analiza aiqbench
GTBench establishes a rigorous, curriculum-grounded benchmark for evaluating LLMs in graph theory, revealing a stark performance gap where only GPT-5 maintains high accuracy across undergraduate to graduate-level proof construction. The study highlights critical failure modes, including execution errors in simpler tasks and significant reliability issues in complex reasoning where automated judges disagree with human experts. This framework offers a necessary standard for assessing the viability of AI assistants in mathematical research and education, moving beyond generic benchmarks to domain-specific validation.
GTBench: A Curriculum-Grounded Benchmark for Evaluating LLMs as Mathematical Research Assistants in Graph Theory
arXiv:2606.03144v1 Announce Type: new Abstract: Large language models (LLMs) are increasingly used as self-study assistants in technical disciplines, yet their reliability as mathematical reasoning assistants remains poorly understood. We introduce GTBench, a curriculum-grounded benchmark for evaluating LLMs as mathematical research assistants in graph theory, comprising 63 problems organized into three groups of increasing difficulty: undergraduate definitions and basic properties (Group 1), algorithm tracing and structural reasoning (Group 2), and graduate-level proof construction (Group 3). Problems are sourced from verified academic materials including Diestel's Graph Theory. We evaluate five frontier models -- GPT-5, Claude Sonnet 4.6, Gemini 2.5 Flash-Lite, Llama 3.3 70B, and Mistral Large 3 -- under zero-shot and chain-of-thought prompting, using exact-match and LLM-as-judge evaluation for Groups 1 and 2, and a hybrid human expert and LLM-as-judge protocol for Group 3. Our results reveal a pronounced performance hierarchy: GPT-5 approaches ceiling on Group 1 (95.8% zero-shot) and maintains meaningful accuracy on graduate proofs (82%), while all other models degrade substantially with difficulty, with Llama achieving 0% under human evaluation on Group 3 zero-shot. Failure mode analysis shows that correct algorithm, wrong execution errors dominate Groups 1 and 2, while Group 3 additionally surfaces incomplete reasoning failures and reveals systematic disagreement between human evaluators and the automated judge, particularly on verbose or near-complete proofs (kappa = 0.48-0.83 across human pairs). GTBench provides the first curriculum-grounded evaluation framework for graph-theoretic reasoning in LLMs, with direct implications for the governance of AI tools in mathematical education and scientific research.
Abstract:Large language models (LLMs) are increasingly used as self-study assistants in technical disciplines, yet their reliability as mathematical reasoning assistants remains poorly understood. We introduce GTBench, a curriculum-grounded benchmark for evaluating LLMs as mathematical research assistants in graph theory, comprising 63 problems organized into three groups of increasing difficulty: undergraduate definitions and basic properties (Group 1), algorithm tracing and structural reasoning (Group 2), and graduate-level proof construction (Group 3). Problems are sourced from verified academic materials including Diestel's Graph Theory. We evaluate five frontier models -- GPT-5, Claude Sonnet 4.6, Gemini 2.5 Flash-Lite, Llama 3.3 70B, and Mistral Large 3 -- under zero-shot and chain-of-thought prompting, using exact-match and LLM-as-judge evaluation for Groups 1 and 2, and a hybrid human expert and LLM-as-judge protocol for Group 3. Our results reveal a pronounced performance hierarchy: GPT-5 approaches ceiling on Group 1 (95.8% zero-shot) and maintains meaningful accuracy on graduate proofs (82%), while all other models degrade substantially with difficulty, with Llama achieving 0% under human evaluation on Group 3 zero-shot. Failure mode analysis shows that correct algorithm, wrong execution errors dominate Groups 1 and 2, while Group 3 additionally surfaces incomplete reasoning failures and reveals systematic disagreement between human evaluators and the automated judge, particularly on verbose or near-complete proofs (kappa = 0.48-0.83 across human pairs). GTBench provides the first curriculum-grounded evaluation framework for graph-theoretic reasoning in LLMs, with direct implications for the governance of AI tools in mathematical education and scientific research.
Artificial Intelligence (cs.AI)
arXiv:2606.03144 [cs.AI]
(or arXiv:2606.03144v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2606.03144 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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