# Some Theoretical Properties of GANs

arXiv: https://arxiv.org/abs/1803.07819 · HTML: https://mlsanity.com/paper/1803.07819/

## Key facts

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

## Built on by (most cited first, 27 of 27)

- [MaGNET: Uniform Sampling from Deep Generative Network Manifolds Without Retraining](https://mlsanity.com/paper/2110.08009/) (2021)
- [Ten Years of Generative Adversarial Nets (GANs): A survey of the state-of-the-art](https://mlsanity.com/paper/2308.16316/) (2023)
- [Rates of convergence for density estimation with generative adversarial networks](https://mlsanity.com/paper/2102.00199/) (2021)
- [A likelihood approach to nonparametric estimation of a singular distribution using deep generative models](https://mlsanity.com/paper/2105.04046/) (2021)
- [Revisiting Energy Based Models as Policies: Ranking Noise Contrastive Estimation and Interpolating Energy Models](https://mlsanity.com/paper/2309.05803/) (2023)
- [Causality Pursuit from Heterogeneous Environments via Neural Adversarial Invariance Learning](https://mlsanity.com/paper/2405.04715/) (2024)
- [Time Series (re)sampling using Generative Adversarial Networks](https://mlsanity.com/paper/2102.00208/) (2021)
- [Does Redundancy in AI Perception Systems Help to Test for Super-Human Automated Driving Performance?](https://mlsanity.com/paper/2112.04758/) (2021)
- [Non-stationary Domain Generalization: Theory and Algorithm](https://mlsanity.com/paper/2405.06816/) (2024)
- [Monte Carlo Simulation of SDEs using GANs](https://mlsanity.com/paper/2104.01437/) (2021)
- [Statistical inference for generative adversarial networks and other minimax problems](https://mlsanity.com/paper/2104.10601/) (2021)
- [Statistical Regeneration Guarantees of the Wasserstein Autoencoder with Latent Space Consistency](https://mlsanity.com/paper/2110.03995/) (2021)
- [Statistically Optimal Generative Modeling with Maximum Deviation from the Empirical Distribution](https://mlsanity.com/paper/2307.16422/) (2023)
- [A Wasserstein perspective of Vanilla GANs](https://mlsanity.com/paper/2403.15312/) (2024)
- [Numerical and statistical analysis of NeuralODE with Runge-Kutta time integration](https://mlsanity.com/paper/2503.10729/) (2025)
- [Learning Brenier Potentials with Convex Generative Adversarial Neural Networks](https://mlsanity.com/paper/2504.19779/) (2025)
- [Asymptotic Statistical Analysis of f-divergence GAN](https://mlsanity.com/paper/2209.06853/) (2022)
- [A Statistical Learning Perspective on Semi-dual Adversarial Neural Optimal Transport Solvers](https://mlsanity.com/paper/2502.01310/) (2025)
- [GAN-MPC: Training Model Predictive Controllers with Parameterized Cost Functions using Demonstrations from Non-identical Experts](https://mlsanity.com/paper/2305.19111/) (2023)
- [PrAda-GAN: A Private Adaptive Generative Adversarial Network with Bayes Network Structure](https://mlsanity.com/paper/2511.07997/) (2025)
- [Investigating Shifts in GAN Output-Distributions](https://mlsanity.com/paper/2112.14061/) (2021)
- [Active Learning for Regression based on Wasserstein distance and GroupSort Neural Networks](https://mlsanity.com/paper/2403.15108/) (2024)
- [Open-Set Heterogeneous Domain Adaptation: Theoretical Analysis and Algorithm](https://mlsanity.com/paper/2412.13036/) (2024)
- [Hellinger loss function for Generative Adversarial Networks](https://mlsanity.com/paper/2512.12267/) (2025)
- [Generative Model via Quantile Assignment](https://mlsanity.com/paper/2602.18216/) (2026)
- [Generative Adversarial Learning from Deterministic Processes](https://mlsanity.com/paper/2605.18425/) (2026)
- [Generative Predictive Distributions for Time Series](https://mlsanity.com/paper/2606.16773/) (2026)

## 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.