Effective Dynamics of Generative Adversarial Networks*

Generative adversarial networks (GANs) are a family of machine-learning models that use adversarial training to generate new samples with the same statistics as the training samples. Mode collapse is a major form of training failure in which the generator fails to reproduce the full diversity of modes in the training data. Here, we present a simplified model of GAN training dynamics, which allows us to study the conditions under which mode collapse occurs. Our effective model replaces the generator neural network with a collection of particles in the output space; particles interact with the target distribution only via the discriminator and mutually couple due to the generator. Our model GAN reveals a mode-collapse transition, the shape of which can be related to the type of discriminator through the frequency principle. Further, we find that gradient regularizers of intermediate strengths can optimally yield convergence through critical damping of the generator dynamics. Our effective GAN model thus provides an interpretable physical framework for understanding and improving adversarial training.