mlsanityData to 14 Oct 2026

Supervised Learning with Quantum-Inspired Tensor Networks

arXiv 1605.05775 ↗First posted 18 May 2016stat.ML cond-mat.str-el cs.LGcited by 36

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Abstract (arXiv)

Tensor networks are efficient representations of high-dimensional tensors which have been very successful for physics and mathematics applications. We demonstrate how algorithms for optimizing such networks can be adapted to supervised learning tasks by using matrix product states (tensor trains) to parameterize models for classifying images. For the MNIST data set we obtain less than 1% test set classification error. We discuss how the tensor network form imparts additional structure to the learned model and suggest a possible generative interpretation.

Key facts. Cited by 36 papers in the map (data through 14 Oct 2026). First posted on arXiv 18 May 2016.

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Citing papers per year: 2021: 9; 2022: 8; 2023: 4; 2024: 5; 2025: 3; 2026: 7.

36 papers.

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  1. 2021An end-to-end trainable hybrid classical-quantum classifiercited by 51
  2. 2022Grokking phase transitions in learning local rules with gradient descentcited by 28
  3. 2022High-Order Pooling for Graph Neural Networks with Tensor Decompositioncited by 24
  4. 2023Tensor networks for quantum machine learningcited by 17
  5. 2021Differentiable Physics: A Position Piececited by 12
  6. 2021Quantum-inspired event reconstruction with Tensor Networks: Matrix Product Statescited by 9
  7. 2023Generative Learning of Continuous Data by Tensor Networkscited by 9
  8. 2024Classification of the Fashion-MNIST Dataset on a Quantum Computercited by 9
  9. 2021More Efficient Sampling for Tensor Decomposition With Worst-Case Guaranteescited by 7
  10. 2022Classical versus Quantum: comparing Tensor Network-based Quantum Circuits on LHC datacited by 7
  11. 2024A Matrix Product State Model for Simultaneous Classification and Generationcited by 6
  12. 2022Optimizing Tensor Network Contraction Using Reinforcement Learningcited by 5
24 more
  1. 2025tn4ml: Tensor Network Training and Customization for Machine Learningcited by 5
  2. 2022Position: Tensor Networks are a Valuable Asset for Green AIcited by 3
  3. 2022Positive unlabeled learning with tensor networkscited by 3
  4. 2021Tensor-Train Networks for Learning Predictive Modeling of Multidimensional Datacited by 2
  5. 2021Neural Tangent Kernel of Matrix Product States: Convergence and Applicationscited by 2
  6. 2022Deep tensor networks with matrix product operatorscited by 2
  7. 2023Distributive Pre-Training of Generative Modeling Using Matrix-Product Statescited by 2
  8. 2024Using matrix-product states for time-series machine learningcited by 2
  9. 2026Deep Sequence Modeling with Quantum Dynamics: Language as a Wave Functioncited by 2
  10. 2021Rademacher Random Projections with Tensor Networkscited by 1
  11. 2021Learning Circular Hidden Quantum Markov Models: A Tensor Network Approachcited by 1
  12. 2022Group-invariant tensor train networks for supervised learningcited by 1
  13. 2023Tensorizing flows: a tool for variational inferencecited by 1
  14. 2026Quantum-Inspired Robust and Scalable SAR Object Classificationcited by 1
  15. 2021Quantum Machine Learning for Health State Diagnosis and Prognosticscited by 0
  16. 2024Entangling Machine Learning with Quantum Tensor Networkscited by 0
  17. 2024FLAASH: Flexible Accelerator Architecture for Sparse High-Order Tensor Contractioncited by 0
  18. 2025HMAE: Self-Supervised Few-Shot Learning for Quantum Spin Systemscited by 0
  19. 2025Quantum-Inspired Stacked Integrated Concept Graph Model (QISICGM) for Diabetes Risk Predictioncited by 0
  20. 2026Entanglement is Half the Story: Post-Selection vs. Partial Tracescited by 0
  21. 2026(MPO)2: Multivariate Polynomial Optimization based on Matrix Product Operatorscited by 0
  22. 2026Tensor Network Machine Learning for Wildfire Susceptibility Mapping: from Grokking Dynamics to Quantum Mixedness of Class Representationscited by 0
  23. 2026Pre-registered tests of solid-state-physics-inspired LLM compression: a cluster-level negative result at small-language-model scalecited by 0
  24. 2026Diversity-Aware Ensemble of Quantum-Classical Models via Combinatorial Fusioncited by 0