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| Main Authors: | , , , , , , , , , , , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.16371 |
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| _version_ | 1866918505484386304 |
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| author | Jing, Jinhao Ma, Zheng Liang, Jinwei Zhao, Qiannian Chen, Shawn Yang, Jing Yee, Por Lip Tiwari, Prayag Bai, Jingjing Wang, Benyou Lu, Lewei Su, Zhan |
| author_facet | Jing, Jinhao Ma, Zheng Liang, Jinwei Zhao, Qiannian Chen, Shawn Yang, Jing Yee, Por Lip Tiwari, Prayag Bai, Jingjing Wang, Benyou Lu, Lewei Su, Zhan |
| contents | Large Multimodal Models (LMMs) often struggle with geometric reasoning due to visual hallucinations and a lack of mathematically precise Chain-of-Thought (CoT) data. To address this, we propose the GeoSym Engine, an automated and scalable neuro-symbolic framework. By leveraging a type-conditional grammar and an analytic SymGT Solver, it derives exact symbolic ground truths and seamlessly integrates with a robust rendering pipeline to produce high-precision geometric diagrams. Using this engine, we construct GeoSym127K, a difficulty-stratified dataset featuring 51K high-resolution images, 127K questions with symbolic ground truths, and 55K answer-verified CoT QA pairs. We also introduce GeoSym-Bench, an expert-curated suite of 511 complex samples for rigorous evaluation. Through extensive supervised fine-tuning (SFT), we demonstrate that GeoSym drives concentrated improvements specifically on diagram-dependent and multi-step geometry tasks. Our Qwen3-VL-8B model gains an absolute +22.21% on the MathVerse Vision-Only subset and reaches 61.52% (+6.19% improvement) on WeMath, mitigating long-horizon logic fragmentation and outperforming advanced closed-source models like Doubao-1.8. Furthermore, applying Reinforcement Learning with Verifiable Rewards (RLVR) via GRPO reveals that initializing from structural SFT checkpoints substantially elevates the performance ceiling over zero-shot RL. Driven by deterministic exact-match signals, this showcases the robust scaling potential of our verifiable reasoning synthesis. Datasets and code are available at https://huggingface.co/datasets/Tomie0506/GeoSym127K and https://github.com/Tomie56/GeoSym127K. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_16371 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | GeoSym127K: Scalable Symbolically-verifiable Synthesis for Multimodal Geometric Reasoning Jing, Jinhao Ma, Zheng Liang, Jinwei Zhao, Qiannian Chen, Shawn Yang, Jing Yee, Por Lip Tiwari, Prayag Bai, Jingjing Wang, Benyou Lu, Lewei Su, Zhan Computer Vision and Pattern Recognition Artificial Intelligence Large Multimodal Models (LMMs) often struggle with geometric reasoning due to visual hallucinations and a lack of mathematically precise Chain-of-Thought (CoT) data. To address this, we propose the GeoSym Engine, an automated and scalable neuro-symbolic framework. By leveraging a type-conditional grammar and an analytic SymGT Solver, it derives exact symbolic ground truths and seamlessly integrates with a robust rendering pipeline to produce high-precision geometric diagrams. Using this engine, we construct GeoSym127K, a difficulty-stratified dataset featuring 51K high-resolution images, 127K questions with symbolic ground truths, and 55K answer-verified CoT QA pairs. We also introduce GeoSym-Bench, an expert-curated suite of 511 complex samples for rigorous evaluation. Through extensive supervised fine-tuning (SFT), we demonstrate that GeoSym drives concentrated improvements specifically on diagram-dependent and multi-step geometry tasks. Our Qwen3-VL-8B model gains an absolute +22.21% on the MathVerse Vision-Only subset and reaches 61.52% (+6.19% improvement) on WeMath, mitigating long-horizon logic fragmentation and outperforming advanced closed-source models like Doubao-1.8. Furthermore, applying Reinforcement Learning with Verifiable Rewards (RLVR) via GRPO reveals that initializing from structural SFT checkpoints substantially elevates the performance ceiling over zero-shot RL. Driven by deterministic exact-match signals, this showcases the robust scaling potential of our verifiable reasoning synthesis. Datasets and code are available at https://huggingface.co/datasets/Tomie0506/GeoSym127K and https://github.com/Tomie56/GeoSym127K. |
| title | GeoSym127K: Scalable Symbolically-verifiable Synthesis for Multimodal Geometric Reasoning |
| topic | Computer Vision and Pattern Recognition Artificial Intelligence |
| url | https://arxiv.org/abs/2605.16371 |