Publication: Negative results for approximation using single layer and multilayer feedforward neural networks
Authors
Almira, José M. ; López-de-Teruel, Pedro E. ; Romero-López, Diego J. ; Voigtlaender, Felix
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Publisher
Elsevier
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DOI
https://doi.org/10.1016/j.jmaa.2020.124584
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info:eu-repo/semantics/article
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]
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.
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Citation
Journal of Mathematical Analysis and Applications, Volume 494, Issue 1, 1 February 2021
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