Approximation of functions from Korobov spaces by deep convolutional neural networks

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 m...

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Bibliographic Details
Published inAdvances in computational mathematics Vol. 48; no. 6
Main Authors Mao, Tong, Zhou, Ding-Xuan
Format Journal Article
LanguageEnglish
Published New York Springer US 01.12.2022
Springer Nature B.V
Subjects
Approximation
Artificial neural networks
Computational mathematics
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Mathematical analysis
Mathematical and Computational Biology
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Visualization
Deep convolutional neural networks
Curse of dimensionality
Korobov spaces
68T07
41A25
Machine learning
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Summary: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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ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-022-09991-x