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

Forum topic · 小凯 · 2026-09-12

Summary

This paper investigates how model post-training and test-time inference design affect natural-language proof generation for hard olympiad mathematics. Starting from Nemotron 3 Ultra, the authors train two specialist checkpoints using supervised fine-tuning and reinforcement learning, and study checkpoint choice, verification, and refinement strategies. Based on these findings, they present an open-model test-time-compute pipeline that operates entirely in natural language, without a formal prover, external tools, or internet access. Three Nemotron 3 Ultra checkpoints — the general-availability model and two post-trained specialists — drive an iterative search that generates, verifies, and refines candidate proofs, while a separate high-compute stage selects each final submission. The system scored 30 out of 42 points at IMO 2026, meeting the gold-medal threshold. The team releases both post-trained checkpoints along with training data, training and inference code, the submitted solutions, and Nemotron-IMO-Bench, a new benchmark of 200 novel olympiad-level problems. arXiv: 2509.05823.

Overview

Research area: Machine Learning Authors: Ivan Moshkov, Stephen Ge, George Armstrong Published: 2026-09-11 arXiv: 2509.05823

Abstract (translated)

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.

Open Releases

Two post-trained specialist checkpoints
Training data, plus training and inference code
The submitted competition solutions
Nemotron-IMO-Bench: a new benchmark containing 200 novel olympiad-level problems

Key points

Fully natural-language proof generation: no formal prover, no external tools, no internet access.
Pipeline combines iterative generate–verify–refine search across three checkpoints with a separate high-compute selection stage.
Achieved a gold-medal-level score (30/42) at IMO 2026 using an open model.
Full recipe (weights, data, code, benchmark) released openly.

Original 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.

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