Geometrically-Constrained Agent for Spatial Reasoning

• URL: http://arxiv.org/abs/2511.22659v1
• Date: Thu, 27 Nov 2025 17:50:37 GMT
• Title: Geometrically-Constrained Agent for Spatial Reasoning
• Authors: Zeren Chen, Xiaoya Lu, Zhijie Zheng, Pengrui Li, Lehan He, Yijin Zhou, Jing Shao, Bohan Zhuang, Lu Sheng,
• Abstract summary: Vision Language Models exhibit a fundamental semantic-to-geometric gap in spatial reasoning.<n>Current paradigms fail to bridge this gap.<n>We propose a training-free agentic paradigm that resolves this gap by introducing a formal task constraint.
• Score: 53.93718394870856
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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