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Quantitative approximation results for complex-valued neural networks

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Caragea, Andrei ; Lee, Dae Gwan ; Maly, Johannes ; Pfander, Götz E. ; Voigtlaender, Felix:
Quantitative approximation results for complex-valued neural networks.
In: SIAM Journal on Mathematics of Data Science. (25. Februar 2021).
ISSN 2577-0187

Volltext

Volltext Link zum Volltext (externe URL):
https://arxiv.org/abs/2102.13092

Kurzfassung/Abstract

Until recently, applications of neural networks in machine learning have almost exclusively relied on real-valued networks. It was recently observed, however, that complex-valued neural networks (CVNNs) exhibit superior performance in applications in which the input is naturally complex-valued, such as MRI fingerprinting. While the mathematical theory of real-valued networks has, by now, reached some level of maturity, this is far from true for complex-valued networks. In this paper, we analyze the expressivity of complex-valued networks by providing explicit quantitative error bounds for approximating Cn functions on compact subsets of Cd by complex-valued neural networks that employ the modReLU activation function, given by σ(z)=ReLU(|z|−1)sgn(z), which is one of the most popular complex activation functions used in practice. We show that the derived approximation rates are optimal (up to log factors) in the class of modReLU networks with weights of moderate growth.

Weitere Angaben

Publikationsform:Artikel
Sprache des Eintrags:Englisch
Institutionen der Universität:Mathematisch-Geographische Fakultät > Mathematik > Lehrstuhl für Mathematik - Wissenschaftliches Rechnen/Informatik
Mathematisch-Geographische Fakultät > Mathematik > Lehrstuhl für Reliable Machine Learning
Peer-Review-Journal:Ja
Verlag:Siam Publications
Die Zeitschrift ist nachgewiesen in:
Titel an der KU entstanden:Ja
KU.edoc-ID:29917
Eingestellt am: 01. Apr 2022 14:26
Letzte Änderung: 01. Apr 2022 14:26
URL zu dieser Anzeige: https://edoc.ku.de/id/eprint/29917/
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