  Generative adversarial networks (GANs) are a class of machine-learning models
that use adversarial training to generate new samples with the same
(potentially very complex) statistics as the training samples. One major form
of training failure, known as mode collapse, involves the generator failing to
reproduce the full diversity of modes in the target probability distribution.
Here, we present an effective model of GAN training, which captures the
learning dynamics by replacing the generator neural network with a collection
of particles in the output space; particles are coupled by a universal kernel
valid for certain wide neural networks and high-dimensional inputs. The
generality of our simplified model allows us to study the conditions under
which mode collapse occurs. Indeed, experiments which vary the effective kernel
of the generator reveal 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.
