QED-Nano: Teaching a Tiny Model to Prove Hard Theorems
Summary: arXiv:2604.04898v1 Announce Type: new
Abstract: Proprietary AI systems have recently demonstrated impressive capabilities on complex proof-based problems, with gold-level performance reported at the 2025 International Mathematical Olympiad (IMO). However, the training pipelines behind these systems remain largely undisclosed, and their reliance on large “internal” models and scaffolds makes them expensive to run, difficult to reproduce, and hard to study or improve upon. This raises a central question: can small, open models also be trained to achieve competitive reasoning performance on difficult Olympiad-level math?
In this paper, we answer this question by building QED-Nano, a 4B model post-trained for Olympiad-level proofs. Our training recipe has three stages:
- Supervised Fine-Tuning: This stage imbues good proof-writing styles by distilling knowledge from DeepSeek-Math-V2.
- Reinforcement Learning (RL): We implement a reinforcement learning approach with rubric-based rewards to enhance proof generation.
- Expanded RL with Reasoning Cache: This final stage decomposes long proofs into iterative summarize-and-refine cycles, enabling stronger test-time reasoning.
The results from these training stages have been promising. QED-Nano surpasses the proof-generation performance of much larger open models, including Nomos-1 and GPT-OSS-120B. Remarkably, it approaches the performance of proprietary models like Gemini 3 Pro, yet does so at a fraction of the inference cost, making it a valuable addition to the field of mathematical reasoning.
Moreover, to support further research on open mathematical reasoning, we are excited to announce that we will release the full QED-Nano pipeline. This includes:
- The QED-Nano model and the QED-Nano-SFT model.
- The FineProofs-SFT and FineProofs-RL datasets.
- Comprehensive training and evaluation code.
This initiative aims to democratize access to advanced mathematical reasoning capabilities, allowing researchers and developers to explore the potential of smaller, open models in this challenging domain. By making QED-Nano publicly available, we hope to spur innovation and collaboration in the AI research community.
As the field of AI continues to evolve, the importance of transparency and accessibility in model training processes cannot be overstated. The development of QED-Nano serves as a step toward more open research practices, ensuring that the advancements in AI are available to a broader audience. We anticipate that this model will offer a solid foundation for further exploration into the intersection of artificial intelligence and mathematical reasoning.
In conclusion, QED-Nano not only exemplifies the potential of small, open models in tackling complex mathematical proofs but also paves the way for future innovations in the field. The release of this model and its accompanying resources marks a significant milestone in the ongoing quest to enhance AI’s capabilities in reasoning and problem-solving.