List of Related Works in between ML and TN

List of Related Works in between ML and TN

1.

Bény C. Deep learning and the renormalization group. arXiv:13013124 [quant-ph] . 2013 Jan 14; http://arxiv.org/abs/1301.3124

2.

Dumoulin V, Goodfellow IJ, Courville A, Bengio Y. On the Challenges of Physical Implementations of RBMs. arXiv:13125258 [cs, stat] . 2013 Dec 18 ;http://arxiv.org/abs/1312.5258

3.

Mehta P, Schwab DJ. An exact mapping between the variational renormalization group and deep learning. arXiv preprint arXiv:14103831 . 2014 ;http://arxiv.org/abs/1410.3831

4.

Steeg GV, Galstyan A. Discovering Structure in High-Dimensional Data Through Correlation Explanation. arXiv:14061222 [cs, stat] . 2014 Jun 4 ;http://arxiv.org/abs/1406.1222

5.

Cichocki A. Tensor Networks for Big Data Analytics and Large-Scale Optimization Problems. arXiv:14073124 [cs, math] . 2014 Jul 11;http://arxiv.org/abs/1407.3124

6.

Arsenault L-F, Lopez-Bezanilla A, von Lilienfeld OA, Millis AJ. Machine learning for many-body physics: The case of the Anderson impurity model. Physical Review B . 2014 Oct 31 ;90(15). http://link.aps.org/doi/10.1103/PhysRevB.90.155136

7.

Tishby N, Zaslavsky N. Deep Learning and the Information Bottleneck Principle. arXiv:150302406 [cs] . 2015 Mar 9; http://arxiv.org/abs/1503.02406

8.

Cai X-D, Wu D, Su Z-E, Chen M-C, Wang X-L, Li L, et al. Entanglement-Based Machine Learning on a Quantum Computer. Physical Review Letters . 2015 Mar 19 ;114(11). http://link.aps.org/doi/10.1103/PhysRevLett.114.110504

9.

Gabrié M, Tramel EW, Krzakala F. Training Restricted Boltzmann Machines via the Thouless-Anderson-Palmer Free Energy. arXiv:150602914 [cond-mat, stat] . 2015 Jun 9 ; http://arxiv.org/abs/1506.02914

10.

Carrasquilla J, Melko RG. Machine learning phases of matter. arXiv preprint arXiv:160501735 . 2016 May ; http://arxiv.org/abs/1605.01735

11.

Stoudenmire EM, Schwab DJ. Supervised Learning with Quantum-Inspired Tensor Networks. arXiv:160505775 [cond-mat, stat] . 2016 May 18 ;http://arxiv.org/abs/1605.05775

12.

Carleo G, Troyer M. Solving the quantum many-body problem with artificial neural networks. Science . 2016 Jun;355(6325):602–6.http://science.sciencemag.org/content/355/6325/602

13.

Wang L. Discovering Phase Transitions with Unsupervised Learning. arXiv:160600318 [cond-mat, stat] . 2016 Jun 1 ; http://arxiv.org/abs/1606.00318

14.

Lin HW, Tegmark M. Why does deep and cheap learning work so well? arXiv:160808225 [cond-mat, stat] . 2016 Aug 29 ; http://arxiv.org/abs/1608.08225

15.

Cichocki A, Lee N, Oseledets IV, Phan A-H, Zhao Q, Mandic D. Low-Rank Tensor Networks for Dimensionality Reduction and Large-Scale Optimization Problems: Perspectives and Challenges PART 1. Foundations and Trends® in Machine Learning . 2016 Sep;9(4–5):249–429.http://arxiv.org/abs/1609.00893

16.

Ch’ng K, Carrasquilla J, Melko RG, Khatami E. Machine Learning Phases of Strongly Correlated Fermions. arXiv:160902552 [cond-mat] . 2016 Sep 8 ;http://arxiv.org/abs/1609.02552

17.

Nieuwenburg V, L EP, Liu Y-H, Huber SD. Learning phase transitions by confusion. 2016 Oct 6 ; https://arxiv.org/abs/1610.02048

18.

Huang L, Wang L. Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines. arXiv:161002746 [cond-mat, physics:physics, stat] . 2016 Oct 9 ; http://arxiv.org/abs/1610.02746

19.

Poggio T, Mhaskar H, Rosasco L, Miranda B, Liao Q. Why and When Can Deep -- but Not Shallow -- Networks Avoid the Curse of Dimensionality: a Review. arXiv:161100740 [cs] . 2016 Nov 2 ; http://arxiv.org/abs/1611.00740

20.

Cichocki A, Phan A-H, Zhao Q, Lee N, Oseledets IV, Sugiyama M, et al. Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives. Foundations and Trends® in Machine Learning . 2017;9(6):249–429. http://arxiv.org/abs/1708.09165

21.

