AIMO3: Tool Integration and Self-Consistent Sampling Strategy in Mathematical Reasoning Competitions

AIMO3 is the winning solution of the third round of the AI Mathematical Olympiad (AIMO Progress Prize 3). Its core is the local deployment of the GPT-OSS 120B open-source model, combined with the vLLM inference framework to achieve efficient service. It solves the limitations of pure text models through tool-integrated reasoning and uses self-consistent sampling and entropy-weighted voting to improve reasoning reliability. The solution is shared in open-source form to promote collaborative progress in the field of AI mathematical reasoning.

The Artificial Intelligence Mathematical Olympiad (AIMO) is an authoritative platform for testing the mathematical reasoning ability of large language models. The questions cover fields such as algebra, geometry, number theory, and combinatorics, requiring complex multi-step reasoning. AIMO Progress Prize 3 attracts top teams to participate, and the winning solutions represent the current advanced level in this field.

The core model of the solution is the GPT-OSS 120B open-source model, which adopts a local deployment strategy and uses the vLLM inference framework. The PagedAttention algorithm of vLLM draws on the idea of virtual memory management, managing attention key-value caches in pages to improve GPU memory utilization and concurrency capabilities. The advantages of local deployment include high cost-effectiveness, strong controllability, and privacy compliance (data does not leave the local environment).

Pure text models have limitations in handling complex mathematical problems, such as long-chain calculation errors, imprecise symbolic operations, and difficulty in visualizing geometric reasoning. The solution uses tool-integrated reasoning to offload computational tasks to specialized tools: Python interpreter for numerical calculations, SymPy library for symbolic algebra, and graphics engine for geometric drawing. The key lies in the model's metacognitive ability to master when to call which tool and how to process the results through prompt templates and few-shot examples.

Large language models have randomness in generation. The solution uses parallel self-consistent sampling to generate multiple candidate solutions, then determines the final answer through voting. Unlike traditional majority voting with equal weights, entropy-weighted voting weights based on the entropy value of the confidence distribution of candidate answers: solutions with low entropy (high confidence) have higher weights, distinguishing between definite answers and random guesses to improve reliability.

The team systematically explored multi-dimensional hyperparameters: model selection (testing different open-source models and analyzing the relationship between scale and reasoning ability), prompt engineering (zero-shot, few-shot, chain-of-thought prompts), temperature parameters (grid search for optimal settings), and aggregation strategies (confidence weighting, reasoning path clustering, etc.), providing references for subsequent research.

Implications from the AIMO3 solution: Optimized open-source models can be comparable to closed-source models; tool integration is an effective path to improve mathematical reasoning; post-processing techniques such as self-consistent sampling and entropy weighting can improve reliability without increasing parameters. The project shares the complete solution in open-source form to promote collaboration in the AI community, facilitate the progress of mathematical AI capabilities, and move towards general artificial intelligence.