VeriGeo: Controllable Geometry Question Generation with Numerical and Analytical Verification

A new framework called VeriGeo aims to solve a persistent challenge in AI-assisted education: generating geometry problems where the text, diagram, constraints, and solution are all mutually consistent [1]. The system uses a multi-stage verification pipeline grounded in executable reasoning traces to catch and repair invalid outputs [2]. The framework, detailed in a paper submitted in 2026, employs a two-agent architecture [1]. An Author agent generates a problem and diagram based on user-specified constraints like target concepts and difficulty, while a Solver agent produces a proof-aligned solution [2]. Both agents use a shared action sequence that links natural language, diagrams, geometric constraints, and proof steps into a single verifiable representation [2]. A three-stage pipeline then checks the output for numerical consistency, analytical realizability, and global consistency [1]. When failures are detected, the system uses verification-guided reflection to repair recoverable issues and rejects those that cannot be fixed [2]. The researchers tested the framework across five different LLM backbones and found that raw generations frequently failed these checks, but VeriGeo was able to repair a substantial fraction of the invalid attempts [2]. The verified synthetic data produced by VeriGeo proved valuable for training other models. The team performed supervised fine-tuning on 8.7k examples generated by the framework [1]. The resulting model achieved what the authors describe as the best reported GeoQA performance among end-to-end multimodal LLM-based solvers and also obtained strong results on the PGPS9K and MathVista-GPS benchmarks [2]. The work addresses a gap in reliable synthetic data generation for multimodal reasoning. A separate 2026 review of generative systems in a different technical domain—quantum circuit generation—found that while many systems address syntactic and semantic correctness, none reported end-to-end evaluation on actual hardware, highlighting a broader challenge in verifying generated artifacts [3]. VeriGeo's approach of using executable traces for verification offers one pathway to closing such reliability gaps in geometry problem synthesis [2]. The paper is available on arXiv, a preprint server that, through integrations with platforms like Hugging Face, allows researchers to link models, datasets, and interactive demos directly to their papers [4][5].