Error bounds for deep ReLU networks using the Kolmogorov–Arnold superposition theorem

Hadrien Montanelli; Haizhao Yang

doi:10.1016/j.neunet.2019.12.013

Error bounds for deep ReLU networks using the Kolmogorov–Arnold superposition theorem

Hadrien Montanelli
, Haizhao Yang

Columbia University
National University of Singapore

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

95 Citations (Scopus)

Résumé

We prove a theorem concerning the approximation of multivariate functions by deep ReLU networks, for which the curse of the dimensionality is lessened. Our theorem is based on a constructive proof of the Kolmogorov–Arnold superposition theorem, and on a subset of multivariate continuous functions whose outer superposition functions can be efficiently approximated by deep ReLU networks.

langue originale	Anglais
Pages (de - à)	1-6
Nombre de pages	6
journal	Neural Networks
Volume	129
Les DOIs	https://doi.org/10.1016/j.neunet.2019.12.013
état	Publié - 1 sept. 2020
Modification externe	Oui

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10.1016/j.neunet.2019.12.013

Contient cette citation

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abstract = "We prove a theorem concerning the approximation of multivariate functions by deep ReLU networks, for which the curse of the dimensionality is lessened. Our theorem is based on a constructive proof of the Kolmogorov{\textendash}Arnold superposition theorem, and on a subset of multivariate continuous functions whose outer superposition functions can be efficiently approximated by deep ReLU networks.",

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AB - We prove a theorem concerning the approximation of multivariate functions by deep ReLU networks, for which the curse of the dimensionality is lessened. Our theorem is based on a constructive proof of the Kolmogorov–Arnold superposition theorem, and on a subset of multivariate continuous functions whose outer superposition functions can be efficiently approximated by deep ReLU networks.

KW - Approximation theory

KW - Curse of dimensionality

KW - Deep ReLU networks

KW - Kolmogorov–Arnold superposition theorem

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DO - 10.1016/j.neunet.2019.12.013

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Error bounds for deep ReLU networks using the Kolmogorov–Arnold superposition theorem

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