# On the Nash equilibrium of moment-matching GANs for stationary Gaussian processes

arXiv: https://arxiv.org/abs/2203.07136 · HTML: https://mlsanity.com/paper/2203.07136/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 35 references that are in the map.
- First posted on arXiv 14 Mar 2022.

## Builds on (most cited first, 21 of 21)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Generative Moment Matching Networks](https://mlsanity.com/paper/1502.02761/) (2015)
- [Generalization and Equilibrium in Generative Adversarial Nets (GANs)](https://mlsanity.com/paper/1703.00573/) (2017)
- [Training generative neural networks via Maximum Mean Discrepancy optimization](https://mlsanity.com/paper/1505.03906/) (2015)
- [The Mechanics of n-Player Differentiable Games](https://mlsanity.com/paper/1802.05642/) (2018)
- [The Numerics of GANs](https://mlsanity.com/paper/1705.10461/) (2017)
- [The Limit Points of (Optimistic) Gradient Descent in Min-Max Optimization](https://mlsanity.com/paper/1807.03907/) (2018)
- [Last-Iterate Convergence: Zero-Sum Games and Constrained Min-Max Optimization](https://mlsanity.com/paper/1807.04252/) (2018)
- [How Well Generative Adversarial Networks Learn Distributions](https://mlsanity.com/paper/1811.03179/) (2018)
- [Gradient descent GAN optimization is locally stable](https://mlsanity.com/paper/1706.04156/) (2017)
- [On Finding Local Nash Equilibria (and Only Local Nash Equilibria) in Zero-Sum Games](https://mlsanity.com/paper/1901.00838/) (2019)
- [On Solving Minimax Optimization Locally: A Follow-the-Ridge Approach](https://mlsanity.com/paper/1910.07512/) (2019)
- [Approximation and Convergence Properties of Generative Adversarial Learning](https://mlsanity.com/paper/1705.08991/) (2017)
- [Approximability of Discriminators Implies Diversity in GANs](https://mlsanity.com/paper/1806.10586/) (2018)
- [A Closer Look at the Optimization Landscapes of Generative Adversarial Networks](https://mlsanity.com/paper/1906.04848/) (2019)
- [Training Generative Adversarial Networks by Solving Ordinary Differential Equations](https://mlsanity.com/paper/2010.15040/) (2020)
- [Towards a Better Global Loss Landscape of GANs](https://mlsanity.com/paper/2011.04926/) (2020)
- [SGD Learns One-Layer Networks in WGANs](https://mlsanity.com/paper/1910.07030/) (2019)
- [Maximum Entropy Models from Phase Harmonic Covariances](https://mlsanity.com/paper/1911.10017/) (2019)
- [Gradient Descent-Ascent Provably Converges to Strict Local Minmax Equilibria with a Finite Timescale Separation](https://mlsanity.com/paper/2009.14820/) (2020)

## Abstract (arXiv)

Generative Adversarial Networks (GANs) learn an implicit generative model from data samples through a two-player game. In this paper, we study the existence of Nash equilibrium of the game which is consistent as the number of data samples grows to infinity. In a realizable setting where the goal is to estimate the ground-truth generator of a stationary Gaussian process, we show that the existence of consistent Nash equilibrium depends crucially on the choice of the discriminator family. The discriminator defined from second-order statistical moments can result in non-existence of Nash equilibrium, existence of consistent non-Nash equilibrium, or existence and uniqueness of consistent Nash equilibrium, depending on whether symmetry properties of the generator family are respected. We further study empirically the local stability and global convergence of gradient descent-ascent methods towards consistent equilibrium.