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 quantum wave function amplitude 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 hand-written digits, (iii) Bayesian networks, and (iv) the stock price fluctuation pattern in S&P500. In (i) and (ii), 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.

翻译：基于张量树网络与玻恩机框架，我们提出了一种通用方法，通过将目标分布函数表示为张量树所表示的量子波函数振幅来构建生成模型。其核心思想是动态优化树结构以最小化键互信息。所提出的方法提供了增强的性能，并揭示了目标数据中隐藏的关系结构。我们通过四个示例说明了潜在的实际应用：(i) 随机模式，(ii) QMNIST手写数字，(iii) 贝叶斯网络，以及 (iv) 标准普尔500指数中的股价波动模式。在 (i) 和 (ii) 中，强相关变量集中在网络中心附近；在 (iii) 中，识别出了因果模式；在 (iv) 中，则浮现出了对应于十一个行业板块的结构。