# On optimal solutions of classical and sliced Wasserstein GANs with non-Gaussian data

arXiv: https://arxiv.org/abs/2509.06505 · HTML: https://mlsanity.com/paper/2509.06505/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 35 references that are in the map.
- First posted on arXiv 8 Sep 2025.

## Builds on (most cited first, 13 of 13)

- [Wasserstein GAN](https://mlsanity.com/paper/1701.07875/) (2017)
- [Generalized Sliced Wasserstein Distances](https://mlsanity.com/paper/1902.00434/) (2019)
- [Generative Modeling using the Sliced Wasserstein Distance](https://mlsanity.com/paper/1803.11188/) (2018)
- [On the Convergence and Robustness of Training GANs with Regularized Optimal Transport](https://mlsanity.com/paper/1802.08249/) (2018)
- [Fast Approximation of the Sliced-Wasserstein Distance Using Concentration of Random Projections](https://mlsanity.com/paper/2106.15427/) (2021)
- [An Aggregation-Free Federated Learning for Tackling Data Heterogeneity](https://mlsanity.com/paper/2404.18962/) (2024)
- [A gradual, semi-discrete approach to generative network training via explicit Wasserstein minimization](https://mlsanity.com/paper/1906.03471/) (2019)
- [Semi-Discrete Optimal Transport: Hardness, Regularization and Numerical Solution](https://mlsanity.com/paper/2103.06263/) (2021)
- [Size-Noise Tradeoffs in Generative Networks](https://mlsanity.com/paper/1810.11158/) (2018)
- [Understanding Entropic Regularization in GANs](https://mlsanity.com/paper/2111.01387/) (2021)
- [GANs as Gradient Flows that Converge](https://mlsanity.com/paper/2205.02910/) (2022)
- [Over-the-Air Design of GAN Training for mmWave MIMO Channel Estimation](https://mlsanity.com/paper/2205.12445/) (2022)
- [Generative Modeling by Minimizing the Wasserstein-2 Loss](https://mlsanity.com/paper/2406.13619/) (2024)

## Abstract (arXiv)

The generative adversarial network (GAN) aims to approximate an unknown distribution via a parameterized neural network (NN). While GANs have been widely applied in reinforcement and semi-supervised learning as well as computer vision tasks, selecting their parameters often needs an exhaustive search, and only a few selection methods have been proven to be theoretically optimal. One of the most promising GAN variants is the Wasserstein GAN (WGAN). Prior work on optimal parameters for population WGAN is limited to the linear-quadratic-Gaussian (LQG) setting, where the generator NN is linear, and the data is Gaussian. In this paper, we focus on the characterization of optimal solutions of population WGAN beyond the LQG setting. As a basic result, closed-form optimal parameters for one-dimensional WGAN are derived when the NN has non-linear activation functions, and the data is non-Gaussian. For high-dimensional data, we adopt the sliced Wasserstein framework and show that the linear generator can be asymptotically optimal. Moreover, the original sliced WGAN only constrains the projected data marginal instead of the whole one in classical WGAN, and thus, we propose another new unprojected sliced WGAN and identify its asymptotic optimality. Empirical studies show that compared to the celebrated r-principal component analysis (r-PCA) solution, which has cubic complexity to the data dimension, our generator for sliced WGAN can achieve better performance with only linear complexity.