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 | |
发表期刊 | NEURAL NETWORKS |
ISSN | 0893-6080 |
卷号 | 147页码:72-80 |
摘要 | 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. |
关键词 | Measure-preserving Neural networks Dynamical systems Approximation theory |
DOI | 10.1016/j.neunet.2021.12.007 |
收录类别 | SCI |
语种 | 英语 |
资助项目 | MOST of China[2018AAA0101002] ; National Natural Science Foundation of China[12171466] ; National Natural Science Foundation of China[11771438] |
WOS研究方向 | Computer Science ; Neurosciences & Neurology |
WOS类目 | Computer Science, Artificial Intelligence ; Neurosciences |
WOS记录号 | WOS:000787888500007 |
出版者 | PERGAMON-ELSEVIER SCIENCE LTD |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/60364 |
专题 | 中国科学院数学与系统科学研究院 |
通讯作者 | Tang, Yifa |
作者单位 | 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 |
推荐引用方式 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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