Generating a synthetic observation at great depth
Certain famous models in neural nets are generative β informally, they produce samples some distribution, in training the distribution of those samples is tweaked until its distribution resembles, in some sense, the distribution of our observed data. There are many attempts now to unify fancy generative techniques such as GANs and VAEs and neural diffusiong into a single unified method, or at least a cordial family of methods, so I had better devise a page for that.
Lilian Weng diagrams some popular generative architectures.
Here I mean generative in the sense that βthis model will (approximately) simulate from the true distribution of interestβ, which is somewhat weaker that the requirements of, e.g., MC Bayesian inference, where we assume that we can access likelihoods, or at least likelihood gradients. In such a case, we might have no likelihood at all, or variational approximations to likelihood or whatever.
Observations arising from unobserved latent factors
Philosophical diversion: probability is a weird abstraction
Tangent: Learning problems involve composition of differentiating and integrating various terms that measure various properties of how well you have approximated the state of the world. Probabilistic neural networks leverage combinations of integrals that we can solve by Monte Carlo, and derivatives that we can solve via automatic differentiation, which are both fast-ish on modern hardware In cunning combination these find approximate solutions to some very interesting problems in calculus. Although⦠There is something odd about that setup. From this perspective the generative models (such as GANs and autoencoders) solve an intractable integral by simulating samples probabilistically from it, in lieu of processing the continuous, unknowable, intractable integral that we actually wish to solve. But that continuous intractable integral was in any case a contrivance, a thought experiment imagining a world populated with such weird Platonic objects as integrals-over-possible-states-of-the-world which only mathematicians would consider reasonable. The world we live in has, as far as I know, no such thing. We do not have a world where the things we observe are stochastic samples from an ineffable probability density, but rather the observations themselves are the phenomena, and the probability density over them is a weird abstraction. It must look deeply odd from the outside when we to talk about how we are solving integrals by looking at data, instead of solving data by looking at integrals.
Generative flow nets
See this page.
References
Adler, Jonas, and Sebastian Lunz. 2018. βBanach Wasserstein GAN,β June.
Anderson, Brian D. O. 1982. βReverse-Time Diffusion Equation Models.β Stochastic Processes and Their Applications 12 (3): 313β26.
Arjovsky, Martin, and LΓ©on Bottou. 2017. βTowards Principled Methods for Training Generative Adversarial Networks.β arXiv:1701.04862 [Stat], January.
Arjovsky, Martin, Soumith Chintala, and LΓ©on Bottou. 2017. βWasserstein Generative Adversarial Networks.β In International Conference on Machine Learning, 214β23.
Arora, Sanjeev, Rong Ge, Yingyu Liang, Tengyu Ma, and Yi Zhang. 2017. βGeneralization and Equilibrium in Generative Adversarial Nets (GANs).β arXiv:1703.00573 [Cs], March.
Arora, Sanjeev, Yingyu Liang, and Tengyu Ma. 2015. βWhy Are Deep Nets Reversible: A Simple Theory, with Implications for Training.β arXiv:1511.05653 [Cs], November.
Bach, Stephen H., Bryan He, Alexander Ratner, and Christopher RΓ©. 2017. βLearning the Structure of Generative Models Without Labeled Data.β In Proceedings of the 34th International Conference on Machine Learning. International Conference on Machine Learning, Sydney, Australia.
Bahadori, Mohammad Taha, Krzysztof Chalupka, Edward Choi, Robert Chen, Walter F. Stewart, and Jimeng Sun. 2017. βNeural Causal Regularization Under the Independence of Mechanisms Assumption.β arXiv:1702.02604 [Cs, Stat], February.
Baydin, AtΔ±lΔ±m GΓΌneΕ, Lei Shao, Wahid Bhimji, Lukas Heinrich, Lawrence Meadows, Jialin Liu, Andreas Munk, et al. 2019. βEtalumis: Bringing Probabilistic Programming to Scientific Simulators at Scale.β In arXiv:1907.03382 [Cs, Stat].
Bora, Ashish, Ajil Jalal, Eric Price, and Alexandros G. Dimakis. 2017. βCompressed Sensing Using Generative Models.β In International Conference on Machine Learning, 537β46.
Bowman, Samuel R., Luke Vilnis, Oriol Vinyals, Andrew M. Dai, Rafal Jozefowicz, and Samy Bengio. 2015. βGenerating Sentences from a Continuous Space.β arXiv:1511.06349 [Cs], November.
