Complex-Valued Multivariate Neural Network (MNN) Approximation by Parameterized Half-Hyperbolic Tangent Function

Seda Karateke ()
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Seda Karateke: Department of Software Engineering, Faculty of Engineering and Natural Sciences, Istanbul Atlas University, 34408 Istanbul, Türkiye

Mathematics, 2025, vol. 13, issue 3, 1-27

Abstract: This paper deals with a family of normalized multivariate neural network (MNN) operators of complex-valued continuous functions for a multivariate context on a box of R N ¯ , N ¯ ∈ N . Moreover, we consider the case of approximation employing iterated MNN operators. In addition, pointwise and uniform convergence results are obtained in Banach spaces thanks to the multivariate versions of trigonometric and hyperbolic-type Taylor formulae on the corresponding feed-forward neural networks (FNNs) based on one or more hidden layers.

Keywords: multi-layer approximation; parameterized half-hyperbolic tangent function; multivariate trigonometric and hyperbolic neural network approximation; multivariate modulus of continuity; iterated approximation; multivariate density function; Ostrowski- and Opial-type inequalities; complex-valued neural network operators; trigonometric- and hyperbolic-type Taylor formulae; activation function; artificial neural networks; feed-forward perceptron; artificial intelligence; machine learning (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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