# Energy-based generative neural network

**Energy-based generative neural networks** ^{[1]}^{[2]} is a class of generative models, which aim to learn explicit probability distributions of data in the form of energy-based models whose energy functions are parameterized by modern deep neural networks. Its name is due to the fact that this model can be derived from the discriminative neural networks. The parameter of the neural network in this model is trained in a generative manner by Markov chain Monte Carlo ^{[3]}(MCMC)-based maximum likelihood estimation. The learning process follows an *analysis by synthesis* scheme, where within each learning iteration, the algorithm samples the synthesized examples from the current model by a gradient-based MCMC method, e.g., Langevin dynamics, and then updates the model parameters based on the difference between the training examples and the synthesized ones. This process can be interpreted as an alternating mode seeking and mode shifting process, and also has an adversarial interpretation ^{[4]}. The first energy-based generative neural network is the generative ConvNet proposed in 2016 for image patterns, where the neural network is a convolutional neural network ^{[5]} ^{[6]}. The model has been generalized to various domains to learn distributions of videos ^{[7]}, and 3D voxels ^{[8]} . They are made more effective in their variants ^{[9]} ^{[10]} ^{[11]} ^{[12]} ^{[13]}^{[14]}. They have proven useful for data generation (e.g., image synthesis , video synthesis, 3D shape synthesis , etc.), data recovery (e.g., recovering videos with missing pixels or image frames , 3D super-resolution, etc), data reconstruction .

## References

- ↑ Xie, Jianwen; Lu, Yang; Zhu, Song-Chun; Wu, Ying Nian (2016). "A theory of generative ConvNet" (PDF).
*ICML*. - ↑ Xie, Jianwen; Zhu, Song-Chun; Wu, Ying Nian (2019). "Learning Energy-based Spatial-Temporal Generative ConvNets for Dynamic Patterns".
*IEEE Transactions on Pattern Analysis and Machine Intelligence*: 1–1. doi:10.1109/tpami.2019.2934852. ISSN 0162-8828. - ↑ Barbu, Adrian; Zhu, Song-Chun (2020).
*Monte Carlo Methods*. Springer. - ↑ Wu, Ying Nian; Xie, Jianwen; Lu, Yang; Zhu, Song-Chun (2018). "Sparse and deep generalizations of the FRAME model".
*Annals of Mathematical Sciences and Applications*.**3**(1): 211–254. doi:10.4310/amsa.2018.v3.n1.a7. ISSN 2380-288X. - ↑ Lecun, Y.; Bottou, L.; Bengio, Y.; Haffner, P. (1998). "Gradient-based learning applied to document recognition".
*Proceedings of the IEEE*.**86**(11): 2278–2324. doi:10.1109/5.726791. ISSN 0018-9219. - ↑ Krizhevsky, Alex; Sutskever, Ilya; Hinton, Geoffrey (2012). "ImageNet classification with deep convolutional neural networks" (PDF).
*NIPS*. - ↑ Xie, Jianwen; Zhu, Song-Chun; Wu, Ying Nian (July 2017). "Synthesizing Dynamic Patterns by Spatial-Temporal Generative ConvNet".
*2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)*. IEEE. doi:10.1109/cvpr.2017.119. ISBN 978-1-5386-0457-1. - ↑ Xie, Jianwen; Zheng, Zilong; Gao, Ruiqi; Wang, Wenguan; Zhu, Song-Chun; Wu, Ying Nian (June 2018). "Learning Descriptor Networks for 3D Shape Synthesis and Analysis".
*2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition*. IEEE. doi:10.1109/cvpr.2018.00900. ISBN 978-1-5386-6420-9. - ↑ Gao, Ruiqi; Lu, Yang; Zhou, Junpei; Zhu, Song-Chun; Wu, Ying Nian (June 2018). "Learning Generative ConvNets via Multi-grid Modeling and Sampling".
*2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition*. IEEE. doi:10.1109/cvpr.2018.00954. ISBN 978-1-5386-6420-9. - ↑ Nijkamp, , Zhu, Song-Chun Wu, Ying Nian, Erik; Hill, Mitch; Zhu, Song-Chun; Wu, Ying Nian (2019).
*On Learning Non-Convergent Non-Persistent Short-Run MCMC Toward Energy-Based Model*. NeurIPS.`{{cite book}}`

: CS1 maint: location missing publisher (link) CS1 maint: multiple names: authors list (link) - ↑ Cai, Xu; Wu, Yang; Li, Guanbin; Chen, Ziliang; Lin, Liang (2019-07-17). "FRAME Revisited: An Interpretation View Based on Particle Evolution".
*Proceedings of the AAAI Conference on Artificial Intelligence*.**33**: 3256–3263. doi:10.1609/aaai.v33i01.33013256. ISSN 2374-3468. - ↑ Xie, Jianwen; Lu, Yang; Gao, Ruiqi; Zhu, Song-Chun; Wu, Ying Nian (2020-01-01). "Cooperative Training of Descriptor and Generator Networks".
*IEEE Transactions on Pattern Analysis and Machine Intelligence*.**42**(1): 27–45. doi:10.1109/tpami.2018.2879081. ISSN 0162-8828. - ↑ Xie, Jianwen; Lu, Yang; Gao, Ruiqi; Gao, Song-Chun (2018). "Cooperative Learning of Energy-Based Model and Latent Variable Model via MCMC Teaching".
*Thirty-Second AAAI Conference on Artificial Intelligence*. - ↑ Han, Tian; Nijkamp, Erik; Fang, Xiaolin; Hill, Mitch; Zhu, Song-Chun; Wu, Ying Nian (June 2019). "Divergence Triangle for Joint Training of Generator Model, Energy-Based Model, and Inferential Model".
*2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)*. IEEE. doi:10.1109/cvpr.2019.00887. ISBN 978-1-7281-3293-8.

This article "Energy-based generative neural network" is from Wikipedia. The list of its authors can be seen in its historical. Articles taken from Draft Namespace on Wikipedia could be accessed on Wikipedia's Draft Namespace.