Privacy-preserving machine learning with tensor networks

Abstract

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.

16 pages, 2 figures. Quantumarticle 6.1. The computational appendix is available at https://www.github.com/apozas/private-tn V3: Published version

References in corpus (4)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Supervised Learning with Projected Entangled Pair States
• Symmetric Tensor Networks for Generative Modeling and Constrained Combinatorial Optimization

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• Tensorization of neural networks for improved privacy and interpretability