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

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 RN¯, N¯∈N. Moreover, we consider the case of approximation employing iterated MNN operators. In addition, pointwise and uniform conve...

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Bibliographic Details
Published in:Mathematics (Basel) Vol. 13; no. 3; p. 453
Main Author: Karateke, Seda
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.02.2025
Subjects:
Algorithms
Approximation
Artificial intelligence
Banach spaces
Continuity (mathematics)
Datasets
Fuzzy sets
Hyperbolic functions
iterated approximation
multi-layer approximation
Multivariate analysis
multivariate density function
multivariate modulus of continuity
multivariate trigonometric and hyperbolic neural network approximation
Neural networks
Neurons
Operators (mathematics)
parameterized half-hyperbolic tangent function
New York
United States
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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Summary: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 RN¯, 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.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math13030453