Quantum-inspired tensor networks in machine learning models
For machine learning researchers, this review clarifies the state and potential of tensor network methods, but it is a survey without new results.
This review examines the integration of tensor networks, originally from quantum many-body physics, into machine learning models, assessing their potential for computational efficiency, explainability, and privacy. It provides a critical overview of current methods, advantages, and challenges.
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.