Wasserstein GAN swMATH ID: 42583 Software Authors: Martin Arjovsky, Soumith Chintala, Léon Bottou Description: WassersteinGAN, Wasserstein GAN: We introduce a new algorithm named WGAN, an alternative to traditional GAN training. In this new model, we show that we can improve the stability of learning, get rid of problems like mode collapse, and provide meaningful learning curves useful for debugging and hyperparameter searches. Furthermore, we show that the corresponding optimization problem is sound, and provide extensive theoretical work highlighting the deep Homepage: https://arxiv.org/abs/1701.07875 Source Code: https://github.com/martinarjovsky/WassersteinGAN Dependencies: Python Related Software: Adam; pix2pix; CycleGAN; TensorFlow; ImageNet; EMD; AlexNet; PyTorch; StyleGAN; GitHub; MNIST; InfoGAN; CIFAR; U-Net; BigGAN; BEGAN; MMD GAN; DGM; torchdiffeq; darch Cited in: 192 Publications all top 5 Cited by 551 Authors 7 Li, Wuchen 5 Osher, Stanley Joel 4 Karniadakis, George Em 3 Arridge, Simon R. 3 Cui, Xiaojun 3 Eckstein, Stephan 3 Maass, Peter 3 Rigollet, Philippe 3 Schönlieb, Carola-Bibiane 3 Veneroni, Marco 2 Amari, Shun-ichi 2 Auricchio, Gennaro 2 Benaim, Sagie 2 Biau, Gérard 2 Bigot, Jéremie 2 Birrell, Jeremiah 2 Chae, Minwoo 2 Chen, Yifan 2 Chen, Yongxin 2 Darve, Eric 2 Dupuis, Paul G. 2 E, Weinan 2 Galanti, Tomer 2 Gualandi, Stefano 2 Guo, Gaoyue 2 Han, Jiequn 2 Hou, Jiagen 2 Katsoulakis, Markos A. 2 Klatt, Marcel 2 Kuhn, Daniel 2 Lin, Alex Tong 2 Matsuda, Takeru 2 Montúfar, Guido F. 2 Mukerji, Tapan 2 Munk, Axel 2 Niles-Weed, Jonathan 2 Oberai, Assad A. 2 Papadakis, Nicolas 2 Patel, Dhruv V. 2 Perdikaris, Paris G. 2 Rey-Bellet, Luc 2 Sangnier, Maxime 2 Sebban, Marc 2 Song, Suihong 2 Tanielian, Ugo 2 Trevisan, Dario 2 Walker, Stephen Grahm 2 Wolf, Lior 2 Wu, Hongguang 2 Xu, Kailai 2 Yang, Yibo 2 Yin, Wotao 2 Zhang, Junyu 2 Zhang, Shuzhong 2 Zhou, Hao-Min 2 Zhu, Guomin 1 Abbasnejad, M. Ehsan 1 Alajaji, Fady 1 Alaya, M. El 1 Aldroubi, Akram 1 Alkousa, Mohammad S. 1 Ambrosio, Luigi 1 An, Wei 1 Angizi, Shaahin 1 Anirudh, Rushil 1 Arbabi, Hassan 1 Azevedo, Leonardo 1 Babu, Gutti Jogesh 1 Balakrishnan, Sivaraman 1 Bang, Duhyeon 1 Bao, Gang 1 Bao, Xuchan 1 Baraniuk, Richard G. 1 Baskerville, Nicholas P. 1 Bassetti, Federico 1 Bayraktar, Erhan 1 Benny, Yaniv 1 Benzi, Michele 1 Berar, M. 1 Bercu, Bernard 1 Berthet, Quentin 1 Bertozzi, Andrea Louise 1 Bhatia, Himesh 1 Blondé, Lionel 1 Blunt, Martin J. 1 Böhm, Axel 1 Bonneel, Nicolas 1 Bortolussi, Luca 1 Boţ, Radu Ioan 1 Burlina, Philippe 1 Cadre, Benoît 1 Cai, Xiangrui 1 Cairoli, Francesca 1 Canchumuni, Smith W. A. 1 Cang, Zixuan 1 Carbone, Ginevra 1 Castiglioni, Valentina 1 Castro, Jose D. B. 1 Cazelles, Elsa 1 Chakraborty, Saptarshi ...and 451 more Authors all top 5 Cited in 89 Serials 13 Journal of Machine Learning Research (JMLR) 9 Machine Learning 8 Journal of Computational Physics 7 International Journal of Computer Vision 7 Computational Geosciences 6 SIAM Journal on Scientific Computing 5 Computer Methods in Applied Mechanics and Engineering 5 SIAM Journal on Imaging Sciences 5 SIAM Journal on Mathematics of Data Science 4 Inverse Problems 4 The Annals of Statistics 4 Information Sciences 4 Data Mining and Knowledge Discovery 3 SIAM Journal on Optimization 3 Electronic Journal of Statistics 3 Mathematical Geosciences 2 Artificial Intelligence 2 Journal of Fluid Mechanics 2 Physics Reports 2 Applied Mathematics and Optimization 2 Statistics & Probability Letters 2 Computer Aided Geometric Design 2 Computational Mechanics 2 Neural Networks 2 Neural Computation 2 Mathematical Programming. Series A. Series B 2 Annals of Mathematics and Artificial Intelligence 2 Bernoulli 2 