机器学习中的范畴论与拓扑斯理论框架：综述
Category-Theoretical and Topos-Theoretical Frameworks in Machine Learning: A Survey
AI总结：
本文从梯度、概率、不变性与等价性及拓扑斯四个视角综述范畴论在机器学习中的应用，更新了过去五年研究并首次系统探讨拓扑斯理论，凸显其在表达网络全局与局部结构及几何逻辑中的深刻作用。
摘要：
在这篇综述中，我们从四个主流视角概述了源自范畴论的机器学习：基于梯度的学习、基于概率的学习、基于不变性与等价性的学习以及基于拓扑斯的学习。对于前三个主题，我们主要回顾了过去五年的研究，更新并扩展了Shiebler等人的先前综述。第四个主题深入探讨了高阶范畴论，特别是拓扑斯理论，在本文中首次被综述。在某些机器学习方法中，函子的组合性发挥着至关重要的作用，促进了特定范畴框架的发展。然而，当考虑网络的全局性质如何反映在局部结构中以及几何性质如何用逻辑表达时，拓扑斯结构变得尤为重要且深刻。
英文摘要：
In this survey, we provide an overview of category theory-derived machine learning from four mainstream perspectives: gradient-based learning, probability-based learning, invariance and equivalence-based learning, and topos-based learning. For the first three topics, we primarily review research in the past five years, updating and expanding on the previous survey by Shiebler et al.. The fourth topic, which delves into higher category theory, particularly topos theory, is surveyed for the first time in this paper. In certain machine learning methods, the compositionality of functors plays a vital role, prompting the development of specific categorical frameworks. However, when considering how the global properties of a network reflect in local structures and how geometric properties are expressed with logic, the topos structure becomes particularly significant and profound.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
