Spatial Reasoning in Language Models

Vision-language models (VLMs) exhibit a striking paradox: they can generate executable code that reconstructs a 3D scene from geometric primitives with correct object counts, classes, and approximate positions, yet the same models fail at simpler spatial questions on the same image. We show that 3D geometric primitives (cubes, spheres, cylinders, expressed in executable code) serve as a powerful intermediate representation for spatial understanding, and exploit this through three contributions. First, we introduce SpatialBabel, a benchmark evaluating fourteen VLMs on primitive-based 3D scene reconstruction across six scene-code languages (programming languages and declarative formats for 3D primitive scenes), revealing that a single model's object-detection F1 can vary by up to $5.7\times$ across languages. Second, we propose Code-CoT (Code Chain-of-Thought), a training-free inference strategy that routes spatial reasoning through primitive-based code generation. Code-CoT lifts the SpatialBabel-QA-Score by up to $+6.4$% on primitive scenes and real-photo CV-Bench-3D accuracy by $+5.0$% for VLMs with strong coding capabilities. Third, we propose \textbf{S$^{3}$-FT} (Self-Supervised Spatial Fine-Tuning), which self-supervisedly distills primitive spatial knowledge into general visual reasoning by parsing the model's own Three.js primitive-reconstructions into structured annotations and fine-tuning on the result, with no human labels and no teacher model. Training on primitive images alone, S$^3$-FT improves Qwen3-VL-8B by $+4.6$ to $+8.6$% on SpatialBabel-Primitive-QA, $+9.7$% on CV-Bench-2D, and $+17$% on HallusionBench; the recipe transfers across model families. These results establish geometric primitives in code as both a diagnostic and a transferable spatial vocabulary for VLMs. We will release all artifacts upon publication.

Multimodal Reasoning Models (MRMs) leveraging Chain-of-Thought (CoT) based thinking have revolutionized mathematical and logical problem-solving. However, we show that this paradigm struggles with generalized spatial intelligence. We perform a comprehensive evaluation of seventeen models across thirteen spatial benchmarks and identify a critical gap: CoT prompting consistently degrades performance in visual spatial reasoning. Furthermore, through a novel No-Image++ ablation, we demonstrate that MRMs and CoT prompted MLMs suffer from severe shortcut learning, and hallucinate visual details from textual priors even when the image is absent. These findings challenge the efficacy of text-only CoT for spatial tasks and underscore the need for vision-centric reasoning paradigms.

When faced with complex spatial problems, humans naturally sketch layouts to organize their thinking, and the act of drawing further sharpens their understanding. In this work, we ask whether a similar principle holds for Large Language Models (LLMs): can learning to construct explicit visual layouts from spatial descriptions instill genuine spatial understanding? We introduce Text2Space, a dataset that pairs natural language descriptions with ground-truth ASCII grid layouts and spatial QA pairs, enabling us to separate failures in constructing spatial representations from failures in reasoning over them. We adopt ASCII because it is human-readable, operates entirely within the token space of language models, and encodes spatial relations in a structurally verifiable form. Our evaluation reveals a pronounced "Read-Write Asymmetry": LLMs interpret ASCII representations effectively but struggle to produce them from text, and these construction errors propagate to incorrect answers downstream. To address this limitation, we train models on layout construction (Text$\rightarrow$ASCII) and find that it significantly improves spatial reasoning from text alone, even without producing any ASCII at inference time. Combining construction with comprehension training further amplifies these gains. Crucially, these improvements transfer to three external spatial reasoning benchmarks, demonstrating that, much as sketching sharpens human spatial thinking, learning to construct explicit layouts instills spatial understanding that generalizes beyond the training format.

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.

Understanding student engagement usually requires time-consuming manual observation or invasive recording that raises privacy concerns. We present a privacy-preserving pipeline that analyzes classroom videos to extract insights about student attention, without storing any identifiable footage. Our system runs on a single GPU, using OpenPose for skeletal extraction and Gaze-LLE for visual attention estimation. Original video frames are deleted immediately after pose extraction, thus only geometric coordinates (stored as JSON) are retained, ensuring compliance with FERPA. The extracted pose and gaze data is processed by QwQ-32B-Reasoning, which performs zero-shot analysis of student behavior across lecture segments. Instructors access results through a web dashboard featuring attention heatmaps and behavioral summaries. Our preliminary findings suggest that LLMs may show promise for multimodal behavior understanding, although they still struggle with spatial reasoning about classroom layouts. We discuss these limitations and outline directions for improving LLM spatial comprehension in educational analytics contexts.

