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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| Published in | Advances in computational mathematics Vol. 48; no. 6 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
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Springer US
01.12.2022
Springer Nature B.V |
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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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| AbstractList | 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. |
| ArticleNumber | 84 |
| Author | Mao, Tong Zhou, Ding-Xuan |
| Author_xml | – sequence: 1 givenname: Tong surname: Mao fullname: Mao, Tong organization: School of Data Science, City University of Hong Kong – sequence: 2 givenname: Ding-Xuan orcidid: 0000-0003-0224-9216 surname: Zhou fullname: Zhou, Ding-Xuan email: dingxuan.zhou@sydney.edu.au organization: School of Mathematics and Statistics, University of Sydney |
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| Cites_doi | 10.1162/neco.2006.18.7.1527 10.1142/S0219530519400074 10.1007/s11633-017-1054-2 10.1109/TIT.2016.2634401 10.3934/mfc.2022021 10.1016/S0893-6080(05)80131-5 10.1016/j.acha.2019.06.004 10.1016/j.neunet.2020.07.029 10.1142/S0219530518500124 10.1007/BF02070821 10.1109/TNNLS.2018.2868980 10.1016/j.neunet.2021.09.027 10.1016/j.neunet.2020.01.018 10.1137/18M1189336 10.1016/j.neunet.2017.07.002 10.1145/3065386 10.1109/TIT.2018.2874447 10.1017/S0962492904000182 10.1109/TNNLS.2020.3027613 10.1002/047134608X.W8424 |
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| References | Feng, Hou, Wei, Zhou (CR6) 2022; 5 Hinton, Osindero, Teh (CR7) 2006; 18 CR19 Yarotsky (CR20) 2017; 94 Poggio, Mhaskar, Rosasco, Miranda, Liao (CR18) 2017; 14 Mao, Shi, Zhou (CR14) 2021; 144 Zhou (CR21) 2020; 48 Klusowski, Barron (CR9) 2018; 64 CR12 Chui, Lin, Zhou (CR3) 2019; 17 Hoefler, Alistarh, Ben-Nun, Dryden, Peste (CR8) 2021; 22 Kohler, Krzyżak (CR10) 2016; 63 Mhaskar (CR15) 1993; 1 Zhou (CR23) 2018; 16 Pinkus (CR17) 1993; 6 Montanelli, Du (CR16) 2019; 1 CR4 Bungartz, Griebel (CR1) 2004; 13 Chui, Lin, Zhang, Zhou (CR2) 2022; 33 CR25 Krizhevsky, Sutskever, Hinton (CR11) 2012; 60 CR24 Lin (CR13) 2019; 30 Zhou (CR22) 2020; 124 Fang, Feng, Huang, Zhou (CR5) 2020; 131 JM Klusowski (9991_CR9) 2018; 64 9991_CR24 9991_CR25 CK Chui (9991_CR3) 2019; 17 H Montanelli (9991_CR16) 2019; 1 T Poggio (9991_CR18) 2017; 14 H-J Bungartz (9991_CR1) 2004; 13 T Hoefler (9991_CR8) 2021; 22 A Pinkus (9991_CR17) 1993; 6 DX Zhou (9991_CR22) 2020; 124 M Kohler (9991_CR10) 2016; 63 T Mao (9991_CR14) 2021; 144 9991_CR4 H Feng (9991_CR6) 2022; 5 HN Mhaskar (9991_CR15) 1993; 1 GE Hinton (9991_CR7) 2006; 18 9991_CR19 DX Zhou (9991_CR21) 2020; 48 Z Fang (9991_CR5) 2020; 131 DX Zhou (9991_CR23) 2018; 16 CK Chui (9991_CR2) 2022; 33 9991_CR12 SB Lin (9991_CR13) 2019; 30 A Krizhevsky (9991_CR11) 2012; 60 D Yarotsky (9991_CR20) 2017; 94 |
