CombiGraph-Vis: A Curated Multimodal Olympiad Benchmark for Discrete Mathematical Reasoning
This addresses the challenge of automated proof grading for mathematical reasoning, which is incremental as it builds on existing LLM capabilities to improve partial credit assessment.
The paper tackles the problem of using LLMs to grade mathematical proofs beyond binary correctness, showing that while models can reliably flag incorrect solutions, they struggle with assigning partial credit consistently. The authors introduce agentic workflows that extract reference solutions and derive problem-specific rubrics, achieving higher agreement with human grades on datasets including 90 Gemini-generated solutions and MathArena IMO/USAMO sets.
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.