GeoSym127K: Scalable Symbolically-verifiable Synthesis for Multimodal Geometric Reasoning

• URL: http://arxiv.org/abs/2605.16371v1
• Date: Sun, 10 May 2026 13:13:47 GMT
• Title: GeoSym127K: Scalable Symbolically-verifiable Synthesis for Multimodal Geometric Reasoning
• Abstract summary: GeoSym Engine is an automated and scalable neuro-symbolic framework.<n>It derives exact symbolic ground truths and seamlessly integrates with a robust rendering pipeline.<n>GeoSym-Bench is an expert-curated suite of 511 complex samples for rigorous evaluation.
• Score: 42.5195033452088
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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