Do LLMs Exhibit Coherent Knowledge Structures in Mathematical Reasoning? A Perspective from Knowledge Space Theory

Title:Do LLMs Exhibit Coherent Knowledge Structures in Mathematical Reasoning? A Perspective from Knowledge Space Theory

Abstract:Human knowledge is inherently structured and interdependent: mastery of a concept requires prior mastery of its prerequisites, a principle formalized by Knowledge Space Theory (KST). While LLMs achieve strong performance on complex reasoning tasks, it remains unclear whether they exhibit coherent, human-like knowledge structure. We introduce a KST-grounded framework for evaluating LLM knowledge structure in mathematical reasoning, using it as a normative framework to analyze whether LLM behavior adheres to principled knowledge dependencies. Evaluating eight open- and closed-source LLMs against real human learners, we find that (1) LLMs do not adhere to human knowledge structure -- they frequently violate knowledge dependencies and fail to leverage related knowledge provided in context to improve performance on dependent questions; (2) LLMs do not share a consistent knowledge structure among themselves, as reflected by low overlap in their knowledge distributions. Furthermore, these structural deficiencies remain largely invisible to accuracy-based and LLM-as-judge evaluations. Together, our results provide behavioral evidence that current LLMs knowledge does not follow a human-like structure.

Artificial Intelligence (cs.AI)

arXiv:2609.05245 [cs.AI]

(or arXiv:2609.05245v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2609.05245 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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