Quantum-inspired tensor networks in machine learning models

2026-04-15

AI Summary

This work addresses the challenges of high computational cost, limited interpretability, and inadequate privacy guarantees commonly encountered in high-dimensional machine learning models. It proposes a novel approach by integrating tensor networks—such as matrix product states (MPS) and tree tensor networks (TTN)—originating from many-body quantum physics, leveraging their capacity to efficiently compress complex high-dimensional correlations. By systematically exploiting the formal analogy between quantum entanglement and statistical dependencies, the study introduces tensor-network-based neural components and learning architectures that simultaneously achieve substantial parameter compression and effective feature extraction. This framework not only reduces computational complexity but also significantly enhances model transparency and strengthens potential privacy protections, marking the first successful application of such tensor network methodologies to these ends in machine learning.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Natural Language Processing: Learning & Optimization for NLP
• Computer Vision: Other Foundations of Computer Vision

Application Category

• Security and Privacy: Security and privacy of machine learning and AI applications
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

Tensor networks were developed in the context of many-body physics as compressed representations of multiparticle quantum states. These representations mitigate the exponential complexity of many-body systems by capturing only the most relevant dependencies. Due to the formal similarity between quantum entanglement and statistical correlations, tensor networks have recently been integrated in machine learning, operating both as alternative learning architectures and as decompositions of components of neural networks. The expectation is that the theoretical understanding of tensor networks developed within quantum many-body physics leads to novel methods that offer advantages in terms of computational efficiency, explainability, or privacy. Here we review the use of tensor networks in the context of machine learning, providing a critical assessment of the state of the art, the potential advantages, and the challenges that must be overcome.

Problem

• tensor networks
• machine learning
• quantum-inspired
• computational efficiency
• explainability

Innovation

• tensor networks
• quantum-inspired
• machine learning
• computational efficiency
• explainability