CombiGraph-Vis: A Curated Multimodal Olympiad Benchmark for Discrete Mathematical Reasoning

TL;DR

This paper evaluates large language models' ability to grade mathematical proofs and solutions, introduces agentic workflows for improved grading accuracy, and demonstrates enhanced agreement with human assessments.

Contribution

It presents novel workflows for automated proof and solution grading, addressing calibration gaps and improving consistency with human judgments.

Findings

Models reliably detect incorrect solutions

Proposed workflows improve grading agreement with humans

Enhanced handling of partial credit in automated grading

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.