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

2026-06-02

AI Summary

Large language models lack native support for continuous spatial representations, hindering their capacity for genuine geometric reasoning. This work proposes the Spatial Language Model (SLM), which for the first time integrates learnable spatial representations as a first-class modality directly into the model’s reasoning process. By leveraging a multimodal architecture, atomic geometric operations, and training with spatial instruction alignment, SLM achieves a paradigm shift from symbolic matching to true geometric reasoning. Accompanied by a newly curated spatial instruction dataset and the SpatialEval benchmark, empirical evaluations demonstrate that SLM substantially outperforms existing approaches—whether based on prompt engineering or textual abstraction—across tasks involving spatial attributes, distance, topology, and relative positioning.

Abstract

Recent large language models (LLMs) often appear to exhibit spatial reasoning ability; however, this capability is largely \emph{symbolic}, arising from pattern matching over spatial language rather than true \emph{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 \emph{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 \emph{Spatial Instruction Dataset} that aligns spatial representations, atomic geometric operations, and natural language instructions. We further propose a new benchmark named \emph{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: \hyperlink{https://github.com/chuchen2017/SLM}{https://github.com/chuchen2017/SLM}.

Problem

• spatial reasoning
• large language models
• geometric reasoning
• symbolic reasoning
• continuous spatial representations

Innovation

• geometric spatial reasoning
• Spatial Language Model
• multimodal LLM
• continuous spatial representation
• SpatialEval