(논문 요약) Gold-medalist Performance in Solving Olympiad Geometry with AlphaGeometry2 (Paper)

핵심 내용

• Expanded Domain Language
  • locus-type theorems
  • linear equations
  • nonconstructive problem statements: Gemini 에 fewshot 활용, 자연어 -> formal language 변환
• Stronger and faster Symbolic Engine
  • handling of double points (double point: a point on a curve where two branches of the curve intersect)
  • a faster implementation in C++
• Multiple search trees with knowledge sharing
  • classic LM search: 각 노드당 LM 이 1개 auxiliary point 생성
  • LM multiple aux search: 각 노드당 LM 이 복수개 auxiliary points 생성
  • LM operator search: 임의의 점 생성 (AB=CD 이고 AEF 가 직선위에 있는 점 A)
• Enhanced Language Models
  • Training from scratch with a custom tokenizer in the domain specific language (Alphageometry 1 setup)
  • Fine-tuning already pre-trained custom math specialized Gemini models in natural language
  • Multimodal training from scratch with a diagram of the given geometry problem
• Larger and more diverse dataset
  

실험 결과