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About this paper
Minfeng Zhu, Zi Wang, Sizhe Ji, Zhengtong Du, Shengqiang Tai, Junming Ke, Xiao Deng, Zanlang Yin and 3 more
GenesisGeo trains a vision-language model on diagrams and formal problems to propose auxiliary constructions, then a symbolic engine verifies them. Its GenesisGeo-2B system solves 29 of 30 IMO-30 problems. Under the same search setting, vision-plus-text training solves 63 of 95 IMO-95 problems versus 59 for text-only training. This supports diagram-grounded training, not visual causation alone.
Key insights
- Integrating visual information from geometric diagrams provides useful geometric cues, leading to more valid auxiliary constructions and enhanced tree search efficiency for neuro-symbolic provers.
- Large-scale synthetic multimodal datasets, meticulously aligning visual representations with formal symbolic deduction and verifiable proof traces, are crucial for training models capable of IMO-level geometric reasoning.
- A multi-task learning strategy that combines continued pre-training on synthetic proofs with supervised fine-tuning on both text-based and diagram-grounded proof generation tasks is essential for robust model performance.
Summary by alphaXiv.
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