mlsanityData to 7 Oct 2026

An error analysis of generative adversarial networks for learning distributions

arXiv 2105.13010 ↗First posted 27 May 2021cs.LG math.ST stat.MLcited by 35

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Abstract (arXiv)

This paper studies how well generative adversarial networks (GANs) learn probability distributions from finite samples. Our main results establish the convergence rates of GANs under a collection of integral probability metrics defined through H"older classes, including the Wasserstein distance as a special case. We also show that GANs are able to adaptively learn data distributions with low-dimensional structures or have H"older densities, when the network architectures are chosen properly. In particular, for distributions concentrated around a low-dimensional set, we show that the learning rates of GANs do not depend on the high ambient dimension, but on the lower intrinsic dimension. Our analysis is based on a new oracle inequality decomposing the estimation error into the generator and discriminator approximation error and the statistical error, which may be of independent interest.

Key facts. Cited by 35 papers in the map (data through 7 Oct 2026). Builds on 30 of its 56 references that are in the map. First posted on arXiv 27 May 2021.

Builds on

30 of 56 references.

References · 30

  1. 2017Progressive Growing of GANs for Improved Quality, Stability, and Variationcited by 2,967
  2. 2017Improved Training of Wasserstein GANscited by 2,223
  3. 2015Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networkscited by 2,048
  4. 2016Generative Adversarial Text to Image Synthesiscited by 735
  5. 2015Generating Sentences from a Continuous Spacecited by 607
  6. 2016Error bounds for approximations with deep ReLU networkscited by 567
  7. 2017Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networkscited by 304
  8. 2018Generative Adversarial Network in Medical Imaging: A Reviewcited by 257
  9. 2015Generative Moment Matching Networkscited by 252
  10. 2017Optimal approximation of piecewise smooth functions using deep ReLU neural networkscited by 176
  11. 2017Generalization and Equilibrium in Generative Adversarial Nets (GANs)cited by 165
  12. 2018Optimal approximation of continuous functions by very deep ReLU networkscited by 165
18 more
  1. 2020Deep Network Approximation for Smooth Functionscited by 163
  2. 2015Training generative neural networks via Maximum Mean Discrepancy optimizationcited by 149
  3. 2019Deep Network Approximation Characterized by Number of Neuronscited by 120
  4. 2019The phase diagram of approximation rates for deep neural networkscited by 86
  5. 2018How Well Generative Adversarial Networks Learn Distributionscited by 78
  6. 2017On the regularization of Wasserstein GANscited by 65
  7. 2018Improving the Improved Training of Wasserstein GANs: A Consistency Term and Its Dual Effectcited by 49
  8. 2017On the Discrimination-Generalization Tradeoff in GANscited by 48
  9. 2019Nonlinear Approximation via Compositionscited by 37
  10. 2017Sobolev GANcited by 29
  11. 2018Approximability of Discriminators Implies Diversity in GANscited by 28
  12. 2020Statistical guarantees for generative models without dominationcited by 27
  13. 2017On the ability of neural nets to express distributionscited by 26
  14. 2018Nonparametric Density Estimation under Adversarial Lossescited by 26
  15. 2019Nonparametric Density Estimation & Convergence Rates for GANs under Besov IPM Lossescited by 22
  16. 2021On the capacity of deep generative networks for approximating distributionscited by 19
  17. 2020Constructive Universal High-Dimensional Distribution Generation through Deep ReLU Networkscited by 13
  18. 2018Size-Noise Tradeoffs in Generative Networkscited by 12

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 3; 2023: 8; 2024: 14; 2025: 6; 2026: 3.

35 papers.

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  1. 2024Deep Generative Models through the Lens of the Manifold Hypothesis: A Survey and New Connectionscited by 47
  2. 2023Convergence of flow-based generative models via proximal gradient descent in Wasserstein spacecited by 34
  3. 2022Approximation bounds for norm constrained neural networks with applications to regression and GANscited by 21
  4. 2024Convergence Analysis of Flow Matching in Latent Space with Transformerscited by 16
  5. 2024Addressing Spectral Bias of Deep Neural Networks by Multi-Grade Deep Learningcited by 14
  6. 2023On Deep Generative Models for Approximation and Estimation of Distributions on Manifoldscited by 12
  7. 2023Wasserstein Generative Regressioncited by 12
  8. 2024Enhancing Accuracy in Generative Models via Knowledge Transfercited by 6
  9. 2023Uniform Convergence of Deep Neural Networks with Lipschitz Continuous Activation Functions and Variable Widthscited by 5
  10. 2023Statistical Guarantees of Group-Invariant GANscited by 4
  11. 2024Hypothesis Spaces for Deep Learningcited by 4
  12. 2024Robust Generative Learning with Lipschitz-Regularized α-Divergences Allows Minimal Assumptions on Target Distributionscited by 4
23 more
  1. 2024Deep Transfer Learning: Model Framework and Error Analysiscited by 4
  2. 2025Deep Generative Models: Complexity, Dimensionality, and Approximationcited by 4
  3. 2025Image Interpolation with Score-based Riemannian Metrics of Diffusion Modelscited by 4
  4. 2023Statistically Optimal Generative Modeling with Maximum Deviation from the Empirical Distributioncited by 3
  5. 2024A Statistical Analysis of Wasserstein Autoencoders for Intrinsically Low-dimensional Datacited by 3
  6. 2024A Wasserstein perspective of Vanilla GANscited by 3
  7. 2026Error Analysis of Neural-Network-Based Engressioncited by 3
  8. 2021Just Least Squares: Binary Compressive Sampling with Low Generative Intrinsic Dimensioncited by 2
  9. 2023LD-GAN: Low-Dimensional Generative Adversarial Network for Spectral Image Generation with Variance Regularizationcited by 2
  10. 2024Statistical Error Bounds for GANs with Nonlinear Objective Functionalscited by 2
  11. 2024Approximation Bounds for Recurrent Neural Networks with Application to Regressioncited by 2
  12. 2026Error Analysis of Bayesian Inverse Problems with Generative Priorscited by 2
  13. 2024Generative adversarial learning with optimal input dimension and its adaptive generator architecturecited by 1
  14. 2024Theoretical Insights into CycleGAN: Analyzing Approximation and Estimation Errors in Unpaired Data Generationcited by 1
  15. 2025PrAda-GAN: A Private Adaptive Generative Adversarial Network with Bayes Network Structurecited by 1
  16. 2022Distribution estimation and change-point estimation for time series via DNN-based GANscited by 0
  17. 2022Distribution Estimation of Contaminated Data via DNN-based MoM-GANscited by 0
  18. 2023Generalization error property of infoGAN for two-layer neural networkcited by 0
  19. 2024A Statistical Analysis of Deep Federated Learning for Intrinsically Low-dimensional Datacited by 0
  20. 2025Nested Annealed Training Scheme for Generative Adversarial Networkscited by 0
  21. 2025Concentration Inequalities for Stochastic Optimization of Unbounded Objective Functions with Application to Denoising Score Matchingcited by 0
  22. 2025Boosting Statistic Learning with Synthetic Data from Pretrained Large Modelscited by 0
  23. 2026Understanding Diffusion Models via Ratio-Based Function Approximation with SignReLU Networkscited by 0