VeriGeo: Controllable Geometry Question Generation with Numerical and Analytical Verification

Computer Science > Artificial Intelligence [Submitted on 12 Jun 2026] VeriGeo: Controllable Geometry Question Generation with Numerical and Analytical Verification Xiaoxian Duan, Zequn Liu, Yingce Xia 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. Comments: 32 pages, 4 figures, 9 tables Subjects: Artificial Intelligence (cs.AI) Cite as: arXiv:2606.14176 [cs.AI]   (or arXiv:2606.14176v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2606.14176 Focus to learn more Submission history From: Xiaoxian Duan [view email] [v1] Fri, 12 Jun 2026 06:59:44 UTC (1,058 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-06 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)