Paper Explained: An Open Recipe for IMO Gold — How Open Models Reached Olympiad Gold with Generate, Verify, Refine

NVIDIA's open recipe uses three Nemotron 3 Ultra checkpoints to generate, verify, and refine proofs, scoring 30/42 (gold-medal level) at IMO 2026. We explain it from scratch as a test-time-compute design.

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

What this paper did

The paper is "An Open Recipe for IMO Gold: Training Nemotron for Olympiad Mathematics" (arXiv:2609.10712, September 2026), by researchers at NVIDIA.

Here is the abstract in brief. The authors study how post-training and test-time inference design affect natural-language proof writing on hard olympiad problems. Starting from Nemotron 3 Ultra, they train two specialist checkpoints with supervised fine-tuning (SFT) and reinforcement learning (RL), then evaluate checkpoint choice, verification, and refinement. The resulting system runs entirely in natural language — no formal prover, no external tools, no internet. Three checkpoints (the general-availability model plus the two specialists) drive an iterative search that generates, verifies, and refines candidate proofs, and a separate high-compute stage picks each final submission. It scored 30 of 42 points at IMO 2026, reaching the gold-medal threshold. The authors release both checkpoints, the training data, the training and inference code, the submitted solutions, and Nemotron-IMO-Bench, a new set of 200 unpublished olympiad-level problems.

In one line: this is not a story about making one big model smarter. It is a report on test-time compute design — combine models with different temperaments and spend heavily on verification.

An analogy: three writers, two strict editors

If "test-time compute" is new to you, picture a publishing house.

• Writers produce lots of drafts (candidate proofs). You employ three with different styles.
• Editors read each draft, grade it "flawless", "close", or "fatal gap", and mark it up in red.
• Writers revise the drafts that come back with notes.
• At the end, a separate panel reads the survivors far more carefully and publishes exactly one.

The punchline, which is the paper's own conclusion (§8): what paid off was not hiring more writers, but strict editors and a variety of styles.

Intuition: why "just write more" isn't enough

Ask a language model the same problem hundreds of times and a correct answer often appears somewhere. The trouble is that you don't know which one it is. A proof can't be checked by comparing a final number; someone has to read it and hunt for logical gaps.

This system makes that "someone" a verification panel of several models, and sets an extreme bar: a proof passes only if every judge gives it full marks. Being that strict also rejects good proofs, but — as we'll see — that only costs time. That trade-off is the heart of the design.

Models and training (§4)

The base is Nemotron-3-Ultra 550B-A55B, a mixture-of-experts model with 550B total parameters and 55B active per token. The paper uses three checkpoints (§4.1):

• GA: the general-availability model, unchanged
• SFT: supervised fine-tuned on proof-focused data
• RL: trained from GA with reinforcement learning for proof generation

The three are siblings from the same base, yet as we'll see they solve different problems and grade with different leniency. Those differences are the resource the whole pipeline runs on.