May 21, 2018
In our recent paper, we present a simple GAN model fed by high-dimensional input data. The dynamics of the training process of the proposed model can be exactly analyzed in the high-dimensional limit. In particular, by using the tool of scaling limits of stochastic processes, we show that the macroscopic quantities measuring the quality of the training process converge to a deterministic process that is characterized as the unique solution of a finite-dimensional ordinary differential equation (ODE). The proposed model is simple, but its training process already exhibits several different phases that can mimic the behaviors of more realistic GAN models used in practice. Specifically, depending on the choice of the learning rates, the training process can reach either a successful, a failed, or an oscillating phase. By studying the steady-state solutions of the limiting ODEs, we obtain a phase diagram that precisely characterizes the conditions under which each phase takes place.