Progress in Machine Learning with Tensor Networks

Edwin Miles Stoudenmire

Timo Felser

Edwin Miles Stoudenmire

Shi-Ju Ran, Gang Su

It is a critical challenge to simultaneously achieve high interpretability and high efficiency with the current schemes of deep machine learning (ML). The tensor network (TN), a well-established mathematical tool originating from quantum mechanics, has shown its unique advantages in developing efficient “white-box” ML schemes. Here, we provide a brief review of the inspiring progress in TN-based ML. On the one hand, the interpretability of TN ML can be accommodated by a solid theoretical foundation based on quantum information and many-body physics. On the other hand, high efficiency can be obtained from powerful TN representations and the advanced computational techniques developed in quantum many-body physics. Keeping pace with the rapid development of quantum computers, TNs are expected to produce novel schemes runnable on quantum hardware in the direction of “quantum artificial intelligence” in the near future.

Ding Liu, Yao, Jiaqi, Z. Jamie Yao +1 more

Tensor networks (TN) have found a wide use in machine learning, and in particular, TN and deep learning bear striking similarities. In this work, we propose the quantum-classical hybrid tensor networks (HTN) which combine tensor networks with classical neural networks in a uniform deep learning framework to overcome the limitations of regular tensor networks in machine learning. We first analyze the limitations of regular tensor networks in the applications of machine learning involving the representation power and architecture scalability. We conclude that in fact the regular tensor networks are not competent to be the basic building blocks of deep learning. Then, we discuss the performance of HTN which overcome all the deficiency of regular tensor networks for machine learning. In this sense, we are able to train HTN in the deep learning way which is the standard combination of algorithms such as Back Propagation and Stochastic Gradient Descent. We finally provide two applicable cases to show the potential applications of HTN, including quantum states classification and quantum-classical autoencoder. These cases also demonstrate the great potentiality to design various HTN in deep learning way.

David E. Sommer, Scott T. Dunham

Progress in the application of machine learning techniques to the prediction of solid-state and molecular materials properties has been greatly facilitated by the development state-of-the-art feature representations and novel deep learning architectures. A large class of atomic structure representations based on expansions of smoothed atomic densities have been shown to correspond to specific choices of basis sets in an abstract many-body Hilbert space. Concurrently, tensor network structures, conventionally the purview of quantum many-body physics and quantum information, have been successfully applied in supervised and unsupervised learning tasks in computer vision and natural language processing. In this work, we argue that architectures based on tensor networks are well-suited to machine learning on Hilbert-space representations of atomic structures. This is demonstrated on supervised learning tasks involving widely available datasets of density functional theory calculations of metal and semiconductor alloys. In particular, we show that certain standard tensor network topologies exhibit strong generalizability even on small training datasets while being parametrically efficient. We further relate this generalizability to the presence of complex entanglement in the trained tensor networks. We also discuss connections to learning with generalized structural kernels and related strategies for compressing large input feature spaces.