Approximation properties of some two-layer feedforward neural networks

Approximation properties of some two-layer feedforward neural networks

In this article, we present a multivariate two-layer feedforward neural networks that approximate continuous functions defined on \([0,1]^d\). We show that the \(L_1\) error of approximation is asymptotically proportional to the modulus of continuity of the underlying function taken at \(\sqrt{d}/n\...

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Main Author: Michał A. Nowak
Format: Article
Language:English
Published: AGH Univeristy of Science and Technology Press 2007-01-01
Series:Opuscula Mathematica
Subjects:
neural networks
approximation of functions
sigmoidal function
Online Access:http://www.opuscula.agh.edu.pl/vol27/1/art/opuscula_math_2706.pdf
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spelling doaj-5b83e170326c473f8b1bdd54b494deba2020-11-25T00:47:10ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742007-01-0127159722706Approximation properties of some two-layer feedforward neural networksMichał A. Nowak0AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Cracow, PolandIn this article, we present a multivariate two-layer feedforward neural networks that approximate continuous functions defined on \([0,1]^d\). We show that the \(L_1\) error of approximation is asymptotically proportional to the modulus of continuity of the underlying function taken at \(\sqrt{d}/n\), where \(n\) is the number of function values used.http://www.opuscula.agh.edu.pl/vol27/1/art/opuscula_math_2706.pdfneural networksapproximation of functionssigmoidal function
collection DOAJ
language English
format Article
sources DOAJ
author Michał A. Nowak
spellingShingle Michał A. Nowak
Approximation properties of some two-layer feedforward neural networks
Opuscula Mathematica
neural networks
approximation of functions
sigmoidal function
author_facet Michał A. Nowak
author_sort Michał A. Nowak
title Approximation properties of some two-layer feedforward neural networks
title_short Approximation properties of some two-layer feedforward neural networks
title_full Approximation properties of some two-layer feedforward neural networks
title_fullStr Approximation properties of some two-layer feedforward neural networks
title_full_unstemmed Approximation properties of some two-layer feedforward neural networks
title_sort approximation properties of some two-layer feedforward neural networks
publisher AGH Univeristy of Science and Technology Press
series Opuscula Mathematica
issn 1232-9274
publishDate 2007-01-01
description In this article, we present a multivariate two-layer feedforward neural networks that approximate continuous functions defined on \([0,1]^d\). We show that the \(L_1\) error of approximation is asymptotically proportional to the modulus of continuity of the underlying function taken at \(\sqrt{d}/n\), where \(n\) is the number of function values used.
topic neural networks
approximation of functions
sigmoidal function
url http://www.opuscula.agh.edu.pl/vol27/1/art/opuscula_math_2706.pdf
work_keys_str_mv AT michałanowak approximationpropertiesofsometwolayerfeedforwardneuralnetworks
_version_ 1725261423743860736

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