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An invertible function is bi-Lipschitz if both the function and its inverse have bounded Lipschitz constants.
Lipschitz Certificates for Layered Network Structures Driven by Averaged Activation Operators
Patrick L. Combettes and Jean-Christophe Pesquet · 1903
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A RAD approach to deep mixture models
Laurent Dinh, Jascha Sohl-Dickstein, Hugo Larochelle, and Razvan Pascanu · 1903
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Improved Precision and Recall Metric for Assessing Generative Models
Tuomas Kynkäänniemi, Tero Karras, Samuli Laine, Jaakko Lehtinen, and Timo Aila · 1904
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Residual Flows for Invertible Generative Modeling
Ricky T. Q. Chen, Jens Behrmann, David Duvenaud, and Jörn-Henrik Jacobsen · 1906
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Approximation Capabilities of Neural ODEs and Invertible Residual Networks
Han Zhang, Xi Gao, Jacob Unterman, and Tom Arodz · 1907
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Relaxing Bijectivity Constraints with Continuously Indexed Normalising Flows
Rob Cornish, Anthony L. Caterini, George Deligiannidis, and Arnaud Doucet · 1909
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Semi-Supervised Learning with Normalizing Flows
Pavel Izmailov, Polina Kirichenko, Marc Finzi, and Andrew Gordon Wilson · 1912
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Geometric measure theory
Herbert Federer · 1969
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The reverse isoperimetric problem for Gaussian measure
Keith Ball · 1993
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On Lipschitz Regularization of Convolutional Layers using Toeplitz Matrix Theory
Alexandre Araujo, Benjamin Negrevergne, Yann Chevaleyre, and Jamal Atif · 2006
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Learning disconnected manifolds: a no GANs land
Ugo Tanielian, Thibaut Issenhuth, Elvis Dohmatob, and Jeremie Mary · 2006
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Learning multiple layers of features from tiny images
Alex Krizhevsky · 2009
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Variational Mixture of Normalizing Flows
Guilherme G. P. Freitas Pires and Mário A. T. Figueiredo · 2009
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MNIST handwritten digit database
Yann LeCun, Corinna Cortes, and CJ Burges · 2010
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Generative Adversarial Networks
Ian J. Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio · 2014
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Intriguing properties of neural networks
Christian Szegedy, Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Erhan, Ian Goodfellow, and Rob Fergus · 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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Assessing Generative Models via Precision and Recall
Mehdi S. M. Sajjadi, Olivier Bachem, Mario Lucic, Olivier Bousquet, and Sylvain Gelly · 2018
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Invertible Residual Networks
Jens Behrmann, Will Grathwohl, Ricky T. Q. Chen, David Duvenaud, and Jörn-Henrik Jacobsen · 2019
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Disconnected Manifold Learning for Generative Adversarial Networks
Mahyar Khayatkhoei, Ahmed Elgammal, and Maneesh Singh · 2019
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Lipschitz regularity of deep neural networks: analysis and efficient estimation
Kevin Scaman and Aladin Virmaux · 2019
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The Expressive Power of a Class of Normalizing Flow Models
Zhifeng Kong and Kamalika Chaudhuri · 2020
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Martin Arjovsky, Soumith Chintala, and Léon Bottou · 2017
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Spectrally-normalized margin bounds for neural networks
Peter Bartlett, Dylan J. Foster, and Matus Telgarsky · 2017
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Generalizable Adversarial Training via Spectral Normalization
Farzan Farnia, Jesse Zhang, and David Tse · 2018
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Glow: Generative Flow with Invertible 1x1 Convolutions
Durk P. Kingma and Prafulla Dhariwal · 2018
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Empirical measures: regularity is a counter-curse to dimensionality
Benoît Kloeckner · 2018
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Spectral Normalization for Generative Adversarial Networks
Takeru Miyato, Toshiki Kataoka, Masanori Koyama, and Yuichi Yoshida · 2018
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Exact lower and upper bounds on the incomplete gamma function
Iosif Pinelis · 2020
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Coupling-based Invertible Neural Networks Are Universal Diffeomorphism Approximators
Takeshi Teshima, Isao Ishikawa, Koichi Tojo, Kenta Oono, Masahiro Ikeda, and Masashi Sugiyama · 2020
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Understanding and Mitigating Exploding Inverses in Invertible Neural Networks
Jens Behrmann, Paul Vicol, Kuan-Chieh Wang, Roger Grosse, and Joern-Henrik Jacobsen · 2021
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The Many Faces of 1-Lipschitz Neural Networks
Louis Béthune, Alberto González-Sanz, Franck Mamalet, and Mathieu Serrurier · 2021
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Representational aspects of depth and conditioning in normalizing flows
Frederic Koehler, Viraj Mehta, and Andrej Risteski · 2021
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Universal Approximation of Residual Flows in Maximum Mean Discrepancy
Zhifeng Kong and Kamalika Chaudhuri · 2021
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