Multimodal large language models (MLLMs) are increasingly being applied to spatial cognition tasks, where they are expected to understand and interact with complex environments. Most existing works improve spatial reasoning by introducing 3D priors or geometric supervision, which enhances performance but incurs substantial data preparation and alignment costs. In contrast, purely 2D approaches often struggle with multi-frame spatial reasoning due to their limited ability to capture cross-frame spatial relationships. To address these limitations, we propose EgoMind, a Chain-of-Thought framework that enables geometry-free spatial reasoning through Role-Play Caption, which jointly constructs a coherent linguistic scene graph across frames, and Progressive Spatial Analysis, which progressively reasons toward task-specific questions. With only 5K auto-generated SFT samples and 20K RL samples, EgoMind achieves competitive results on VSI-Bench, SPAR-Bench, SITE-Bench, and SPBench, demonstrating its effectiveness in strengthening the spatial reasoning capabilities of MLLMs and highlighting the potential of linguistic reasoning for spatial cognition. Code and data are released at https://github.com/Hyggge/EgoMind.

Structured spatial navigation is a core benchmark for Large Language Models (LLMs) spatial reasoning. Existing paradigms like Visualization-of-Thought (VoT) are prone to cascading errors in complex topologies. To solve this, we propose STAR, a two-stage framework grounded on topological anchors, and introduce the RedMaze-23K dataset with human-inspired turnpoint annotations. The first stage uses supervised fine-tuning to help models internalize spatial semantics and prune redundant paths. The second adopts Spatial-aware Segment-level Direct Preference Optimization (SDPO) to refine self-correction in long-horizon navigation. Experiments show STAR achieves state-of-the-art performance among open-source models: its 32B variant outperforms DeepSeek-V3 (29.27% vs. 25.00%) and reaches 82.4% of GPT-4's performance.

Humans build shared spatial understanding by communicating partial, viewpoint-dependent observations. We ask whether Multimodal Large Language Models (MLLMs) can do the same, aligning distinct egocentric views through dialogue to form a coherent, allocentric mental model of a shared environment. To study this systematically, we introduce COSMIC, a benchmark for Collaborative Spatial Communication. In this setting, two static MLLM agents observe a 3D indoor environment from different viewpoints and exchange natural-language messages to solve spatial queries. COSMIC contains 899 diverse scenes and 1250 question-answer pairs spanning five tasks. We find a capability hierarchy, MLLMs are most reliable at identifying shared anchor objects across views, perform worse on relational reasoning, and largely fail at building globally consistent maps, performing near chance, even for frontier models. Moreover, we find thinking capability yields gains in anchor grounding, but is insufficient for higher-level spatial communication. To contextualize model behavior, we collect 250 human-human dialogues. Humans achieve 95% aggregate accuracy, while the best model, Gemini-3-Pro-Thinking, reaches 72%, leaving substantial room for improvement. Moreover, human conversations grow more precise as partners align on a shared spatial understanding, whereas MLLMs keep exploring without converging, suggesting limited capacity to form and sustain a robust shared mental model throughout the dialogue. Our code and data is available at https://github.com/ankursikarwar/Cosmic.

As spatial intelligence becomes an increasingly important capability for foundation models, it remains unclear whether large language models' (LLMs) performance on spatial reasoning benchmarks reflects structured internal spatial representations or reliance on linguistic heuristics. We address this question from a mechanistic perspective by examining how spatial information is internally represented and used. Drawing on computational theories of human spatial cognition, we decompose spatial reasoning into three primitives, relational composition, representational transformation, and stateful spatial updating, and design controlled task families for each. We evaluate multilingual LLMs in English, Chinese, and Arabic under single pass inference, and analyze internal representations using linear probing, sparse autoencoder based feature analysis, and causal interventions. We find that task relevant spatial information is encoded in intermediate layers and can causally influence behavior, but these representations are transient, fragmented across task families, and weakly integrated into final predictions. Cross linguistic analysis further reveals mechanistic degeneracy, where similar behavioral performance arises from distinct internal pathways. Overall, our results suggest that current LLMs exhibit limited and context dependent spatial representations rather than robust, general purpose spatial reasoning, highlighting the need for mechanistic evaluation beyond benchmark accuracy.

