Two-hidden-layer Feedforward Neural Networks are Universal Approximators: A Constructive Approach

It is well known that Artificial Neural Networks are universal approximators. The classical result proves that, given a continuous function on a compact set on an n-dimensional space, then there exists a one-hidden-layer feedforward network which approximates the function. Such result proves the exi...

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Autores: González Díaz, Rocío, Gutiérrez Naranjo, Miguel Ángel, Paluzo Hidalgo, Eduardo
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2019
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/97963
Acceso en línea:https://hdl.handle.net/11441/97963
Access Level:acceso abierto
Palabra clave:Universal approximation theorem
Simplicial approximation theorem
Multilayer feedforward network
Simplicial Complexes
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spelling Two-hidden-layer Feedforward Neural Networks are Universal Approximators: A Constructive ApproachGonzález Díaz, RocíoGutiérrez Naranjo, Miguel ÁngelPaluzo Hidalgo, EduardoUniversal approximation theoremSimplicial approximation theoremMultilayer feedforward networkSimplicial ComplexesIt is well known that Artificial Neural Networks are universal approximators. The classical result proves that, given a continuous function on a compact set on an n-dimensional space, then there exists a one-hidden-layer feedforward network which approximates the function. Such result proves the existence, but it does not provide a method for finding it. In this paper, a constructive approach to the proof of this property is given for the case of two-hidden-layer feedforward networks. This approach is based on an approximation of continuous functions by simplicial maps. Once a triangulation of the space is given, a concrete architecture and set of weights can be obtained. The quality of the approximation depends on the refinement of the covering of the space by simplicial complexes.Cornell UniversityMatemática Aplicada ICiencias de la Computación e Inteligencia Artificial2019info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/97963reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésArXiv.org, arXiv:1907.11457https://arxiv.org/abs/1907.11457info:eu-repo/semantics/openAccessoai:idus.us.es:11441/979632026-06-17T12:51:07Z
dc.title.none.fl_str_mv Two-hidden-layer Feedforward Neural Networks are Universal Approximators: A Constructive Approach
title Two-hidden-layer Feedforward Neural Networks are Universal Approximators: A Constructive Approach
spellingShingle Two-hidden-layer Feedforward Neural Networks are Universal Approximators: A Constructive Approach
González Díaz, Rocío
Universal approximation theorem
Simplicial approximation theorem
Multilayer feedforward network
Simplicial Complexes
title_short Two-hidden-layer Feedforward Neural Networks are Universal Approximators: A Constructive Approach
title_full Two-hidden-layer Feedforward Neural Networks are Universal Approximators: A Constructive Approach
title_fullStr Two-hidden-layer Feedforward Neural Networks are Universal Approximators: A Constructive Approach
title_full_unstemmed Two-hidden-layer Feedforward Neural Networks are Universal Approximators: A Constructive Approach
title_sort Two-hidden-layer Feedforward Neural Networks are Universal Approximators: A Constructive Approach
dc.creator.none.fl_str_mv González Díaz, Rocío
Gutiérrez Naranjo, Miguel Ángel
Paluzo Hidalgo, Eduardo
author González Díaz, Rocío
author_facet González Díaz, Rocío
Gutiérrez Naranjo, Miguel Ángel
Paluzo Hidalgo, Eduardo
author_role author
author2 Gutiérrez Naranjo, Miguel Ángel
Paluzo Hidalgo, Eduardo
author2_role author
author
dc.contributor.none.fl_str_mv Matemática Aplicada I
Ciencias de la Computación e Inteligencia Artificial
dc.subject.none.fl_str_mv Universal approximation theorem
Simplicial approximation theorem
Multilayer feedforward network
Simplicial Complexes
topic Universal approximation theorem
Simplicial approximation theorem
Multilayer feedforward network
Simplicial Complexes
description It is well known that Artificial Neural Networks are universal approximators. The classical result proves that, given a continuous function on a compact set on an n-dimensional space, then there exists a one-hidden-layer feedforward network which approximates the function. Such result proves the existence, but it does not provide a method for finding it. In this paper, a constructive approach to the proof of this property is given for the case of two-hidden-layer feedforward networks. This approach is based on an approximation of continuous functions by simplicial maps. Once a triangulation of the space is given, a concrete architecture and set of weights can be obtained. The quality of the approximation depends on the refinement of the covering of the space by simplicial complexes.
publishDate 2019
dc.date.none.fl_str_mv 2019
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/97963
url https://hdl.handle.net/11441/97963
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv ArXiv.org, arXiv:1907.11457
https://arxiv.org/abs/1907.11457
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Cornell University
publisher.none.fl_str_mv Cornell University
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301629

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