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.

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.

Annotated text datasets are increasingly reused as classifier targets, annotation candidates, and inputs to aggregate profiles, yet their labels often circulate without enough information about how they were produced. This article presents a reproducible benchmark and validation workflow for the public SASB-Aligned ESG Sentences corpus, a sentence-level sustainability disclosure dataset organized around standards-based categories such as those used in Sustainability Accounting Standards Board (SASB) analytics. Using the downloaded 6460-row version of the corpus, we construct fixed train/validation/test splits, map released child labels to parent categories, and evaluate label reuse through supervised classifiers, prompted GPT-4o classification, blind and candidate-visible Claude annotation, and Monte Carlo aggregation into ESG/Non-ESG category profiles. The reproducibility artifacts provide split metadata, label mappings, prompt templates, model predictions, LLM annotation outputs, profile sensitivity outputs, figure inputs, and scripts for reproducing the reported tables and figures. Results show that label reproduction is strongest at coarser label levels, blind annotation flags 40.3% of held-out sentences as ambiguous, candidate-visible annotation increases agreement while changing the task format, and aggregate profiles remain sensitive to label source. The benchmark supports transparent reuse of sentence-level ESG labels by reporting label source, annotation condition, prompt family, and aggregation level.