Burda, Yuri, Roger Grosse, and Ruslan Salakhutdinov. 2016. βImportance Weighted Autoencoders.β In arXiv:1509.00519 [Cs, Stat].
Caterini, Anthony L., Arnaud Doucet, and Dino Sejdinovic. 2018. βHamiltonian Variational Auto-Encoder.β In Advances in Neural Information Processing Systems.
Chen, Xi, Yan Duan, Rein Houthooft, John Schulman, Ilya Sutskever, and Pieter Abbeel. 2016. βInfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets.β In Advances in Neural Information Processing Systems 29, edited by D. D. Lee, M. Sugiyama, U. V. Luxburg, I. Guyon, R. Garnett, and R. Garnett, 2172β80. Curran Associates, Inc.
Chen, Xi, Diederik P. Kingma, Tim Salimans, Yan Duan, Prafulla Dhariwal, John Schulman, Ilya Sutskever, and Pieter Abbeel. 2016. βVariational Lossy Autoencoder.β In PRoceedings of ICLR.
Dasgupta, Sakyasingha, Takayuki Yoshizumi, and Takayuki Osogami. 2016. βRegularized Dynamic Boltzmann Machine with Delay Pruning for Unsupervised Learning of Temporal Sequences.β arXiv:1610.01989 [Cs, Stat], September.
Denton, Emily, Soumith Chintala, Arthur Szlam, and Rob Fergus. 2015. βDeep Generative Image Models Using a Laplacian Pyramid of Adversarial Networks.β arXiv:1506.05751 [Cs], June.
Dhariwal, Prafulla, and Alex Nichol. 2021. βDiffusion Models Beat GANs on Image Synthesis.β arXiv:2105.05233 [Cs, Stat], June.
Donahue, Chris, Julian McAuley, and Miller Puckette. 2019. βAdversarial Audio Synthesis.β In ICLR 2019.
Dosovitskiy, Alexey, Jost Tobias Springenberg, Maxim Tatarchenko, and Thomas Brox. 2014. βLearning to Generate Chairs, Tables and Cars with Convolutional Networks.β arXiv:1411.5928 [Cs], November.
Dutordoir, Vincent, James Hensman, Mark van der Wilk, Carl Henrik Ek, Zoubin Ghahramani, and Nicolas Durrande. 2021. βDeep Neural Networks as Point Estimates for Deep Gaussian Processes.β arXiv:2105.04504 [Cs, Stat], May.
Dutordoir, Vincent, Alan Saul, Zoubin Ghahramani, and Fergus Simpson. 2022. βNeural Diffusion Processes.β arXiv.
Dziugaite, Gintare Karolina, Daniel M. Roy, and Zoubin Ghahramani. 2015. βTraining Generative Neural Networks via Maximum Mean Discrepancy Optimization.β In Proceedings of the Thirty-First Conference on Uncertainty in Artificial Intelligence, 258β67. UAIβ15. Arlington, Virginia, United States: AUAI Press.
Engel, Jesse, Kumar Krishna Agrawal, Shuo Chen, Ishaan Gulrajani, Chris Donahue, and Adam Roberts. 2019. βGANSynth: Adversarial Neural Audio Synthesis.β In Seventh International Conference on Learning Representations.
Engel, Jesse, Lamtharn (Hanoi) Hantrakul, Chenjie Gu, and Adam Roberts. 2019. βDDSP: Differentiable Digital Signal Processing.β In.
Engel, Jesse, Cinjon Resnick, Adam Roberts, Sander Dieleman, Douglas Eck, Karen Simonyan, and Mohammad Norouzi. 2017. βNeural Audio Synthesis of Musical Notes with WaveNet Autoencoders.β In PMLR.
FrΓΌhstΓΌck, Anna, Ibraheem Alhashim, and Peter Wonka. 2019. βTileGAN: Synthesis of Large-Scale Non-Homogeneous Textures.β arXiv:1904.12795 [Cs], April.
Gal, Yarin, and Zoubin Ghahramani. 2015. βOn Modern Deep Learning and Variational Inference.β In Advances in Approximate Bayesian Inference Workshop, NIPS.
Genevay, Aude, Gabriel PeyrΓ©, and Marco Cuturi. 2017. βLearning Generative Models with Sinkhorn Divergences.β arXiv:1706.00292 [Stat], October.
