On the Nash equilibrium of moment-matching GANs for stationary Gaussian processes. (arXiv:2203.07136v3 [stat.ML] UPDATED)

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 …

arxiv equilibrium gans gaussian processes nash equilibrium processes