Euclid's Gift: Enhancing Spatial Perception and Reasoning in
  Vision-Language Models via Geometric Surrogate Tasks
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.
68db44add2bf1f4b15ec7378
Shijie Lian
claimed_verified
2025-10-01T10:24:59.122Z
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Shijie Lian
user
LiamLian0727
68db44add2bf1f4b15ec7379
Changti Wu
claimed_verified
2025-09-30T06:30:31.203Z
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Changti Wu
user
MaplesWCT
68db44add2bf1f4b15ec737a
Laurence Tianruo Yang
68db44add2bf1f4b15ec737b
Hang Yuan
68db44add2bf1f4b15ec737c
Bin Yu
claimed_verified
2025-10-22T15:47:11.453Z
63d3b5f1640bb0f77173baea
https://cdn-avatars.huggingface.co/v1/production/uploads/1674819020331-noauth.jpeg
yubin
user
VLyb
68db44add2bf1f4b15ec737d
Lei Zhang
68db44add2bf1f4b15ec737e
Kai Chen
Euclid's Gift: Enhancing Spatial Perception and Reasoning in
  Vision-Language Models via Geometric Surrogate Tasks
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.
Geometry-centric fine-tuning using the Euclid30K dataset significantly improves spatial reasoning abilities in multimodal large language models across multiple benchmarks.
Euclidean geometry Group Relative Policy Optimization (GRPO) Qwen2.5VL RoboBrain2.0 zero-shot gains spatial reasoning benchmarks Super-CLEVR Omni3DBench VSI-Bench MindCube vision-language models