Standard attribution heatmaps show where a vision-language model (VLM) focuses, but they do not reveal whether the recovered evidence is organized by the queried spatial relation or merely reflects image layout. To address this problem, we introduce CREG (Compass Relational Evidence Graph), a training-free diagnostic framework that converts token-level attribution into a reference-centered compass distribution and measures its directional alignment. CREG provides a shared directional readout across attribution methods and makes comparison with geometric controls explicit. Across three spatial-relation benchmarks, box-only geometry achieves Direction Alignment Error 28.4 to 34.4 degrees lower than the best current model-based attribution method on each dataset, leaving a substantial gap between attribution structure and simple target localization. To examine this gap, we apply a diagnostic battery including target intervention, reference-center randomization, and variance partition. Taken together, the results suggest that the directional structure recoverable from current attribution methods is limited and often mixed with image layout. We further find that higher task accuracy does not reliably coincide with better directional attribution: small-scale LoRA training and newer model generations can improve task accuracy while leaving Direction Alignment Error unchanged or worse. These findings characterize what current attribution methods reveal rather than the model's internal spatial representation. CREG provides a controlled protocol for testing whether improvements in spatial reasoning are accompanied by more directionally organized evidence.

Large Language Models (LLMs) achieve strong performance on many reasoning benchmarks, yet these evaluations typically focus on isolated tasks that differ from real-world usage in task-oriented dialogue (TOD). In this setting, LLMs must perform reasoning inherently while generating text and adhering to instructions on role, format, and style. This mismatch raises concerns about whether benchmark performance accurately reflects models' reasoning robustness in TOD setting. We investigate how framing reasoning tasks within TOD affects LLM performance by introducing BOULDER, a new dynamic benchmark covering eight travel-related tasks that require arithmetic, spatial, and temporal reasoning with both commonsense and formal aspects. Each problem is presented in both isolated and dialogue-based variants, enabling controlled comparison while mitigating data contamination. Experiments on eight LLMs reveal a substantial and consistent performance gap between isolated and dialogue settings. Through ablations and qualitative analysis, we show that this gap is largely driven by the multi-turn nature of dialogue, with additional effects from role conditioning and tool-use requirements. Our results highlight the need to evaluate LLM reasoning in realistic interactive scenarios.

In this work, we probe the ability of a language model to demonstrate spatial reasoning from unstructured text, mimicking human capabilities and automating a process that benefits many downstream media applications. Concretely, we study the narrative-to-play task: inferring stage-play layouts (scenes, speaker positions, movements, and room types) from text that lacks explicit spatial, positional, or relational cues. We then introduce a dramaturgy-inspired deterministic evaluation suite and, finally, a training and inference recipe that combines rejection SFT using Best-of-N sampling with RL from verifiable rewards via GRPO. Experiments on a text-only corpus of classical English literature demonstrate improvements over vanilla models across multiple metrics (character attribution, spatial plausibility, and movement economy), as well as alignment with an LLM-as-a-judge and subjective human preferences.

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.

Vision-language models (VLMs) have advanced rapidly, yet they still struggle with basic spatial reasoning. Despite strong performance on general benchmarks, modern VLMs remain brittle at understanding 2D spatial relationships such as relative position, layout, and counting. We argue that this failure is not merely a data problem, but is closely tied to dominant design choices in current VLM pipelines: reliance on CLIP-style image encoders and the flattening of images into 1D token sequences with 1D positional encoding. We present a controlled diagnostic study within the LLaVA framework to isolate how these choices affect spatial grounding. We evaluate frontier models and LLaVA variants on a suite of spatial benchmarks, comparing CLIP-based encoders against alternatives trained with denser or generative objectives, as well as variants augmented with 2D positional encoding. Our results show consistent spatial performance gaps across models, and indicate that encoder objectives and positional structure shape spatial behavior, but do not fully resolve it.

Current Large Language Models have achieved Olympiad-level logic, yet Vision-Language Models paradoxically falter on elementary spatial tasks like block counting. This capability mismatch reveals a critical spatial intelligence gap,'' where models fail to construct coherent 3D mental representations from 2D observations. We uncover this gap via diagnostic analyses showing the bottleneck is a missing view-consistent spatial interface rather than insufficient visual features or weak reasoning. To bridge this, we introduce **3ViewSense**, a framework that grounds spatial reasoning in Orthographic Views. Drawing on engineering cognition, we propose a Simulate-and-Reason'' mechanism that decomposes complex scenes into canonical orthographic projections to resolve geometric ambiguities. By aligning egocentric perceptions with these allocentric references, our method facilitates explicit mental rotation and reconstruction. Empirical results on spatial reasoning benchmarks demonstrate that our method significantly outperforms existing baselines, with consistent gains on occlusion-heavy counting and view-consistent spatial reasoning. The framework also improves the stability and consistency of spatial descriptions, offering a scalable path toward stronger spatial intelligence in multimodal systems.~\footnote{https://github.com/Jasaxion/3ViewSense}

