Explaining Anomalies with Tensor Networks

TL;DR

This paper extends tensor network methods for explainable anomaly detection from discrete to real-valued data, introducing tree tensor networks and demonstrating their effectiveness on benchmark problems.

Contribution

It introduces tree tensor networks for explainable anomaly detection on real-valued data, expanding the application scope of tensor networks.

Findings

Adequate predictive performance on benchmark problems

Both tensor network architectures effectively explain anomalies

Extended tensor network applications to broader problem classes

Abstract

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.