Chen J, Cheng S, Xie H, Wang L, Xiang T. On the Equivalence of Restricted Boltzmann Machines and Tensor Network States. arXiv:170104831 [cond-mat, physics:quant-ph, stat] . 2017 Jan 17; http://arxiv.org/abs/1701.04831

22.

Gao X, Duan L-M. Efficient Representation of Quantum Many-body States with Deep Neural Networks. arXiv:170105039 [cond-mat, physics:quant-ph] . 2017 Jan 18 ; http://arxiv.org/abs/1701.05039

23.

Huang Y, Moore JE. Neural network representation of tensor network and chiral states. arXiv:170106246 [cond-mat] . 2017 Jan 22;http://arxiv.org/abs/1701.06246

24.

Mills K, Spanner M, Tamblyn I. Deep learning and the Schr\"odinger equation. arXiv:170201361 [cond-mat, physics:physics] . 2017 Feb 4 ;http://arxiv.org/abs/1702.01361

25.

Wetzel SJ. Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders. arXiv:170302435 [cond-mat, stat] . 2017 Mar 7 ; http://arxiv.org/abs/1703.02435

26.

Levine Y, Yakira D, Cohen N, Shashua A. Deep Learning and Quantum Entanglement: Fundamental Connections with Implications to Network Design. arXiv:170401552 [quant-ph] . 2017 Apr 5; http://arxiv.org/abs/1704.01552

27.

Schindler F, Regnault N, Neupert T. Probing many-body localization with neural networks. arXiv:170401578 [cond-mat] . 2017 Apr 5 ;http://arxiv.org/abs/1704.01578

28.

Koch-Janusz M, Ringel Z. Mutual Information, Neural Networks and the Renormalization Group. arXiv:170406279 [cond-mat] . 2017 Apr 20;http://arxiv.org/abs/1704.06279

29.

Bradde S, Bialek W. PCA meets RG. Journal of Statistical Physics . 2017 May;167(3–4):462–75. http://arxiv.org/abs/1610.09733

30.

Lu S, Huang S, Li K, Li J, Chen J, Lu D, et al. A Separability-Entanglement Classifier via Machine Learning. arXiv:170501523 [quant-ph] . 2017 May 3 ;http://arxiv.org/abs/1705.01523

31.

Cohen N, Sharir O, Levine Y, Tamari R, Yakira D, Shashua A. Analysis and Design of Convolutional Networks via Hierarchical Tensor Decompositions. arXiv:170502302 [cs] . 2017 May 5; http://arxiv.org/abs/1705.02302

32.

Deng D-L, Li X, Sarma SD. Quantum Entanglement in Neural Network States. Physical Review X . 2017 May 11;7(2). http://arxiv.org/abs/1701.04844

33.

Rolnick D, Tegmark M. The power of deeper networks for expressing natural functions. arXiv:170505502 [cs, stat] . 2017 May 15 ;http://arxiv.org/abs/1705.05502

34.

Cristoforetti M, Jurman G, Nardelli AI, Furlanello C. Towards meaningful physics from generative models. arXiv:170509524 [cond-mat, physics:hep-lat] . 2017 May 26 ; http://arxiv.org/abs/1705.09524

35.

Oprisa D, Toth P. Criticality & Deep Learning II: Momentum Renormalisation Group. arXiv:170511023 [cond-mat] . 2017 May 31;http://arxiv.org/abs/1705.11023

36.

Broecker P, Assaad FF, Trebst S. Quantum phase recognition via unsupervised machine learning. arXiv:170700663 [cond-mat] . 2017 Jul 3 ;http://arxiv.org/abs/1707.00663

37.

Gallego AJ, Orus R. The physical structure of grammatical correlations: equivalences, formalizations and consequences. arXiv:170801525 [cond-mat, physics:physics, physics:quant-ph] . 2017 Aug 4; http://arxiv.org/abs/1708.01525

38.

Morningstar A, Melko RG. Deep Learning the Ising Model Near Criticality. arXiv:170804622 [cond-mat, stat] . 2017 Aug 15 ;http://arxiv.org/abs/1708.04622

39.

You Y-Z, Yang Z, Qi X-L. Machine Learning Spatial Geometry from Entanglement Features. arXiv:170901223 [cond-mat, physics:gr-qc, physics:hep-th, physics:quant-ph] . 2017 Sep 4; http://arxiv.org/abs/1709.01223

40.

Han Z-Y, Wang J, Fan H, Wang L, Zhang P. Unsupervised Generative Modeling Using Matrix Product States. arXiv:170901662 [cond-mat, physics:quant-ph, stat] . 2017 Sep 5; http://arxiv.org/abs/1709.01662

41.

