# Grid Spatial Understanding: A Dataset for Textual Spatial Reasoning over Grids, Embodied Settings, and Coordinate Structures

arXiv: https://arxiv.org/abs/2603.17333 · HTML: https://mlsanity.com/paper/2603.17333/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 44 of its 51 references that are in the map.
- First posted on arXiv 18 Mar 2026.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)

## Builds on (most cited first, 30 of 44)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2-VL: Enhancing Vision-Language Model's Perception of the World at Any Resolution](https://mlsanity.com/paper/2409.12191/) (2024)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Scaling Instruction-Finetuned Language Models](https://mlsanity.com/paper/2210.11416/) (2022)
- [Qwen-VL: A Versatile Vision-Language Model for Understanding, Localization, Text Reading, and Beyond](https://mlsanity.com/paper/2308.12966/) (2023)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [Gemini: A Family of Highly Capable Multimodal Models](https://mlsanity.com/paper/2312.11805/) (2023)
- [ALFRED: A Benchmark for Interpreting Grounded Instructions for Everyday Tasks](https://mlsanity.com/paper/1912.01734/) (2019)
- [SpatialVLM: Endowing Vision-Language Models with Spatial Reasoning Capabilities](https://mlsanity.com/paper/2401.12168/) (2024)
- [BLINK: Multimodal Large Language Models Can See but Not Perceive](https://mlsanity.com/paper/2404.12390/) (2024)
- [SpatialRGPT: Grounded Spatial Reasoning in Vision Language Models](https://mlsanity.com/paper/2406.01584/) (2024)
- [Visual Spatial Reasoning](https://mlsanity.com/paper/2205.00363/) (2022)
- [Large Language Models for Mathematical Reasoning: Progresses and Challenges](https://mlsanity.com/paper/2402.00157/) (2024)
- [Vision-and-Dialog Navigation](https://mlsanity.com/paper/1907.04957/) (2019)
- [EmbodiedBench: Comprehensive Benchmarking Multi-modal Large Language Models for Vision-Driven Embodied Agents](https://mlsanity.com/paper/2502.09560/) (2025)
- [G-LLaVA: Solving Geometric Problem with Multi-Modal Large Language Model](https://mlsanity.com/paper/2312.11370/) (2023)
- [TEACh: Task-driven Embodied Agents that Chat](https://mlsanity.com/paper/2110.00534/) (2021)
- [Pixtral 12B](https://mlsanity.com/paper/2410.07073/) (2024)
- [Scene-LLM: Extending Language Model for 3D Visual Understanding and Reasoning](https://mlsanity.com/paper/2403.11401/) (2024)
- [UniGeo: Unifying Geometry Logical Reasoning via Reformulating Mathematical Expression](https://mlsanity.com/paper/2212.02746/) (2022)
- [Olmo 3](https://mlsanity.com/paper/2512.13961/) (2025)
- [Is A Picture Worth A Thousand Words? Delving Into Spatial Reasoning for Vision Language Models](https://mlsanity.com/paper/2406.14852/) (2024)
- [Vision-and-Language Navigation Today and Tomorrow: A Survey in the Era of Foundation Models](https://mlsanity.com/paper/2407.07035/) (2024)
- [Evaluating Cognitive Maps and Planning in Large Language Models with CogEval](https://mlsanity.com/paper/2309.15129/) (2023)
- [StepGame: A New Benchmark for Robust Multi-Hop Spatial Reasoning in Texts](https://mlsanity.com/paper/2204.08292/) (2022)

## Abstract (arXiv)

We introduce GSU, a text-only grid dataset to evaluate the spatial reasoning capabilities of LLMs over 3 core tasks: navigation, object localization, and structure composition. By forgoing visual inputs, isolating spatial reasoning from perception, we show that while most models grasp basic grid concepts, they struggle with frames of reference relative to an embodied agent and identifying 3D shapes from coordinate lists. We also find that exposure to a visual modality does not provide a generalizable understanding of 3D space that VLMs are able to utilize for these tasks. Finally, we show that while the very latest frontier models can solve the provided tasks (though harder variants may still stump them), fully fine-tuning a small LM or LORA fine-tuning a small LLM show potential to match frontier model performance, suggesting an avenue for specialized embodied agents.