# Category-Theoretical and Topos-Theoretical Frameworks in Machine Learning: A Survey

arXiv: https://arxiv.org/abs/2408.14014 · HTML: https://mlsanity.com/paper/2408.14014/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Aug 2024.

## Built on by (most cited first, 3 of 3)

- [A Categorical Analysis of Large Language Models and Why LLMs Circumvent the Symbol Grounding Problem](https://mlsanity.com/paper/2512.09117/) (2025)
- [Polymorphic Combinatorial Frameworks (PCF): Guiding the Design of Mathematically-Grounded, Adaptive AI Agents](https://mlsanity.com/paper/2508.01581/) (2025)
- [Ternary Gamma Semirings: From Neural Implementation to Categorical Foundations](https://mlsanity.com/paper/2603.19317/) (2026)

## Abstract (arXiv)

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.