# Quantum-inspired tensor networks in machine learning models

arXiv: https://arxiv.org/abs/2604.14287 · HTML: https://mlsanity.com/paper/2604.14287/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 56 of its 144 references that are in the map.
- First posted on arXiv 15 Apr 2026.

## Builds on (most cited first, 30 of 56)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Energy and Policy Considerations for Deep Learning in NLP](https://mlsanity.com/paper/1906.02243/) (2019)
- [Extracting Training Data from Diffusion Models](https://mlsanity.com/paper/2301.13188/) (2023)
- [Pruning and Quantization for Deep Neural Network Acceleration: A Survey](https://mlsanity.com/paper/2101.09671/) (2021)
- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [TensorLy: Tensor Learning in Python](https://mlsanity.com/paper/1610.09555/) (2016)
- [Unsupervised Generative Modeling Using Matrix Product States](https://mlsanity.com/paper/1709.01662/) (2017)
- [A Tensorized Transformer for Language Modeling](https://mlsanity.com/paper/1906.09777/) (2019)
- [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)
- [Expressive power of tensor-network factorizations for probabilistic modeling, with applications from hidden Markov models to quantum machine learning](https://mlsanity.com/paper/1907.03741/) (2019)
- [Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives](https://mlsanity.com/paper/1708.09165/) (2017)
- [Towards Efficient Tensor Decomposition-Based DNN Model Compression with Optimization Framework](https://mlsanity.com/paper/2107.12422/) (2021)
- [Learning Relevant Features of Data with Multi-scale Tensor Networks](https://mlsanity.com/paper/1801.00315/) (2017)
- [An end-to-end trainable hybrid classical-quantum classifier](https://mlsanity.com/paper/2102.02416/) (2021)
- [Quantum Entanglement in Deep Learning Architectures](https://mlsanity.com/paper/1803.09780/) (2018)
- [Machine Learning by Unitary Tensor Network of Hierarchical Tree Structure](https://mlsanity.com/paper/1710.04833/) (2017)
- [From probabilistic graphical models to generalized tensor networks for supervised learning](https://mlsanity.com/paper/1806.05964/) (2018)
- [Tensor Networks Meet Neural Networks: A Survey and Future Perspectives](https://mlsanity.com/paper/2302.09019/) (2023)
- [CompactifAI: Extreme Compression of Large Language Models using Quantum-Inspired Tensor Networks](https://mlsanity.com/paper/2401.14109/) (2024)
- [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)
- [Compressing deep neural networks by matrix product operators](https://mlsanity.com/paper/1904.06194/) (2019)
- [Anomaly Detection with Tensor Networks](https://mlsanity.com/paper/2006.02516/) (2020)
- [Generative Tensor Network Classification Model for Supervised Machine Learning](https://mlsanity.com/paper/1903.10742/) (2019)
- [TensorNetwork: A Library for Physics and Machine Learning](https://mlsanity.com/paper/1905.01330/) (2019)

## Abstract (arXiv)

Tensor networks were developed in the context of many-body physics as compressed representations of multiparticle quantum states. These representations mitigate the exponential complexity of many-body systems by capturing only the most relevant dependencies. Due to the formal similarity between quantum entanglement and statistical correlations, tensor networks have recently been integrated in machine learning, operating both as alternative learning architectures and as decompositions of components of neural networks. The expectation is that the theoretical understanding of tensor networks developed within quantum many-body physics leads to novel methods that offer advantages in terms of computational efficiency, explainability, or privacy. Here we review the use of tensor networks in the context of machine learning, providing a critical assessment of the state of the art, the potential advantages, and the challenges that must be overcome.