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arXiv · 2509.21896

GenesisGeo: Technical Report

Minfeng Zhu·Zi Wang·Sizhe Ji·Zhengtong Du·Shengqiang Tai·Junming Ke·Xiao Deng·Zanlang Yin·Xiuqi Huang·Heyu Wang·Wei Chen
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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.

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Minfeng Zhu, Zi Wang, Sizhe Ji, Zhengtong Du, Shengqiang Tai, Junming Ke, Xiao Deng, Zanlang Yin, Xiuqi Huang, Heyu Wang, Wei Chen. 2025-09-26. GenesisGeo: Technical Report. https://arxiv.org/abs/2509.21896

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