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.

本文研究了作为机器学习系统的一系列机器学习元素及其之间的关系，填补了当前研究中对机器学习系统转化方法的不足。通过对等价关系、聚类等系统转化的分析，提出了一种优化问题解决方案的新视角，对机器学习中的代数结构与单子性质也进行了深入探讨，具有重要的理论和实践意义。

人工智能的方面：自然转变机器学习系统