Learning disconnected manifolds: a no GANs land

8 Jun 2020  ·  Ugo Tanielian, Thibaut Issenhuth, Elvis Dohmatob, Jeremie Mary ·

Typical architectures of Generative AdversarialNetworks make use of a unimodal latent distribution transformed by a continuous generator. Consequently, the modeled distribution always has connected support which is cumbersome when learning a disconnected set of manifolds. We formalize this problem by establishing a no free lunch theorem for the disconnected manifold learning stating an upper bound on the precision of the targeted distribution. This is done by building on the necessary existence of a low-quality region where the generator continuously samples data between two disconnected modes. Finally, we derive a rejection sampling method based on the norm of generators Jacobian and show its efficiency on several generators including BigGAN.

PDF Abstract
No code implementations yet. Submit your code now

Tasks


Results from the Paper


  Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers.

Methods