KMS Of Academy of mathematics and systems sciences, CAS
Approximation capabilities of measure-preserving neural networks | |
Zhu, Aiqing; Jin, Pengzhan; Tang, Yifa1 | |
2022-03-01 | |
Source Publication | NEURAL NETWORKS
![]() |
ISSN | 0893-6080 |
Volume | 147Pages: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 |
Citation statistics | |
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. |
Files in This Item: | There are no files associated with this item. |
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.
Edit Comment