Quantum-inspired tensor networks in machine learning models

TL;DR

This paper reviews how tensor networks, originally from quantum physics, are applied in machine learning to improve efficiency, explainability, and privacy, highlighting current methods, benefits, and challenges.

Contribution

It provides a comprehensive review of tensor networks in machine learning, emphasizing their potential advantages and the challenges faced in integrating quantum-inspired methods.

Findings

Tensor networks can effectively compress neural network components.

Quantum-inspired tensor methods offer computational efficiency benefits.

Challenges include adapting quantum concepts to classical machine learning.

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.