Geometrically-Constrained Agent for Spatial Reasoning

TL;DR

The paper introduces GCA, a training-free agentic approach that bridges the semantic-to-geometric gap in spatial reasoning by decoupling semantic analysis and task solving, leading to state-of-the-art results.

Contribution

GCA presents a novel formal task constraint framework that enhances spatial reasoning accuracy without training, outperforming existing methods.

Findings

GCA achieves approximately 27% improvement over previous methods.

GCA provides a robust, verifiable reasoning pathway for spatial tasks.

GCA surpasses training-based and tool-integrated methods on multiple benchmarks.

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.