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With the discovery of Wasserstein GANs, Optimal Transport (OT) has become a powerful tool for large-scale generative modeling tasks.
On a problem of monge
Leonid Vitalevich Kantorovich · 1948
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Integral functionals, normal integrands and measurable selections
R Tyrrell Rockafellar · 1976
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The fréchet distance between multivariate normal distributions
DC Dowson and BV Landau · 1982
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Polar factorization and monotone rearrangement of vector-valued functions
Yann Brenier · 1991
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Gradient-based learning applied to document recognition
Yann LeCun, Léon Bottou, Yoshua Bengio, and Patrick Haffner · 1998
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Optimal transport: old and new , volume 338
Cédric Villani · 2008
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Learning multiple layers of features from tiny images
Alex Krizhevsky, Geoffrey Hinton, et al · 2009
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Regularity of optimal transportation between spaces with different dimensions
Brendan Pass · 2010
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Auto-encoding variational bayes
Diederik P Kingma and Max Welling · 2013
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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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Adam: A method for stochastic optimization
Diederik P Kingma and Jimmy Ba · 2014
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Deep learning face attributes in the wild
Ziwei Liu, Ping Luo, Xiaogang Wang, and Xiaoou Tang · 2015
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Optimal transport for applied mathematicians
Filippo Santambrogio · 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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Improved techniques for training gans
Tim Salimans, Ian Goodfellow, Wojciech Zaremba, Vicki Cheung, Alec Radford, and Xi Chen · 2016
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Rethinking the inception architecture for computer vision
Christian Szegedy, Vincent Vanhoucke, Sergey Ioffe, Jon Shlens, and Zbigniew Wojna · 2016
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Input convex neural networks
Brandon Amos, Lei Xu, and J Zico Kolter · 2017
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Towards principled methods for training generative adversarial networks
Martin Arjovsky and Léon Bottou · 2017
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Wasserstein generative adversarial networks
Martin Arjovsky, Soumith Chintala, and Léon Bottou · 2017
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Began: Boundary equilibrium generative adversarial networks
David Berthelot, Thomas Schumm, and Luke Metz · 2017
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Improved training of wasserstein gans
Ishaan Gulrajani, Faruk Ahmed, Martin Arjovsky, Vincent Dumoulin, and Aaron Courville · 2017
Cited alongside, same era.
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
Cited alongside, same era.
On convergence and stability of gans
Naveen Kodali, Jacob Abernethy, James Hays, and Zsolt Kira · 2017
Cited alongside, same era.
Least squares generative adversarial networks
Xudong Mao, Qing Li, Haoran Xie, Raymond YK Lau, Zhen Wang, and Stephen Paul Smolley · 2017
Cited alongside, same era.
Ilya Tolstikhin, Olivier Bousquet, Sylvain Gelly, and Bernhard Schoelkopf · 2017
Cited alongside, same era.
A geometric view of optimal transportation and generative model
Na Lei, Kehua Su, Li Cui, Shing-Tung Yau, and Xianfeng David Gu · 2019
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Wasserstein gan with quadratic transport cost
Huidong Liu, Xianfeng Gu, and Dimitris Samaras · 2019
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Guiding the one-to-one mapping in cyclegan via optimal transport
Guansong Lu, Zhiming Zhou, Yuxuan Song, Kan Ren, and Yong Yu · 2019
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(q, p)-wasserstein gans: Comparing ground metrics for wasserstein gans
Anton Mallasto, Jes Frellsen, Wouter Boomsma, and Aasa Feragen · 2019
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Threeplayer wasserstein gan via amortised duality
Quan Hoang Nhan Dam, Trung Le, Tu Dinh Nguyen, Hung Bui, and Dinh Phung · 2019
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Generative modeling by estimating gradients of the data distribution
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Jun-Yan Zhu, Taesung Park, Phillip Isola, and Alexei A Efros · 2017
Cited alongside, same era.
Generative modeling using the sliced wasserstein distance
Ishan Deshpande, Ziyu Zhang, and Alexander G Schwing · 2018
Cited alongside, same era.
Learning generative models with sinkhorn divergences
Aude Genevay, Gabriel Peyré, and Marco Cuturi · 2018
Cited alongside, same era.
W2gan: Recovering an optimal transport map with a gan
Leygonie Jacob, Jennifer She, Amjad Almahairi, Sai Rajeswar, and Aaron Courville · 2018
Cited alongside, same era.
Spectral normalization for generative adversarial networks
Takeru Miyato, Toshiki Kataoka, Masanori Koyama, and Yuichi Yoshida · 2018
Cited alongside, same era.
Autoregressive quantile networks for generative modeling
Georg Ostrovski, Will Dabney, and Rémi Munos · 2018
Cited alongside, same era.
On the regularization of wasserstein gans
Henning Petzka, Asja Fischer, and Denis Lukovnikov · 2018
Cited alongside, same era.
Yang Song and Stefano Ermon · 2019
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Amirhossein Taghvaei and Amin Jalali · 2019
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On scalable and efficient computation of large scale optimal transport
Yujia Xie, Minshuo Chen, Haoming Jiang, Tuo Zhao, and Hongyuan Zha · 2019
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Large-scale optimal transport via adversarial training with cycle-consistency
Guansong Lu, Zhiming Zhou, Jian Shen, Cheng Chen, Weinan Zhang, and Yong Yu · 2020
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Optimal transport mapping via input convex neural networks
Ashok Makkuva, Amirhossein Taghvaei, Sewoong Oh, and Jason Lee · 2020
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Optimal transportation between unequal dimensions
Robert J McCann and Brendan Pass · 2020
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Sinkhorn autoencoders
Giorgio Patrini, Rianne van den Berg, Patrick Forre, Marcello Carioni, Samarth Bhargav, Max Welling, Tim Genewein, and Frank Nielsen · 2020
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Nvae: A deep hierarchical variational autoencoder
Arash Vahdat and Jan Kautz · 2020
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Ncp-vae: Variational autoencoders with noise contrastive priors
Jyoti Aneja, Alexander Schwing, Jan Kautz, and Arash Vahdat · 2021
Closest in time.
Cyclegan through the lens of (dynamical) optimal transport
Emmanuel de Bézenac, Ibrahim Ayed, and Patrick Gallinari · 2021
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Sliced iterative normalizing flows
Biwei Dai and Uros Seljak · 2021
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Scalable computation of monge maps with general costs
Jiaojiao Fan, Shu Liu, Shaojun Ma, Yongxin Chen, and Haomin Zhou · 2021
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Local stability of wasserstein gans with abstract gradient penalty
Cheolhyeong Kim, Seungtae Park, and Hyung Ju Hwang · 2021
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Learning high dimensional wasserstein geodesics
Shu Liu, Shaojun Ma, Yongxin Chen, Hongyuan Zha, and Haomin Zhou · 2021
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Approximating lipschitz continuous functions with groupsort neural networks
Ugo Tanielian and Gerard Biau · 2021
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