Multivariate information theory provides a general and principled framework for understanding how the components of a complex system are connected. Existing analyses are coarse in nature -- built up from characterizations of discrete subsystems -- and can be computationally prohibitive. In this work, we propose to study the continuous space of possible descriptions of a composite system as a window into its organizational structure. A description consists of specific information conveyed about each of the components, and the space of possible descriptions is equivalent to the space of lossy compression schemes of the components. We introduce a machine learning framework to optimize descriptions that extremize key information theoretic quantities used to characterize organization, such as total correlation and O-information. Through case studies on spin systems, Sudoku boards, and letter sequences from natural language, we identify extremal descriptions that reveal how system-wide variation emerges from individual components. By integrating machine learning into a fine-grained information theoretic analysis of composite random variables, our framework opens a new avenues for probing the structure of real-world complex systems.

本研究解决了现有分析对复杂系统组件连接性理解的粗糙性和计算限制问题。通过引入一种机器学习框架，优化描述以极大化关键信息论量（如总相关性和O信息），我们发现了揭示系统整体变异如何从各个组成部分中产生的极值描述。这一方法为深入探测现实世界复杂系统的结构开辟了新途径。

使用机器学习研究复合系统描述空间