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Symmetry
Volume 16
Issue 12
10.3390/sym16121568
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Parametrized Half-Hyperbolic Tangent Function-Activated Complex-Valued Neural Network Approximation

by
George A. Anastassiou
1,* and
Seda Karateke
2
1
Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA
2
Department of Software Engineering, Faculty of Engineering and Natural Sciences, Istanbul Atlas University, Kagithane, Istanbul 34408, Türkiye
*
Author to whom correspondence should be addressed.
Symmetry 2024, 16(12), 1568; https://doi.org/10.3390/sym16121568
Submission received: 21 October 2024 / Revised: 6 November 2024 / Accepted: 19 November 2024 / Published: 23 November 2024
(This article belongs to the Special Issue Functional Analysis, Fractional Operators and Symmetry/Asymmetry: Second Edition)
Versions Notes

Abstract

In this paper, we create a family of neural network (NN) operators employing a parametrized and deformed half-hyperbolic tangent function as an activation function and a density function produced by the same activation function. Moreover, we consider the univariate quantitative approximations by complex-valued neural network (NN) operators of complex-valued functions on a compact domain. Pointwise and uniform convergence results on Banach spaces are acquired through trigonometric, hyperbolic, and hybrid-type hyperbolic–trigonometric approaches.
Keywords: parametrized half-hyperbolic tangent function; Banach space-valued neural network approximation; Ostrowski- and Opial-type inequalities; complex-valued neural network operators; trigonometric- and hyperbolic-type Taylor formulae; activation function; neural networks parametrized half-hyperbolic tangent function; Banach space-valued neural network approximation; Ostrowski- and Opial-type inequalities; complex-valued neural network operators; trigonometric- and hyperbolic-type Taylor formulae; activation function; neural networks

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MDPI and ACS Style

Anastassiou, G.A.; Karateke, S. Parametrized Half-Hyperbolic Tangent Function-Activated Complex-Valued Neural Network Approximation. Symmetry 2024, 16, 1568. https://doi.org/10.3390/sym16121568

AMA Style

Anastassiou GA, Karateke S. Parametrized Half-Hyperbolic Tangent Function-Activated Complex-Valued Neural Network Approximation. Symmetry. 2024; 16(12):1568. https://doi.org/10.3390/sym16121568

Chicago/Turabian Style

Anastassiou, George A., and Seda Karateke. 2024. "Parametrized Half-Hyperbolic Tangent Function-Activated Complex-Valued Neural Network Approximation" Symmetry 16, no. 12: 1568. https://doi.org/10.3390/sym16121568

APA Style

Anastassiou, G. A., & Karateke, S. (2024). Parametrized Half-Hyperbolic Tangent Function-Activated Complex-Valued Neural Network Approximation. Symmetry, 16(12), 1568. https://doi.org/10.3390/sym16121568

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