| References_xml | – volume: 18 start-page: 1527 year: 2006 end-page: 1554 ident: CR7 article-title: A fast learning algorithm for deep belief nets publication-title: Neural Comput. doi: 10.1162/neco.2006.18.7.1527 – volume: 17 start-page: 737 year: 2019 end-page: 772 ident: CR3 article-title: Deep neural networks for rotation-invariance approximation and learning publication-title: Anal. Appl. doi: 10.1142/S0219530519400074 – ident: CR4 – ident: CR12 – volume: 14 start-page: 503 year: 2017 end-page: 519 ident: CR18 article-title: Why and when can deep—but not shallow—networks avoid the curse of dimensionality: a review publication-title: Internat. J. Automation Comput. doi: 10.1007/s11633-017-1054-2 – volume: 22 start-page: 1 year: 2021 end-page: 124 ident: CR8 article-title: Sparsity in deep learning: Pruning and growth for efficient inference and training in neural networks publication-title: J. Mach. Learn. Res. – volume: 63 start-page: 1620 year: 2016 end-page: 1630 ident: CR10 article-title: Nonparametric regression based on hierarchical interaction models publication-title: IEEE Trans. Inf. Theory doi: 10.1109/TIT.2016.2634401 – volume: 5 start-page: 351 year: 2022 end-page: 362 ident: CR6 article-title: CNN models for readability of Chinese texts publication-title: Math. Found. Comp. doi: 10.3934/mfc.2022021 – volume: 6 start-page: 861 year: 1993 end-page: 867 ident: CR17 article-title: Multilayer feedforward networks with a nonpolynomial activation function can approximate any function publication-title: Neural Netw. doi: 10.1016/S0893-6080(05)80131-5 – volume: 48 start-page: 787 year: 2020 end-page: 794 ident: CR21 article-title: Universality of deep convolutional neural networks publication-title: Appl. Comput. Harmon. Anal. doi: 10.1016/j.acha.2019.06.004 – ident: CR25 – volume: 131 start-page: 154 year: 2020 end-page: 162 ident: CR5 article-title: Theory of deep convolutional neural networks II: spherical analysis publication-title: Neural Netw. doi: 10.1016/j.neunet.2020.07.029 – volume: 16 start-page: 895 year: 2018 end-page: 919 ident: CR23 article-title: Deep distributed convolutional neural networks: universality publication-title: Anal. Appl. doi: 10.1142/S0219530518500124 – volume: 1 start-page: 61 year: 1993 end-page: 80 ident: CR15 article-title: Approximation properties of a multilayered feedforward artificial neural network publication-title: Adv. Comput. Math. doi: 10.1007/BF02070821 – ident: CR19 – volume: 30 start-page: 1392 year: 2019 end-page: 1406 ident: CR13 article-title: Generalization and expressivity for deep nets publication-title: IEEE Trans. Neural Netw. Learn Syst. doi: 10.1109/TNNLS.2018.2868980 – volume: 144 start-page: 778 year: 2021 end-page: 790 ident: CR14 article-title: Theory of deep convolutional neural networks III: Approximating radial functions publication-title: Neural Netw. doi: 10.1016/j.neunet.2021.09.027 – volume: 124 start-page: 319 year: 2020 end-page: 327 ident: CR22 article-title: Theory of deep convolutional neural networks: Downsampling publication-title: Neural Netw. doi: 10.1016/j.neunet.2020.01.018 – volume: 1 start-page: 78 year: 2019 end-page: 92 ident: CR16 article-title: New error bounds for deep reLU networks using sparse grids publication-title: SIAM Journal on Mathematics of Data Science doi: 10.1137/18M1189336 – volume: 94 start-page: 103 year: 2017 end-page: 114 ident: CR20 article-title: Error bounds for approximations with deep reLU networks publication-title: Neural Netw. doi: 10.1016/j.neunet.2017.07.002 – volume: 60 start-page: 84 year: 2012 end-page: 90 ident: CR11 article-title: Imagenet classification with deep convolutional neural networks publication-title: Commun. ACM doi: 10.1145/3065386 – volume: 64 start-page: 7649 year: 2018 end-page: 7656 ident: CR9 article-title: Approximation by combinations of reLU and squared reLU ridge