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.
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.
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.
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.
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.
arXiv:2608. 07838v1 Announce Type: new Abstract: Large language models (LLMs) have increasingly supported response generation grounded in user-provided knowledge spanning heterogeneous structures.
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.
arXiv:2607. 01431v1 Announce Type: cross Abstract: We introduce ISOSCI, a benchmark of isomorphic cross-domain science problem pairs that separates reasoning ability from domain knowledge retrieval in LLM evaluation.
arXiv:2606. 27378v1 Announce Type: cross Abstract: We introduce an axiomatic evaluation framework for latent thought representations in LLMs, comprising metrics that are independent of downstream benchmark scores and reveal representational failures that benchmark accuracy masks.
arXiv:2604. 27540v2 Announce Type: replace Abstract: Scientific reasoning rarely stops at what is directly observable; it often requires uncovering hidden structure from data.
LiveMathematicianBench is a dynamic multiple‑choice benchmark for research‑level mathematical reasoning, built from recent arXiv papers published after model training cutoffs. It introduces a thirteen‑category logical taxonomy of theorem types and uses a proof‑sketch‑guided distractor pipeline to create plausible but invalid answer choices, enhancing sensitivity to genuine reasoning. Evaluation shows current large language models perform poorly, with the best model scoring 43.5% overall and only 17.6% under substitution‑resistant conditions, indicating the benchmark’s difficulty and realism.
arXiv:2607. 08393v1 Announce Type: new Abstract: Fine-tuning LLMs to inject new knowledge faces a critical challenge: LLMs can quickly memorize new facts, yet fail to use them for downstream reasoning tasks.
The paper argues that large language models (LLMs) organize their internal mathematical reasoning by reusable reasoning approaches rather than by the benchmark topics they are tested on. Using a generation‑replay protocol, the authors extract activation‑importance signatures from eight models across five math sources, cluster these signatures, and find that the resulting groups align more closely with reasoning approaches than with topics. The study shows that changing the requested reasoning approach shifts cluster assignments, while paraphrasing the prompt does not, underscoring the primacy of approach over topic in LLM reasoning.