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

2025/08/08 by Alejandro Moreno R., R., Alejandro Moreno, Desale Fentaw +16 · 1 citation
Computer Science · Decision Sciences · #Artificial Intelligence (cs.AI) #Big Data Technologies and Applications #Cryptography and Security (cs.CR) #Data Visualization and Analytics #Digital and Cyber Forensics #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning (cs.LG) #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2508.06251

openalex publication_date 2025/08/08 · openalex created_date 2025/10/15 · openalex updated_date 2026/07/28

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 Rényi 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.

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