Exponential convergence of the deep neural network approximation for analytic functions

E. Weinan; Qingcan Wang

doi:10.1007/s11425-018-9387-x

Exponential convergence of the deep neural network approximation for analytic functions

E. Weinan
, Qingcan Wang

Mathematics

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

58 Scopus citations

Abstract

We prove that for analytic functions in low dimension, the convergence rate of the deep neural network approximation is exponential.

Original language	English (US)
Pages (from-to)	1733-1740
Number of pages	8
Journal	Science China Mathematics
Volume	61
Issue number	10
DOIs	https://doi.org/10.1007/s11425-018-9387-x
State	Published - Oct 1 2018

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Primary 65D15
analytic functions
approximation theory
neural networks
secondary 41-04

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10.1007/s11425-018-9387-x

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title = "Exponential convergence of the deep neural network approximation for analytic functions",

abstract = "We prove that for analytic functions in low dimension, the convergence rate of the deep neural network approximation is exponential.",

keywords = "Primary 65D15, analytic functions, approximation theory, neural networks, secondary 41-04",

author = "E. Weinan and Qingcan Wang",

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AB - We prove that for analytic functions in low dimension, the convergence rate of the deep neural network approximation is exponential.

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KW - approximation theory

KW - neural networks

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Exponential convergence of the deep neural network approximation for analytic functions

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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