Approximation capabilities of measure-preserving neural networks

doi:10.1016/j.neunet.2021.12.007

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	Approximation capabilities of measure-preserving neural networks
	Zhu, Aiqing ; Jin, Pengzhan ; Tang, Yifa 1
	2022-03-01
Source Publication	NEURAL NETWORKS
ISSN	0893-6080
Volume	147 Pages:72-80
Abstract	Measure-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.
Keyword	Measure-preserving Neural networks Dynamical systems Approximation theory
DOI	10.1016/j.neunet.2021.12.007
Indexed By	SCI
Language	英语
Funding Project	MOST of China[2018AAA0101002] ; National Natural Science Foundation of China[12171466] ; National Natural Science Foundation of China[11771438]
WOS Research Area	Computer Science ; Neurosciences & Neurology
WOS Subject	Computer Science, Artificial Intelligence ; Neurosciences
WOS ID	WOS:000787888500007
Publisher	PERGAMON-ELSEVIER SCIENCE LTD
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Document Type	期刊论文
Identifier	http://ir.amss.ac.cn/handle/2S8OKBNM/60364
Collection	中国科学院数学与系统科学研究院
Corresponding Author	Tang, Yifa
Affiliation	1.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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