Solver-Driven AI Improves Verifiable Geometry Problem Solving

Solving geometry problems with AI often involves a neuro-symbolic approach, combining neural intuition with symbolic rigor. However, current systems face two major hurdles: converting natural language problems into formal, solvable expressions (autoformalization) and generating new theorems when existing rule libraries are insufficient. This research introduces SD-GPS (Solver-Driven Geometry Problem Solving), a framework that uses a symbolic solver as an active oracle throughout both stages. SD-GPS's "Solver-Driven Autoformalization" module, built on QwenVL3-2B, integrates supervised formal-language adaptation with reinforcement learning guided by solvability. This ensures that the generated formal expressions are not just syntactically correct but also executable by the downstream solver. For theorem prediction, the "Verified Theorem Proposing" component features an agent that identifies deductive impasses and proposes auxiliary lemmas. Crucially, all proposed theorems are filtered through symbolic verification to guarantee their soundness. Empirical evaluations on challenging geometry benchmarks demonstrate that SD-GPS consistently outperforms existing methods, proving that tightly coupling multimodal perception with symbolic execution leads to significantly improved and verifiable geometric reasoning.