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Learning disconnected manifolds: no GAN's land

Ugo Tanielian
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Thibaut Issenhuth
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Elvis Dohmatob
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Jérémie Mary


Typical architectures of Generative Adversarial Networks make use of a unimodal latent/input 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 generator's Jacobian and show its efficiency on several generators including BigGAN.
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hal-02778441 , version 1 (05-06-2020)



Ugo Tanielian, Thibaut Issenhuth, Elvis Dohmatob, Jérémie Mary. Learning disconnected manifolds: no GAN's land. International Conference on Machine Learning 2020, Jul 2020, Vienna, Austria. ⟨hal-02778441⟩
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