mlsanityData to 7 Oct 2026

Machine Learning by Unitary Tensor Network of Hierarchical Tree Structure

arXiv 1710.04833 ↗First posted 13 Oct 2017stat.ML cond-mat.str-el physics.comp-phcited by 39

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Abstract (arXiv)

The resemblance between the methods used in quantum-many body physics and in machine learning has drawn considerable attention. In particular, tensor networks (TNs) and deep learning architectures bear striking similarities to the extent that TNs can be used for machine learning. Previous results used one-dimensional TNs in image recognition, showing limited scalability and flexibilities. In this work, we train two-dimensional hierarchical TNs to solve image recognition problems, using a training algorithm derived from the multi-scale entanglement renormalization ansatz. This approach introduces mathematical connections among quantum many-body physics, quantum information theory, and machine learning. While keeping the TN unitary in the training phase, TN states are defined, which encode classes of images into quantum many-body states. We study the quantum features of the TN states, including quantum entanglement and fidelity. We find these quantities could be properties that characterize the image classes, as well as the machine learning tasks.

Key facts. Cited by 39 papers in the map (data through 7 Oct 2026). First posted on arXiv 13 Oct 2017.

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Citing papers per year: 2021: 7; 2022: 9; 2023: 7; 2024: 4; 2025: 8; 2026: 4.

39 papers.

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  1. 2021Variational Quantum Reinforcement Learning via Evolutionary Optimizationcited by 50
  2. 2022Grokking phase transitions in learning local rules with gradient descentcited by 28
  3. 2021Tensor networks for unsupervised machine learningcited by 20
  4. 2023Tensor networks for quantum machine learningcited by 16
  5. 2023Tensor networks for interpretable and efficient quantum-inspired machine learningcited by 16
  6. 2023Machine learning with tree tensor networks, CP rank constraints, and tensor dropoutcited by 14
  7. 2022Quantum-Inspired Tensor Neural Networks for Partial Differential Equationscited by 9
  8. 2022Privacy-preserving machine learning with tensor networkscited by 8
  9. 2021More Efficient Sampling for Tensor Decomposition With Worst-Case Guaranteescited by 7
  10. 2021Explainable Natural Language Processing with Matrix Product Statescited by 7
  11. 2022Classical versus Quantum: comparing Tensor Network-based Quantum Circuits on LHC datacited by 7
  12. 2022Unsupervised Recognition of Informative Features via Tensor Network Machine Learning and Quantum Entanglement Variationscited by 7
27 more
  1. 2023TensorKrowch: Smooth integration of tensor networks in machine learningcited by 5
  2. 2021Entangled q-Convolutional Neural Netscited by 4
  3. 2021Automatically Differentiable Quantum Circuit for Many-qubit State Preparationcited by 4
  4. 2022Interaction Decompositions for Tensor Network Regressioncited by 4
  5. 2025Deep Tree Tensor Networkscited by 4
  6. 2025Tensorization of neural networks for improved privacy and interpretabilitycited by 3
  7. 2025Tensorization is a powerful but underexplored tool for compression and interpretability of neural networkscited by 3
  8. 2025Riemannian Optimization on Tree Tensor Networks with Application in Machine Learningcited by 3
  9. 2021Non-parametric Semi-Supervised Learning in Many-body Hilbert Space with Rescaled Logarithmic Fidelitycited by 2
  10. 2022Deep tensor networks with matrix product operatorscited by 2
  11. 2024Tensor-Networks-based Learning of Probabilistic Cellular Automata Dynamicscited by 2
  12. 2022Quantum-Inspired Tensor Neural Networks for Option Pricingcited by 1
  13. 2023T-ADAF: Adaptive Data Augmentation Framework for Image Classification Network based on Tensor T-product Operatorcited by 1
  14. 2024Cons-training Tensor Networks: Embedding and Optimization Over Discrete Linear Constraintscited by 1
  15. 2024Universal scaling laws in quantum-probabilistic machine learning by tensor network towards interpreting representation and generalization powerscited by 1
  16. 2022Stack operation of tensor networkscited by 0
  17. 2023Intelligent diagnostic scheme for lung cancer screening with Raman spectra data by tensor network machine learningcited by 0
  18. 2023Application of Tensor Neural Networks to Pricing Bermudan Swaptionscited by 0
  19. 2024Entangling Machine Learning with Quantum Tensor Networkscited by 0
  20. 2025Trainable Quantum Neural Network for Multiclass Image Classification with the Power of Pre-trained Tree Tensor Networkscited by 0
  21. 2025HMAE: Self-Supervised Few-Shot Learning for Quantum Spin Systemscited by 0
  22. 2025Explaining Anomalies with Tensor Networkscited by 0
  23. 2025Hybrid quantum tensor networks for aeroelastic applicationscited by 0
  24. 2026Efficient Generative Modeling with Unitary Matrix Product States Using Riemannian Optimizationcited by 0
  25. 2026Quantum-Inspired Tensor Network Autoencoders for Anomaly Detection: A MERA-Based Approachcited by 0
  26. 2026Tensor-Augmented Convolutional Neural Networks: Enhancing Expressivity with Generic Tensor Kernelscited by 0
  27. 2026Quantum-inspired tensor networks in machine learning modelscited by 0