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:2609. 25710v1 Announce Type: cross Abstract: The statistical accuracy of neural networks depends on both their approximation power and the complexity of the class fitted from data.
By Baicheng Li, Zuowei Shen, Haizhao Yang, Shijun Zhang
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
arXiv:2609.39020v1 Announce Type: new
Abstract: We study how well deep neural networks approximate and learn spectral Barron functions. Recent studies have shown that these function classes can be ef...
By Songqiu Ma, Yunfei Yang
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
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:2510. 04060v3 Announce Type: replace-cross Abstract: We establish two related but logically distinct results for shallow ReLU$^k$ neural networks on the unit sphere $\SS^d$.
By Tong Mao, Jinchao Xu
arXiv:2510. 02779v4 Announce Type: replace Abstract: Recent advances have significantly improved our understanding of the generalization performance of gradient descent (GD) methods in deep neural networks.
By Yuanfan Li, Yunwen Lei, Zheng-Chu Guo, Yiming Ying
arXiv:2605. 31152v2 Announce Type: replace-cross Abstract: This paper studies how efficiently deep ReLU neural networks can approximate and learn smooth functions.
By Yunfei Yang, Jun Fan
arXiv:2604. 20219v2 Announce Type: replace Abstract: Depth is widely viewed as a central contributor to the success of deep neural networks, whereas standard neural network approximation theory typically provides guarantees only for the final output and leaves the role of intermediate layers largely unclear.
By Shijun Zhang, Zuowei Shen, Yuesheng Xu
This paper investigates the ρ^p-Lipschitz constants of deep ReLU neural networks with random weights drawn from a He‑style initialization. For zero‑bias networks, it provides high‑probability upper and lower bounds that differ by at most a logarithmic factor in depth, and shows a sharp contrast between the regimes p∈[1,2) and p∈[2,∞], with the former behaving like the Euclidean norm of a Gaussian vector and the latter like its dual norm. The analysis is extended to networks with non‑zero biases from symmetric distributions, yielding bounds that differ by a logarithmic factor in width and a linear factor in depth.
By Sjoerd Dirksen, Patrick Finke, Paul Geuchen, Dominik St\"oger, Felix Voigtlaender
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