Learning disconnected manifolds: a no GANs land

• URL: http://arxiv.org/abs/2006.04596v3
• Date: Thu, 10 Dec 2020 12:46:25 GMT
• Title: Learning disconnected manifolds: a no GANs land
• Authors: Ugo Tanielian, Thibaut Issenhuth, Elvis Dohmatob, Jeremie Mary
• Abstract summary: Generative AdversarialNetworks make use of a unimodal latent distribution transformed by a continuous generator. We establish a no free lunch theorem for the disconnected manifold learning stating an upper bound on the precision of the targeted distribution. We derive a rejection sampling method based on the norm of generators Jacobian and show its efficiency on several generators including BigGAN.
• Score: 15.4867805276559
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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