QED-Nano: A 4-Billion Parameter Model That Proves Hard Olympiad-Level Math Theorems

A new paper introduces QED-Nano, a 4-billion parameter language model that can prove Olympiad-level mathematical theorems — matching or surpassing models 30x its size. The work demonstrates that mathematical reasoning ability doesn't necessarily require massive scale.

The Achievement

QED-Nano is a 4B parameter model post-trained specifically for Olympiad-level proofs. Despite its small size, it:

• Surpasses much larger open models including Nomos-1 and GPT-OSS-120B
• Approaches the performance of proprietary models like Gemini 3 Pro
• Operates at a fraction of the inference cost
• Is fully open-source with released code, models, and datasets

The Training Recipe

The three-stage training pipeline is the key innovation:

1. Supervised Fine-Tuning (SFT) — Distills proof-writing style from DeepSeek-Math-V2, teaching the model good mathematical argumentation
2. Reinforcement Learning (RL) — Uses rubric-based rewards to improve proof quality iteratively
3. Reasoning Cache RL — Decomposes long proofs into summarize-and-refine cycles, enabling stronger test-time reasoning

Why This Matters

Efficiency

• 4B parameters vs. 120B+ for comparable performance
• Dramatically lower inference costs
• Can run on consumer hardware

Reproducibility

• Proprietary systems (Gemini, GPT) have undisclosed training pipelines
• QED-Nano releases everything: model weights, training code, datasets, evaluation code
• Enables the research community to study and improve mathematical reasoning

Open Source Impact

• Released components: QED-Nano model, QED-Nano-SFT model, FineProofs-SFT dataset, FineProofs-RL dataset, training and evaluation code
• Complete pipeline for future research on open mathematical reasoning

The Bigger Picture

This work challenges the assumption that bigger is always better for AI reasoning. A well-designed training pipeline focused on the right skills (proof writing, iterative refinement) can achieve remarkable results with small models.