# Tensor networks for interpretable and efficient quantum-inspired machine learning

arXiv: https://arxiv.org/abs/2311.11258 · HTML: https://mlsanity.com/paper/2311.11258/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 57 of its 192 references that are in the map.
- First posted on arXiv 19 Nov 2023.

## Builds on (most cited first, 30 of 57)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [The Mythos of Model Interpretability](https://mlsanity.com/paper/1606.03490/) (2016)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [One pixel attack for fooling deep neural networks](https://mlsanity.com/paper/1710.08864/) (2017)
- [Explaining Explanations: An Overview of Interpretability of Machine Learning](https://mlsanity.com/paper/1806.00069/) (2018)
- [Opening the Black Box of Deep Neural Networks via Information](https://mlsanity.com/paper/1703.00810/) (2017)
- [Post-hoc Interpretability for Neural NLP: A Survey](https://mlsanity.com/paper/2108.04840/) (2021)
- [Visual Interpretability for Deep Learning: a Survey](https://mlsanity.com/paper/1802.00614/) (2018)
- [Tensor Ring Decomposition](https://mlsanity.com/paper/1606.05535/) (2016)
- [Theory of overparametrization in quantum neural networks](https://mlsanity.com/paper/2109.11676/) (2021)
- [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)
- [Tensor-Train Recurrent Neural Networks for Video Classification](https://mlsanity.com/paper/1707.01786/) (2017)
- [q-means: A quantum algorithm for unsupervised machine learning](https://mlsanity.com/paper/1812.03584/) (2018)
- [Convolutional Tensor-Train LSTM for Spatio-temporal Learning](https://mlsanity.com/paper/2002.09131/) (2020)
- [Learning Relevant Features of Data with Multi-scale Tensor Networks](https://mlsanity.com/paper/1801.00315/) (2017)
- [Wide Compression: Tensor Ring Nets](https://mlsanity.com/paper/1802.09052/) (2018)
- [Tensor Ring Decomposition with Rank Minimization on Latent Space: An Efficient Approach for Tensor Completion](https://mlsanity.com/paper/1809.02288/) (2018)
- [Enhancing Generative Models via Quantum Correlations](https://mlsanity.com/paper/2101.08354/) (2021)
- [Machine Learning by Unitary Tensor Network of Hierarchical Tree Structure](https://mlsanity.com/paper/1710.04833/) (2017)
- [Compressing Recurrent Neural Networks with Tensor Ring for Action Recognition](https://mlsanity.com/paper/1811.07503/) (2018)
- [Mutual Information, Neural Networks and the Renormalization Group](https://mlsanity.com/paper/1704.06279/) (2017)
- [Information Perspective to Probabilistic Modeling: Boltzmann Machines versus Born Machines](https://mlsanity.com/paper/1712.04144/) (2017)
- [Tensor Networks Meet Neural Networks: A Survey and Future Perspectives](https://mlsanity.com/paper/2302.09019/) (2023)
- [Neural-Network Quantum States, String-Bond States, and Chiral Topological States](https://mlsanity.com/paper/1710.04045/) (2017)
- [Quantum-inspired Machine Learning on high-energy physics data](https://mlsanity.com/paper/2004.13747/) (2020)
- [Supervised Learning with Projected Entangled Pair States](https://mlsanity.com/paper/2009.09932/) (2020)
- [Compressing Recurrent Neural Network with Tensor Train](https://mlsanity.com/paper/1705.08052/) (2017)

## Built on by (most cited first, 17 of 17)

- [Tensor Networks for Explainable Machine Learning in Cybersecurity](https://mlsanity.com/paper/2401.00867/) (2023)
- [Interpretable Machine Learning in Physics: A Review](https://mlsanity.com/paper/2503.23616/) (2025)
- [SHAP Meets Tensor Networks: Provably Tractable Explanations with Parallelism](https://mlsanity.com/paper/2510.21599/) (2025)
- [Federated Hierarchical Tensor Networks: a Collaborative Learning Quantum AI-Driven Framework for Healthcare](https://mlsanity.com/paper/2405.07735/) (2024)
- [Deep Tree Tensor Networks](https://mlsanity.com/paper/2502.09928/) (2025)
- [tn4ml: Tensor Network Training and Customization for Machine Learning](https://mlsanity.com/paper/2502.13090/) (2025)
- [Tensor Network for Anomaly Detection in the Latent Space of Proton Collision Events at the LHC](https://mlsanity.com/paper/2506.00102/) (2025)
- [Hardware-Aware Tensor Networks for Real-Time Quantum-Inspired Anomaly Detection at Particle Colliders](https://mlsanity.com/paper/2603.26604/) (2026)
- [Universal scaling laws in quantum-probabilistic machine learning by tensor network towards interpreting representation and generalization powers](https://mlsanity.com/paper/2410.09703/) (2024)
- [Tensor Network Estimation of Distribution Algorithms](https://mlsanity.com/paper/2412.19780/) (2024)
- [A Quantum Tensor Network-Based Viewpoint for Modeling and Analysis of Time Series Data](https://mlsanity.com/paper/2511.13514/) (2025)
- [Dimension reduction with structure-aware quantum circuits for hybrid machine learning](https://mlsanity.com/paper/2508.00048/) (2025)
- [Structured Unitary Tensor Network Representations for Circuit-Efficient Quantum Data Encoding](https://mlsanity.com/paper/2602.16266/) (2026)
- [Quantum-inspired tensor networks in machine learning models](https://mlsanity.com/paper/2604.14287/) (2026)
- [A Hamiltonian-Inspired Local-Operator Ansatz for Slimming Large Language Models](https://mlsanity.com/paper/2605.25344/) (2026)
- [LLMs Interpret, Embeddings Organize, Graphs Emerge: Agent-Driven Compilation of Scientific Knowledge](https://mlsanity.com/paper/2608.29612/) (2026)
- [Gaussian Universality and Its Breakdown in Tensor-Network Machine Learning](https://mlsanity.com/paper/2610.06080/) (2026)

## Abstract (arXiv)

It is a critical challenge to simultaneously gain high interpretability and efficiency with the current schemes of deep machine learning (ML). Tensor network (TN), which is a well-established mathematical tool originating from quantum mechanics, has shown its unique advantages on developing efficient ``white-box'' ML schemes. Here, we give a brief review on the inspiring progresses made in TN-based ML. On one hand, interpretability of TN ML is accommodated with the solid theoretical foundation based on quantum information and many-body physics. On the other hand, high efficiency can be rendered from the powerful TN representations and the advanced computational techniques developed in quantum many-body physics. With the fast development on quantum computers, TN is expected to conceive novel schemes runnable on quantum hardware, heading towards the ``quantum artificial intelligence'' in the forthcoming future.