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

TL;DR

This paper introduces a novel tensor network-based method using Matrix Product States for generating high-quality, privacy-preserving synthetic tabular data, outperforming existing models under strict differential privacy constraints.

Contribution

It presents the first application of Tensor Networks, specifically MPS, for differentially private synthetic data generation, demonstrating superior performance over classical models.

Findings

MPS-based model outperforms CTGAN, VAE, PrivBayes in fidelity and privacy.

Differential privacy achieved via noise injection and gradient clipping.

Scalable, interpretable approach suitable for sensitive data domains.

Abstract

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.