# Tensor networks in machine learning

arXiv: https://arxiv.org/abs/2207.02851 · HTML: https://mlsanity.com/paper/2207.02851/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 49 references that are in the map.
- First posted on arXiv 6 Jul 2022.

## Builds on (most cited first, 6 of 6)

- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives](https://mlsanity.com/paper/1708.09165/) (2017)
- [Machine Learning Phase Transitions with a Quantum Processor](https://mlsanity.com/paper/1906.10155/) (2019)
- [Quantum-machine-learning channel discrimination](https://mlsanity.com/paper/2206.09933/) (2022)

## Built on by (most cited first, 7 of 7)

- [Ultra-low latency quantum-inspired machine learning predictors implemented on FPGA](https://mlsanity.com/paper/2409.16075/) (2024)
- [Automating Data Science Pipelines with Tensor Completion](https://mlsanity.com/paper/2410.06408/) (2024)
- [MetaLoRA: Tensor-Enhanced Adaptive Low-Rank Fine-tuning](https://mlsanity.com/paper/2504.00460/) (2025)
- [Application of Tensorized Neural Networks for Cloud Classification](https://mlsanity.com/paper/2405.10946/) (2024)
- [Quantum-based QoE Optimization in Advanced Cellular Networks: Integration and Cloud Gaming Use Case](https://mlsanity.com/paper/2509.01008/) (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)

## Abstract (arXiv)

A tensor network is a type of decomposition used to express and approximate large arrays of data. A given data-set, quantum state or higher dimensional multi-linear map is factored and approximated by a composition of smaller multi-linear maps. This is reminiscent to how a Boolean function might be decomposed into a gate array: this represents a special case of tensor decomposition, in which the tensor entries are replaced by 0, 1 and the factorisation becomes exact. The collection of associated techniques are called, tensor network methods: the subject developed independently in several distinct fields of study, which have more recently become interrelated through the language of tensor networks. The tantamount questions in the field relate to expressability of tensor networks and the reduction of computational overheads. A merger of tensor networks with machine learning is natural. On the one hand, machine learning can aid in determining a factorization of a tensor network approximating a data set. On the other hand, a given tensor network structure can be viewed as a machine learning model. Herein the tensor network parameters are adjusted to learn or classify a data-set. In this survey we recover the basics of tensor networks and explain the ongoing effort to develop the theory of tensor networks in machine learning.