Analytic Function Approximation by Path-Norm-Regularized Deep Neural Networks

We show that neural networks with an absolute value activation function and with network path norm, network sizes and network weights having logarithmic dependence on [Formula: see text] can [Formula: see text]-approximate functions that are analytic on certain regions of [Formula: see text].

Detalles Bibliográficos
Autor principal: Beknazaryan, Aleksandr
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9407526/
https://www.ncbi.nlm.nih.gov/pubmed/36010799
http://dx.doi.org/10.3390/e24081136
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author Beknazaryan, Aleksandr
author_facet Beknazaryan, Aleksandr
author_sort Beknazaryan, Aleksandr
collection PubMed
description We show that neural networks with an absolute value activation function and with network path norm, network sizes and network weights having logarithmic dependence on [Formula: see text] can [Formula: see text]-approximate functions that are analytic on certain regions of [Formula: see text].
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spelling pubmed-94075262022-08-26 Analytic Function Approximation by Path-Norm-Regularized Deep Neural Networks Beknazaryan, Aleksandr Entropy (Basel) Article We show that neural networks with an absolute value activation function and with network path norm, network sizes and network weights having logarithmic dependence on [Formula: see text] can [Formula: see text]-approximate functions that are analytic on certain regions of [Formula: see text]. MDPI 2022-08-16 /pmc/articles/PMC9407526/ /pubmed/36010799 http://dx.doi.org/10.3390/e24081136 Text en © 2022 by the author. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Beknazaryan, Aleksandr
Analytic Function Approximation by Path-Norm-Regularized Deep Neural Networks
title Analytic Function Approximation by Path-Norm-Regularized Deep Neural Networks
title_full Analytic Function Approximation by Path-Norm-Regularized Deep Neural Networks
title_fullStr Analytic Function Approximation by Path-Norm-Regularized Deep Neural Networks
title_full_unstemmed Analytic Function Approximation by Path-Norm-Regularized Deep Neural Networks
title_short Analytic Function Approximation by Path-Norm-Regularized Deep Neural Networks
title_sort analytic function approximation by path-norm-regularized deep neural networks
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9407526/
https://www.ncbi.nlm.nih.gov/pubmed/36010799
http://dx.doi.org/10.3390/e24081136
work_keys_str_mv AT beknazaryanaleksandr analyticfunctionapproximationbypathnormregularizeddeepneuralnetworks

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