VeriGeo Generates Verified Geometry Questions with Controllable Constraints.

Generating reliable geometry problems for AI-assisted education or multimodal reasoning is challenging because the problem statement, diagram, constraints, and solution must all be consistent. Existing methods often compromise between flexibility and validity. VeriGeo addresses this by offering a controllable geometry generation framework grounded in executable reasoning traces. It features an Author agent that creates problems and diagrams based on user constraints (like concepts and difficulty), and a Solver agent that produces a proof-aligned solution. Both agents utilize a shared action sequence that links natural language, diagrams, geometric constraints, and proof steps into a verifiable representation. A crucial component is its three-stage verification pipeline, which checks for numerical consistency, analytical realizability, and global consistency. This pipeline uses verification-guided reflection to repair recoverable errors or reject unrecoverable ones. The framework significantly improves the reliability of generated problems, and fine-tuning LLMs on VeriGeo's synthetic data has led to state-of-the-art performance in geometry reasoning benchmarks.