mlsanityData to 7 Oct 2026

Approximation capabilities of measure-preserving neural networks

arXiv 2106.10911 ↗First posted 21 Jun 2021cs.LGcited by 4

Not on the map. Why?

Abstract (arXiv)

Measure-preserving neural networks are well-developed invertible models, however, their approximation capabilities remain unexplored. This paper rigorously analyses the approximation capabilities of existing measure-preserving neural networks including NICE and RevNets. It is shown that for compact U subset RD with D≥ 2, the measure-preserving neural networks are able to approximate arbitrary measure-preserving map psi: U→ RD which is bounded and injective in the Lp-norm. In particular, any continuously differentiable injective map with ± 1 determinant of Jacobian are measure-preserving, thus can be approximated.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 25 of its 44 references that are in the map. First posted on arXiv 21 Jun 2021.

Builds on

25 of 44 references.

References · 25

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13 more
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 1; 2023: 0; 2024: 1; 2025: 0; 2026: 1.

4 papers.

  1. 2021Locally-symplectic neural networks for learning volume-preserving dynamicscited by 9
  2. 2024Adaptive deep density approximation for stochastic dynamical systemscited by 4
  3. 2022VPNets: Volume-preserving neural networks for learning source-free dynamicscited by 2
  4. 2026Learning symplectic model reduction based on an approximation theorem of symplectic embeddingscited by 0