Dunjko V, Briegel HJ. Machine learning \& artificial intelligence in the quantum domain. arXiv:170902779 [quant-ph] . 2017 Sep 8;http://arxiv.org/abs/1709.02779

42.

Gan W-C, Shu F-W. Holography as deep learning. International Journal of Modern Physics D . 2017 Oct ;26(12):1743020. http://arxiv.org/abs/1705.05750

43.

Robeva E, Seigal A. Duality of Graphical Models and Tensor Networks. arXiv:171001437 [quant-ph, stat] . 2017 Oct 3; http://arxiv.org/abs/1710.01437

44.

Clark SR. Unifying Neural-network Quantum States and Correlator Product States via Tensor Networks. arXiv:171003545 [cond-mat, physics:quant-ph] . 2017 Oct 10; http://arxiv.org/abs/1710.03545

45.

Kaubruegger R, Pastori L, Budich JC. Chiral Topological Phases from Artificial Neural Networks. arXiv:171004713 [cond-mat, physics:quant-ph] . 2017 Oct 12 ; http://arxiv.org/abs/1710.04713

46.

Liu D, Ran S-J, Wittek P, Peng C, García RB, Su G, et al. Machine Learning by Two-Dimensional Hierarchical Tensor Networks: A Quantum Information Theoretic Perspective on Deep Architectures. arXiv:171004833 [cond-mat, physics:physics, physics:quant-ph, stat] . 2017 Oct 13;http://arxiv.org/abs/1710.04833

47.

Zhang Y-H. Entanglement Entropy of Target Functions for Image Classification and Convolutional Neural Network. arXiv:171005520 [cond-mat] . 2017 Oct 16 ; http://arxiv.org/abs/1710.05520

48.

Wang C, Zhai H. Unsupervised Learning of Frustrated Classical Spin Models I: Principle Component Analysis. Physical Review B . 2017 Oct 26 ;96(14).http://arxiv.org/abs/1706.07977

49.

Pestun V, Vlassopoulos Y. Tensor network language model. arXiv:171010248 [cond-mat, stat] . 2017 Oct 27; http://arxiv.org/abs/1710.10248

50.

Gao X, Zhang Z, Duan L. An efficient quantum algorithm for generative machine learning. arXiv:171102038 [quant-ph, stat] . 2017 Nov 6;http://arxiv.org/abs/1711.02038

51.

Hallam A, Grant E, Stojevic V, Severini S, Green AG. Compact Neural Networks based on the Multiscale Entanglement Renormalization Ansatz. arXiv:171103357 [quant-ph] . 2017 Nov 9 ; http://arxiv.org/abs/1711.03357

52.

Huang Y. Provably efficient neural network representation for image classification. arXiv:171104606 [cs] . 2017 Nov 13; http://arxiv.org/abs/1711.04606

53.

Nomura Y, Darmawan AS, Yamaji Y, Imada M. Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems. Physical Review B . 2017 Nov 29 ;96(20). http://arxiv.org/abs/1709.06475

54.

Cheng S, Chen J, Wang L. Information Perspective to Probabilistic Modeling: Boltzmann Machines versus Born Machines. arXiv:171204144 [cond-mat, physics:physics, physics:quant-ph, stat] . 2017 Dec 12 ; http://arxiv.org/abs/1712.04144

55.

Miyahara H, Sughiyama Y. A Quantum Extension of Variational Bayes Inference. arXiv:171204709 [cond-mat, physics:quant-ph, stat] . 2017 Dec 13 ;http://arxiv.org/abs/1712.04709

56.

Verdon G, Broughton M, Biamonte J. A quantum algorithm to train neural networks using low-depth circuits. arXiv:171205304 [cond-mat, physics:quant-ph] . 2017 Dec 14 ; http://arxiv.org/abs/1712.05304

57.

Stoudenmire EM. Learning Relevant Features of Data with Multi-scale Tensor Networks. arXiv:180100315 [cond-mat, stat] . 2017 Dec 31 ;http://arxiv.org/abs/1801.00315

58.

Glasser I, Pancotti N, August M, Rodriguez ID, Cirac JI. Neural Networks Quantum States, String-Bond States and chiral topological states. Physical Review X . 2018 Jan 11 ;8(1). http://arxiv.org/abs/1710.04045

59.

Li S-H, Wang L. Neural Network Renormalization Group. arXiv:180202840 [cond-mat, stat] . 2018 Feb 8 ; http://arxiv.org/abs/1802.02840

60.

Bény C. Inferring relevant features: from QFT to PCA. arXiv:180205756 [quant-ph, stat] . 2018 Feb 16 ; http://arxiv.org/abs/1802.05756

61.

Torlai G, Mazzola G, Carrasquilla J, Troyer M, Melko R, Carleo G. Many-body quantum state tomography with neural networks. Nature Physics . 2018 Feb 26 ; http://arxiv.org/abs/1703.05334