{"ID":2865050,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.21896","arxiv_id":"2509.21896","title":"GenesisGeo: Technical Report","abstract":"Recent neuro-symbolic geometry theorem provers have made significant progress on Euclidean problems by coupling neural guidance with symbolic verification. However, most existing systems operate almost exclusively in a symbolic space, leaving diagram-based intuition largely unused during reasoning. For humans, geometric diagrams provide essential heuristics for identifying non-trivial auxiliary constructions. Meanwhile, visual language models (VLMs) still struggle with geometry due to the lack of high-quality data with geometric diagrams and reasoning supervision. In this paper, we introduce GenesisGeo-1M, a large-scale synthetic dataset for visual geometric reasoning that contains 1M multimodal geometry problems paired with machine-checkable proof traces. Building on this dataset, we formulate geometric learning as a multi-task training paradigm that jointly optimizes text-based proof generation and diagram-grounded proof generation, encouraging models to learn visual grounding and symbolic deduction. Extensive experiments show that our GenesisGeo-2B model achieves gold-medal-level performance on Olympiad geometry benchmarks, solving 29/30 problems on IMO-30, 63/95 on IMO-95, and 278/409 on HAGeo-409.","short_abstract":"Recent neuro-symbolic geometry theorem provers have made significant progress on Euclidean problems by coupling neural guidance with symbolic verification. However, most existing systems operate almost exclusively in a symbolic space, leaving diagram-based intuition largely unused during reasoning. For humans, geometri...","url_abs":"https://arxiv.org/abs/2509.21896","url_pdf":"https://arxiv.org/pdf/2509.21896v2","authors":"[\"Minfeng Zhu\",\"Zi Wang\",\"Sizhe Ji\",\"Zhengtong Du\",\"Shengqiang Tai\",\"Junming Ke\",\"Xiao Deng\",\"Zanlang Yin\",\"Xiuqi Huang\",\"Heyu Wang\",\"Wei Chen\"]","published":"2025-09-26T05:30:43Z","proceeding":"cs.AI","tasks":"[\"cs.AI\"]","methods":"[\"Language Model\"]","has_code":false}