BrGANs: Stabilizing GANs' Training Process with Brownian Motion Control

The training process of generative adversarial networks (GANs) is unstable and does not converge globally. In this paper, we propose a universal higher order noise based control called Brownian Motion Control (BMC) that is invariant to GANs frameworks so that the training process of GANs is exponential stable almost surely. Specifically, starting with the prototypical case of Dirac-GANs, we design a BMC and propose Dirac-BrGANs that retrieve exactly the same but reachable optimal equilibrium regardless of GANs' framework. The optimal equilibrium of our Dirac-BrGANs' training system is globally unique and always exists. Furthermore, the training process of Dirac-BrGANs achieve exponentially stability almost surely for any arbitrary initial value. Then we extend our BMC to normal GANs' settings and propose BrGANs. We provide numerical experiments showing that our BrGANs effectively stabilizes GANs's training process and obtains state-of-the art performance compared to other stabilizing methods.