# SATURN: Symbolic Spatial Reasoning for Multi-Perspective Grounding

arXiv: https://arxiv.org/abs/2606.22694 · HTML: https://mlsanity.com/paper/2606.22694/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 43 of its 82 references that are in the map.
- First posted on arXiv 21 Jun 2026.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)
- Multimodal LLMs / vision-language models / [Embodied and 3D vision-language models](https://mlsanity.com/mllm/embodied-and-3d-vision-language-models/)

## Builds on (most cited first, 30 of 43)

- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Expanding Performance Boundaries of Open-Source Multimodal Models with Model, Data, and Test-Time Scaling](https://mlsanity.com/paper/2412.05271/) (2024)
- [DeepSeek-V4: Towards Highly Efficient Million-Token Context Intelligence](https://mlsanity.com/paper/2606.19348/) (2026)
- [OpenAI GPT-5 System Card](https://mlsanity.com/paper/2601.03267/) (2025)
- [Cambrian-1: A Fully Open, Vision-Centric Exploration of Multimodal LLMs](https://mlsanity.com/paper/2406.16860/) (2024)
- [Depth Anything 3: Recovering the Visual Space from Any Views](https://mlsanity.com/paper/2511.10647/) (2025)
- [BLINK: Multimodal Large Language Models Can See but Not Perceive](https://mlsanity.com/paper/2404.12390/) (2024)
- [GLM-4.5V and GLM-4.1V-Thinking: Towards Versatile Multimodal Reasoning with Scalable Reinforcement Learning](https://mlsanity.com/paper/2507.01006/) (2025)
- [VLM-3R: Vision-Language Models Augmented with Instruction-Aligned 3D Reconstruction](https://mlsanity.com/paper/2505.20279/) (2025)
- [Cosmos-Reason1: From Physical Common Sense To Embodied Reasoning](https://mlsanity.com/paper/2503.15558/) (2025)
- [3DSRBench: A Comprehensive 3D Spatial Reasoning Benchmark](https://mlsanity.com/paper/2412.07825/) (2024)
- [Molmo2: Open Weights and Data for Vision-Language Models with Video Understanding and Grounding](https://mlsanity.com/paper/2601.10611/) (2026)
- [From Flatland to Space: Teaching Vision-Language Models to Perceive and Reason in 3D](https://mlsanity.com/paper/2503.22976/) (2025)
- [ViewSpatial-Bench: Evaluating Multi-perspective Spatial Localization in Vision-Language Models](https://mlsanity.com/paper/2505.21500/) (2025)
- [SAT: Dynamic Spatial Aptitude Training for Multimodal Language Models](https://mlsanity.com/paper/2412.07755/) (2024)
- [OmniSpatial: Towards Comprehensive Spatial Reasoning Benchmark for Vision Language Models](https://mlsanity.com/paper/2506.03135/) (2025)
- [EmbSpatial-Bench: Benchmarking Spatial Understanding for Embodied Tasks with Large Vision-Language Models](https://mlsanity.com/paper/2406.05756/) (2024)
- [SpatialLadder: Progressive Training for Spatial Reasoning in Vision-Language Models](https://mlsanity.com/paper/2510.08531/) (2025)
- [MM-Spatial: Exploring 3D Spatial Understanding in Multimodal LLMs](https://mlsanity.com/paper/2503.13111/) (2025)
- [Spatial Reasoning with Vision-Language Models in Ego-Centric Multi-View Scenes](https://mlsanity.com/paper/2509.06266/) (2025)
- [SpatialSense: An Adversarially Crowdsourced Benchmark for Spatial Relation Recognition](https://mlsanity.com/paper/1908.02660/) (2019)
- [An Empirical Analysis on Spatial Reasoning Capabilities of Large Multimodal Models](https://mlsanity.com/paper/2411.06048/) (2024)
- [LEGO-Puzzles: How Good Are MLLMs at Multi-Step Spatial Reasoning?](https://mlsanity.com/paper/2503.19990/) (2025)
- [How Far are VLMs from Visual Spatial Intelligence? A Benchmark-Driven Perspective](https://mlsanity.com/paper/2509.18905/) (2025)
- [Spatial457: A Diagnostic Benchmark for 6D Spatial Reasoning of Large Multimodal Models](https://mlsanity.com/paper/2502.08636/) (2025)
- [GSR-BENCH: A Benchmark for Grounded Spatial Reasoning Evaluation via Multimodal LLMs](https://mlsanity.com/paper/2406.13246/) (2024)
- [SPHERE: Unveiling Spatial Blind Spots in Vision-Language Models Through Hierarchical Evaluation](https://mlsanity.com/paper/2412.12693/) (2024)
- [TIGeR: Tool-Integrated Geometric Reasoning in Vision-Language Models for Robotics](https://mlsanity.com/paper/2510.07181/) (2025)
- [Geometrically-Constrained Agent for Spatial Reasoning](https://mlsanity.com/paper/2511.22659/) (2025)
- [SpaCE-10: A Comprehensive Benchmark for Multimodal Large Language Models in Compositional Spatial Intelligence](https://mlsanity.com/paper/2506.07966/) (2025)

## Built on by (most cited first, 2 of 2)

- [Spatial Reasoning via Modality Switching Between Language and Symbolic Representations](https://mlsanity.com/paper/2606.31285/) (2026)
- [CLAMP: Constrained Decoding for Vision-Language Embodied Planning](https://mlsanity.com/paper/2609.08602/) (2026)

## Abstract (arXiv)

Vision-Language Models (VLMs) remain unreliable when spatial reasoning requires composing relations whose meanings depend on frames of reference. Existing tool-augmented spatial reasoning methods make reasoning more explicit, but often rely on low-level geometric procedures and hard binary 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 for 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 degrades the least and outperforms every baseline at each depth. On the real-world MindCube benchmark, SATURN achieves (78.06%) overall accuracy, outperforming the strongest baseline by (14) percentage points.