Approximation capabilities of measure-preserving neural networks. (March 2022)

• Record Type: Journal Article
• Authors: Zhu, Aiqing; Jin, Pengzhan; Tang, Yifa
• Is Part Of: Neural networks. Volume 147(2022)
• Page Start: 72
• Page End: 80
• Publication Date: 2022-03
• Subjects: Measure-preserving -- Neural networks -- Dynamical systems -- Approximation theory; Neural computers -- Periodicals; Neural networks (Computer science) -- Periodicals; Neural networks (Neurobiology) -- Periodicals; Nervous System -- Periodicals; Ordinateurs neuronaux -- Périodiques; Réseaux neuronaux (Informatique) -- Périodiques; Réseaux neuronaux (Neurobiologie) -- Périodiques; Neural computers; Neural networks (Computer science); Neural networks (Neurobiology); Periodicals; 006.32
• DOI: 10.1016/j.neunet.2021.12.007
• Languages: English
• ISSNs: 0893-6080

Abstract

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 ⊂ R D with D ≥ 2, the measure-preserving neural networks are able to approximate arbitrary measure-preserving map ψ : 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.