arXiv AI September 7, 2026 By Peng Cui, Heejin Do, Mrinmaya Sachan

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

The paper investigates whether large language models (LLMs) possess coherent, human-like knowledge structures in mathematical reasoning by applying Knowledge Space Theory (KST). Using a KST-based framework, the authors evaluate eight open- and closed-source LLMs and find that they frequently violate knowledge dependencies, fail to leverage related context, and exhibit low overlap in knowledge distributions compared to real human learners. These structural deficiencies remain largely invisible to standard accuracy or LLM-as-judge evaluations, suggesting that current LLMs do not follow a human-like knowledge structure.

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llms

arXiv AI

Jun 2

KnowledgeBerg: Evaluating Systematic Knowledge Coverage and Compositional Reasoning in Large Language Models

arXiv:2604. 17621v2 Announce Type: replace Abstract: Many real-world questions appear deceptively simple yet implicitly demand two capabilities: (i) systematic coverage of a bounded knowledge universe and (ii) compositional set-based reasoning over that universe, a phenomenon we term "the tip of the iceberg.

By Xiao Zhang, Qianru Meng, Yongjian Chen, Yumeng Wang, Johan Bos

llms benchmarks

arXiv AI

Jul 8

Mathematical Reasoning in Large Language Models: Benchmarks, Architectures, Evaluation, and Open Challenges

arXiv:2605. 19723v2 Announce Type: replace-cross Abstract: Mathematical reasoning is essential for problem-solving in education, science, and industry, serving as a crucial benchmark for evaluating artificial intelligence systems.

By Husnain Amjad, Raja Khurram Shahzad, Aamir Shahzad, Mehwish Fatima

llms fine-tuning benchmarks

arXiv Machine Learning

3d ago

The Missing Primitive: Diagnosing and Repairing Mathematical Reasoning in Large Language Models

arXiv:2610. 02191v1 Announce Type: new Abstract: While Large Language Models (LLMs) have demonstrated striking capabilities on frontier mathematical problems, it remains unclear whether they possess the structural mathematical understanding underlying their solutions.

By Shuo Xing, Zilin Dai, Chengyuan Qian, Fangzhou Lin, Wenjing Chen, Ping He, Pan Lu, Alvaro Velasquez, Mohit Bansal, Zhengzhong Tu

llms efficiency benchmarks

arXiv AI

Jun 10

RealMath-Eval: Why SOTA Judges Struggle with Real Human Reasoning

arXiv:2606. 10254v1 Announce Type: new Abstract: While Large Language Models (LLMs) have achieved near-perfect performance in \emph{solving} high-school mathematics, their ability to \emph{evaluate} the diverse reasoning processes of real human students remains under-examined.

By Yiteng Mao, Kenan Xu, Yijia Lyu, Wenhao Li, Jianlong Chen, Xiangfeng Wang

llms rag benchmarks

arXiv AI

Aug 11

Counterfactual Benchmarking and Training for Factuality Consistency and Order-Robust Grounded Reasoning in LLMs over Heterogeneous Knowledge

arXiv:2608. 07838v1 Announce Type: new Abstract: Large language models (LLMs) have increasingly supported response generation grounded in user-provided knowledge spanning heterogeneous structures.

By Shibo Chu, Yuze Liu, Tiehua Zhang, Zhishu Shen, Lianghua He, Haofen Wang, Zhijun Ding

llms fine-tuning benchmarks safety

arXiv AI

Aug 19

Structure-Internalized Rule Language Model for Faithful Knowledge Graph Reasoning

The paper introduces the Structure-Internalized Rule Language Model (SIRLM) to improve Knowledge Graph Reasoning (KGR) by addressing the mismatch between KG structural context and Large Language Model (LLM) parametric knowledge. SIRLM centers on a Structure-Internalized Rule Generator (SIRG) that uses in-context learning, a structural relation memory, a KG tokenizer, and a neuro-symbolic reasoner to generate structural rules and provide faithful rule-execution feedback. Experiments on 36 datasets against 17 state‑of‑the‑art KGR methods show that SIRLM achieves significant performance gains.

By Xingrui Zhuo, Jiapu Wang, Manzong Huang, Gongqing Wu, Xindong Wu

llms nlp fine-tuning benchmarks

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KnowledgeBerg: Evaluating Systematic Knowledge Coverage and Compositional Reasoning in Large Language Models

Mathematical Reasoning in Large Language Models: Benchmarks, Architectures, Evaluation, and Open Challenges

The Missing Primitive: Diagnosing and Repairing Mathematical Reasoning in Large Language Models

RealMath-Eval: Why SOTA Judges Struggle with Real Human Reasoning

Counterfactual Benchmarking and Training for Factuality Consistency and Order-Robust Grounded Reasoning in LLMs over Heterogeneous Knowledge

Structure-Internalized Rule Language Model for Faithful Knowledge Graph Reasoning