  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.
