mlsanityData to 7 Oct 2026

Universal Approximation of Residual Flows in Maximum Mean Discrepancy

arXiv 2103.05793 ↗First posted 10 Mar 2021cs.LG stat.MLcited by 7

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Abstract (arXiv)

Normalizing flows are a class of flexible deep generative models that offer easy likelihood computation. Despite their empirical success, there is little theoretical understanding of their expressiveness. In this work, we study residual flows, a class of normalizing flows composed of Lipschitz residual blocks. We prove residual flows are universal approximators in maximum mean discrepancy. We provide upper bounds on the number of residual blocks to achieve approximation under different assumptions.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 29 of its 39 references that are in the map. First posted on arXiv 10 Mar 2021.

Builds on

29 of 39 references.

References · 29

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2018Neural Ordinary Differential Equationscited by 3,733
  3. 2015Variational Inference with Normalizing Flowscited by 2,161
  4. 2017Masked Autoregressive Flow for Density Estimationcited by 680
  5. 2016Improving Variational Inference with Inverse Autoregressive Flowcited by 636
  6. 2019Augmented Neural ODEscited by 396
  7. 2014On the Number of Linear Regions of Deep Neural Networkscited by 378
  8. 2018Invertible Residual Networkscited by 364
  9. 2017The Expressive Power of Neural Networks: A View from the Widthcited by 318
  10. 2015MADE: Masked Autoencoder for Distribution Estimationcited by 306
  11. 2016On the Expressive Power of Deep Neural Networkscited by 302
  12. 2019Residual Flows for Invertible Generative Modelingcited by 256
17 more
  1. 2018Sorting out Lipschitz function approximationcited by 211
  2. 2018Neural Autoregressive Flowscited by 207
  3. 2017Universal Function Approximation by Deep Neural Nets with Bounded Width and ReLU Activationscited by 104
  4. 2020Coupling-based Invertible Neural Networks Are Universal Diffeomorphism Approximatorscited by 85
  5. 2015Representation Benefits of Deep Feedforward Networkscited by 84
  6. 2018ResNet with one-neuron hidden layers is a Universal Approximatorcited by 78
  7. 2018Sylvester Normalizing Flows for Variational Inferencecited by 71
  8. 2019Sum-of-Squares Polynomial Flowcited by 62
  9. 2020The Expressive Power of a Class of Normalizing Flow Modelscited by 35
  10. 2020Approximating Lipschitz continuous functions with GroupSort neural networkscited by 27
  11. 2017On the ability of neural nets to express distributionscited by 26
  12. 2020Representational aspects of depth and conditioning in normalizing flowscited by 25
  13. 2020Constructive Universal High-Dimensional Distribution Generation through Deep ReLU Networkscited by 13
  14. 2018Size-Noise Tradeoffs in Generative Networkscited by 12
  15. 2019Universal Lipschitz Approximation in Bounded Depth Neural Networkscited by 11
  16. 2020A Universal Approximation Theorem of Deep Neural Networks for Expressing Probability Distributionscited by 7
  17. 2019On the space-time expressivity of ResNetscited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 2; 2023: 2; 2024: 0; 2025: 1; 2026: 1.

7 papers.

  1. 2022Universal approximation property of invertible neural networkscited by 30
  2. 2021On the expressivity of bi-Lipschitz normalizing flowscited by 15
  3. 2023Minimum Width of Leaky-ReLU Neural Networks for Uniform Universal Approximationcited by 13
  4. 2025Efficient Regression-Based Training of Normalizing Flows for Boltzmann Generatorscited by 6
  5. 2022Learning to Bound: A Generative Cram'er-Rao Boundcited by 2
  6. 2023Arbitrary Distributions Mapping via SyMOT-Flow: A Flow-based Approach Integrating Maximum Mean Discrepancy and Optimal Transportcited by 0
  7. 2026Expressivity of Bi-Lipschitz Normalizing Flows: A Score-Based Diffusion Perspectivecited by 0