Tensor tree learns hidden relational structures in data to construct generative models

Abstract

Based on the tensor tree network with the Born machine framework, we propose a general method for constructing a generative model by expressing the target distribution function as the amplitude of the quantum wave function represented by a tensor tree. The key idea is dynamically optimizing the tree structure that minimizes the bond mutual information. The proposed method offers enhanced performance and uncovers hidden relational structures in the target data. We illustrate potential practical applications with four examples: (i) random patterns, (ii) QMNIST handwritten digits, (iii) Bayesian networks, and (iv) the pattern of stock price fluctuation pattern in S&P500. In (i) and (ii), the strongly correlated variables were concentrated near the center of the network; in (iii), the causality pattern was identified; and in (iv), a structure corresponding to the eleven sectors emerged.

10 pages, 3 figures

References in corpus (14)

• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Classical simulation of quantum many-body systems with a tree tensor network
• A generative modeling approach for benchmarking and training shallow quantum circuits
• Differentiable Learning of Quantum Circuit Born Machine
• Unsupervised Generative Modeling Using Matrix Product States
• The Born Supremacy: Quantum Advantage and Training of an Ising Born Machine
• Correlations in local measurements on a quantum state, and complementarity as an explanation of nonclassicality
• Tree Tensor Networks for Generative Modeling
• Synergy Between Quantum Circuits and Tensor Networks: Short-cutting the Race to Practical Quantum Advantage
• Variational inference with a quantum computer
• A Framework for Demonstrating Practical Quantum Advantage: Racing Quantum against Classical Generative Models
• Automatic structural optimization of tree tensor networks
• Mutual Information Scaling for Tensor Network Machine Learning
• Decohering Tensor Network Quantum Machine Learning Models

Cited by in corpus (3)

• The State Preparation of Multivariate Normal Distributions using Tree Tensor Network
• Improving accuracy of tree-tensor network approach by optimization of network structure
• Trainable Quantum Neural Network for Multiclass Image Classification with the Power of Pre-trained Tree Tensor Networks