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

• URL: http://arxiv.org/abs/2609.05245v1
• Date: Fri, 04 Sep 2026 15:11:56 GMT
• Title: Do LLMs Exhibit Coherent Knowledge Structures in Mathematical Reasoning? A Perspective from Knowledge Space Theory
• Abstract summary: We introduce a KST-grounded framework for evaluating knowledge structure in mathematical reasoning.<n>We evaluate eight open- and closed-source LLMs against real human learners.
• Score: 64.45080465635783
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• Mirage of Mastery: Memorization Tricks LLMs into Artificially Inflated Self-Knowledge [0.0]
  Existing studies treat memorization and self-knowledge deficits in LLMs as separate issues.<n>We utilize a novel framework to ascertain if LLMs genuinely learn reasoning patterns from training data.<n>Our analysis shows a noteworthy problem in generalization: LLMs draw confidence from memorized solutions to infer a higher self-knowledge.
  arXiv  Detail & Related papers  (2025-06-23T18:01:16Z)
• LLM Cannot Discover Causality, and Should Be Restricted to Non-Decisional Support in Causal Discovery [30.24849564413826]
  We demonstrate that LLMs' autoregressive, correlation-driven modeling inherently lacks the theoretical grounding for causal reasoning.<n>We show that deliberate prompt engineering could overstate their performance, helping to explain the consistently favorable results reported in much of the current literature.<n>We conclude with a call for the community to shift focus from naively applying LLMs to developing specialized models and training method that respect the core principles of causal discovery.
  arXiv  Detail & Related papers  (2025-06-01T05:38:56Z)
• LLM Inference Enhanced by External Knowledge: A Survey [16.319049759753106]
  This study explores strategies for using external knowledge to enhance large language models (LLMs)<n>Our comparative analysis highlights the trade-offs among interpretability, scalability, and performance.
  arXiv  Detail & Related papers  (2025-05-30T09:08:51Z)
• Line of Duty: Evaluating LLM Self-Knowledge via Consistency in Feasibility Boundaries [0.0]
  This study aims to obtain intrinsic insights into different types of LLM self-knowledge with a novel methodology.<n>We find that even frontier models like GPT-4o and Mistral Large are not sure of their own capabilities more than 80% of the time.
  arXiv  Detail & Related papers  (2025-03-14T10:07:07Z)
• Refine Knowledge of Large Language Models via Adaptive Contrastive Learning [54.61213933999464]
  A mainstream category of methods is to reduce hallucinations by optimizing the knowledge representation of Large Language Models.<n>We believe that the process of models refining knowledge can greatly benefit from the way humans learn.<n>In our work, by imitating the human learning process, we design an Adaptive Contrastive Learning strategy.
  arXiv  Detail & Related papers  (2025-02-11T02:19:13Z)
• Decoding Knowledge in Large Language Models: A Framework for Categorization and Comprehension [14.039653386385519]
  Large language models (LLMs) acquire, retain, and apply knowledge.<n>This paper introduces a novel framework, K-(CSA)2, which categorizes LLM knowledge along two dimensions: correctness and confidence.
  arXiv  Detail & Related papers  (2025-01-02T16:34:10Z)
• KaLM: Knowledge-aligned Autoregressive Language Modeling via Dual-view Knowledge Graph Contrastive Learning [74.21524111840652]
  This paper proposes textbfKaLM, a textitKnowledge-aligned Language Modeling approach.<n>It fine-tunes autoregressive large language models to align with KG knowledge via the joint objective of explicit knowledge alignment and implicit knowledge alignment.<n> Notably, our method achieves a significant performance boost in evaluations of knowledge-driven tasks.
  arXiv  Detail & Related papers  (2024-12-06T11:08:24Z)
• Knowledge Mechanisms in Large Language Models: A Survey and Perspective [88.51320482620679]
  This paper reviews knowledge mechanism analysis from a novel taxonomy including knowledge utilization and evolution.<n>We discuss what knowledge LLMs have learned, the reasons for the fragility of parametric knowledge, and the potential dark knowledge (hypothesis) that will be challenging to address.
  arXiv  Detail & Related papers  (2024-07-22T06:15:59Z)
• Untangle the KNOT: Interweaving Conflicting Knowledge and Reasoning Skills in Large Language Models [51.72963030032491]
  Knowledge documents for large language models (LLMs) may conflict with the memory of LLMs due to outdated or incorrect knowledge. We construct a new dataset, dubbed KNOT, for knowledge conflict resolution examination in the form of question answering.
  arXiv  Detail & Related papers  (2024-04-04T16:40:11Z)
• KnowTuning: Knowledge-aware Fine-tuning for Large Language Models [83.5849717262019]
  We propose a knowledge-aware fine-tuning (KnowTuning) method to improve fine-grained and coarse-grained knowledge awareness of LLMs. KnowTuning generates more facts with less factual error rate under fine-grained facts evaluation.
  arXiv  Detail & Related papers  (2024-02-17T02:54:32Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.