Leveraging Online Olympiad-Level Math Problems for LLMs Training and Contamination-Resistant Evaluation

TL;DR

This paper introduces AoPS-Instruct, a large dataset of Olympiad-level math QA pairs extracted from AoPS forum, and a contamination-resistant benchmark LiveAoPSBench, to improve and reliably evaluate LLMs' advanced math reasoning abilities.

Contribution

It presents an automated pipeline for extracting high-quality math QA data from AoPS forum and creates a dynamic, contamination-resistant benchmark for LLM evaluation.

Findings

Fine-tuning on AoPS-Instruct enhances LLM reasoning skills.

LLMs show performance decline over time on the benchmark.

Pre-training exposure may influence LLM success on older problems.

Abstract

Advances in Large Language Models (LLMs) have sparked interest in their ability to solve Olympiad-level math problems. However, the training and evaluation of these models are constrained by the limited size and quality of available datasets, as creating large-scale data for such advanced problems requires extensive effort from human experts. In addition, current benchmarks are prone to contamination, leading to unreliable evaluations. In this paper, we present an automated pipeline that leverages the rich resources of the Art of Problem Solving (AoPS) forum, which predominantly features Olympiad-level problems and community-driven solutions. Using open-source LLMs, we develop a method to extract question-answer pairs from the forum, resulting in AoPS-Instruct, a dataset of more than 600,000 high-quality QA pairs. Our experiments demonstrate that fine-tuning LLMs on AoPS-Instruct improves their reasoning abilities across various benchmarks. Moreover, we build an automatic pipeline that introduces LiveAoPSBench, an evolving evaluation set with timestamps, derived from the latest forum data, providing a contamination-resistant benchmark for assessing LLM performance. Notably, we observe a significant decline in LLM performance over time, suggesting their success on older examples may stem from pre-training exposure rather than true reasoning ability. Our work presents a scalable approach to creating and maintaining large-scale, high-quality datasets for advanced math reasoning, offering valuable insights into the capabilities and limitations of LLMs in this domain. Our benchmark and code is available at https://github.com/DSL-Lab/aops