  Generative Adversarial Nets (GANs) represent an important milestone for
effective generative models, which has inspired numerous variants seemingly
different from each other. One of the main contributions of this paper is to
reveal a unified geometric structure in GAN and its variants. Specifically, we
show that the adversarial generative model training can be decomposed into
three geometric steps: separating hyperplane search, discriminator parameter
update away from the separating hyperplane, and the generator update along the
normal vector direction of the separating hyperplane. This geometric intuition
reveals the limitations of the existing approaches and leads us to propose a
new formulation called geometric GAN using SVM separating hyperplane that
maximizes the margin. Our theoretical analysis shows that the geometric GAN
converges to a Nash equilibrium between the discriminator and generator. In
addition, extensive numerical results show that the superior performance of
geometric GAN.
