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This work builds the connection between the regularity theory of optimal transportation map, Monge-Amp\`{e}re equation and GANs, which gives a theoretic understanding of the major drawbacks of GANs: convergence difficulty and mode collapse.
Polar factorization and monotone rearrangement of vector-valued functions
Yann Brenier · 1991
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The regularity of mappings with a convex potential
Luis A Caffarelli · 1992
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The monge-kantorovitch mass transfer and its computational fluid mechanics formulation
Y. Brenier J.D. Benamou and K. Guittet · 2002
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Convex polyhedra
Aleksandr D Alexandrov · 2005
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Optimal transport: old and new
Cédric Villani · 2008
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From knothe’s rearrangement to brenier’s optimal transport map
Nicolas Bonnotte · 2013
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Sinkhorn distances: Lightspeed computation of optimal transport
Marco Cuturi · 2013
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Generative adversarial nets
Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio · 2014
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Numerical solution of the optimal transportation problem using the monge-ampère equation
Brittany D. Froese Jean-David Benamou and Adam M. Oberman · 2014
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Optimal transport with proximal splitting
Gabriel Peyré Nicolas Papadakis and Edouard Oudet · 2014
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Convolutional wasserstein distances: Efficient optimal transportation on geometric domains
Fernando de Goes Gabriel Peyré Marco Cuturi Adrian Butscher Andy Nguyen Tao Du Solomon, Justin and Leonidas Guibas · 2015
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Mode regularized generative adversarial networks
Tong Che, Yanran Li, Athul Paul Jacob, Yoshua Bengio, and Wenjie Li · 2016
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Jeff Donahue, Philipp Krähenbühl, and Trevor Darrell · 2016
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Adversarially learned inference
Vincent Dumoulin, Ishmael Belghazi, Ben Poole, Olivier Mastropietro, Alex Lamb, Martin Arjovsky, and Aaron Courville · 2016
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Nips 2016 tutorial: Generative adversarial networks
Ian Goodfellow · 2016
Cited alongside, same era.
Variational principles for minkowski type problems, discrete optimal transport, and discrete monge–ampère equations
David Xianfeng Gu, Feng Luo, jian Sun, and Shing-Tung Yau · 2016
Cited alongside, same era.
Improved training of wasserstein gans
Ishaan Gulrajani, Faruk Ahmed, Martin Arjovsky, Vincent Dumoulin, and Aaron C Courville · 2017
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Relaxed wasserstein with applications to gans
Xin Guo, Johnny Hong, Tianyi Lin, and Nan Yang · 2017
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Progressive growing of gans for improved quality, stability, and variation
Tero Karras, Timo Aila, Samuli Laine, and Jaakko Lehtinen · 2017
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A geometric view of optimal transportation and generative mode
Na Lei, Kehua Su, Li Cui, Shing-Tung Yau, and David Xianfeng Gu · 2017
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Towards understanding the dynamics of generative adversarial networks
Jerry Li, Aleksander Madry, John Peebles, and Ludwig Schmidt · 2017
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Luke Metz, Ben Poole, David Pfau, and Jascha Sohl-Dickstein · 2016
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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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Generative adversarial text to image synthesis
Scott Reed, Zeynep Akata, Xinchen Yan, Lajanugen Logeswaran, Bernt Schiele, and Honglak Lee · 2016
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Improved techniques for training gans
Tim Salimans, Ian Goodfellow, Wojciech Zaremba, Vicki Cheung, Alec Radford, and Xi Chen · 2016
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Amortised map inference for image super-resolution
Casper Kaae Sønderby, Jose Caballero, Lucas Theis, Wenzhe Shi, and Ferenc Huszár · 2016
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Wasserstein generative adversarial networks
Martin Arjovsky, Soumith Chintala, and Léon Bottou · 2017
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Generalization and equilibrium in generative adversarial nets (gans)
Sanjeev Arora, Rong Ge, Yingyu Liang, Tengyu Ma, and Yi Zhang · 2017
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Do gans actually learn the distribution? an empirical study
Sanjeev Arora and Yi Zhang · 2017
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Veegan: Reducing mode collapse in gans using implicit variational learning
Akash Srivastava, Lazar Valkov, Chris Russell, Michael U Gutmann, and Charles Sutton · 2017
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Adagan: Boosting generative models
Ilya O Tolstikhin, Sylvain Gelly, Olivier Bousquet, Carl-Johann Simon-Gabriel, and Bernhard Schölkopf · 2017
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Unpaired image-to-image translation using cycle-consistent adversarial networks
Jun-Yan Zhu, Taesung Park, Phillip Isola, and Alexei A Efros · 2017
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Pacgan: The power of two samples in generative adversarial networks
Zinan Lin, Ashish Khetan, Giulia Fanti, and Sewoong Oh · 2018
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Which training methods for gans do actually converge?
Lars Mescheder, Andreas Geiger, and Sebastian Nowozin · 2018
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Computational Optimal Transport
Gabriel Peyré and Marco Cuturi · 2018
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Optimal Transport on Discrete Domains
Justin Solomon · 2018
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