Euclid's Gift: Enhancing Spatial Perception and Reasoning in
  Vision-Language Models via Geometric Surrogate Tasks
Authors: name: Shijie Lian, name: Changti Wu, name: Laurence Tianruo Yang, name: Hang Yuan, name: Bin Yu, name: Lei Zhang, name: Kai Chen
Organization: Zhongguancun Academy

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. To enable the model to acquire and apply Euclidean
principles from these geometry problems, we employed Group Relative Policy
Optimization (GRPO) to finetune the Qwen2.5VL family and RoboBrain2.0 family,
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 of all evaluated models
rose from 34.5% to 40.5%, improving by 5.5 percentage points. Among them,
RoboBrain2.0-Euclid-7B achieves 49.6\% accuracy, surpassing the previous
state-of-the-art model, Spatial-MLLM.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 https://zgca-ai4edu.github.io/Euclids_Gift.