用几何题训练视觉语言模型，显著提升空间推理能力。
Euclid's Gift: Enhancing Spatial Perception and Reasoning in Vision-Language Models via Geometric Surrogate Tasks
- 以欧氏几何问题为代理任务，构建3万道多模态几何题数据集。
- 微调后模型在4个基准上零样本提升，空间推理准确率最高增6.7%。
- 首次证明几何训练可让模型获得通用空间智能，适合研究多模态推理者。
空间智能涵盖形状可视化、物体旋转、位置关系判断、包含关系及数量估计等丰富能力，但仍是多模态大语言模型（MLLMs）的核心挑战。为此，本文提出将欧氏几何求解作为代理任务。我们精心构建了名为Euclid30K的多模态数据集，包含约3万道平面与立体几何题。为使模型从这些题目中学习并应用欧氏原理，我们使用组相对策略优化（GRPO）对来自Qwen2.5VL、Qwen3VL和RoboBrain2.0系列的七个模型变体（参数量3–72B）进行微调，使其能识别形状、计数、关联实体，并基于欧氏原理进行多步演绎推理。实验表明，微调后的模型在四个空间推理基准（Super-CLEVR、Omni3DBench、VSI-Bench、MindCube）上实现显著零样本提升，无需特定任务适配。值得注意的是，经Euclid30K训练后，VSI-Bench平均准确率从36.6%升至41.8%（+5.2%），MindCube平均准确率从31.4%升至38.1%（+6.7%）。据我们所知，这是首个系统性证明几何中心微调可赋予视觉语言模型广泛可迁移空间技能的研究。代码与数据集见：https://zgca-ai4edu.github.io/Euclids_Gift
原文摘要 · Abstract (English)
Spatial intelligence spans a rich suite of abilities, including visualising and transforming shapes, mentally rotating objects, judging relational positions and containment, and estimating numerosity. However, it still remains a critical unresolved challenge for Multimodal Large Language Models (MLLMs). To fill this gap, we propose to treat Euclidean geometry problem-solving as a surrogate task. Specifically, we meticulously constructed a curated multimodal dataset, called Euclid30K, comprising approximately 30K plane and solid geometry problems. Furthermore, to enable the model to learn and apply Euclidean principles from these geometry problems, we fine-tuned seven model variants (spanning 3--72B parameters) from the Qwen2.5VL, Qwen3VL, and RoboBrain2.0 families using Group Relative Policy Optimization (GRPO), inspiring the models to identify shapes, count, and relate entities, and perform multi-step deductive reasoning using Euclidean principles. Our experiments demonstrate that the resulting models achieve substantial zero-shot gains across four spatial reasoning benchmarks (Super-CLEVR, Omni3DBench, VSI-Bench, and MindCube) without any task-specific adaptations. Notably, after training on the Euclid30K, the mean VSI-Bench accuracy rose from 36.6\% to 41.8\% (+5.2\%), and the mean MindCube accuracy rose from 31.4\% to 38.1\% (+6.7\%). To our knowledge, this is the first systematic study showing that geometry-centric fine-tuning can confer vision-language models with broadly transferable spatial skills. Code and Euclid30K dataset can be found in \href{https://zgca-ai4edu.github.io/Euclids_Gift}{this}.
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