FGeo-TP: A Language Model-Enhanced Solver for Geometry Problems

Abstract: The application of contemporary artificial intelligence techniques to address geometric problems and automated deductive proof has always been a grand challenge to the interdiscipline field of mathematics and artificial Intelligence. This is the fourth article in a series of our works, in our previous work, we established of a geometric formalized system known as FormalGeo. Moreover we annotated approximately 7000 geometric problems, forming the FormalGeo7k dataset. Despite the FGPS (Formal Geometry Problem Solver) can achieve interpretable algebraic equation solving and human-like deductive reasoning, it often experiences timeouts due to the complexity of the search strategy. In this paper, we introduced FGeo-TP (Theorem Predictor), which utilizes the LLM to predict theorem sequences for solving geometry problems. We compared the effectiveness of various Transformer architectures, such as BART or T5, in theorem prediction, implementing pruning in the search process of FGPS, thereby improving its performance in solving geometry problems. Our results demonstrate a significant increase in the problem-solving rate of the LLM-enhanced FGeo-TP on the FormalGeo7k dataset, rising from 39.7% to 80.86%. Furthermore, FGeo-TP exhibits notable reductions in solving time and search steps across problems of varying difficulty levels.