Achieving Olympiad-Level Geometry Large Language Model Agent via Complexity Boosting Reinforcement Learning

The researchers proposed a large language model agent in the field of geometry named InternGeometry, designed to solve problems at the level of the International Mathematical Olympiad (IMO). This agent was built based on InternThinker-32B and interacted with a symbol engine more than two hundred times through a dynamic memory mechanism. The Complexity Enhancement Reinforcement Learning (CBRL) technique was introduced to accelerate training. With only 13,000 pieces of training data, InternGeometry successfully solved 44 out of 50 IMO geometry problems (covering the years 2000–2024), achieving a score of 44 points, which exceeded the average score of 40.9 points for gold medalists. The auxiliary construction methods proposed by it were not seen in human solutions, and the amount of data used was only 0.004% of that used in AlphaGeometry 2.