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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	78-92
Number of pages	15
Journal	SIAM Journal on Mathematics of Data Science
Volume	1
Issue number	1
DOIs	https://doi.org/10.1137/18M1189336
Publication status	Published - 1 Jan 2019
Externally published	Yes

Keywords

approximation theory
curse of dimensionality
deep networks
machine learning
neural networks
sparse grids

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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 - deep networks

KW - machine learning

KW - neural networks

KW - sparse grids

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New Error Bounds for Deep ReLU Networks Using Sparse Grids

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Keywords

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