Negative results for approximation using single layer and multilayer feedforward neural networks

Almira, José M.; López-de-Teruel, Pedro E.; Romero-López, Diego J.; Voigtlaender, Felix

Publication:
Negative results for approximation using single layer and multilayer feedforward neural networks

dc.contributor.author	Almira, José M.
dc.contributor.author	López-de-Teruel, Pedro E.
dc.contributor.author	Romero-López, Diego J.
dc.contributor.author	Voigtlaender, Felix
dc.contributor.department	Ingeniería y Tecnología de Computadores
dc.date.accessioned	2024-02-07T13:29:23Z
dc.date.available	2024-02-07T13:29:23Z
dc.date.issued	2021-02-01
dc.description	©<2021>. This manuscript version is made available under the CC-BY-NC-ND license http://creativecommons.org/licenses/ccby-nc-nd/4.0/ This document is the Acepted version of a Published Work that appeared in final form in [Journal of Mathematical Analysis and Applications]. To access the final edited and published work see [https://doi.org/ 10.1016/j.jmaa.2020.124584]
dc.description.abstract	We prove a negative result for the approximation of functions defined on compact subsets of R^d (where d >=2) using feedforward neural networks with one hidden layer and arbitrary continuous activation function. In a nutshell, this result claims the existence of target functions that are as difficult to approximate using these neural networks as one may want. We also demonstrate an analogous result (for general d in N) for neural networks with an arbitrary number of hidden layers, for activation functions that are either rational functions or continuous splines with finitely many pieces.	es
dc.format	application/pdf	es
dc.format.extent	12 páginas	es
dc.identifier.citation	Journal of Mathematical Analysis and Applications, Volume 494, Issue 1, 1 February 2021
dc.identifier.doi	https://doi.org/10.1016/j.jmaa.2020.124584
dc.identifier.issn	Print: 0022-247X
dc.identifier.issn	Electrónico: 1096-0813
dc.identifier.uri	http://hdl.handle.net/10201/138913
dc.language	eng	es
dc.publisher	Elsevier	es
dc.relation	Sin financiación externa a la Universidad	es
dc.relation.publisherversion	https://www.sciencedirect.com/science/article/pii/S0022247X20307460	es
dc.relation.replaces	https://arxiv.org/pdf/1810.10032.pdf	es
dc.rights	info:eu-repo/semantics/openAccess	es
dc.rights	Attribution-NoDerivatives 4.0 Internacional	*
dc.rights.uri	http://creativecommons.org/licenses/by-nd/4.0/	*
dc.subject	Feedforward neural networks	es
dc.subject	Function approximation
dc.subject	Compact sets
dc.subject.other	CDU::5 - Ciencias puras y naturales::51 - Matemáticas	es
dc.subject.other	CDU::6 - Ciencias aplicadas::62 - Ingeniería. Tecnología	es
dc.title	Negative results for approximation using single layer and multilayer feedforward neural networks	es
dc.type	info:eu-repo/semantics/article	es
dspace.entity.type	Publication	es