# On some theoretical limitations of Generative Adversarial Networks

arXiv: https://arxiv.org/abs/2110.10915 · HTML: https://mlsanity.com/paper/2110.10915/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 16 references that are in the map.
- First posted on arXiv 21 Oct 2021.

## Builds on (most cited first, 5 of 5)

- [Adversarial vulnerability for any classifier](https://mlsanity.com/paper/1802.08686/) (2018)
- [Random Matrix Theory Proves that Deep Learning Representations of GAN-data Behave as Gaussian Mixtures](https://mlsanity.com/paper/2001.08370/) (2020)
- [Pareto GAN: Extending the Representational Power of GANs to Heavy-Tailed Distributions](https://mlsanity.com/paper/2101.09113/) (2021)
- [Copula & Marginal Flows: Disentangling the Marginal from its Joint](https://mlsanity.com/paper/1907.03361/) (2019)
- [Improved Estimation of Concentration Under ℓp-Norm Distance Metrics Using Half Spaces](https://mlsanity.com/paper/2103.12913/) (2021)

## Built on by (most cited first, 2 of 2)

- [3D GANs and Latent Space: A comprehensive survey](https://mlsanity.com/paper/2304.03932/) (2023)
- [Generalized Regression with Conditional GANs](https://mlsanity.com/paper/2404.13500/) (2024)

## Abstract (arXiv)

Generative Adversarial Networks have become a core technique in Machine Learning to generate unknown distributions from data samples. They have been used in a wide range of context without paying much attention to the possible theoretical limitations of those models. Indeed, because of the universal approximation properties of Neural Networks, it is a general assumption that GANs can generate any probability distribution. Recently, people began to question this assumption and this article is in line with this thinking. We provide a new result based on Extreme Value Theory showing that GANs can't generate heavy tailed distributions. The full proof of this result is given.