiv:2610.22693v1 Announce Type: cross
Abstract: We study uniform approximation of the H\"older ball $\mathcal H_1^s([0,1]^D)$ by fully connected ReLU networks. Except in the one-dimensional Lipschi...
By Thomas Nagler
Recent studies have shown that smooth functions can be well approximated by ReLU neural networks with path norm constraint on the weights. We extend these results from uniform approximation to approximation in Sobolev norm.
arXiv:2609. 19937v1 Announce Type: cross Abstract: Recent studies have shown that smooth functions can be well approximated by ReLU neural networks with path norm constraint on the weights.
By Xianjun Li, Yunfei Yang
arXiv:2407.11353v5 Announce Type: replace
Abstract: We study nonparametric regression using an over-parameterized two-layer neural network trained with algorithmic guarantees in this paper. We consid...
By Yingzhen Yang, Ping Li
arXiv:2610.02253v1 Announce Type: new
Abstract: The universal approximation property of dropout neural networks does not by itself describe the network size required for an accurate random realizatio...
By Jia-He Yao