Approximation of functions from Korobov spaces by deep convolutional neural networks

Tong Mao; Ding-Xuan Zhou

doi:10.1007/s10444-022-09991-x

Approximation of functions from Korobov spaces by deep convolutional neural networks

Tong Mao, Ding-Xuan Zhou^*

^*Corresponding author for this work

Department of Data Science

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

14 Citations (Scopus)

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Abstract

The efficiency of deep convolutional neural networks (DCNNs) has been demonstrated empirically in many practical applications. In this paper, we establish a theory for approximating functions from Korobov spaces by DCNNs. It verifies rigorously the efficiency of DCNNs in approximating functions of many variables with some variable structures and their abilities in overcoming the curse of dimensionality.

Original language	English
Article number	84
Journal	Advances in Computational Mathematics
Volume	48
Issue number	6
Online published	7 Dec 2022
DOIs	https://doi.org/10.1007/s10444-022-09991-x
Publication status	Published - Dec 2022

Research Keywords

Curse of dimensionality
Deep convolutional neural networks
Korobov spaces
Machine learning

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This full text is made available under CC-BY 4.0. https://creativecommons.org/licenses/by/4.0/

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abstract = "The efficiency of deep convolutional neural networks (DCNNs) has been demonstrated empirically in many practical applications. In this paper, we establish a theory for approximating functions from Korobov spaces by DCNNs. It verifies rigorously the efficiency of DCNNs in approximating functions of many variables with some variable structures and their abilities in overcoming the curse of dimensionality.",

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KW - Deep convolutional neural networks

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KW - Machine learning

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Approximation of functions from Korobov spaces by deep convolutional neural networks

Abstract

Research Keywords

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Ger/HKJRS: Theoretical Research on Deep Learning from a Mathematical Approximation Theory Viewpoint

GRF: Theory of Deep Learning: from CNNs to RNNs

NSFC: Approximation Analysis of Deep Learning and Related Topics

Cite this

Approximation of functions from Korobov spaces by deep convolutional neural networks

Abstract

Research Keywords

Publisher's Copyright Statement

Access Output

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Ger/HKJRS: Theoretical Research on Deep Learning from a Mathematical Approximation Theory Viewpoint

GRF: Theory of Deep Learning: from CNNs to RNNs

NSFC: Approximation Analysis of Deep Learning and Related Topics

Cite this