Category-Theoretical and Topos-Theoretical Frameworks in Machine Learning: A Survey
It synthesizes recent advances in categorical frameworks for machine learning, serving as a resource for researchers interested in theoretical foundations, but it is incremental as a survey.
This survey provides an overview of category theory-derived machine learning from four perspectives, including a first-time review of topos theory, updating and expanding on previous work.
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.