# Privacy-preserving machine learning with tensor networks

arXiv: https://arxiv.org/abs/2202.12319 · HTML: https://mlsanity.com/paper/2202.12319/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 59 references that are in the map.
- First posted on arXiv 24 Feb 2022.

## Builds on (most cited first, 21 of 21)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/1610.05820/) (2016)
- [Stealing Machine Learning Models via Prediction APIs](https://mlsanity.com/paper/1609.02943/) (2016)
- [High Accuracy and High Fidelity Extraction of Neural Networks](https://mlsanity.com/paper/1909.01838/) (2019)
- [Hacking Smart Machines with Smarter Ones: How to Extract Meaningful Data from Machine Learning Classifiers](https://mlsanity.com/paper/1306.4447/) (2013)
- [A Tensorized Transformer for Language Modeling](https://mlsanity.com/paper/1906.09777/) (2019)
- [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)
- [Universal Quantum Control through Deep Reinforcement Learning](https://mlsanity.com/paper/1803.01857/) (2018)
- [Machine Learning by Unitary Tensor Network of Hierarchical Tree Structure](https://mlsanity.com/paper/1710.04833/) (2017)
- [Inverse statistical problems: from the inverse Ising problem to data science](https://mlsanity.com/paper/1702.01522/) (2017)
- [From probabilistic graphical models to generalized tensor networks for supervised learning](https://mlsanity.com/paper/1806.05964/) (2018)
- [Supervised Learning with Projected Entangled Pair States](https://mlsanity.com/paper/2009.09932/) (2020)
- [Anomaly Detection with Tensor Networks](https://mlsanity.com/paper/2006.02516/) (2020)
- [Tensor Networks for Medical Image Classification](https://mlsanity.com/paper/2004.10076/) (2020)
- [Parallelized Tensor Train Learning of Polynomial Classifiers](https://mlsanity.com/paper/1612.06505/) (2016)
- [Large-Scale Learning with Fourier Features and Tensor Decompositions](https://mlsanity.com/paper/2109.01545/) (2021)
- [Preserving Differential Privacy in Convolutional Deep Belief Networks](https://mlsanity.com/paper/1706.08839/) (2017)
- [A Prior of a Googol Gaussians: a Tensor Ring Induced Prior for Generative Models](https://mlsanity.com/paper/1910.13148/) (2019)
- [A Deterministic and Generalized Framework for Unsupervised Learning with Restricted Boltzmann Machines](https://mlsanity.com/paper/1702.03260/) (2017)
- [Efficient training of energy-based models via spin-glass control](https://mlsanity.com/paper/1910.01592/) (2019)

## Built on by (most cited first, 9 of 9)

- [A Matrix Product State Model for Simultaneous Classification and Generation](https://mlsanity.com/paper/2406.17441/) (2024)
- [Tensorization of neural networks for improved privacy and interpretability](https://mlsanity.com/paper/2501.06300/) (2025)
- [Quantum-inspired Techniques in Tensor Networks for Industrial Contexts](https://mlsanity.com/paper/2404.11277/) (2024)
- [Cons-training Tensor Networks: Embedding and Optimization Over Discrete Linear Constraints](https://mlsanity.com/paper/2405.09005/) (2024)
- [Universal scaling laws in quantum-probabilistic machine learning by tensor network towards interpreting representation and generalization powers](https://mlsanity.com/paper/2410.09703/) (2024)
- [T'ecnicas Quantum-Inspired en Tensor Networks para Contextos Industriales](https://mlsanity.com/paper/2404.17645/) (2024)
- [Private and interpretable clinical prediction with quantum-inspired tensor train models](https://mlsanity.com/paper/2602.06110/) (2026)
- [Quantum-inspired tensor networks in machine learning models](https://mlsanity.com/paper/2604.14287/) (2026)
- [Gaussian Universality and Its Breakdown in Tensor-Network Machine Learning](https://mlsanity.com/paper/2610.06080/) (2026)

## Abstract (arXiv)

Tensor networks, widely used for providing efficient representations of low-energy states of local quantum many-body systems, have been recently proposed as machine learning architectures which could present advantages with respect to traditional ones. In this work we show that tensor network architectures have especially prospective properties for privacy-preserving machine learning, which is important in tasks such as the processing of medical records. First, we describe a new privacy vulnerability that is present in feedforward neural networks, illustrating it in synthetic and real-world datasets. Then, we develop well-defined conditions to guarantee robustness to such vulnerability, which involve the characterization of models equivalent under gauge symmetry. We rigorously prove that such conditions are satisfied by tensor-network architectures. In doing so, we define a novel canonical form for matrix product states, which has a high degree of regularity and fixes the residual gauge that is left in the canonical forms based on singular value decompositions. We supplement the analytical findings with practical examples where matrix product states are trained on datasets of medical records, which show large reductions on the probability of an attacker extracting information about the training dataset from the model's parameters. Given the growing expertise in training tensor-network architectures, these results imply that one may not have to be forced to make a choice between accuracy in prediction and ensuring the privacy of the information processed.