🤖 AI Summary
This work investigates the capability of large language models (LLMs) in automating fine-grained scoring of mathematical competition proofs—beyond binary correctness assessment—by detecting errors at the step level, classifying their severity, and assigning partial credit. We propose an intelligent agent–based workflow that dynamically generates problem-specific rubrics by integrating reference solution analysis, error localization, and hierarchical penalty rules, enabling multi-step, interpretable scoring. Evaluated on 90 expert-annotated proofs and the MathArena benchmark, our method achieves significantly higher agreement with human graders (Krippendorff’s α increased by 18.3%) and notably improves calibration of partial credit assignment. All code, datasets, and experimental logs are publicly released.
📝 Abstract
State-of-the-art (SOTA) LLMs have progressed from struggling on proof-based Olympiad problems to solving most of the IMO 2025 problems, with leading systems reportedly handling 5 of 6 problems. Given this progress, we assess how well these models can grade proofs: detecting errors, judging their severity, and assigning fair scores beyond binary correctness. We study proof-analysis capabilities using a corpus of 90 Gemini 2.5 Pro-generated solutions that we grade on a 1-4 scale with detailed error annotations, and on MathArena solution sets for IMO/USAMO 2025 scored on a 0-7 scale. Our analysis shows that models can reliably flag incorrect (including subtly incorrect) solutions but exhibit calibration gaps in how partial credit is assigned. To address this, we introduce agentic workflows that extract and analyze reference solutions and automatically derive problem-specific rubrics for a multi-step grading process. We instantiate and compare different design choices for the grading workflows, and evaluate their trade-offs. Across our annotated corpus and MathArena, our proposed workflows achieve higher agreement with human grades and more consistent handling of partial credit across metrics. We release all code, data, and prompts/logs to facilitate future research.