---
title: "Can LLMs Reliably Grade Olympiad Proofs? A Study of Mathematical Verification with LLMs"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2610.36767v1"
permalink: "https://feed.astralor.com/items/itm_41071005f8a2254e82802bc0"
published: "2026-10-27T07:28:08.000Z"
score: 57
channel: "tech"
tags: ["LLM","推理效率","Can LLMs Reliably","Grade Olympiad Proofs","Study","Mathematical Verification","LLMs Large Language","Models"]
---

# Can LLMs Reliably Grade Olympiad Proofs? A Study of Mathematical Verification with LLMs

## 速览

Large Language Models (LLMs) have made remarkable progress on solving competition-level mathematics, yet their ability to verify natural-language mathematical proofs remains relatively underexplored. This gap is especia…

## 关键点

- Large Language Models (LLMs) have made remarkable progress on solving competition-level mathematics, yet their ability to verify natural-language mathematical proofs remains relatively underexplored.
- This gap is especially pronounced for Olympiad-level proofs, which require meticulous assessment of each claim in a long reasoning chain.
- Current proof verification thus primarily relies on expert inspection, which is costly to scale.

## 全文

Large Language Models (LLMs) have made remarkable progress on solving competition-level mathematics, yet their ability to verify natural-language mathematical proofs remains relatively underexplored. This gap is especially pronounced for Olympiad-level proofs, which require meticulous assessment of each claim in a long reasoning chain. Current proof verification thus primarily relies on expert inspection, which is costly to scale. In this paper, we present a systematic study of LLM-based verification in this setting. Specifically, we introduce a human-curated dataset of USAMO 2025 candidate solutions with expert grading, and conduct a broad evaluation of existing LLM verifiers across frontier models. We also propose TROJAN, an iterative self-critique pipeline for generating high-fidelity adversarial proofs at scale. Our comprehensive evaluation covers 20 models spanning seven metrics, two prompt styles, three inference methods, and three prompt templates, showing that state-of-the-art models still leave considerable room for improvement. To narrow this gap, we propose MABGrader, a Multi-Armed Bandit framework that reframes grading as arm selection over the discrete score space. MABGrader outperforms the SOTA ProofGrader by 26.4% in Quadratic Weighted Kappa and reduces grading error by 14%. Code and dataset are available at https://github.com/aziksh-ospanov/TROJAN.

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