# Wasserstein GAN Can Perform PCA

arXiv: https://arxiv.org/abs/1902.09073 · HTML: https://mlsanity.com/paper/1902.09073/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Feb 2019.

## Built on by (most cited first, 4 of 4)

- [Neural networks trained with SGD learn distributions of increasing complexity](https://mlsanity.com/paper/2211.11567/) (2022)
- [Wasserstein GANs Work Because They Fail (to Approximate the Wasserstein Distance)](https://mlsanity.com/paper/2103.01678/) (2021)
- [WGAN with an Infinitely Wide Generator Has No Spurious Stationary Points](https://mlsanity.com/paper/2102.07541/) (2021)
- [On the Optimization Landscape of Maximum Mean Discrepancy](https://mlsanity.com/paper/2110.13452/) (2021)

## Abstract (arXiv)

Generative Adversarial Networks (GANs) have become a powerful framework to learn generative models that arise across a wide variety of domains. While there has been a recent surge in the development of numerous GAN architectures with distinct optimization metrics, we are still lacking in our understanding on how far away such GANs are from optimality. In this paper, we make progress on a theoretical understanding of the GANs under a simple linear-generator Gaussian-data setting where the optimal maximum-likelihood generator is known to perform Principal Component Analysis (PCA). We find that the original GAN by Goodfellow et. al. fails to recover the optimal PCA solution. On the other hand, we show that Wasserstein GAN can approach the PCA solution in the limit of sample size, and hence it may serve as a basis for an optimal GAN architecture that yields the optimal generator for a wide range of data settings.