Goodfellow, Ian J., Jonathon Shlens, and Christian Szegedy. 2014. βExplaining and Harnessing Adversarial Examples.β arXiv:1412.6572 [Cs, Stat], December.
Goodfellow, Ian, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. 2014. βGenerative Adversarial Nets.β In Advances in Neural Information Processing Systems 27, edited by Z. Ghahramani, M. Welling, C. Cortes, N. D. Lawrence, and K. Q. Weinberger, 2672β80. NIPSβ14. Cambridge, MA, USA: Curran Associates, Inc.
Gulrajani, Ishaan, Faruk Ahmed, Martin Arjovsky, Vincent Dumoulin, and Aaron Courville. 2017. βImproved Training of Wasserstein GANs.β arXiv:1704.00028 [Cs, Stat], March.
Guo, Xin, Johnny Hong, Tianyi Lin, and Nan Yang. 2017. βRelaxed Wasserstein with Applications to GANs.β arXiv:1705.07164 [Cs, Stat], May.
Han, Xizewen, Huangjie Zheng, and Mingyuan Zhou. 2022. βCARD: Classification and Regression Diffusion Models.β arXiv.
He, Kun, Yan Wang, and John Hopcroft. 2016. βA Powerful Generative Model Using Random Weights for the Deep Image Representation.β In Advances in Neural Information Processing Systems.
Hinton, Geoffrey E. 2007. βLearning Multiple Layers of Representation.β Trends in Cognitive Sciences 11 (10): 428β34.
Ho, Jonathan, Ajay Jain, and Pieter Abbeel. 2020. βDenoising Diffusion Probabilistic Models.β arXiv:2006.11239 [Cs, Stat], December.
Hoffman, Matthew D, and Matthew J Johnson. 2016. βELBO Surgery: Yet Another Way to Carve up the Variational Evidence Lower Bound.β In Advances In Neural Information Processing Systems, 4.
Hoogeboom, Emiel, Alexey A. Gritsenko, Jasmijn Bastings, Ben Poole, Rianne van den Berg, and Tim Salimans. 2021. βAutoregressive Diffusion Models.β arXiv:2110.02037 [Cs, Stat], October.
Hu, Zhiting, Zichao Yang, Ruslan Salakhutdinov, and Eric P. Xing. 2018. βOn Unifying Deep Generative Models.β In arXiv:1706.00550 [Cs, Stat].
Husain, Hisham. 2020. βDistributional Robustness with IPMs and Links to Regularization and GANs.β arXiv:2006.04349 [Cs, Stat], June.
Husain, Hisham, Richard Nock, and Robert C. Williamson. 2019. βA Primal-Dual Link Between GANs and Autoencoders.β In Advances in Neural Information Processing Systems, 32:415β24.
HuszΓ‘r, Ferenc. 2015. βHow (Not) to Train Your Generative Model: Scheduled Sampling, Likelihood, Adversary?β arXiv:1511.05101 [Cs, Math, Stat], November.
HyvΓ€rinen, Aapo. 2005. βEstimation of Non-Normalized Statistical Models by Score Matching.β The Journal of Machine Learning Research 6 (December): 695β709.
Isola, Phillip, Jun-Yan Zhu, Tinghui Zhou, and Alexei A. Efros. 2017. βImage-to-Image Translation with Conditional Adversarial Networks.β In 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 5967β76.
Jalal, Ajil, Marius Arvinte, Giannis Daras, Eric Price, Alexandros G Dimakis, and Jon Tamir. 2021. βRobust Compressed Sensing MRI with Deep Generative Priors.β In Advances in Neural Information Processing Systems, 34:14938β54. Curran Associates, Inc.
Jayaram, Vivek, and John Thickstun. 2020. βSource Separation with Deep Generative Priors.β arXiv:2002.07942 [Cs, Stat], February.
Jetchev, Nikolay, Urs Bergmann, and Roland Vollgraf. 2016. βTexture Synthesis with Spatial Generative Adversarial Networks.β In Advances in Neural Information Processing Systems 29.
Ji, Kaiyi, and Yingbin Liang. 2018. βMinimax Estimation of Neural Net Distance,β November.
Jolicoeur-Martineau, Alexia, RΓ©mi PichΓ©-Taillefer, Ioannis Mitliagkas, and Remi Tachet des Combes. 2022. βAdversarial Score Matching and Improved Sampling for Image Generation.β In.
