# Generative Tensor Network Classification Model for Supervised Machine Learning

arXiv: https://arxiv.org/abs/1903.10742 · HTML: https://mlsanity.com/paper/1903.10742/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Mar 2019.

## Built on by (most cited first, 22 of 22)

- [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)
- [Tensor networks for quantum machine learning](https://mlsanity.com/paper/2303.11735/) (2023)
- [Tensor networks for interpretable and efficient quantum-inspired machine learning](https://mlsanity.com/paper/2311.11258/) (2023)
- [Machine learning with tree tensor networks, CP rank constraints, and tensor dropout](https://mlsanity.com/paper/2305.19440/) (2023)
- [Quantum-Inspired Tensor Neural Networks for Partial Differential Equations](https://mlsanity.com/paper/2208.02235/) (2022)
- [Unsupervised Recognition of Informative Features via Tensor Network Machine Learning and Quantum Entanglement Variations](https://mlsanity.com/paper/2207.06031/) (2022)
- [QuFeX: Quantum feature extraction module for hybrid quantum-classical deep neural networks](https://mlsanity.com/paper/2501.13165/) (2025)
- [Positive unlabeled learning with tensor networks](https://mlsanity.com/paper/2211.14085/) (2022)
- [Tensor-Networks-based Learning of Probabilistic Cellular Automata Dynamics](https://mlsanity.com/paper/2404.11768/) (2024)
- [Tensor-Train Networks for Learning Predictive Modeling of Multidimensional Data](https://mlsanity.com/paper/2101.09184/) (2021)
- [Non-parametric Semi-Supervised Learning in Many-body Hilbert Space with Rescaled Logarithmic Fidelity](https://mlsanity.com/paper/2107.00195/) (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)
- [Quantum-Inspired Tensor Neural Networks for Option Pricing](https://mlsanity.com/paper/2212.14076/) (2022)
- [Density peak clustering using tensor network](https://mlsanity.com/paper/2302.00192/) (2023)
- [Universal scaling laws in quantum-probabilistic machine learning by tensor network towards interpreting representation and generalization powers](https://mlsanity.com/paper/2410.09703/) (2024)
- [Intelligent diagnostic scheme for lung cancer screening with Raman spectra data by tensor network machine learning](https://mlsanity.com/paper/2303.06340/) (2023)
- [Application of Tensor Neural Networks to Pricing Bermudan Swaptions](https://mlsanity.com/paper/2304.09750/) (2023)
- [Explaining Anomalies with Tensor Networks](https://mlsanity.com/paper/2505.03911/) (2025)
- [Quantum-inspired tensor networks in machine learning models](https://mlsanity.com/paper/2604.14287/) (2026)
- [On the Approximation Complexity of Matrix Product Operator (MPO) Born Machines](https://mlsanity.com/paper/2605.11471/) (2026)

## Abstract (arXiv)

Tensor network (TN) has recently triggered extensive interests in developing machine-learning models in quantum many-body Hilbert space. Here we purpose a generative TN classification (GTNC) approach for supervised learning. The strategy is to train the generative TN for each class of the samples to construct the classifiers. The classification is implemented by comparing the distance in the many-body Hilbert space. The numerical experiments by GTNC show impressive performance on the MNIST and Fashion-MNIST dataset. The testing accuracy is competitive to the state-of-the-art convolutional neural network while higher than the naive Bayes classifier (a generative classifier) and support vector machine. Moreover, GTNC is more efficient than the existing TN models that are in general discriminative. By investigating the distances in the many-body Hilbert space, we find that (a) the samples are naturally clustering in such a space; and (b) bounding the bond dimensions of the TN's to finite values corresponds to removing redundant information in the image recognition. These two characters make GTNC an adaptive and universal model of excellent performance.