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The mathematical forces at work behind Generative Adversarial Networks raise challenging theoretical issues.
On a space of completely additive functions
L.V. Kantorovich and G.S. Rubinstein · 1958
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Strong limit theorems for maximal spacings from a general univariate distribution
P. Deheuvels · 1984
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On the influence of the extremes of an i.i.d. sequence on the maximal spacings
P. Deheuvels · 1986
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Growth rates of Euclidean minimal spanning trees with power weighted edges
J.M. Steele · 1988
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Integral probability metrics and their generating classes of functions
A. Müller · 1997
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Minkowski-type theorems and least-squares clustering
F. Aurenhammer, F. Hoffmann, and B. Aronov · 1998
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Asymptotics for weighted minimal spanning trees on random points
J.E. Yukich · 2000
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On the equality between Monge’s infimum and Kantorovich’s minimum in optimal mass transportation
A. Pratelli · 2007
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Optimal Transport: Old and New
C. Villani · 2008
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A user’s guide to optimal transport
L. Ambrosio and N. Gigli · 2013
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Optimally solving a transportation problem using Voronoi diagrams
D. Geiß, R. Klein, R. Penninger, and G. Rote · 2013
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Generative adversarial nets
I.J. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio · 2014
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Measure Theory and Fine Properties of Functions
L.C. Evans and R.F. Gariepy · 2015
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On the rate of convergence in Wasserstein distance of the empirical measure
N. Fournier and A. Guillin · 2015
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Optimal Transport for Applied Mathematicians
F. Santambrogio · 2015
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Testing the manifold hypothesis
C. Fefferman, S. Mitter, and H. Narayanan · 2016
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Unsupervised representation learning with deep convolutional generative adversarial networks
A. Radford, L. Metz, and S. Chintala · 2016
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Generating videos with scene dynamics
C. Vondrick, H. Pirsiavash, and A. Torralba · 2016
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Wasserstein generative adversarial networks
M. Arjovsky, S. Chintala, and L. Bottou · 2017
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Estimating the intrinsic dimension of datasets by a minimal neighborhood information
E. Facco, M. d’Errico, A. Rodriguez, and A. Laio · 2017
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Pros and cons of GAN evaluation measures
A. Borji · 2019
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Towards GAN benchmarks which require generalization
I. Gulrajani, C. Raffel, and L. Metz · 2019
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A style-based generator architecture for generative adversarial networks
T. Karras, S. Laine, and T. Aila · 2019
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Nonparametric density estimation and convergence rates for GANs under Besov IPM losses
A. Uppal, S. Singh, and B. Poczos · 2019
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Lipschitz generative adversarial nets
Z. Zhou, J. Liang, Y. Song, L. Yu, H. Wang, W. Zhang, Y. Yu, and Z. Zhang · 2019
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Semi-discrete optimal transport: A solution procedure for the unsquared Euclidean distance case
V. Hartmann and D. Schuhmacher · 2020
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Improved training of Wasserstein GANs
I. Gulrajani, F. Ahmed, M. Arjovsky, V. Dumoulin, and A.C. Courville · 2017
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On convergence and stability of GANs
N. Kodali, J. Abernethy, J. Hays, and Z. Kira · 2017
Cited alongside, same era.
SeqGAN: Sequence generative adversarial nets with policy gradient
L. Yu, W. Zhang, J. Wang, and Y. Yu · 2017
Cited alongside, same era.
Progressive growing of GANs for improved quality, stability, and variation
T. Karras, T. Aila, S. Laine, and J. Lehtinen · 2018
Cited alongside, same era.
Are GANs created equal? A large-scale study
M. Lucic, K. Kurach, M. Michalski, S. Gelly, and O. Bousquet · 2018
Cited alongside, same era.
Which training methods for GANs do actually converge?
L. Mescheder, A. Geiger, and S. Nowozin · 2018
Cited alongside, same era.
Generalization properties of optimal transport GANs with latent distribution learning
G. Luise, M. Pontil, and C. Ciliberto · 2020
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Learning disconnected manifolds: A no GAN’s land
U. Tanielian, T. Issenhuth, E. Dohmatob, and J. Mary · 2020
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Some theoretical insights into Wasserstein GANs
G. Biau, M. Sangnier, and U. Tanielian · 2021
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How well generative adversarial networks learn distributions
T. Liang · 2021
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Statistical guarantees for generative models without domination
N. Schreuder, V.-E. Brunel, and A. Dalalyan · 2021
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Reversible Gromov-Monge sampler for simulation-based inference
H. YoonHaeng, W. Guo, and T. Liang · 2021
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Supplement to “Optimal 1 1 -Wasserstein distance for WGANs”
A. Stéphanovitch, U. Tanielian, B. Cadre, N. Klutchnikoff, and G. Biau · 2023
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