Geometrically-Constrained Agent for Spatial Reasoning
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arXiv
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| Main Authors: | , , , , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915642781728768 |
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| author | Chen, Zeren Lu, Xiaoya Zheng, Zhijie Li, Pengrui He, Lehan Zhou, Yijin Shao, Jing Zhuang, Bohan Sheng, Lu |
| author_facet | Chen, Zeren Lu, Xiaoya Zheng, Zhijie Li, Pengrui He, Lehan Zhou, Yijin Shao, Jing Zhuang, Bohan Sheng, Lu |
| contents | Vision Language Models (VLMs) exhibit a fundamental semantic-to-geometric gap in spatial reasoning: they excel at qualitative semantic inference but their reasoning operates within a lossy semantic space, misaligned with high-fidelity geometry. Current paradigms fail to bridge this gap. Training-based methods suffer from an ``oracle paradox,'' learning flawed spatial logic from imperfect oracles. Tool-integrated methods constrain the final computation but critically leave the VLM's planning process unconstrained, resulting in geometrically flawed plans. In this work, we propose Geometrically-Constrained Agent (GCA), a training-free agentic paradigm that resolves this gap by introducing a formal task constraint. Specifically, we strategically decouples the VLM's role into two stages. First, acting as a semantic analyst, the VLM translates the user's ambiguous query into the formal, verifiable task constraint, which defines the reference frame and objective. Second, acting as a task solver, the VLM generates and executes tool calls strictly within the deterministic bounds defined by the constraint. This geometrically-constrained reasoning strategy successfully resolve the semantic-to-geometric gap, yielding a robust and verifiable reasoning pathway for spatial reasoning. Comprehensive experiments demonstrate that GCA achieves SOTA performance on multiple spatial reasoning benchmarks, surpassing existing training-based and tool-integrated methods by ~27%. Please see our homepage at https://gca-spatial-reasoning.github.io. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22659 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometrically-Constrained Agent for Spatial Reasoning Chen, Zeren Lu, Xiaoya Zheng, Zhijie Li, Pengrui He, Lehan Zhou, Yijin Shao, Jing Zhuang, Bohan Sheng, Lu Artificial Intelligence Computer Vision and Pattern Recognition Vision Language Models (VLMs) exhibit a fundamental semantic-to-geometric gap in spatial reasoning: they excel at qualitative semantic inference but their reasoning operates within a lossy semantic space, misaligned with high-fidelity geometry. Current paradigms fail to bridge this gap. Training-based methods suffer from an ``oracle paradox,'' learning flawed spatial logic from imperfect oracles. Tool-integrated methods constrain the final computation but critically leave the VLM's planning process unconstrained, resulting in geometrically flawed plans. In this work, we propose Geometrically-Constrained Agent (GCA), a training-free agentic paradigm that resolves this gap by introducing a formal task constraint. Specifically, we strategically decouples the VLM's role into two stages. First, acting as a semantic analyst, the VLM translates the user's ambiguous query into the formal, verifiable task constraint, which defines the reference frame and objective. Second, acting as a task solver, the VLM generates and executes tool calls strictly within the deterministic bounds defined by the constraint. This geometrically-constrained reasoning strategy successfully resolve the semantic-to-geometric gap, yielding a robust and verifiable reasoning pathway for spatial reasoning. Comprehensive experiments demonstrate that GCA achieves SOTA performance on multiple spatial reasoning benchmarks, surpassing existing training-based and tool-integrated methods by ~27%. Please see our homepage at https://gca-spatial-reasoning.github.io. |
| title | Geometrically-Constrained Agent for Spatial Reasoning |
| topic | Artificial Intelligence Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2511.22659 |