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| Autores principales: | , , , , , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2509.21896 |
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| _version_ | 1866912916840644608 |
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| author | Zhu, Minfeng Wang, Zi Ji, Sizhe Du, Zhengtong Tai, Shengqiang Ke, Junming Deng, Xiao Yin, Zanlang Huang, Xiuqi Wang, Heyu Chen, Wei |
| author_facet | Zhu, Minfeng Wang, Zi Ji, Sizhe Du, Zhengtong Tai, Shengqiang Ke, Junming Deng, Xiao Yin, Zanlang Huang, Xiuqi Wang, Heyu Chen, Wei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21896 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | GenesisGeo: Technical Report Zhu, Minfeng Wang, Zi Ji, Sizhe Du, Zhengtong Tai, Shengqiang Ke, Junming Deng, Xiao Yin, Zanlang Huang, Xiuqi Wang, Heyu Chen, Wei Artificial Intelligence 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. |
| title | GenesisGeo: Technical Report |
| topic | Artificial Intelligence |
| url | https://arxiv.org/abs/2509.21896 |