Keep it SymPL: Symbolic Projective Layout for Allocentric Spatial Reasoning in Vision-Language Models

Vision-Language Models (VLMs) remain unreliable when spatial reasoning requires composing relations whose meanings depend on frames of reference. Existing neuro-symbolic methods make reasoning more explicit, but often depend on brittle geometric procedures and hard decisions over noisy perception. We propose SATURN, a neuro-symbolic framework for perspective-aware compositional spatial reasoning. SATURN reconstructs an approximate 3D scene, derives soft perspective-aware spatial predicates, and composes them with a training-free Pythonic symbolic executor, separating perception from reasoning while preserving uncertainty through multi-hop inference. We also introduce 3D FORCE, a diagnostic benchmark that controls reasoning depth, view, and perspective composition across spatial arrangement grounding (SAG) and referring expression grounding (REF). On 3D FORCE, VLMs and spatially trained models degrade sharply as depth and perspective complexity increase, whereas SATURN remains stable and outperforms strong baselines. On the real-world MindCube benchmark, SATURN achieves 78.57% overall accuracy, outperforming the strongest baseline by 14 pp.

Current Large Language Models have achieved Olympiad-level logic, yet Vision-Language Models paradoxically falter on elementary spatial tasks like block counting. This capability mismatch reveals a critical spatial intelligence gap,'' where models fail to construct coherent 3D mental representations from 2D observations. We uncover this gap via diagnostic analyses showing the bottleneck is a missing view-consistent spatial interface rather than insufficient visual features or weak reasoning. To bridge this, we introduce **3ViewSense**, a framework that grounds spatial reasoning in Orthographic Views. Drawing on engineering cognition, we propose a Simulate-and-Reason'' mechanism that decomposes complex scenes into canonical orthographic projections to resolve geometric ambiguities. By aligning egocentric perceptions with these allocentric references, our method facilitates explicit mental rotation and reconstruction. Empirical results on spatial reasoning benchmarks demonstrate that our method significantly outperforms existing baselines, with consistent gains on occlusion-heavy counting and view-consistent spatial reasoning. The framework also improves the stability and consistency of spatial descriptions, offering a scalable path toward stronger spatial intelligence in multimodal systems.~\footnote{https://github.com/Jasaxion/3ViewSense}

Existing approaches to multi-view spatial reasoning operate largely on sparse input views. Vision-language models (VLMs) are thus restricted to understand a scene and infer spatial relations within these fixed views, leading to fragile cross-view alignment and geometry-to-language bottleneck. To address these issues, we formulate a novel Seek-and-View reasoning approach to find implicit cross-view spatial evidence by locating a question-relevant view to support the spatial reasoning. To realize this approach, we propose Vantage, a training-free model-agnostic reasoning framework that pairs a VLM with a 3D foundation model: a viewpoint-grounded reasoning stage for question analysis and view planning, followed by a geometry-grounded evidence augmentation stage to effectively synthesize and incorporate visual evidence into the final reasoning. Comprehensive experiments on six VLMs demonstrate consistent improvements on five benchmarks without fine-tuning. Overall, by revealing spatial evidence through view-grounded reasoning, Vantage can largely reduce reliance on language-based cross-view alignment and improve multi-view spatial understanding. Our code is available at https://github.com/q1xiangchen/Vantage.