模型訓練與數學推理
Nemotron Wins IMO Gold With a Three-Model Generate–Verify–Revise Pipeline, but the Full Competition Run Consumed 2.31B Tokens
NVIDIA has released the weights for two Nemotron 3 Ultra math specialists, their training data, and a resumable natural-language proof pipeline. The system’s official score was 30 out of 42. The results also expose a shared blind spot among model-based verifiers: internal evaluations overestimated performance on two problems, while high precision came at the cost of extensive false rejections and substantial compute.
NVIDIA’s research team has released the weights, data, and inference recipe for its IMO 2026 system. The system is based on Nemotron 3 Ultra, which has 550B total parameters and activates approximately 55B per inference, with two additional math specialists trained through SFT and RL. The SFT model supports sequences of up to 425,984 tokens. Its corpus began with 15,879 difficult proof problems, for which DeepSeek V4 Pro generated initial drafts, revision trajectories, verification data, and meta-verification data.
The competition pipeline did not rely on one-shot answers. In the first stage, three checkpoints combined with eight prompting strategies generated 384 candidate proofs. The RL and SFT models then each performed eight evaluations without access to reference answers. A proof was accepted early only if all 16 votes judged it correct. For candidates that did not pass, the system selected high-scoring proofs from the pool and sent them, together with critiques, back to the three models for revision, for up to eight rounds. In the final stage, all three models assigned IMO-style scores to each finalist 16 times, and the submission was selected according to the average of the resulting 48 judgments. The publicly available NeMo-Skills recipe can connect to OpenAI-compatible endpoints and saves each record in JSONL format, allowing interrupted runs to resume.
This purely natural-language system, which used neither a formal proof assistant nor internet access, received an official score of 30 out of 42, clearing the gold-medal cutoff of 29. Identifying the final submissions consumed approximately 707M tokens and 1,464 GB200 GPU-hours, while the complete workload launched within the competition time limit reached 2.31B tokens and roughly 4,800 GPU-hours. The result therefore reflects a combination of post-training, checkpoint diversity, and extremely high test-time compute—not the one-shot generation capability of a single model.
Verification remains the central risk. Both internal evaluations and post hoc model judging estimated a score of approximately 32, but they shared the same failure mode and overlooked flaws in Problems 3 and 6. In an audit of 300 proofs, the unanimous 16-vote rule reduced the false-acceptance rate to 1.1%, but the false-rejection rate reached 81.3%. The next questions are whether third parties can reproduce the result under fixed token and GPU budgets, and whether adding formal checkers or heterogeneous model judges can reduce correlated errors.