Quantitative Finance 2 Oberwolfach Reports 2 Communications in Computational Physics 2 Inverse Problems and Imaging 2 Journal of Computational and Graphical Statistics 2 SIAM/ASA Journal on Uncertainty Quantification 2 Research in the Mathematical Sciences 2 Information Geometry 1 Computers and Fluids 1 Journal of the Franklin Institute 1 Journal of Statistical Physics 1 Nonlinearity 1 Annals of the Institute of Statistical Mathematics 1 Archiv der Mathematik 1 BIT 1 IEEE Transactions on Computers 1 Journal of Applied Probability 1 Journal of Differential Equations 1 Journal of Optimization Theory and Applications 1 Numerische Mathematik 1 Quarterly of Applied Mathematics 1 SIAM Journal on Control and Optimization 1 SIAM Journal on Numerical Analysis 1 Transactions of the American Mathematical Society 1 Physica D 1 Constructive Approximation 1 Statistical Science 1 Computers & Operations Research 1 Journal of Scientific Computing 1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 1 Annals of Operations Research 1 The Annals of Applied Probability 1 Differential Geometry and its Applications 1 SIAM Journal on Applied Mathematics 1 SIAM Journal on Mathematical Analysis 1 SIAM Review 1 Journal of Mathematical Imaging and Vision 1 Calculus of Variations and Partial Differential Equations 1 Mathematical Methods of Statistics 1 Computational and Applied Mathematics 1 The Journal of Artificial Intelligence Research (JAIR) 1 Complexity 1 Engineering Analysis with Boundary Elements 1 Electronic Journal of Probability 1 Electronic Communications in Probability 1 Optimization Methods & Software 1 Mathematical Methods of Operations Research 1 Journal of the Royal Statistical Society. Series B. Statistical Methodology 1 Annales Henri Poincaré 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 International Journal of Wavelets, Multiresolution and Information Processing 1 Acta Numerica 1 Mathematical Biosciences and Engineering 1 Journal of Statistical Theory and Practice 1 SIAM Journal on Financial Mathematics 1 Statistics and Computing 1 Journal of Theoretical Biology 1 Journal of the Operations Research Society of China 1 Foundations of Data Science 1 Sampling Theory, Signal Processing, and Data Analysis 1 Frontiers of Mathematical Finance all top 5 Cited in 37 Fields 103 Computer science (68-XX) 55 Statistics (62-XX) 33 Probability theory and stochastic processes (60-XX) 33 Numerical analysis (65-XX) 28 Operations research, mathematical programming (90-XX) 22 Calculus of variations and optimal control; optimization (49-XX) 17 Geophysics (86-XX) 16 Information and communication theory, circuits (94-XX) 12 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 11 Partial differential equations (35-XX) 11 Biology and other natural sciences (92-XX) 8 Fluid mechanics (76-XX) 4 Differential geometry (53-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Combinatorics (05-XX) 3 Functional analysis (46-XX) 2 General and overarching topics; collections (00-XX) 2 Measure and integration (28-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Difference and functional equations (39-XX) 2 Approximations and expansions (41-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Operator theory (47-XX) 2 General topology (54-XX) 2 Mechanics of deformable solids (74-XX) 2 Quantum theory (81-XX) 2 Systems theory; control (93-XX) 1 Mathematical logic and foundations (03-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Category theory; homological algebra (18-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Ordinary differential equations (34-XX) 1 Geometry (51-XX) 1 Algebraic topology (55-XX) 1 Optics, electromagnetic theory (78-XX) Citations by Year