Genuine spatial reasoning relies on the capacity to construct and manipulate coherent internal spatial representations, often conceptualized as mental models, rather than merely processing surface linguistic associations. While large language models exhibit advanced capabilities across various domains, existing benchmarks fail to isolate this intrinsic spatial cognition from statistical language heuristics. Furthermore, multimodal evaluations frequently conflate genuine spatial reasoning with visual perception. To systematically investigate whether models construct flexible spatial mental models, we introduce SpatialText, a theory-driven diagnostic framework. Rather than functioning simply as a dataset, SpatialText isolates text-based spatial reasoning through a dual-source methodology. It integrates human-annotated descriptions of real 3D indoor environments, which capture natural ambiguities, perspective shifts, and functional relations, with code-generated, logically precise scenes designed to probe formal spatial deduction and epistemic boundaries. Systematic evaluation across state-of-the-art models reveals fundamental representational limitations. Although models demonstrate proficiency in retrieving explicit spatial facts and operating within global, allocentric coordinate systems, they exhibit critical failures in egocentric perspective transformation and local reference frame reasoning. These systematic errors provide strong evidence that current models rely heavily on linguistic co-occurrence heuristics rather than constructing coherent, verifiable internal spatial representations. SpatialText thus serves as a rigorous instrument for diagnosing the cognitive boundaries of artificial spatial intelligence.

Recent advances in training-free visual prompting, such as Set-of-Mark, have emerged as a promising direction for enhancing the grounding capabilities of multimodal language models (MLMs). These techniques operate by partitioning the input image into object regions and annotating them with marks, predominantly boxes with numeric identifiers, before feeding the augmented image to the MLM. However, these approaches treat marked objects as isolated entities, failing to capture the relationships between them. On these premises, we propose Graph-of-Mark (GoM), the first pixel-level visual prompting technique that overlays scene graphs onto the input image for spatial reasoning tasks. We evaluate GoM across 3 open-source MLMs and 4 different datasets, conducting extensive ablations on drawn components and investigating the impact of auxiliary graph descriptions in the text prompt. Our results demonstrate that GoM consistently improves the zero-shot capability of MLMs in interpreting object positions and relative directions, improving base accuracy in visual question answering and localization up to 11 percentage points.

We present a simple experiment that exposes a fundamental limitation in vision-language models (VLMs): the inability to accurately localize filled cells in binary grids when those cells lack textual identity. We generate fifteen 15x15 grids with varying density (10.7%-41.8% filled cells) and render each as two image types -- text symbols (. and #) and filled squares without gridlines -- then ask three frontier VLMs (Claude Opus, ChatGPT 5.2, and Gemini 3 Thinking) to transcribe them. In the text-symbol condition, Claude and ChatGPT achieve approximately 91% cell accuracy and 84% F1, while Gemini achieves 84% accuracy and 63% F1. In the filled-squares condition, all three models collapse to 60-73% accuracy and 29-39% F1. Critically, all conditions pass through the same visual encoder -- the text symbols are images, not tokenized text. The text-vs-squares F1 gap ranges from 34 to 54 points across models, demonstrating that VLMs behave as if they possess a high-fidelity text-recognition pathway for spatial reasoning that dramatically outperforms their native visual pathway. Each model exhibits a distinct failure mode in the squares condition -- systematic under-counting (Claude), massive over-counting (ChatGPT), and template hallucination (Gemini) -- but all share the same underlying deficit: severely degraded spatial localization for non-textual visual elements.

Multimodal large language models (MLLMs) have achieved remarkable progress in vision-language tasks, but continue to struggle with spatial reasoning. Existing spatial MLLMs rely on large-scale datasets, explicit 3D inputs, architecture-specific modifications, or sparse Reinforcement Learning (RL) methods that provide insufficient guidance for spatially-grounded reasoning. We introduce SpatialThinker. To our knowledge, it is the first MLLM unifying Scene Graph Generation (SGG) and visual reasoning in a single pass via online RL. The model simulates human-like spatial perception by constructing a mental scene graph of task-relevant objects and relations, and reasoning toward an answer via dense spatial rewards. Our contributions are threefold: (1) SGG-grounded reasoning: integrating SGG directly within the reasoning chain rather than as a disjoint preprocessing step; (2) STVQA-7K: a high-quality spatial VQA training dataset via a scalable synthesis pipeline; and (3) a dense spatial reward design that enforces structured grounding during RL and generalizes to improve broad visual perception. SpatialThinker-7B achieves 3.6$\times$ larger gains over SFT and $1.7\times$ better in- and out-of-distribution generalization than sparse RL. Trained on only 7K samples, SpatialThinker-7B matches GPT-5 and outperforms GPT-4o, while SpatialThinker-30B surpasses both GPT-5 and Claude 4 Sonnet on average across 14 spatial and real-world benchmarks, demonstrating that structured spatial grounding with reward-aligned reasoning enables robust spatial understanding with limited data.