# From Symbolic to Geometric: Enabling Spatial Reasoning in Large Language Models

arXiv: https://arxiv.org/abs/2606.04381 · HTML: https://mlsanity.com/paper/2606.04381/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 16 of its 33 references that are in the map.
- First posted on arXiv 3 Jun 2026.

## Placed in

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

## Builds on (most cited first, 16 of 16)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [PointLLM: Empowering Large Language Models to Understand Point Clouds](https://mlsanity.com/paper/2308.16911/) (2023)
- [Hallucination is Inevitable: An Innate Limitation of Large Language Models](https://mlsanity.com/paper/2401.11817/) (2024)
- [Language Models Represent Space and Time](https://mlsanity.com/paper/2310.02207/) (2023)
- [GPT4GEO: How a Language Model Sees the World's Geography](https://mlsanity.com/paper/2306.00020/) (2023)
- [GeoLLM: Extracting Geospatial Knowledge from Large Language Models](https://mlsanity.com/paper/2310.06213/) (2023)
- [Large Language Model for Participatory Urban Planning](https://mlsanity.com/paper/2402.17161/) (2024)
- [FoNE: Precise Single-Token Number Embeddings via Fourier Features](https://mlsanity.com/paper/2502.09741/) (2025)
- [UrbanLLaVA: A Multi-modal Large Language Model for Urban Intelligence with Spatial Reasoning and Understanding](https://mlsanity.com/paper/2506.23219/) (2025)
- [Geo-Llama: Leveraging LLMs for Human Mobility Trajectory Generation with Spatiotemporal Constraints](https://mlsanity.com/paper/2408.13918/) (2024)
- [Harnessing the Synergy between LLM Agents and Knowledge Graphs for Urban Socioeconomic Prediction](https://mlsanity.com/paper/2411.00028/) (2024)

## Built on by (most cited first, 1 of 1)

- [Geospatial Vector Geometry as a Native Spatial Modality for Vision-Language Models](https://mlsanity.com/paper/2610.16769/) (2026)

## Abstract (arXiv)

Recent large language models (LLMs) often appear to exhibit spatial reasoning ability; however, this capability is largely symbolic, arising from pattern matching over spatial language rather than true geometric reasoning over space. Because LLMs operate on discrete tokens, they lack native support for continuous spatial representations, explicit geometric computation, and structured spatial operators. To address this limitation, we introduce the Spatial Language Model (SLM), the first multimodal LLM that treats location information as a first-class modality and enables geometric spatial reasoning within the model's inference process. SLM directly operates on learned spatial representations rather than textual descriptions of spatial relations. To support effective training, we construct a Spatial Instruction Dataset that aligns spatial representations, atomic geometric operations, and natural language instructions. We further propose a new benchmark named SpatialEval, which is designed to evaluate spatial reasoning across attributes, distance, topology, and relative-position tasks. Extensive experiments show that SLM significantly outperforms existing LLM-based approaches that rely on symbolic reasoning via prompt engineering or textual abstraction, demonstrating the benefits of integrating geometric spatial representations for robust spatial reasoning. Our instruction dataset, evaluation benchmark, model training codes, and models' checkpoints can be found at: hyperlinkhttps://github.com/chuchen2017/SLMhttps://github.com/chuchen2017/SLM.