VeriGeo: Controllable Geometry Question Generation with Numerical and Analytical Verification
For researchers and educators in AI-assisted education and multimodal reasoning, VeriGeo provides a reliable method to generate verified geometry problems with user-specified constraints, improving the quality of synthetic training data for geometry solvers.
VeriGeo introduces a controllable geometry problem generation framework that uses executable reasoning traces and a three-stage verification pipeline to ensure consistency between problem statements, diagrams, constraints, and solutions. The method repairs a substantial fraction of invalid generations across five LLM backbones, and supervised fine-tuning on 8.7k generated examples achieves the best reported GeoQA performance among end-to-end multimodal LLM-based solvers.
Geometry problem generation is useful for AI-assisted education and multimodal mathematical reasoning, but reliable synthesis remains difficult because the problem statement, diagram, constraints, and solution should be mutually consistent. Existing methods often trade off controllability and reliability: seed-based rewriting is flexible but weakly verifiable, whereas diagram-first construction improves validity but is less suited to arbitrary user-specified constraints. We introduce VeriGeo, a controllable geometry generation framework grounded in executable reasoning traces. Given user constraints such as target concepts and difficulty, an Author agent generates a problem and diagram, and a Solver agent produces a proof-aligned solution. Both agents use a shared action sequence that connects natural language, diagrams, geometric constraints, and proof steps into a verifiable representation. A three-stage pipeline checks numerical consistency, analytical realizability, and global consistency, using verification-guided reflection to repair recoverable failures and reject unrecoverable ones. Across five LLM backbones, raw generations frequently fail these checks, while VeriGeo repairs a substantial fraction of the invalid attempts. Supervised fine-tuning on 8.7k examples generated by VeriGeo achieves the best reported GeoQA performance among end-to-end multimodal LLM-based solvers, and obtains strong results on PGPS9K and MathVista-GPS, demonstrating the effectiveness of verified synthetic data for improving multimodal geometry reasoning.