在解决奥林匹克几何问题中取得金牌成绩，使用AlphaGeometry2。

Gold-medalist Performance in Solving Olympiad Geometry with AlphaGeometry2

February 5, 2025

作者: Yuri Chervonyi, Trieu H. Trinh, Miroslav Olšák, Xiaomeng Yang, Hoang Nguyen, Marcelo Menegali, Junehyuk Jung, Vikas Verma, Quoc V. Le, Thang Luong

cs.AI

摘要

我们介绍AlphaGeometry2，这是Trinh等人（2024年）介绍的AlphaGeometry的显着改进版本，已经超越了解决奥林匹克几何问题的平均金牌得主。为了实现这一点，我们首先扩展了原始的AlphaGeometry语言，以解决涉及物体运动以及包含角度、比例和距离线性方程的更难问题。这些改进与其他增强功能一起，显着提高了AlphaGeometry语言在2000-2024年国际数学奥林匹克几何问题上的覆盖率，从66%提高到88%。AlphaGeometry2的搜索过程也通过使用Gemini架构进行了极大改进，以获得更好的语言建模，并采用结合多个搜索树的新颖知识共享机制。再加上对符号引擎和合成数据生成的进一步增强，我们将AlphaGeometry2对过去25年所有几何问题的整体解决率显着提高到84%，而之前为54%。AlphaGeometry2还是在IMO 2024年获得银牌标准的系统的一部分。最后，我们报告了使用AlphaGeometry2作为完全自动化系统的一部分，可可靠地直接从自然语言输入解决几何问题的进展。

English

We present AlphaGeometry2, a significantly improved version of AlphaGeometry introduced in Trinh et al. (2024), which has now surpassed an average gold medalist in solving Olympiad geometry problems. To achieve this, we first extend the original AlphaGeometry language to tackle harder problems involving movements of objects, and problems containing linear equations of angles, ratios, and distances. This, together with other additions, has markedly improved the coverage rate of the AlphaGeometry language on International Math Olympiads (IMO) 2000-2024 geometry problems from 66% to 88%. The search process of AlphaGeometry2 has also been greatly improved through the use of Gemini architecture for better language modeling, and a novel knowledge-sharing mechanism that combines multiple search trees. Together with further enhancements to the symbolic engine and synthetic data generation, we have significantly boosted the overall solving rate of AlphaGeometry2 to 84% for all geometry problems over the last 25 years, compared to 54% previously. AlphaGeometry2 was also part of the system that achieved silver-medal standard at IMO 2024 https://dpmd.ai/imo-silver. Last but not least, we report progress towards using AlphaGeometry2 as a part of a fully automated system that reliably solves geometry problems directly from natural language input.