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Polar factorization of maps on riemannian manifolds
McCann, Robert J · 2001
Earlier work this paper cites.
Optimal transport: old and new , volume 338
Villani, Cédric · 2008
Earlier work this paper cites.
Differential topology , volume 370
Guillemin, Victor and Pollack, Alan · 2010
Earlier work this paper cites.
Sample complexity of testing the manifold hypothesis
Narayanan, Hariharan and Mitter, Sanjoy · 2010
Earlier work this paper cites.
Five lectures on optimal transportation: geometry, regularity and applications
McCann, Robert J and Guillen, Nestor · 2011
Earlier work this paper cites.
Auto-encoding variational bayes
Original
Kingma, Diederik P and Welling, Max · 2013
Earlier work this paper cites.

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Then

Do gans actually learn the distribution? an empirical study
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Generalization and equilibrium in generative adversarial nets (gans)
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2017

Implicit Manifold Learning on Generative Adversarial Networks

Lui, Kry Yik Chau, Cao, Yanshuai, Gazeau, Maxime et al.

Understand

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 $\mathcal{M}_{\theta}$, perfectly match with $\mathcal{M}_{r}$, the support of the real data distribution.

We show that optimizing Jensen-Shannon divergence forces $\mathcal{M}_{\theta}$ to perfectly match with $\mathcal{M}_{r}$, 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.

Built on

Polar factorization of maps on riemannian manifolds
McCann, Robert J · 2001
Earlier work this paper cites.
Optimal transport: old and new , volume 338
Villani, Cédric · 2008
Earlier work this paper cites.
Differential topology , volume 370
Guillemin, Victor and Pollack, Alan · 2010
Earlier work this paper cites.
Sample complexity of testing the manifold hypothesis
Narayanan, Hariharan and Mitter, Sanjoy · 2010
Earlier work this paper cites.
Five lectures on optimal transportation: geometry, regularity and applications
McCann, Robert J and Guillen, Nestor · 2011
Earlier work this paper cites.
Auto-encoding variational bayes
Original
Kingma, Diederik P and Welling, Max · 2013
Earlier work this paper cites.

Similar

Generative adversarial nets
Goodfellow, Ian, Pouget-Abadie, Jean, Mirza, Mehdi, Xu, Bing, Warde-Farley, David, Ozair, Sherjil, Courville, Aaron, and Bengio, Yoshua · 2014
Cited alongside, same era.
Unsupervised representation learning with deep convolutional generative adversarial networks
Original
Radford, Alec, Metz, Luke, and Chintala, Soumith · 2015
Cited alongside, same era.
Nips 2016 tutorial: Generative adversarial networks
Original
Goodfellow, Ian · 2016
Cited alongside, same era.
f-gan: Training generative neural samplers using variational divergence minimization
Original
Nowozin, Sebastian, Cseke, Botond, and Tomioka, Ryota · 2016
Cited alongside, same era.
Towards principled methods for training generative adversarial networks
Arjovsky, Martin and Bottou, Léon · 2017
Cited alongside, same era.