Non-Parametric Structural Priors for Geometry Theorem Prediction

The paper introduces a novel approach for multi-step theorem prediction using Theorem Precedence Graphs, which encode historical solution dependencies as directed graphs to enhance reasoning capabilities without gradient-based optimization. This method addresses the scalability issue known as Structural Drift, allowing LLMs to maintain performance as reasoning depth increases, achieving 89.29% accuracy on the FormalGeo7k benchmark, surpassing traditional in-context learning baselines and competing with state-of-the-art supervised models. The findings suggest that integrating explicit structural priors can significantly improve LLM-based symbolic reasoning, offering a new avenue for practitioners in AI and geometry problem-solving.