# Anomaly Detection with Tensor Networks

arXiv: https://arxiv.org/abs/2006.02516 · HTML: https://mlsanity.com/paper/2006.02516/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jun 2020.

## Built on by (most cited first, 26 of 26)

- [Grokking phase transitions in learning local rules with gradient descent](https://mlsanity.com/paper/2210.15435/) (2022)
- [Tensor networks for quantum machine learning](https://mlsanity.com/paper/2303.11735/) (2023)
- [Tensor networks for interpretable and efficient quantum-inspired machine learning](https://mlsanity.com/paper/2311.11258/) (2023)
- [Tensor Networks for Explainable Machine Learning in Cybersecurity](https://mlsanity.com/paper/2401.00867/) (2023)
- [Quantum-Inspired Machine Learning: a Survey](https://mlsanity.com/paper/2308.11269/) (2023)
- [Quantum-inspired event reconstruction with Tensor Networks: Matrix Product States](https://mlsanity.com/paper/2106.08334/) (2021)
- [Privacy-preserving machine learning with tensor networks](https://mlsanity.com/paper/2202.12319/) (2022)
- [Improvements to Gradient Descent Methods for Quantum Tensor Network Machine Learning](https://mlsanity.com/paper/2203.03366/) (2022)
- [Unsupervised Recognition of Informative Features via Tensor Network Machine Learning and Quantum Entanglement Variations](https://mlsanity.com/paper/2207.06031/) (2022)
- [TensorKrowch: Smooth integration of tensor networks in machine learning](https://mlsanity.com/paper/2306.08595/) (2023)
- [tn4ml: Tensor Network Training and Customization for Machine Learning](https://mlsanity.com/paper/2502.13090/) (2025)
- [Positive unlabeled learning with tensor networks](https://mlsanity.com/paper/2211.14085/) (2022)
- [Tensorization of neural networks for improved privacy and interpretability](https://mlsanity.com/paper/2501.06300/) (2025)
- [Deep tensor networks with matrix product operators](https://mlsanity.com/paper/2209.09098/) (2022)
- [Quantum-inspired Techniques in Tensor Networks for Industrial Contexts](https://mlsanity.com/paper/2404.11277/) (2024)
- [Using matrix-product states for time-series machine learning](https://mlsanity.com/paper/2412.15826/) (2024)
- [Hardware-Aware Tensor Networks for Real-Time Quantum-Inspired Anomaly Detection at Particle Colliders](https://mlsanity.com/paper/2603.26604/) (2026)
- [Cons-training Tensor Networks: Embedding and Optimization Over Discrete Linear Constraints](https://mlsanity.com/paper/2405.09005/) (2024)
- [No-Free-Lunch Theories for Tensor-Network Machine Learning Models](https://mlsanity.com/paper/2412.05674/) (2024)
- [Intelligent diagnostic scheme for lung cancer screening with Raman spectra data by tensor network machine learning](https://mlsanity.com/paper/2303.06340/) (2023)
- [Efficient Finite Initialization with Partial Norms for Tensorized Neural Networks and Tensor Networks Algorithms](https://mlsanity.com/paper/2309.06577/) (2023)
- [T'ecnicas Quantum-Inspired en Tensor Networks para Contextos Industriales](https://mlsanity.com/paper/2404.17645/) (2024)
- [Anomaly Detection from a Tensor Train Perspective](https://mlsanity.com/paper/2409.15030/) (2024)
- [Private and interpretable clinical prediction with quantum-inspired tensor train models](https://mlsanity.com/paper/2602.06110/) (2026)
- [SMT-AD: a scalable quantum-inspired anomaly detection approach](https://mlsanity.com/paper/2604.06265/) (2026)
- [Quantum-inspired tensor networks in machine learning models](https://mlsanity.com/paper/2604.14287/) (2026)

## Abstract (arXiv)

Originating from condensed matter physics, tensor networks are compact representations of high-dimensional tensors. In this paper, the prowess of tensor networks is demonstrated on the particular task of one-class anomaly detection. We exploit the memory and computational efficiency of tensor networks to learn a linear transformation over a space with dimension exponential in the number of original features. The linearity of our model enables us to ensure a tight fit around training instances by penalizing the model's global tendency to a predict normality via its Frobenius norm---a task that is infeasible for most deep learning models. Our method outperforms deep and classical algorithms on tabular datasets and produces competitive results on image datasets, despite not exploiting the locality of images.