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.
Subject
Statistics and Probability,Statistical and Nonlinear Physics,Analysis
Cited by
1 articles.
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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