A Game of Snakes and Gans

Generative adversarial networks (GANs) comprise generator and discriminator networks trained adversarially to learn the underlying distribution of a dataset. Recently, we have shown that the optimal GAN discriminator can be obtained in closed-form as the solution to the Poisson partial differential equation (PDE). While existing approaches either train a network or solve the PDE in closed-form, we propose training the generator through the gradient field of the optimal discriminator. In this paper, we establish a connection between active contour models (snakes) and GANs. We evolve a set of snake points over the gradient field of radial basis function (RBF) Coulomb GAN. The generator is then trained to follow the trajectory of the snake. The proposed approach benefits from both the sample diversity seen in flow-based approaches and the fast sampling capability of GANs. Experimental validation on 2-D synthetic data shows that the proposed approach leads to accelerated convergence, compared against the baseline approaches that either employ network or kernel-based discriminators.