mlsanityData to 14 Oct 2026

Some Theoretical Properties of GANs

arXiv 1803.07819 ↗First posted 21 Mar 2018stat.ML cs.LGcited by 27

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Abstract (arXiv)

Generative Adversarial Networks (GANs) are a class of generative algorithms that have been shown to produce state-of-the art samples, especially in the domain of image creation. The fundamental principle of GANs is to approximate the unknown distribution of a given data set by optimizing an objective function through an adversarial game between a family of generators and a family of discriminators. In this paper, we offer a better theoretical understanding of GANs by analyzing some of their mathematical and statistical properties. We study the deep connection between the adversarial principle underlying GANs and the Jensen-Shannon divergence, together with some optimality characteristics of the problem. An analysis of the role of the discriminator family via approximation arguments is also provided. In addition, taking a statistical point of view, we study the large sample properties of the estimated distribution and prove in particular a central limit theorem. Some of our results are illustrated with simulated examples.

Key facts. Cited by 27 papers in the map (data through 14 Oct 2026). First posted on arXiv 21 Mar 2018.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 9; 2022: 1; 2023: 4; 2024: 5; 2025: 5; 2026: 3.

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  1. 2021MaGNET: Uniform Sampling from Deep Generative Network Manifolds Without Retrainingcited by 23
  2. 2023Ten Years of Generative Adversarial Nets (GANs): A survey of the state-of-the-artcited by 14
  3. 2021Rates of convergence for density estimation with generative adversarial networkscited by 13
  4. 2021A likelihood approach to nonparametric estimation of a singular distribution using deep generative modelscited by 12
  5. 2023Revisiting Energy Based Models as Policies: Ranking Noise Contrastive Estimation and Interpolating Energy Modelscited by 10
  6. 2024Causality Pursuit from Heterogeneous Environments via Neural Adversarial Invariance Learningcited by 7
  7. 2021Time Series (re)sampling using Generative Adversarial Networkscited by 4
  8. 2021Does Redundancy in AI Perception Systems Help to Test for Super-Human Automated Driving Performance?cited by 4
  9. 2024Non-stationary Domain Generalization: Theory and Algorithmcited by 4
  10. 2021Monte Carlo Simulation of SDEs using GANscited by 3
  11. 2021Statistical inference for generative adversarial networks and other minimax problemscited by 3
  12. 2021Statistical Regeneration Guarantees of the Wasserstein Autoencoder with Latent Space Consistencycited by 3
15 more
  1. 2023Statistically Optimal Generative Modeling with Maximum Deviation from the Empirical Distributioncited by 3
  2. 2024A Wasserstein perspective of Vanilla GANscited by 3
  3. 2025Numerical and statistical analysis of NeuralODE with Runge-Kutta time integrationcited by 3
  4. 2025Learning Brenier Potentials with Convex Generative Adversarial Neural Networkscited by 3
  5. 2022Asymptotic Statistical Analysis of f-divergence GANcited by 2
  6. 2025A Statistical Learning Perspective on Semi-dual Adversarial Neural Optimal Transport Solverscited by 2
  7. 2023GAN-MPC: Training Model Predictive Controllers with Parameterized Cost Functions using Demonstrations from Non-identical Expertscited by 1
  8. 2025PrAda-GAN: A Private Adaptive Generative Adversarial Network with Bayes Network Structurecited by 1
  9. 2021Investigating Shifts in GAN Output-Distributionscited by 0
  10. 2024Active Learning for Regression based on Wasserstein distance and GroupSort Neural Networkscited by 0
  11. 2024Open-Set Heterogeneous Domain Adaptation: Theoretical Analysis and Algorithmcited by 0
  12. 2025Hellinger loss function for Generative Adversarial Networkscited by 0
  13. 2026Generative Model via Quantile Assignmentcited by 0
  14. 2026Generative Adversarial Learning from Deterministic Processescited by 0
  15. 2026Generative Predictive Distributions for Time Seriescited by 0