mlsanityData to 14 Oct 2026

Non-Asymptotic Error Bounds for Bidirectional GANs

arXiv 2110.12319 ↗First posted 24 Oct 2021cs.LG math.ST stat.MLcited by 3

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Abstract (arXiv)

We derive nearly sharp bounds for the bidirectional GAN (BiGAN) estimation error under the Dudley distance between the latent joint distribution and the data joint distribution with appropriately specified architecture of the neural networks used in the model. To the best of our knowledge, this is the first theoretical guarantee for the bidirectional GAN learning approach. An appealing feature of our results is that they do not assume the reference and the data distributions to have the same dimensions or these distributions to have bounded support. These assumptions are commonly assumed in the existing convergence analysis of the unidirectional GANs but may not be satisfied in practice. Our results are also applicable to the Wasserstein bidirectional GAN if the target distribution is assumed to have a bounded support. To prove these results, we construct neural network functions that push forward an empirical distribution to another arbitrary empirical distribution on a possibly different-dimensional space. We also develop a novel decomposition of the integral probability metric for the error analysis of bidirectional GANs. These basic theoretical results are of independent interest and can be applied to other related learning problems.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 19 of its 36 references that are in the map. First posted on arXiv 24 Oct 2021.

Builds on

19 of 36 references.

References · 19

  1. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 6,013
  2. 2017Progressive Growing of GANs for Improved Quality, Stability, and Variationcited by 2,988
  3. 2018Large Scale GAN Training for High Fidelity Natural Image Synthesiscited by 2,626
  4. 2015Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networkscited by 2,054
  5. 2016Generative Adversarial Text to Image Synthesiscited by 735
  6. 2015Adversarial Autoencoderscited by 364
  7. 2016Adversarial Feature Learningcited by 350
  8. 2016Adversarially Learned Inferencecited by 216
  9. 2017Generalization and Equilibrium in Generative Adversarial Nets (GANs)cited by 166
  10. 2019Deep Network Approximation Characterized by Number of Neuronscited by 122
  11. 2018How Well Generative Adversarial Networks Learn Distributionscited by 78
  12. 2017On the Discrimination-Generalization Tradeoff in GANscited by 48
7 more
  1. 2017Approximation and Convergence Properties of Generative Adversarial Learningcited by 28
  2. 2018Approximability of Discriminators Implies Diversity in GANscited by 28
  3. 2019Nonparametric Density Estimation & Convergence Rates for GANs under Besov IPM Lossescited by 22
  4. 2021On the capacity of deep generative networks for approximating distributionscited by 19
  5. 2020Bounding the expectation of the supremum of empirical processes indexed by H"older classescited by 8
  6. 2020A Universal Approximation Theorem of Deep Neural Networks for Expressing Probability Distributionscited by 7
  7. 2020Bidirectional Generative Modeling Using Adversarial Gradient Estimationcited by 3

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Cited by year

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

3 papers.

  1. 2024A Statistical Analysis of Wasserstein Autoencoders for Intrinsically Low-dimensional Datacited by 4
  2. 2025A Statistical Learning Perspective on Semi-dual Adversarial Neural Optimal Transport Solverscited by 2
  3. 2022Distribution estimation and change-point estimation for time series via DNN-based GANscited by 0