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Generative adversarial networks, or GANs, commonly display unstable behavior during training.
Über die zusammenziehende und Lipschitzsche Transformationen
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Edward James McShane · 1934
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Hassler Whitney · 1934
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The Principles of Mathematical Analysis
Walter Rudin · 1964
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J-B Hiriart-Urruty · 1980
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The operation of infimal convolution
Thomas Strömberg · 1996
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Integral probability metrics and their generating classes of functions
Alfred Müller · 1997
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Variational Analysis , volume 317 of Grundlehren der mathematischen Wissenschaften
R. T. Rockafeller and R. J-B Wets · 1998
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Nonlinear Programming
Dimitri P. Bertsekas · 1999
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Convex optimization
Stephen Boyd and Lieven Vandenberghe · 2004
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Gradient Flows in Metric Spaces and in the Space of Probability Measures
Luigi Ambrosio, Nicola Gigli, and Giuseppe Savaré · 2008
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Kernel choice and classifiability for rkhs embeddings of probability distributions
Bharath K Sriperumbudur, Kenji Fukumizu, Arthur Gretton, Gert R Lanckriet, and Bernhard Schölkopf · 2009
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Optimal Transport: Old and New
Cédrik Villani · 2009
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Convex Analysis and Monotone Operator Theory in Hilbert Spaces
Heinz H. Bauschke and Patrick L. Combettes · 2011
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Reproducing kernels of generalized Sobolev spaces via a Green function approach with distributional operators
Gregory E Fasshauer and Qi Ye · 2011
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A kernel two-sample test
Arthur Gretton, Karsten M. Borgwardt, Malte J. Rasch, Bernhard Schölkopf, and Alexander Smola · 2012
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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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Convex optimization: Algorithms and complexity
Sébastien Bubeck · 2015
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Generative moment matching networks
Yujia Li, Kevin Swersky, and Rich Zemel · 2015
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Unsupervised representation learning with deep convolutional generative adversarial networks
Alec Radford, Luke Metz, and Soumith Chintala · 2015
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Fast and accurate deep network learning by exponential linear units (ELUs)
Djork-Arné Clevert, Thomas Unterthiner, and Sepp Hochreiter · 2016
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f-GAN: Training generative neural samplers using variational divergence minimization
Geometrical insights for implicit generative modeling
Leon Bottou, Martin Arjovsky, David Lopez-Paz, and Maxime Oquab · 2018
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A convex duality framework for GANs
Farzan Farnia and David Tse · 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 Goodfellow · 2018
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An online learning approach to generative adversarial networks
Paulina Grnarova, Kfir Y Levy, Aurelien Lucchi, Thomas Hofmann, and Andreas Krause · 2018
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Progressive growing of GANs for improved quality, stability, and variation
Tero Karras, Timo Aila, Samuli Laine, and Jaakko Lehtinen · 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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Sebastian Nowozin, Botond Cseke, and Ryota Tomioka · 2016
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Towards principled methods for training generative adversarial networks
Martin Arjovsky and Leon Bottou · 2017
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Wasserstein generative adversarial networks
Martin Arjovsky, Soumith Chintala, and Léon Bottou · 2017
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Improved training of Wasserstein GANs
Ishaan Gulrajani, Faruk Ahmed, Martin Arjovsky, Vincent Dumoulin, and Aaron C Courville · 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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On convergence and stability of GANs
Naveen Kodali, Jacob Abernethy, James Hays, and Zsolt Kira · 2017
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Approximation and convergence properties of generative adversarial learning
Shuang Liu, Olivier Bousquet, and Kamalika Chaudhuri · 2017
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Spectral normalization for generative adversarial networks
Takeru Miyato, Toshiki Kataoka, Masanori Koyama, and Yuichi Yoshida · 2018
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Reproducing kernels of Sobolev spaces on ℝ d \mathbb{R}^{d} and applications to embedding constants and tractability
Erich Novak, Mario Ullrich, Henryk Woźniakowski, and Shun Zhang · 2018
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Beyond local Nash equilibria for adversarial networks
Frans A Oliehoek, Rahul Savani, Jose Gallego, Elise van der Pol, and Roderich Groß · 2018
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On the convergence and robustness of training GANs with regularized optimal transport
Maziar Sanjabi, Jimmy Ba, Meisam Razaviyayn, and Jason D Lee · 2018
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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 Fenchel duality between strong convexity and Lipschitz continuous gradient
Xingyu Zhou · 2018
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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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Probability functional descent: A unifying perspective on GANs, variational inference, and reinforcement learning
Casey Chu, Jose Blanchet, and Peter Glynn · 2019
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How to combine WGAN and spectral norm?
Takeru Miyato · 2019
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