Karras, Tero, Samuli Laine, and Timo Aila. 2018. βA Style-Based Generator Architecture for Generative Adversarial Networks.β arXiv:1812.04948 [Cs, Stat], December.
Kim, Yoon, Sam Wiseman, Andrew C. Miller, David Sontag, and Alexander M. Rush. 2018. βSemi-Amortized Variational Autoencoders.β arXiv:1802.02550 [Cs, Stat], February.
Kingma, Durk P, and Prafulla Dhariwal. 2018. βGlow: Generative Flow with Invertible 1x1 Convolutions.β In Advances in Neural Information Processing Systems 31, edited by S. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi, and R. Garnett, 10236β45. Curran Associates, Inc.
Kodali, Naveen, Jacob Abernethy, James Hays, and Zsolt Kira. 2017. βOn Convergence and Stability of GANs.β arXiv:1705.07215 [Cs], December.
Krishnan, Rahul G., Uri Shalit, and David Sontag. 2017. βStructured Inference Networks for Nonlinear State Space Models.β In Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence, 2101β9.
Kulkarni, Tejas D., Will Whitney, Pushmeet Kohli, and Joshua B. Tenenbaum. 2015. βDeep Convolutional Inverse Graphics Network.β arXiv:1503.03167 [Cs], March.
Lee, Holden, Rong Ge, Tengyu Ma, Andrej Risteski, and Sanjeev Arora. 2017. βOn the Ability of Neural Nets to Express Distributions.β In arXiv:1702.07028 [Cs].
Lee, Honglak, Roger Grosse, Rajesh Ranganath, and Andrew Y. Ng. 2009. βConvolutional Deep Belief Networks for Scalable Unsupervised Learning of Hierarchical Representations.β In Proceedings of the 26th Annual International Conference on Machine Learning, 609β16. ICML β09. New York, NY, USA: ACM.
Lee, Hung-yi, and Yu Tsao. n.d. βGenerative Adversarial Network.β In, 222.
Li, Chun-Liang, Wei-Cheng Chang, Yu Cheng, Yiming Yang, and Barnabas Poczos. 2017. βMMD GAN: Towards Deeper Understanding of Moment Matching Network.β In Advances in Neural Information Processing Systems 30, edited by I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, 2203β13. Curran Associates, Inc.
Liang, Dawen, Rahul G. Krishnan, Matthew D. Hoffman, and Tony Jebara. 2018. βVariational Autoencoders for Collaborative Filtering.β In Proceedings of the 2018 World Wide Web Conference, 689β98. WWW β18. Republic and Canton of Geneva, CHE: International World Wide Web Conferences Steering Committee.
Louizos, Christos, and Max Welling. 2016. βStructured and Efficient Variational Deep Learning with Matrix Gaussian Posteriors.β In arXiv Preprint arXiv:1603.04733, 1708β16.
Mirza, Mehdi, and Simon Osindero. 2014. βConditional Generative Adversarial Nets.β arXiv:1411.1784 [Cs, Stat], November.
Miyato, Takeru, Toshiki Kataoka, Masanori Koyama, and Yuichi Yoshida. 2018. βSpectral Normalization for Generative Adversarial Networks.β In ICLR 2018.
Mnih, Andriy, and Karol Gregor. 2014. βNeural Variational Inference and Learning in Belief Networks.β In Proceedings of The 31st International Conference on Machine Learning.
Mohamed, A. r, G. E. Dahl, and G. Hinton. 2012. βAcoustic Modeling Using Deep Belief Networks.β IEEE Transactions on Audio, Speech, and Language Processing 20 (1): 14β22.
Mohamed, Shakir, and Balaji Lakshminarayanan. 2016. βLearning in Implicit Generative Models,β November.
Nichol, Alex, and Prafulla Dhariwal. 2021. βImproved Denoising Diffusion Probabilistic Models.β arXiv:2102.09672 [Cs, Stat], February.
Oord, Aaron van den, Sander Dieleman, Heiga Zen, Karen Simonyan, Oriol Vinyals, Alex Graves, Nal Kalchbrenner, Andrew Senior, and Koray Kavukcuoglu. 2016. βWaveNet: A Generative Model for Raw Audio.β In 9th ISCA Speech Synthesis Workshop.
Oord, AΓ€ron van den, Nal Kalchbrenner, and Koray Kavukcuoglu. 2016. βPixel Recurrent Neural Networks.β arXiv:1601.06759 [Cs], January.
