Disentangling the factors of variation in data is a fundamental concept in machine learning and has been studied in various ways by different researchers, leading to a multitude of definitions. Despite the numerous empirical studies, more theoretical research is needed to fully understand the defining properties of disentanglement and how different definitions relate to each other. This paper presents a meta-analysis of existing definitions of disentanglement, using category theory as a unifying and rigorous framework. We propose that the concepts of the cartesian and monoidal products should serve as the core of disentanglement. With these core concepts, we show the similarities and crucial differences in dealing with (i) functions, (ii) equivariant maps, (iii) relations, and (iv) stochastic maps. Overall, our meta-analysis deepens our understanding of disentanglement and its various formulations and can help researchers navigate different definitions and choose the most appropriate one for their specific context.

翻译：数据中变因解缠是机器学习中的一个基本概念，不同研究者通过多种方式对其进行了研究，导致了众多定义的产生。尽管已有大量实证研究，但仍需要更多理论工作来全面理解解缠的定义属性及不同定义之间的关系。本文利用范畴理论作为统一且严谨的框架，对现有解缠定义进行了元分析。我们提出笛卡尔积和幺半群积应作为解缠的核心概念。基于这些核心概念，我们展示了在处理（i）函数、（ii）等变映射、（iii）关系以及（iv）随机映射时的相似性和关键差异。总体而言，我们的元分析加深了对解缠及其不同表述的理解，并能帮助研究人员在众多定义中进行导航，选择最适合其特定场景的定义。