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About this paper
Chi Zhang, Jiajun Song, Siyu Li, Yitao Liang, Yuxi Ma, Wei Wang, Yixin Zhu, Song-Chun Zhu
TongGeometry, developed by Beijing Institute for General Artificial Intelligence (BIGAI) and Peking University, is a neuro-symbolic AI system capable of both solving and generating olympiad-level geometry problems. It successfully solved all problems in the IMO-AG-30 benchmark, surpassing human gold medalists, and demonstrated the ability to propose competition-worthy problems selected for real-world mathematical contests.
Key insights
- Large Language Models (LLMs) can effectively guide complex combinatorial search in geometry, significantly improving efficiency by suggesting promising constructions and evaluating solution proximity.
- A neuro-symbolic architecture combining a deductive database with LLM-guided tree search can enable an AI system to solve olympiad-level geometry problems, including those requiring auxiliary constructions.
- Automated forward exploration for theorem discovery combined with backward problem construction and filtering can generate novel, high-quality geometry problems suitable for competitions.
Summary by alphaXiv.
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