Panaretos, Victor M., and Yoav Zemel. 2019. βStatistical Aspects of Wasserstein Distances.β Annual Review of Statistics and Its Application 6 (1): 405β31.
Papamakarios, George, Eric Nalisnick, Danilo Jimenez Rezende, Shakir Mohamed, and Balaji Lakshminarayanan. 2021. βNormalizing Flows for Probabilistic Modeling and Inference.β Journal of Machine Learning Research 22 (57): 1β64.
Pascual, Santiago, Joan SerrΓ , and Antonio Bonafonte. 2019. βTowards Generalized Speech Enhancement with Generative Adversarial Networks.β arXiv:1904.03418 [Cs, Eess], April.
Pfau, David, and Oriol Vinyals. 2016. βConnecting Generative Adversarial Networks and Actor-Critic Methods.β arXiv:1610.01945 [Cs, Stat], October.
Poole, Ben, Alexander A. Alemi, Jascha Sohl-Dickstein, and Anelia Angelova. 2016. βImproved Generator Objectives for GANs.β In Advances in Neural Information Processing Systems 29.
Prenger, Ryan, Rafael Valle, and Bryan Catanzaro. 2018. βWaveGlow: A Flow-Based Generative Network for Speech Synthesis.β arXiv:1811.00002 [Cs, Eess, Stat], October.
Radford, Alec, Luke Metz, and Soumith Chintala. 2015. βUnsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks.β In arXiv:1511.06434 [Cs].
Ramasinghe, Sameera, Kanchana Nisal Ranasinghe, Salman Khan, Nick Barnes, and Stephen Gould. 2020. βConditional Generative Modeling via Learning the Latent Space.β In.
Ranganath, Rajesh, Dustin Tran, Jaan Altosaar, and David Blei. 2016. βOperator Variational Inference.β In Advances in Neural Information Processing Systems 29, edited by D. D. Lee, M. Sugiyama, U. V. Luxburg, I. Guyon, and R. Garnett, 496β504. Curran Associates, Inc.
Rezende, Danilo Jimenez, Shakir Mohamed, and Daan Wierstra. 2015. βStochastic Backpropagation and Approximate Inference in Deep Generative Models.β In Proceedings of ICML.
Salakhutdinov, Ruslan. 2015. βLearning Deep Generative Models.β Annual Review of Statistics and Its Application 2 (1): 361β85.
Salimans, Tim, Diederik Kingma, and Max Welling. 2015. βMarkov Chain Monte Carlo and Variational Inference: Bridging the Gap.β In Proceedings of the 32nd International Conference on Machine Learning (ICML-15), 1218β26. ICMLβ15. Lille, France: JMLR.org.
Sohl-Dickstein, Jascha, Eric A. Weiss, Niru Maheswaranathan, and Surya Ganguli. 2015. βDeep Unsupervised Learning Using Nonequilibrium Thermodynamics.β arXiv:1503.03585 [Cond-Mat, q-Bio, Stat], November.
Song, Jiaming, Chenlin Meng, and Stefano Ermon. 2021. βDenoising Diffusion Implicit Models.β arXiv:2010.02502 [Cs], November.
Song, Yang, Conor Durkan, Iain Murray, and Stefano Ermon. 2021. βMaximum Likelihood Training of Score-Based Diffusion Models.β In Advances in Neural Information Processing Systems.
Song, Yang, and Stefano Ermon. 2020a. βGenerative Modeling by Estimating Gradients of the Data Distribution.β In Advances In Neural Information Processing Systems. arXiv.
βββ. 2020b. βImproved Techniques for Training Score-Based Generative Models.β In Advances In Neural Information Processing Systems. arXiv.
Song, Yang, Sahaj Garg, Jiaxin Shi, and Stefano Ermon. 2019. βSliced Score Matching: A Scalable Approach to Density and Score Estimation.β arXiv.
Song, Yang, Liyue Shen, Lei Xing, and Stefano Ermon. 2022. βSolving Inverse Problems in Medical Imaging with Score-Based Generative Models.β In. arXiv.
Song, Yang, Jascha Sohl-Dickstein, Diederik P. Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. 2022. βScore-Based Generative Modeling Through Stochastic Differential Equations.β In.
