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

Forum topic · 小凯 · 2026-09-12

Summary

Researchers at NVIDIA describe how post-training and test-time inference design affect natural-language proof generation for hard olympiad mathematics. Starting from Nemotron 3 Ultra, the team trained two specialist checkpoints using supervised fine-tuning and reinforcement learning, evaluating checkpoint choice, verification, and refinement strategies. Based on these findings, they built an open-model test-time-compute pipeline that operates entirely in natural language—with no formal prover, external tools, or internet access. Three Nemotron 3 Ultra checkpoints (the general-availability model plus two post-trained specialists) power an iterative search loop that generates, verifies, and refines candidate proofs, followed by a separate high-compute stage that selects each final submission. The system scored 30 out of 42 points at IMO 2026, exceeding the gold-medal threshold. The authors release both post-trained checkpoints along with training data, training and inference code, submitted solutions, and Nemotron-IMO-Bench, a new benchmark of 200 novel olympiad-level problems. Paper: arXiv:2509.05823.

Overview

This paper (arXiv: 2509.05823) studies how model post-training and test-time inference design affect natural-language proof generation for hard olympiad mathematics.

Field: Machine Learning Authors: Ivan Moshkov, Stephen Ge, George Armstrong Published: 2026-09-11

Key Points

Starting from Nemotron 3 Ultra, the authors train two specialist checkpoints using supervised fine-tuning (SFT) and reinforcement learning (RL), and evaluate checkpoint choice, verification, and refinement strategies.
They present an open-model test-time-compute pipeline that runs entirely in natural language — no formal prover, external tools, or internet access.
Three Nemotron 3 Ultra checkpoints (the general-availability model plus the two post-trained specialists) drive an iterative search that generates, verifies, and refines candidate proofs.
A separate high-compute selection stage then chooses each final submission.
The system scored 30 out of 42 points at IMO 2026, surpassing the gold-medal threshold.

Open Releases

The team publishes:

The two post-trained checkpoints
Training data, plus training and inference code
The submitted solutions
Nemotron-IMO-Bench — a new benchmark of 200 novel olympiad-level problems

Original Abstract (excerpt)

> 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.

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*Auto-collected on 2026-09-12.*