Geometric GAN

TL;DR

This paper uncovers a unified geometric perspective of GANs, introduces a new geometric GAN model based on SVM hyperplanes, and demonstrates its theoretical convergence and superior performance.

Contribution

It reveals the geometric structure underlying GANs, proposes a novel geometric GAN formulation using SVM, and provides theoretical and empirical validation.

Findings

Geometric structure unifies GAN variants

Geometric GAN converges to Nash equilibrium

Geometric GAN outperforms existing models

Abstract

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.