mlsanityData to 14 Oct 2026

Quantum-inspired tensor networks in machine learning models

arXiv 2604.14287 ↗First posted 15 Apr 2026cs.LG cs.AI quant-phcited by 0

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Abstract (arXiv)

Tensor networks were developed in the context of many-body physics as compressed representations of multiparticle quantum states. These representations mitigate the exponential complexity of many-body systems by capturing only the most relevant dependencies. Due to the formal similarity between quantum entanglement and statistical correlations, tensor networks have recently been integrated in machine learning, operating both as alternative learning architectures and as decompositions of components of neural networks. The expectation is that the theoretical understanding of tensor networks developed within quantum many-body physics leads to novel methods that offer advantages in terms of computational efficiency, explainability, or privacy. Here we review the use of tensor networks in the context of machine learning, providing a critical assessment of the state of the art, the potential advantages, and the challenges that must be overcome.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 56 of its 144 references that are in the map. First posted on arXiv 15 Apr 2026.

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References · 56

  1. 2017Attention Is All You Needcited by 60,361
  2. 2014Very Deep Convolutional Networks for Large-Scale Image Recognitioncited by 15,364
  3. 2021LoRA: Low-Rank Adaptation of Large Language Modelscited by 14,380
  4. 2019Energy and Policy Considerations for Deep Learning in NLPcited by 1,254
  5. 2023Extracting Training Data from Diffusion Modelscited by 732
  6. 2021Pruning and Quantization for Deep Neural Network Acceleration: A Surveycited by 263
  7. 2015Tensorizing Neural Networkscited by 250
  8. 2016TensorLy: Tensor Learning in Pythoncited by 104
  9. 2017Unsupervised Generative Modeling Using Matrix Product Statescited by 88
  10. 2019A Tensorized Transformer for Language Modelingcited by 86
  11. 2018Towards Quantum Machine Learning with Tensor Networkscited by 76
  12. 2019Tree Tensor Networks for Generative Modelingcited by 64
38 more
  1. 2017Tensor-Train Recurrent Neural Networks for Video Classificationcited by 59
  2. 2019Expressive power of tensor-network factorizations for probabilistic modeling, with applications from hidden Markov models to quantum machine learningcited by 55
  3. 2017Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectivescited by 54
  4. 2021Towards Efficient Tensor Decomposition-Based DNN Model Compression with Optimization Frameworkcited by 52
  5. 2017Learning Relevant Features of Data with Multi-scale Tensor Networkscited by 51
  6. 2021An end-to-end trainable hybrid classical-quantum classifiercited by 51
  7. 2018Quantum Entanglement in Deep Learning Architecturescited by 50
  8. 2017Machine Learning by Unitary Tensor Network of Hierarchical Tree Structurecited by 40
  9. 2018From probabilistic graphical models to generalized tensor networks for supervised learningcited by 32
  10. 2023Tensor Networks Meet Neural Networks: A Survey and Future Perspectivescited by 32
  11. 2024CompactifAI: Extreme Compression of Large Language Models using Quantum-Inspired Tensor Networkscited by 32
  12. 2020Quantum-inspired Machine Learning on high-energy physics datacited by 31
  13. 2020Supervised Learning with Projected Entangled Pair Statescited by 31
  14. 2017Compressing Recurrent Neural Network with Tensor Traincited by 28
  15. 2019Compressing deep neural networks by matrix product operatorscited by 28
  16. 2020Anomaly Detection with Tensor Networkscited by 26
  17. 2019Generative Tensor Network Classification Model for Supervised Machine Learningcited by 22
  18. 2019TensorNetwork: A Library for Physics and Machine Learningcited by 21
  19. 2020Tensorizing GAN with High-Order Pooling for Alzheimer's Disease Assessmentcited by 21
  20. 2021Tensor networks for unsupervised machine learningcited by 21
  21. 2023Tensor networks for quantum machine learningcited by 17
  22. 2023Tensor networks for interpretable and efficient quantum-inspired machine learningcited by 17
  23. 2016Parallelized Tensor Train Learning of Polynomial Classifierscited by 16
  24. 2023Machine learning with tree tensor networks, CP rank constraints, and tensor dropoutcited by 15
  25. 2023Tensor Networks for Explainable Machine Learning in Cybersecuritycited by 14
  26. 2024LoRETTA: Low-Rank Economic Tensor-Train Adaptation for Ultra-Low-Parameter Fine-Tuning of Large Language Modelscited by 12
  27. 2021Quantum Tensor Network in Machine Learning: An Application to Tiny Object Classificationcited by 9
  28. 2021TedNet: A Pytorch Toolkit for Tensor Decomposition Networkscited by 9
  29. 2022Privacy-preserving machine learning with tensor networkscited by 9
  30. 2023Generative Learning of Continuous Data by Tensor Networkscited by 9
  31. 2025SHAP Meets Tensor Networks: Provably Tractable Explanations with Parallelismcited by 8
  32. 2021Explainable Natural Language Processing with Matrix Product Statescited by 7
  33. 2022tntorch: Tensor Network Learning with PyTorchcited by 7
  34. 2022Tensor networks in machine learningcited by 7
  35. 2021Tensor-Train Recurrent Neural Networks for Interpretable Multi-Way Financial Forecastingcited by 6
  36. 2021Efficient Tensor Robust PCA under Hybrid Model of Tucker and Tensor Traincited by 6
  37. 2024A Matrix Product State Model for Simultaneous Classification and Generationcited by 6
  38. 2024Discrete generative diffusion models without stochastic differential equations: a tensor network approachcited by 6

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