  In this paper, we show that Generative Adversarial Networks (GANs) suffer
from catastrophic forgetting even when they are trained to approximate a single
target distribution. We show that GAN training is a continual learning problem
in which the sequence of changing model distributions is the sequence of tasks
to the discriminator. The level of mismatch between tasks in the sequence
determines the level of forgetting. Catastrophic forgetting is interrelated to
mode collapse and can make the training of GANs non-convergent. We investigate
the landscape of the discriminator's output in different variants of GANs and
find that when a GAN converges to a good equilibrium, real training datapoints
are wide local maxima of the discriminator. We empirically show the
relationship between the sharpness of local maxima and mode collapse and
generalization in GANs. We show how catastrophic forgetting prevents the
discriminator from making real datapoints local maxima, and thus causes
non-convergence. Finally, we study methods for preventing catastrophic
forgetting in GANs.
