# Explaining Anomalies with Tensor Networks

arXiv: https://arxiv.org/abs/2505.03911 · HTML: https://mlsanity.com/paper/2505.03911/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 46 references that are in the map.
- First posted on arXiv 6 May 2025.

## Builds on (most cited first, 21 of 21)

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [ADBench: Anomaly Detection Benchmark](https://mlsanity.com/paper/2206.09426/) (2022)
- [Unsupervised Generative Modeling Using Matrix Product States](https://mlsanity.com/paper/1709.01662/) (2017)
- [Towards Quantum Machine Learning with Tensor Networks](https://mlsanity.com/paper/1803.11537/) (2018)
- [Tree Tensor Networks for Generative Modeling](https://mlsanity.com/paper/1901.02217/) (2019)
- [Learning Relevant Features of Data with Multi-scale Tensor Networks](https://mlsanity.com/paper/1801.00315/) (2017)
- [Machine Learning by Unitary Tensor Network of Hierarchical Tree Structure](https://mlsanity.com/paper/1710.04833/) (2017)
- [A Survey on Explainable Anomaly Detection](https://mlsanity.com/paper/2210.06959/) (2022)
- [From probabilistic graphical models to generalized tensor networks for supervised learning](https://mlsanity.com/paper/1806.05964/) (2018)
- [CompactifAI: Extreme Compression of Large Language Models using Quantum-Inspired Tensor Networks](https://mlsanity.com/paper/2401.14109/) (2024)
- [Tensor-Train Density Estimation](https://mlsanity.com/paper/2108.00089/) (2021)
- [Generative Tensor Network Classification Model for Supervised Machine Learning](https://mlsanity.com/paper/1903.10742/) (2019)
- [T-Net: Parametrizing Fully Convolutional Nets with a Single High-Order Tensor](https://mlsanity.com/paper/1904.02698/) (2019)
- [Tensor networks for quantum machine learning](https://mlsanity.com/paper/2303.11735/) (2023)
- [Tensor Networks for Explainable Machine Learning in Cybersecurity](https://mlsanity.com/paper/2401.00867/) (2023)
- [Generative modeling via tensor train sketching](https://mlsanity.com/paper/2202.11788/) (2022)
- [Generative Learning of Continuous Data by Tensor Networks](https://mlsanity.com/paper/2310.20498/) (2023)
- [Generative Modeling via Hierarchical Tensor Sketching](https://mlsanity.com/paper/2304.05305/) (2023)
- [Quantum Large Language Models via Tensor Network Disentanglers](https://mlsanity.com/paper/2410.17397/) (2024)
- [Shortcut Matrix Product States and its applications](https://mlsanity.com/paper/1812.05248/) (2018)

## 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.