用范畴论统一建模机器学习系统，揭示其内在结构与变换规律。
Aspects of Artificial Intelligence: Transforming Machine Learning Systems Naturally
- 以代数运算和范畴关系构建机器学习系统框架
- 通过商、嵌入等变换保持系统关系不变性
- 利用伴随与单子揭示通用结构，适合理论研究者
本文将机器学习系统视为由一组学习元素及其相互关系构成的整体，关注的关系包括代数运算、二元关系及可范畴化推理的复合关系。系统间的变换是保持这些关系的映射，重点讨论了商/聚类、可表示函子和Yoneda嵌入等变换方式，并通过机器学习实例加以说明。机器学习系统间的伴随关系——一种特殊的变换闭环——提供了最优问题求解路径。通过2-细胞层面的自然变换，不同变换得以关联与比较。由伴随生成的单子所体现的泛性质与代数结构，为系统分析提供了新视角。
原文摘要 · Abstract (English)
In this paper, we study the machine learning elements which we are interested in together as a machine learning system, consisting of a collection of machine learning elements and a collection of relations between the elements. The relations we concern are algebraic operations, binary relations, and binary relations with composition that can be reasoned categorically. A machine learning system transformation between two systems is a map between the systems, which preserves the relations we concern. The system transformations given by quotient or clustering, representable functor, and Yoneda embedding are highlighted and discussed by machine learning examples. An adjunction between machine learning systems, a special machine learning system transformation loop, provides the optimal way of solving problems. Machine learning system transformations are linked and compared by their maps at 2-cell, natural transformations. New insights and structures can be obtained from universal properties and algebraic structures given by monads, which are generated from adjunctions.
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