2024 SolvingOlympiadGeometryWithoutH
- (Trinh, 2024) ⇒ Trieu H. Trinh, Yuhuai Wu, Quoc V. Le, He He, and Thang Luong. (2024). “Solving Olympiad Geometry Without Human Demonstrations.” In: Nature Journal, 625. doi:10.1038/s41586-023-06747-5
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Notes
- The paper introduces AlphaGeometry, a novel theorem prover for Euclidean plane geometry.
- It is a neuro-symbolic system that combines a neural language model with a symbolic deduction engine.
- It uses synthetic data generation to overcome the geometry training data scarcity - it "learns" geometry independently of human instruction.
- It showcases the language model suggesting intuitive ideas and the symbolic engine providing rational, deliberate decision-making.
- It solves Olympiad-level geometry problems with capabilities close to an International Mathematical Olympiad (IMO) gold medalist.
- It can generate human-readable proofs.
Cited By
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Abstract
Proving mathematical theorems at the olympiad level represents a notable milestone in human-level automated reasoning1,2,3,4, owing to their reputed difficulty among the world’s best talents in pre-university mathematics. Current machine-learning approaches, however, are not applicable to most mathematical domains owing to the high cost of translating human proofs into machine-verifiable format. The problem is even worse for geometry because of its unique translation challenges1,5, resulting in severe scarcity of training data. We propose AlphaGeometry, a theorem prover for Euclidean plane geometry that sidesteps the need for human demonstrations by synthesizing millions of theorems and proofs across different levels of complexity. AlphaGeometry is a neuro-symbolic system that uses a neural language model, trained from scratch on our large-scale synthetic data, to guide a symbolic deduction engine through infinite branching points in challenging problems. On a test set of 30 latest olympiad-level problems, AlphaGeometry solves 25, outperforming the previous best method that only solves ten problems and approaching the performance of an average International Mathematical Olympiad (IMO) gold medallist. Notably, AlphaGeometry produces human-readable proofs, solves all geometry problems in the IMO 2000 and 2015 under human expert evaluation and discovers a generalized version of a translated IMO theorem in 2004.
References
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| Author | volume | Date Value | title | type | journal | titleUrl | doi | note | year | |
|---|---|---|---|---|---|---|---|---|---|---|
| 2024 SolvingOlympiadGeometryWithoutH | Quoc V. Le Thang Luong Yuhuai Wu Trieu H. Trinh He He | Solving Olympiad Geometry Without Human Demonstrations | 10.1038/s41586-023-06747-5 | 2024 |