Evaluating Automated Geometric Problem Solving with Formal Language Generation on Large Multimodal Models

In recent years, research on automatic analytic geometry problems has gained considerable attention. The key areas of focus include the analysis of natural language problems, graph analysis, and multi-modal information fusion reasoning. With the increasing advantages of large multi-modal models in cross-modal data scenarios, they offer a novel technical approach for solving geometric problems. Unlike traditional rule-based methods, which typically parse problem text and graphics into a formal language and solve them using a symbolic solver, our approach leverages large multi-modal models. In our experiment, we first use these models to integrate text and graphical information, generate the corresponding formal language, and then invite three annotators to evaluate its accuracy. Next, we optimize the formal language using graphical location data and, finally, test the effectiveness of the optimized formal language in solving geometric problems using large multi-modal models with prompt-based inputs. Extensive experiments on public datasets demonstrate that the use of formal languages improves the accuracy of geometric problem-solving in large multi-modal models.