Implicit Manifold Learning on Generative Adversarial Networks
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This paper raises an implicit manifold learning perspective in Generative Adversarial Networks (GANs), by studying how the support of the learned distribution, modelled as a submanifold M_θ, perfectly match with M_r, the support of the real data distribution. We show that optimizing Jensen-Shannon divergence forces M_θ to perfectly match with M_r, while optimizing Wasserstein distance does not. On the other hand, by comparing the gradients of the Jensen-Shannon divergence and the Wasserstein distances (W_1 and W_2^2) in their primal forms, we conjecture that Wasserstein W_2^2 may enjoy desirable properties such as reduced mode collapse. It is therefore interesting to design new distances that inherit the best from both distances.
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