The following is the abstract for the research paper titled Improved Training of Wasserstein GANs
Generative Adversarial Networks (GANs) are powerful generative models, but suffer from training instability. The recently proposed Wasserstein GAN (WGAN) makes progress toward stable training of GANs, but sometimes can still generate only poor samples or fail to converge. We find that these problems are often due to the use of weight clipping in WGAN to enforce a Lipschitz constraint on the critic, which can lead to undesired behavior. We propose an alternative to clipping weights: penalize the norm of gradient of the critic with respect to its input. Our proposed method performs better than standard WGAN and enables stable training of a wide variety of GAN architectures with almost no hyperparameter tuning, including 101-layer ResNets and language models with continuous generators. We also achieve high quality generations on CIFAR-10 and LSUN bedrooms.
Here, the critic stands for discriminator of the GAN. I understood that the discriminator must obey Lipschitz constraint and hence weight clipping is generally done before this paper. The paper provides an alternative way, penalizing the norm of the gradient of the critic with respect to its input, to enforce the desired Lipschitz constraint.
What actually is Lipschitz constraint and why is it mandatory for a discriminator to obey it?