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Within a broad class of generative adversarial networks, we show that discriminator optimization process increases a lower bound of the dual cost function for the Wasserstein distance between the target distribution $p$ and the generator distribution $p_G$.
The geometry of optimal transportation
Wilfrid Gangbo and Robert J McCann · 1996
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Constructing optimal maps for monge’s transport problem as a limit of strictly convex costs
Luis Caffarelli, Mikhail Feldman, and Robert McCann · 2002
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Topics in optimal transportation
Cédric Villani · 2003
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Optimal transport: old and new
Cédric Villani · 2008
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Generative adversarial nets
Ian J. Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron C. Courville, and Yoshua Bengio · 2014
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Auto-encoding variational bayes
Diederik P. Kingma and Max Welling · 2014
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Intriguing properties of neural networks
Christian Szegedy, Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Erhan, Ian J. Goodfellow, and Rob Fergus · 2014
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Conditional generative adversarial nets
Mehdi Mirza and Simon Osindero · 2014
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Explaining and harnessing adversarial examples
Ian J. Goodfellow, Jonathon Shlens, and Christian Szegedy · 2015
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Unsupervised representation learning with deep convolutional generative adversarial networks
Alec Radford, Luke Metz, and Soumith Chintala · 2016
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f-gan: Training generative neural samplers using variational divergence minimization
Sebastian Nowozin, Botond Cseke, and Ryota Tomioka · 2016
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Energy-based generative adversarial network
Junbo Jake Zhao, Michaël Mathieu, and Yann LeCun · 2016
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Improved techniques for training gans
Tim Salimans, Ian J. Goodfellow, Wojciech Zaremba, Vicki Cheung, Alec Radford, and Xi Chen · 2016
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Martín Arjovsky, Soumith Chintala, and Léon Bottou · 2017
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Jae Hyun Lim and Jong Chul Ye · 2017
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The cramer distance as a solution to biased wasserstein gradients
Marc G. Bellemare, Ivo Danihelka, Will Dabney, Shakir Mohamed, Balaji Lakshminarayanan, Stephan Hoyer, and Rémi Munos · 2017
Cited alongside, same era.
Improved training of wasserstein gans
Ishaan Gulrajani, Faruk Ahmed, Martín Arjovsky, Vincent Dumoulin, and Aaron C. Courville · 2017
Cited alongside, same era.
Spectral normalization for generative adversarial networks
Takeru Miyato, Toshiki Kataoka, Masanori Koyama, and Yuichi Yoshida · 2018
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Many paths to equilibrium: Gans do not need to decrease a divergence at every step
William Fedus, Mihaela Rosca, Balaji Lakshminarayanan, Andrew M. Dai, Shakir Mohamed, and Ian J. Goodfellow · 2018
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Improving gans using optimal transport
Tim Salimans, Han Zhang, Alec Radford, and Dimitris N. Metaxas · 2018
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cgans with projection discriminator
Takeru Miyato and Masanori Koyama · 2018
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Self-attention generative adversarial networks
Han Zhang, Ian J. Goodfellow, Dimitris N. Metaxas, and Augustus Odena · 2019
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Discriminator rejection sampling
Samaneh Azadi, Catherine Olsson, Trevor Darrell, Ian J. Goodfellow, and Augustus Odena · 2019
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Unrolled generative adversarial networks
Luke Metz, Ben Poole, David Pfau, and Jascha Sohl-Dickstein · 2017
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Gans trained by a two time-scale update rule converge to a local nash equilibrium
Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, and Sepp Hochreiter · 2017
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Pot python optimal transport library, 2017
R’emi Flamary and Nicolas Courty · 2017
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Coulomb gans: Provably optimal nash equilibria via potential fields
Thomas Unterthiner, Bernhard Nessler, Calvin Seward, Günter Klambauer, Martin Heusel, Hubert Ramsauer, and Sepp Hochreiter · 2018
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On the regularization of wasserstein gans
Henning Petzka, Asja Fischer, and Denis Lukovnikov · 2018
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Improving the improved training of wasserstein gans: A consistency term and its dual effect
Xiang Wei, Boqing Gong, Zixia Liu, Wei Lu, and Liqiang Wang · 2018
Cited alongside, same era.
Progressive growing of gans for improved quality, stability, and variation
Tero Karras, Timo Aila, Samuli Laine, and Jaakko Lehtinen · 2018
Cited alongside, same era.
Metropolis-hastings generative adversarial networks
Ryan D. Turner, Jane Hung, Eric Frank, Yunus Saatchi, and Jason Yosinski · 2019
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Computational optimal transport
Gabriel Peyré and Marco Cuturi · 2019
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Optimal transport maps for distribution preserving operations on latent spaces of generative models
Eirikur Agustsson, Alexander Sage, Radu Timofte, and Luc Van Gool · 2019
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Large scale GAN training for high fidelity natural image synthesis
Andrew Brock, Jeff Donahue, and Karen Simonyan · 2019
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Yuxuan Song, Qiwei Ye, Minkai Xu, and Tie-Yan Liu · 2020
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