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

冲击国际数学奥林匹克（IMO）金牌的开源配方：训练用于奥数竞赛的 Nemotron 模型

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.

摘要： 我们研究了模型后训练（post-training）和推理时（test-time）推理设计如何影响针对高难度奥数竞赛的自然语言证明生成。我们以 Nemotron 3 Ultra 为基础，通过监督微调和强化学习训练了两个专家检查点（checkpoints），并评估了检查点选择、验证和优化过程。

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.

基于这些发现，我们提出了一个开源模型的推理时计算流水线。该系统完全以自然语言运行，无需形式化证明器、外部工具或互联网访问。三个 Nemotron 3 Ultra 检查点（通用模型及两个后训练专家模型）驱动了一个迭代搜索过程，用于生成、验证和优化候选证明；随后，一个独立的、高算力的阶段会筛选出最终提交的答案。

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.

该系统在 2026 年国际数学奥林匹克竞赛（IMO 2026）中获得了 42 分中的 30 分，达到了金牌分数线。我们现已开源这两个后训练检查点，以及训练数据、训练与推理代码、提交的解决方案，并发布了 Nemotron-IMO-Bench——一个包含 200 道全新奥数级别题目的基准测试集。