🤖 AI Summary
This paper addresses interpretable modeling of implicit structural relationships—such as causality, clustering, and centrality induced by strong correlations—in high-dimensional data.
Method: We propose a generative modeling paradigm integrating tensor tree networks with Born machines, where the target distribution is represented as the squared amplitude of a quantum wavefunction. A mutual information minimization objective dynamically optimizes the tree topology, enabling data-driven topological learning without structural priors.
Contribution/Results: Our key innovation is the first “joint structure-parameter optimization” mechanism, which automatically discovers interpretable latent structures without domain-specific assumptions. Evaluated on four diverse tasks—synthetic random patterns, QMNIST, synthetic Bayesian networks, and S&P500 stock volatility—we demonstrate successful identification of variable centrality distributions, causal graphs, and an 11-sector industry clustering. Results validate the framework’s effectiveness and generalizability for interpretable generative modeling.
📝 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.