The universal approximation theorem for complex-valued neural networks

We generalize the classical universal approximation theorem for neural networks to the case of complex-valued neural networks. Precisely, we consider feedforward networks with a complex activation function σ:C→C in which each neuron performs the operation CN→C,z↦σ(b+wTz) with weights w∈CN and a bias...

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Bibliographic Details

Published in:	Applied and computational harmonic analysis Vol. 64; pp. 33 - 61
Main Author:	Voigtlaender, Felix
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01.05.2023
Subjects:	Complex-valued neural networks Deep neural networks Holomorphic functions Polyharmonic functions Universal approximation theorem 30E10 Deep neural networks 41A30 41A63 31A30 Complex-valued neural networks Universal approximation theorem 68T07 Holomorphic functions Polyharmonic functions
ISSN:	1063-5203, 1096-603X
Online Access:	Get full text
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