Sun, Zheng, Jiaqi Liu, Zewang Zhang, Jingwen Chen, Zhao Huo, Ching Hua Lee, and Xiao Zhang. 2016. βComposing Music with Grammar Argumented Neural Networks and Note-Level Encoding.β arXiv:1611.05416 [Cs], November.
Sutherland, Dougal J., Hsiao-Yu Tung, Heiko Strathmann, Soumyajit De, Aaditya Ramdas, Alex Smola, and Arthur Gretton. 2017. βGenerative Models and Model Criticism via Optimized Maximum Mean Discrepancy.β In Proceedings of ICLR.
Swersky, Kevin, MarcβAurelio Ranzato, David Buchman, Nando D. Freitas, and Benjamin M. Marlin. 2011. βOn Autoencoders and Score Matching for Energy Based Models.β In Proceedings of the 28th International Conference on Machine Learning (ICML-11), 1201β8.
Theis, Lucas, and Matthias Bethge. 2015. βGenerative Image Modeling Using Spatial LSTMs.β arXiv:1506.03478 [Cs, Stat], June.
Tran, Dustin, Matthew D. Hoffman, Rif A. Saurous, Eugene Brevdo, Kevin Murphy, and David M. Blei. 2017. βDeep Probabilistic Programming.β In ICLR.
Ullrich, K. 2020. βA Coding Perspective on Deep Latent Variable Models.β
Vincent, Pascal. 2011. βA connection between score matching and denoising autoencoders.β Neural Computation 23 (7): 1661β74.
Wang, Chuang, Hong Hu, and Yue M. Lu. 2019. βA Solvable High-Dimensional Model of GAN.β arXiv:1805.08349 [Cond-Mat, Stat], October.
Wang, Prince Zizhuang, and William Yang Wang. 2019. βRiemannian Normalizing Flow on Variational Wasserstein Autoencoder for Text Modeling.β In Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers), 284β94. Minneapolis, Minnesota: Association for Computational Linguistics.
Wu, Yan, Mihaela Rosca, and Timothy Lillicrap. 2019. βDeep Compressed Sensing.β In International Conference on Machine Learning, 6850β60.
Xie, Jianwen, Ruiqi Gao, Erik Nijkamp, Song-Chun Zhu, and Ying Nian Wu. 2020. βRepresentation Learning: A Statistical Perspective.β Annual Review of Statistics and Its Application 7 (1): 303β35.
Yang, Li-Chia, Szu-Yu Chou, and Yi-Hsuan Yang. 2017. βMidiNet: A Convolutional Generative Adversarial Network for Symbolic-Domain Music Generation.β In Proceedings of the 18th International Society for Music Information Retrieval Conference (ISMIRβ2017), Suzhou, China.
Yang, Ling, Zhilong Zhang, Shenda Hong, Runsheng Xu, Yue Zhao, Yingxia Shao, Wentao Zhang, Ming-Hsuan Yang, and Bin Cui. 2022. βDiffusion Models: A Comprehensive Survey of Methods and Applications.β arXiv.
Yang, Liu, Dongkun Zhang, and George Em Karniadakis. 2020. βPhysics-Informed Generative Adversarial Networks for Stochastic Differential Equations.β SIAM Journal on Scientific Computing 42 (1): A292β317.
Yang, Mengyue, Furui Liu, Zhitang Chen, Xinwei Shen, Jianye Hao, and Jun Wang. 2020. βCausalVAE: Disentangled Representation Learning via Neural Structural Causal Models.β arXiv:2004.08697 [Cs, Stat], July.
YΔ±ldΔ±z, ΓaΔatay, Markus Heinonen, and Harri LΓ€hdesmΓ€ki. 2019. βODE\(^2\)VAE: Deep Generative Second Order ODEs with Bayesian Neural Networks.β arXiv:1905.10994 [Cs, Stat], October.
Zhou, Cong, Michael Horgan, Vivek Kumar, Cristina Vasco, and Dan Darcy. 2018. βVoice Conversion with Conditional SampleRNN.β arXiv:1808.08311 [Cs, Eess], August.
Zhu, B., J. Jiao, and D. Tse. 2020. βDeconstructing Generative Adversarial Networks.β IEEE Transactions on Information Theory 66 (11): 7155β79.
Zhu, Jun-Yan, Philipp KrΓ€henbΓΌhl, Eli Shechtman, and Alexei A. Efros. 2016. βGenerative Visual Manipulation on the Natural Image Manifold.β In Proceedings of European Conference on Computer Vision.
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