AlphaProof uses a pre-trained language model coupled with the AlphaZero reinforcement learning algorithm, which allows it to prove mathematical statements in the formal language Lean. AlphaGeometry 2 is a neuro-symbolic hybrid system that uses a symbolic engine to tackle complex geometry problems. The article also mentions a natural language reasoning system that doesn't require problems to be translated into a formal language. The development teams are continuing to explore multiple AI approaches for advancing mathematical reasoning.
Key takeaways:
- AlphaProof, a new reinforcement-learning based system for formal math reasoning, and AlphaGeometry 2, an improved version of a geometry-solving system, have been developed. Together, these systems solved four out of six problems from this year’s International Mathematical Olympiad (IMO), achieving the same level as a silver medalist in the competition.
- AlphaProof trains itself to prove mathematical statements in the formal language Lean, coupling a pre-trained language model with the AlphaZero reinforcement learning algorithm. It generates solution candidates and then proves or disproves them by searching over possible proof steps in Lean.
- AlphaGeometry 2 is a significantly improved version of AlphaGeometry, a neuro-symbolic hybrid system. It employs a symbolic engine that is two orders of magnitude faster than its predecessor and uses a novel knowledge-sharing mechanism to enable advanced combinations of different search trees to tackle more complex problems.
- As part of the IMO work, a natural language reasoning system was also experimented with, built upon Gemini and the latest research to enable advanced problem-solving skills. This system doesn’t require the problems to be translated into a formal language and could be combined with other AI systems.