# Synthetic Data Generation and Differential Privacy using Tensor Networks' Matrix Product States (MPS)

arXiv: https://arxiv.org/abs/2508.06251 · HTML: https://mlsanity.com/paper/2508.06251/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 5 references that are in the map.
- First posted on arXiv 8 Aug 2025.

## Builds on (most cited first, 3 of 3)

- [Synthesizing Tabular Data using Generative Adversarial Networks](https://mlsanity.com/paper/1811.11264/) (2018)
- [A Unified Framework for Quantifying Privacy Risk in Synthetic Data](https://mlsanity.com/paper/2211.10459/) (2022)
- [High Epsilon Synthetic Data Vulnerabilities in MST and PrivBayes](https://mlsanity.com/paper/2402.06699/) (2024)

## Built on by (most cited first, 1 of 1)

- [Optimizer Dynamics at the Edge of Stability with Differential Privacy](https://mlsanity.com/paper/2512.19019/) (2025)

## Abstract (arXiv)

Synthetic data generation is a key technique in modern artificial intelligence, addressing data scarcity, privacy constraints, and the need for diverse datasets in training robust models. In this work, we propose a method for generating privacy-preserving high-quality synthetic tabular data using Tensor Networks, specifically Matrix Product States (MPS). We benchmark the MPS-based generative model against state-of-the-art models such as CTGAN, VAE, and PrivBayes, focusing on both fidelity and privacy-preserving capabilities. To ensure differential privacy (DP), we integrate noise injection and gradient clipping during training, enabling privacy guarantees via R'enyi Differential Privacy accounting. Across multiple metrics analyzing data fidelity and downstream machine learning task performance, our results show that MPS outperforms classical models, particularly under strict privacy constraints. This work highlights MPS as a promising tool for privacy-aware synthetic data generation. By combining the expressive power of tensor network representations with formal privacy mechanisms, the proposed approach offers an interpretable and scalable alternative for secure data sharing. Its structured design facilitates integration into sensitive domains where both data quality and confidentiality are critical.