arXiv:2609. 05263v1 Announce Type: cross Abstract: We investigate the best $L_2$ approximation of mixed Sobolev spaces by shallow neural networks with $n$ neurons and general activation functions.
By Yuwen Li, Guozhi Zhang
arXiv:2608. 19584v1 Announce Type: new Abstract: We study landscapes for complex-parameterized networks.
By Andrew Gracyk
arXiv:2610.18166v1 Announce Type: cross
Abstract: Randomly initialised neural networks of width $m$ converge to Gaussian processes as $m \to \infty$, with two types of quantitative bounds characteris...
By Luis Wiederhold, Nil Ayday, Debarghya Ghoshdastidar
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:2603. 00819v2 Announce Type: replace-cross Abstract: This paper surveys recent developments at the intersection of operator learning, statistical learning theory, and approximation theory.
By Simone Brugiapaglia, Nicola Rares Franco, Nicholas H. Nelsen
arXiv:2106. 04770v2 Announce Type: replace Abstract: We study parameter nonuniqueness in continuous-width depth-two fully connected neural networks.
By Sho Sonoda, Isao Ishikawa, Masahiro Ikeda