An Open Recipe for IMO Gold: Training Nemotron for Olympiad Mathematics

2026-09-09

AI Summary

研究通过模型后训练和测试时推理设计改进Nemotron在奥林匹克数学证明生成中的表现，使用自然语言处理技术达到IMO金牌水平。

Abstract

We study how model post-training and test-time inference design affect natural-language proof generation for hard olympiad mathematics. Starting from Nemotron 3 Ultra, we train two specialist checkpoints using supervised fine-tuning and reinforcement learning, and evaluate checkpoint choice, verification, and refinement. Based on these findings, we present an open-model test-time-compute pipeline. The system operates entirely in natural language, with no formal prover, external tools, or internet access. Three Nemotron 3 Ultra checkpoints - the general-availability model and two post-trained specialists - power an iterative search that generates, verifies, and refines candidate proofs; a separate high-compute stage then selects each final submission. The system scored 30 out of 42 points at IMO 2026, reaching the gold-medal threshold. We release the two post-trained checkpoints as well as the training data, the training and inference code, the submitted solutions, and Nemotron-IMO-Bench, a new benchmark of 200 novel olympiad-level problems.

Problem

• model post-training
• test-time inference design
• natural-language proof generation
• olympiad mathematics

Innovation

• natural-language proof generation
• supervised fine-tuning
• reinforcement learning
• open-model test-time-compute pipeline
• Nemotron-IMO-Bench