functions with ℓ1 and ℓ0 controls publication-title: IEEE Trans. Inf. Theory doi: 10.1109/TIT.2018.2874447 – volume: 13 start-page: 147 year: 2004 end-page: 269 ident: CR1 article-title: Sparse grids publication-title: Acta Numer. doi: 10.1017/S0962492904000182 – volume: 33 start-page: 229 year: 2022 end-page: 243 ident: CR2 article-title: Realization of spatial sparseness by deep reLU nets with massive data publication-title: IEEE Trans. Neural Netw. Learn. Syst. doi: 10.1109/TNNLS.2020.3027613 – ident: CR24 – volume: 1 start-page: 61 year: 1993 ident: 9991_CR15 publication-title: Adv. Comput. Math. doi: 10.1007/BF02070821 – volume: 13 start-page: 147 year: 2004 ident: 9991_CR1 publication-title: Acta Numer. doi: 10.1017/S0962492904000182 – volume: 60 start-page: 84 year: 2012 ident: 9991_CR11 publication-title: Commun. ACM doi: 10.1145/3065386 – ident: 9991_CR4 – ident: 9991_CR19 – volume: 18 start-page: 1527 year: 2006 ident: 9991_CR7 publication-title: Neural Comput. doi: 10.1162/neco.2006.18.7.1527 – volume: 144 start-page: 778 year: 2021 ident: 9991_CR14 publication-title: Neural Netw. doi: 10.1016/j.neunet.2021.09.027 – volume: 30 start-page: 1392 year: 2019 ident: 9991_CR13 publication-title: IEEE Trans. Neural Netw. Learn Syst. doi: 10.1109/TNNLS.2018.2868980 – volume: 17 start-page: 737 year: 2019 ident: 9991_CR3 publication-title: Anal. Appl. doi: 10.1142/S0219530519400074 – ident: 9991_CR24 doi: 10.1002/047134608X.W8424 – volume: 64 start-page: 7649 year: 2018 ident: 9991_CR9 publication-title: IEEE Trans. Inf. Theory doi: 10.1109/TIT.2018.2874447 – volume: 131 start-page: 154 year: 2020 ident: 9991_CR5 publication-title: Neural Netw. doi: 10.1016/j.neunet.2020.07.029 – volume: 124 start-page: 319 year: 2020 ident: 9991_CR22 publication-title: Neural Netw. doi: 10.1016/j.neunet.2020.01.018 – volume: 22 start-page: 1 year: 2021 ident: 9991_CR8 publication-title: J. Mach. Learn. Res. – volume: 33 start-page: 229 year: 2022 ident: 9991_CR2 publication-title: IEEE Trans. Neural Netw. Learn. Syst. doi: 10.1109/TNNLS.2020.3027613 – volume: 63 start-page: 1620 year: 2016 ident: 9991_CR10 publication-title: IEEE Trans. Inf. Theory doi: 10.1109/TIT.2016.2634401 – ident: 9991_CR12 – volume: 14 start-page: 503 year: 2017 ident: 9991_CR18 publication-title: Internat. J. Automation Comput. doi: 10.1007/s11633-017-1054-2 – volume: 48 start-page: 787 year: 2020 ident: 9991_CR21 publication-title: Appl. Comput. Harmon. Anal. doi: 10.1016/j.acha.2019.06.004 – volume: 16 start-page: 895 year: 2018 ident: 9991_CR23 publication-title: Anal. Appl. doi: 10.1142/S0219530518500124 – volume: 94 start-page: 103 year: 2017 ident: 9991_CR20 publication-title: Neural Netw. doi: 10.1016/j.neunet.2017.07.002 – ident: 9991_CR25 – volume: 1 start-page: 78 year: 2019 ident: 9991_CR16 publication-title: SIAM Journal on Mathematics of Data Science doi: 10.1137/18M1189336 – volume: 5 start-page: 351 year: 2022 ident: 9991_CR6 publication-title: Math. Found. Comp. doi: 10.3934/mfc.2022021 – volume: 6 start-page: 861 year: 1993 ident: 9991_CR17 publication-title: Neural Netw. doi: 10.1016/S0893-6080(05)80131-5 |
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| SubjectTerms | 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 |
| Title | Approximation of functions from Korobov spaces by deep convolutional neural networks |
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