# TensorNetwork for Machine Learning

arXiv: https://arxiv.org/abs/1906.06329 · HTML: https://mlsanity.com/paper/1906.06329/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jun 2019.

## Built on by (most cited first, 29 of 29)

- [An end-to-end trainable hybrid classical-quantum classifier](https://mlsanity.com/paper/2102.02416/) (2021)
- [Variational Quantum Reinforcement Learning via Evolutionary Optimization](https://mlsanity.com/paper/2109.00540/) (2021)
- [Grokking phase transitions in learning local rules with gradient descent](https://mlsanity.com/paper/2210.15435/) (2022)
- [Machine learning with tree tensor networks, CP rank constraints, and tensor dropout](https://mlsanity.com/paper/2305.19440/) (2023)
- [Quantum-Inspired Machine Learning: a Survey](https://mlsanity.com/paper/2308.11269/) (2023)
- [Quantum Tensor Network in Machine Learning: An Application to Tiny Object Classification](https://mlsanity.com/paper/2101.03154/) (2021)
- [Quantum-inspired event reconstruction with Tensor Networks: Matrix Product States](https://mlsanity.com/paper/2106.08334/) (2021)
- [Classical versus Quantum: comparing Tensor Network-based Quantum Circuits on LHC data](https://mlsanity.com/paper/2202.10471/) (2022)
- [Quantized Fourier and Polynomial Features for more Expressive Tensor Network Models](https://mlsanity.com/paper/2309.05436/) (2023)
- [A Matrix Product State Model for Simultaneous Classification and Generation](https://mlsanity.com/paper/2406.17441/) (2024)
- [Entangled q-Convolutional Neural Nets](https://mlsanity.com/paper/2103.11785/) (2021)
- [Tensor network to learn the wavefunction of data](https://mlsanity.com/paper/2111.08014/) (2021)
- [Interaction Decompositions for Tensor Network Regression](https://mlsanity.com/paper/2208.06029/) (2022)
- [Ultra-low latency quantum-inspired machine learning predictors implemented on FPGA](https://mlsanity.com/paper/2409.16075/) (2024)
- [Segmenting two-dimensional structures with strided tensor networks](https://mlsanity.com/paper/2102.06900/) (2021)
- [Residual Tensor Train: A Quantum-inspired Approach for Learning Multiple Multilinear Correlations](https://mlsanity.com/paper/2108.08659/) (2021)
- [Classical Simulation of Variational Quantum Classifiers using Tensor Rings](https://mlsanity.com/paper/2201.08878/) (2022)
- [Non-parametric Semi-Supervised Learning in Many-body Hilbert Space with Rescaled Logarithmic Fidelity](https://mlsanity.com/paper/2107.00195/) (2021)
- [Patch-based Medical Image Segmentation using Matrix Product State Tensor Networks](https://mlsanity.com/paper/2109.07138/) (2021)
- [Differentiable Programming of Isometric Tensor Networks](https://mlsanity.com/paper/2110.03898/) (2021)
- [Deep tensor networks with matrix product operators](https://mlsanity.com/paper/2209.09098/) (2022)
- [Representation Theorem for Matrix Product States](https://mlsanity.com/paper/2103.08277/) (2021)
- [The cross-sectional stock return predictions via quantum neural network and tensor network](https://mlsanity.com/paper/2304.12501/) (2023)
- [No-Free-Lunch Theories for Tensor-Network Machine Learning Models](https://mlsanity.com/paper/2412.05674/) (2024)
- [Tensor Network for Supervised Learning at Finite Temperature](https://mlsanity.com/paper/2104.05439/) (2021)
- [Stack operation of tensor networks](https://mlsanity.com/paper/2203.16338/) (2022)
- [Noisy Tensor Ring approximation for computing gradients of Variational Quantum Eigensolver for Combinatorial Optimization](https://mlsanity.com/paper/2307.03884/) (2023)
- [A Tensor Network Implementation of Multi Agent Reinforcement Learning](https://mlsanity.com/paper/2401.03896/) (2024)
- [(MPO)2: Multivariate Polynomial Optimization based on Matrix Product Operators](https://mlsanity.com/paper/2607.15916/) (2026)

## Abstract (arXiv)

We demonstrate the use of tensor networks for image classification with the TensorNetwork open source library. We explain in detail the encoding of image data into a matrix product state form, and describe how to contract the network in a way that is parallelizable and well-suited to automatic gradients for optimization. Applying the technique to the MNIST and Fashion-MNIST datasets we find out-of-the-box performance of 98% and 88% accuracy, respectively, using the same tensor network architecture. The TensorNetwork library allows us to seamlessly move from CPU to GPU hardware, and we see a factor of more than 10 improvement in computational speed using a GPU.