Learning disconnected manifolds: a no GAN’s land
Ugo Tanielian, Thibaut Issenhuth, Elvis Dohmatob, Jeremie Mary
Abstract
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.
BibTeX
@InProceedings{pmlr-v119-tanielian20a,
title = {Learning disconnected manifolds: a no {GAN}’s land},
author = {Tanielian, Ugo and Issenhuth, Thibaut and Dohmatob, Elvis and Mary, Jeremie},
booktitle = {Proceedings of the 37th International Conference on Machine Learning},
pages = {9418--9427},
year = {2020},
editor = {III, Hal Daumé and Singh, Aarti},
volume = {119},
series = {Proceedings of Machine Learning Research},
month = {13--18 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v119/tanielian20a/tanielian20a.pdf},
url = {https://proceedings.mlr.press/v119/tanielian20a.html},
abstract = {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.}
}