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Keywords = functorial manifold learning

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59 pages, 1333 KB  
Review
Category-Theoretical and Topos-Theoretical Frameworks in Machine Learning: A Survey
by Yiyang Jia, Guohong Peng, Zheng Yang and Tianhao Chen
Axioms 2025, 14(3), 204; https://doi.org/10.3390/axioms14030204 - 10 Mar 2025
Cited by 1 | Viewed by 4814
Abstract
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 [...] Read more.
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 and semantics are expressed with logic, the topos structure becomes particularly significant and profound. Full article
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