Approximation capabilities of measure-preserving neural networks
Zhu, Aiqing; Jin, Pengzhan; Tang, Yifa1
Source PublicationNEURAL NETWORKS
AbstractMeasure-preserving neural networks are well-developed invertible models, however, their approximation capabilities remain unexplored. This paper rigorously analyzes the approximation capabilities of existing measure-preserving neural networks including NICE and RevNets. It is shown that for compact U c R-D with D >= 2, the measure-preserving neural networks are able to approximate arbitrary measure-preserving map psi : U -> R-D which is bounded and injective in the L-p-norm. In particular, any continuously differentiable injective map with +/- 1 determinant of Jacobian is measure-preserving, thus can be approximated. (C) 2021 Elsevier Ltd. All rights reserved.
KeywordMeasure-preserving Neural networks Dynamical systems Approximation theory
Indexed BySCI
Funding ProjectMOST of China[2018AAA0101002] ; National Natural Science Foundation of China[12171466] ; National Natural Science Foundation of China[11771438]
WOS Research AreaComputer Science ; Neurosciences & Neurology
WOS SubjectComputer Science, Artificial Intelligence ; Neurosciences
WOS IDWOS:000787888500007
Citation statistics
Document Type期刊论文
Corresponding AuthorTang, Yifa
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Zhu, Aiqing,Jin, Pengzhan,Tang, Yifa. Approximation capabilities of measure-preserving neural networks[J]. NEURAL NETWORKS,2022,147:72-80.
APA Zhu, Aiqing,Jin, Pengzhan,&Tang, Yifa.(2022).Approximation capabilities of measure-preserving neural networks.NEURAL NETWORKS,147,72-80.
MLA Zhu, Aiqing,et al."Approximation capabilities of measure-preserving neural networks".NEURAL NETWORKS 147(2022):72-80.
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