LLM Knowledge Structure in Math Reasoning
Do LLMs Exhibit Coherent Knowledge Structures in Mathematical Reasoning? A Perspective from Knowledge Space Theory
Researchers can use this framework to diagnose knowledge structure gaps in LLMs, potentially improving math reasoning training methods.
The paper evaluates eight open- and closed-source LLMs using Knowledge Space Theory to analyze mathematical reasoning. LLMs violate knowledge dependencies and fail to leverage related context for dependent questions. The models show low overlap in knowledge distributions compared to human learners. Accuracy-based evaluations miss these structural deficiencies.
Do LLMs Exhibit Coherent Knowledge Structures in Mathematical Reasoning? A Perspective from Knowledge Space Theory
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.
