New Error Bounds for Deep ReLU Networks Using Sparse Grids

Hadrien Montanelli; Qiang Du

doi:10.1137/18M1189336

New Error Bounds for Deep ReLU Networks Using Sparse Grids

Hadrien Montanelli
, Qiang Du

Columbia University

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

Résumé

We prove a theorem concerning the approximation of multivariate functions by deep ReLU networks. We present new error estimates for which the curse of dimensionality is lessened by establishing a connection with sparse grids.

langue originale	Anglais
Pages (de - à)	78-92
Nombre de pages	15
journal	SIAM Journal on Mathematics of Data Science
Volume	1
Numéro de publication	1
Les DOIs	https://doi.org/10.1137/18M1189336
état	Publié - 1 janv. 2019
Modification externe	Oui

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10.1137/18M1189336

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title = "New Error Bounds for Deep ReLU Networks Using Sparse Grids",

abstract = "We prove a theorem concerning the approximation of multivariate functions by deep ReLU networks. We present new error estimates for which the curse of dimensionality is lessened by establishing a connection with sparse grids.",

keywords = "approximation theory, curse of dimensionality, deep networks, machine learning, neural networks, sparse grids",

author = "Hadrien Montanelli and Qiang Du",

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KW - approximation theory

KW - curse of dimensionality

KW - deep networks

KW - machine learning

KW - neural networks

KW - sparse grids

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DO - 10.1137/18M1189336

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New Error Bounds for Deep ReLU Networks Using Sparse Grids

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