# Understanding GANs: the LQG Setting

arXiv: https://arxiv.org/abs/1710.10793 · HTML: https://mlsanity.com/paper/1710.10793/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Oct 2017.

## Built on by (most cited first, 12 of 12)

- [Understanding Overparameterization in Generative Adversarial Networks](https://mlsanity.com/paper/2104.05605/) (2021)
- [Rates of convergence for density estimation with generative adversarial networks](https://mlsanity.com/paper/2102.00199/) (2021)
- [Learning (Very) Simple Generative Models Is Hard](https://mlsanity.com/paper/2205.16003/) (2022)
- [Understanding Entropic Regularization in GANs](https://mlsanity.com/paper/2111.01387/) (2021)
- [Minimax Optimality (Probably) Doesn't Imply Distribution Learning for GANs](https://mlsanity.com/paper/2201.07206/) (2022)
- [Fine-tuning of Pre-trained End-to-end Speech Recognition with Generative Adversarial Networks](https://mlsanity.com/paper/2103.13329/) (2021)
- [Pursuit of a Discriminative Representation for Multiple Subspaces via Sequential Games](https://mlsanity.com/paper/2206.09120/) (2022)
- [Synthetic Data for Portfolios: A Throw of the Dice Will Never Abolish Chance](https://mlsanity.com/paper/2501.03993/) (2025)
- [Learning Polynomial Transformations](https://mlsanity.com/paper/2204.04209/) (2022)
- [Dissecting adaptive methods in GANs](https://mlsanity.com/paper/2210.04319/) (2022)
- [On the Optimization Landscape of Maximum Mean Discrepancy](https://mlsanity.com/paper/2110.13452/) (2021)
- [Graph-Informed Adversarial Modeling: Infimal Subadditivity of Interpolative Divergences](https://mlsanity.com/paper/2603.20025/) (2026)

## Abstract (arXiv)

Generative Adversarial Networks (GANs) have become a popular method to learn a probability model from data. In this paper, we aim to provide an understanding of some of the basic issues surrounding GANs including their formulation, generalization and stability on a simple benchmark where the data has a high-dimensional Gaussian distribution. Even in this simple benchmark, the GAN problem has not been well-understood as we observe that existing state-of-the-art GAN architectures may fail to learn a proper generative distribution owing to (1) stability issues (i.e., convergence to bad local solutions or not converging at all), (2) approximation issues (i.e., having improper global GAN optimizers caused by inappropriate GAN's loss functions), and (3) generalizability issues (i.e., requiring large number of samples for training). In this setup, we propose a GAN architecture which recovers the maximum-likelihood solution and demonstrates fast generalization. Moreover, we analyze global stability of different computational approaches for the proposed GAN optimization and highlight their pros and cons. Finally, we outline an extension of our model-based approach to design GANs in more complex setups than the considered Gaussian benchmark.