From Human Cognition to Neural Activations: Probing the Computational Primitives of Spatial Reasoning in LLMs

Multimodal language models (MLLMs) exhibit promising spatial reasoning capabilities, yet the internal mechanisms supporting them remain poorly understood. We uncover S-Space, a linear representation subspace in which object-token representations encode continuous coordinates along horizontal, vertical, and distance axes. Although we identify these axes by differentiating spatial-answer scores with respect to object-token activations, S-Space is intrinsic rather than induced by specific data or prompts, remaining readable under non-spatial questions. We show that S-Space functions as an internal spatial workspace of MLLMs. Perception encodes object locations into it, forming spatial representations that can be directly read out to support accurate spatial judgments. Internal reasoning transforms it for changing viewpoints. Verbal responses selectively access it, evidenced by causal interventions that alter spatial judgments while largely preserving non-spatial responses. Case studies further show that S-Space assigns locations to unseen entities and the observer, and connects physical directions with abstract linguistic meanings, suggesting both the capabilities and limitations of large-scale language training. Finally, we use S-Space as a diagnostic tool for spatial reasoning failures. Direction-word readouts reveal systematic coupling between cardinal and image-relative reference frames. More importantly, a perception-computation decomposition exposes a key bottleneck: MLLMs can form capable spatial representations, yet fall short in the spatial transformations required to reason reliably across viewpoint changes.

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: \hyperlink{https://github.com/chuchen2017/SLM}{https://github.com/chuchen2017/SLM}.

Foundation models have shown remarkable performance across diverse tasks, yet their ability to construct internal spatial world models for reasoning and planning remains unclear. We systematically evaluate the spatial understanding of large language models through maze tasks, a controlled testing context requiring multi-step planning and spatial abstraction. Across comprehensive experiments with Gemini-2.5-Flash, GPT-5-mini, Claude-Haiku-4.5, and DeepSeek-Chat, we uncover significant discrepancies in spatial reasoning that challenge assumptions about LLM planning capabilities. Using chain-of-thought prompting, Gemini achieves 80-86% accuracy on smaller mazes (5x5 to 7x7 grids) with tokenized adjacency representations, but performance collapses to 16-34% with visual grid formats, which is a 2-5x difference, suggesting representation-dependent rather than format-invariant spatial reasoning. We further probe spatial understanding through sequential proximity questions and compositional distance comparisons. Despite achieving 96-99% semantic coverage in reasoning traces, models fail to leverage this understanding for consistent spatial computations, indicating that they treat each question independently rather than building cumulative spatial knowledge. Our findings based on the maze-solving tasks suggest that LLMs do not develop robust spatial world models, but rather exhibit representation-specific and prompting-dependent reasoning that succeeds only under narrow conditions. These results have critical implications for deploying foundation models in applications requiring spatial abstraction.