Abstract. The classic Generative Adversarial Net and its variants can
be roughly categorized into two large families: the unregularized versus regularized GANs. By relaxing the non-parametric assumption on
the discriminator in the classic GAN, the regularized GANs have better
generalization ability to produce new samples drawn from the real distribution. It is well known that the real data like natural images are not
uniformly distributed over the whole data space. Instead, they are often
restricted to a low-dimensional manifold of the ambient space. Such a
manifold assumption suggests the distance over the manifold should be
a better measure to characterize the distinct between real and fake samples. Thus, we define a pullback operator to map samples back to their
data manifold, and a manifold margin is defined as the distance between
the pullback representations to distinguish between real and fake samples and learn the optimal generators. We justify the effectiveness of the
proposed model both theoretically and empirically