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Cheng, S1; Wang, L; Xiang, T; Zhang, P2
Tree tensor networks for generative modeling
Source PublicationPHYSICAL REVIEW B
AbstractMatrix product states (MPSs), a tensor network designed for one-dimensional quantum systems, were recently proposed for generative modeling of natural data (such as images) in terms of the "Born machine." However, the exponential decay of correlation in MPSs restricts its representation power heavily for modeling complex data such as natural images. In this work, we push forward the effort of applying tensor networks to machine learning by employing the tree tensor network (TTN), which exhibits balanced performance in expressibility and efficient training and sampling. We design the tree tensor network to utilize the two-dimensional prior of the natural images and develop sweeping learning and sampling algorithms which can be efficiently implemented utilizing graphical processing units. We apply our model to random binary patterns and the binary MNIST data sets of handwritten digits. We show that the TTN is superior to MPSs for generative modeling in keeping the correlation of pixels in natural images, as well as giving better log-likelihood scores in standard data sets of handwritten digits. We also compare its performance with state-of-the-art generative models such as variational autoencoders, restricted Boltzmann machines, and PixelCNN. Finally, we discuss the future development of tensor network states in machine learning problems.
Subject AreaMaterials Science ; Physics
MOST Discipline CatalogueMaterials Science, Multidisciplinary ; Physics, Applied ; Physics, Condensed Matter
Indexed BySCIE
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Cited Times:9[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Affiliation1.Chinese Acad Sci, Inst Phys, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Beijing 100049, Peoples R China
3.Chinese Acad Sci, Inst Theoret Phys, CAS Key Lab Theoret Phys, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Cheng, S,Wang, L,Xiang, T,et al. Tree tensor networks for generative modeling[J]. PHYSICAL REVIEW B,2019,99(15):155131.
APA Cheng, S,Wang, L,Xiang, T,&Zhang, P.(2019).Tree tensor networks for generative modeling.PHYSICAL REVIEW B,99(15),155131.
MLA Cheng, S,et al."Tree tensor networks for generative modeling".PHYSICAL REVIEW B 99.15(2019):155131.
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