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Wu's Method Can Boost AlphaGeometry to Outperform Gold Medalists at IMO Geometry (arxiv.org)
7 points by mnk47 on Apr 13, 2024 | hide | past | pdf | 1 comment on HN

In plain words: Wu's method turns geometry problems into equations and eliminates variables to test whether a statement is always true. Paired with classic symbolic rules it nearly matched AlphaGeometry on a laptop, and adding it to AlphaGeometry solved 27 of 30 olympiad problems.

Abstract · Wu's Method can Boost Symbolic AI to Rival Silver Medalists and AlphaGeometry to Outperform Gold Medalists at IMO Geometry

Proving geometric theorems constitutes a hallmark of visual reasoning combining both intuitive and logical skills. Therefore, automated theorem proving of Olympiad-level geometry problems is considered a notable milestone in human-level automated reasoning. The introduction of AlphaGeometry, a neuro-symbolic model trained with 100 million synthetic samples, marked a major breakthrough. It solved 25 of 30 International Mathematical Olympiad (IMO) problems whereas the reported baseline based on Wu's method solved only ten. In this note, we revisit the IMO-AG-30 Challenge introduced with AlphaGeometry, and find that Wu's method is surprisingly strong. Wu's method alone can solve 15 problems, and some of them are not solved by any of the other methods. This leads to two key findings: (i) Combining Wu's method with the classic synthetic methods of deductive databases and angle, ratio, and distance chasing solves 21 out of 30 methods by just using a CPU-only laptop with a time limit of 5 minutes per problem. Essentially, this classic method solves just 4 problems less than AlphaGeometry and establishes the first fully symbolic baseline strong enough to rival the performance of an IMO silver medalist. (ii) Wu's method even solves 2 of the 5 problems that AlphaGeometry failed to solve. Thus, by combining AlphaGeometry with Wu's method we set a new state-of-the-art for automated theorem proving on IMO-AG-30, solving 27 out of 30 problems, the first AI method which outperforms an IMO gold medalist.

Shiven Sinha, Ameya Prabhu, Ponnurangam Kumaraguru, Siddharth Bhat, Matthias Bethge
arXiv:2404.06405 · cs.AI, cs.CG, cs.CL, cs.LG · submitted Apr 9, 2024 · updated Apr 11, 2024
abstract · pdf · html · Work in Progress. Released for wider feedback

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full title: Wu's Method can Boost Symbolic AI to Rival Silver Medalists and AlphaGeometry to Outperform Gold Medalists at IMO Geometry