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https://doi.org/10.1016/j.jmaa.2020.124584
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Título: | Negative results for approximation using single layer and multilayer feedforward neural networks |
Fecha de publicación: | 1-feb-2021 |
Editorial: | Elsevier |
Cita bibliográfica: | Journal of Mathematical Analysis and Applications, Volume 494, Issue 1, 1 February 2021 |
ISSN: | Print: 0022-247X Electrónico: 1096-0813 |
Materias relacionadas: | CDU::5 - Ciencias puras y naturales::51 - Matemáticas CDU::6 - Ciencias aplicadas::62 - Ingeniería. Tecnología |
Palabras clave: | Feedforward neural networks Function approximation Compact sets |
Resumen: | 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. |
Autor/es principal/es: | Almira, José M. López-de-Teruel, Pedro E. Romero-López, Diego J. Voigtlaender, Felix |
Facultad/Departamentos/Servicios: | Facultades, Departamentos, Servicios y Escuelas::Departamentos de la UMU::Ingeniería y Tecnología de Computadores |
Versiones anteriores del documento: | https://arxiv.org/pdf/1810.10032.pdf |
Versión del editor: | https://www.sciencedirect.com/science/article/pii/S0022247X20307460 |
URI: | http://hdl.handle.net/10201/138913 |
DOI: | https://doi.org/10.1016/j.jmaa.2020.124584 |
Tipo de documento: | info:eu-repo/semantics/article |
Número páginas / Extensión: | 12 páginas |
Derechos: | info:eu-repo/semantics/openAccess Attribution-NoDerivatives 4.0 Internacional |
Descripción: | ©<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] |
Aparece en las colecciones: | Artículos: Ingeniería y Tecnología de Computadores |
Ficheros en este ítem:
Fichero | Descripción | Tamaño | Formato | |
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1810.10032.pdf | 214,19 kB | Adobe PDF | Visualizar/Abrir |
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