Geometric GAN
This provides a foundational insight for researchers in generative models, though it is incremental as it builds on existing GAN variants.
The paper tackled the problem of unifying and improving Generative Adversarial Nets (GANs) by revealing a geometric structure in their training, proposing a new formulation called geometric GAN that maximizes the margin using SVM, and showing it converges to a Nash equilibrium with superior performance in numerical results.
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.