A Precise Text-to-Diagram Generation Method for Elementary Geometry

Geometric problems hold significant importance in the fields of machine reasoning and AI education. Contrasting with the current widespread interest in the field of general natural language text-to-image research, the unique nature of the mathematical domain requires that geometric text-to-diagram generation involves human-like mathematical abstraction and logical reasoning capabilities. This necessity arises because machines must parse propositional text, infer and reason mathematical conditions essential for diagram generation. Yet, current AI systems are not sufficiently advanced in this aspect. This paper establishes a connection between entity relationship extraction and analytic geometry, introducing a novel approach that redefines the challenge of diagram generation as an equivalent problem of solving systems of equations. This method effectively circumvents some of the difficulties associated with mathematical reasoning. The paper have developed a highly precise entity relationship extraction model based on BERT and knowledge graph, showcasing outstanding efficacy in the realm of elementary geometry. To address the complexity of solving large-scale systems of equations, this paper also proposes an algorithm designed to expedite the computation by reducing the computational path while maintaining accuracy. Experiments results validate the superiority of our method over previous studies, achieving an average correctness rate of 93.5% in the generation of geometric diagrams.