mlsanityData to 14 Oct 2026

Explaining Anomalies with Tensor Networks

arXiv 2505.03911 ↗First posted 6 May 2025cs.LG quant-phcited by 0

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Abstract (arXiv)

Tensor networks, a class of variational quantum many-body wave functions have attracted considerable research interest across many disciplines, including classical machine learning. Recently, Aizpurua et al. demonstrated explainable anomaly detection with matrix product states on a discrete-valued cyber-security task, using quantum-inspired methods to gain insight into the learned model and detected anomalies. Here, we extend this framework to real-valued data domains. We furthermore introduce tree tensor networks for the task of explainable anomaly detection. We demonstrate these methods with three benchmark problems, show adequate predictive performance compared to several baseline models and both tensor network architectures' ability to explain anomalous samples. We thereby extend the application of tensor networks to a broader class of potential problems and open a pathway for future extensions to more complex tensor network architectures.

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References · 21

  1. 2019Optuna: A Next-generation Hyperparameter Optimization Frameworkcited by 2,501
  2. 2015Tensorizing Neural Networkscited by 250
  3. 2022ADBench: Anomaly Detection Benchmarkcited by 232
  4. 2017Unsupervised Generative Modeling Using Matrix Product Statescited by 88
  5. 2018Towards Quantum Machine Learning with Tensor Networkscited by 76
  6. 2019Tree Tensor Networks for Generative Modelingcited by 64
  7. 2017Learning Relevant Features of Data with Multi-scale Tensor Networkscited by 51
  8. 2017Machine Learning by Unitary Tensor Network of Hierarchical Tree Structurecited by 40
  9. 2022A Survey on Explainable Anomaly Detectioncited by 39
  10. 2018From probabilistic graphical models to generalized tensor networks for supervised learningcited by 32
  11. 2024CompactifAI: Extreme Compression of Large Language Models using Quantum-Inspired Tensor Networkscited by 32
  12. 2021Tensor-Train Density Estimationcited by 30
9 more
  1. 2019Generative Tensor Network Classification Model for Supervised Machine Learningcited by 22
  2. 2019T-Net: Parametrizing Fully Convolutional Nets with a Single High-Order Tensorcited by 22
  3. 2023Tensor networks for quantum machine learningcited by 17
  4. 2023Tensor Networks for Explainable Machine Learning in Cybersecuritycited by 14
  5. 2022Generative modeling via tensor train sketchingcited by 13
  6. 2023Generative Learning of Continuous Data by Tensor Networkscited by 9
  7. 2023Generative Modeling via Hierarchical Tensor Sketchingcited by 8
  8. 2024Quantum Large Language Models via Tensor Network Disentanglerscited by 7
  9. 2018Shortcut Matrix Product States and its applicationscited by 4

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