Abstract Univariate Neural Network Approximation Using a q-Deformed and λ-Parametrized Hyperbolic Tangent Activation Function

Author:

Anastassiou George A.1ORCID

Affiliation:

1. Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA

Abstract

In this work, we perform univariate approximation with rates, basic and fractional, of continuous functions that take values into an arbitrary Banach space with domain on a closed interval or all reals, by quasi-interpolation neural network operators. These approximations are achieved by deriving Jackson-type inequalities via the first modulus of continuity of the on hand function or its abstract integer derivative or Caputo fractional derivatives. Our operators are expressed via a density function based on a q-deformed and λ-parameterized hyperbolic tangent activation sigmoid function. The convergences are pointwise and uniform. The associated feed-forward neural networks are with one hidden layer.

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

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Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Brownian motion approximation by parametrized and deformed neural networks;Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas;2023-10-24

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