Daily Papers

Distinguishing spatial relations is a basic part of human cognition which requires fine-grained perception on cross-instance. Although benchmarks like MME, MMBench and SEED comprehensively have evaluated various capabilities which already include visual spatial reasoning(VSR). There is still a lack of sufficient quantity and quality evaluation and optimization datasets for Vision Large Language Models(VLLMs) specifically targeting visual positional reasoning. To handle this, we first diagnosed current VLLMs with the VSR dataset and proposed a unified test set. We found current VLLMs to exhibit a contradiction of over-sensitivity to language instructions and under-sensitivity to visual positional information. By expanding the original benchmark from two aspects of tunning data and model structure, we mitigated this phenomenon. To our knowledge, we expanded spatially positioned image data controllably using diffusion models for the first time and integrated original visual encoding(CLIP) with other 3 powerful visual encoders(SigLIP, SAM and DINO). After conducting combination experiments on scaling data and models, we obtained a VLLM VSR Expert(VSRE) that not only generalizes better to different instructions but also accurately distinguishes differences in visual positional information. VSRE achieved over a 27\% increase in accuracy on the VSR test set. It becomes a performant VLLM on the position reasoning of both the VSR dataset and relevant subsets of other evaluation benchmarks. We open-sourced the expanded model with data and Appendix at https://github.com/peijin360/vsre and hope it will accelerate advancements in VLLM on VSR learning.

Game playing has long served as a fundamental benchmark for evaluating Artificial General Intelligence (AGI). While Large Language Models (LLMs) have demonstrated impressive capabilities in general reasoning, their effectiveness in spatial strategic reasoning, which is critical for complex and fully observable board games, remains insufficiently explored. In this work, we adopt Chinese Chess (Xiangqi) as a challenging and rich testbed due to its intricate rules and spatial complexity. To advance LLMs' strategic competence in such environments, we propose a training framework tailored to Xiangqi, built upon a large-scale dataset of five million board-move pairs enhanced with expert annotations and engine evaluations. Building on this foundation, we introduce Xiangqi-R1, a 7B-parameter model trained in multi-stage manner: (1) fine-tuning for legal move prediction to capture basic spatial rules, (2) incorporating strategic annotations to improve decision-making, and (3) applying reinforcement learning via Group Relative Policy Optimization (GRPO) with multi-dimensional reward signals to enhance reasoning stability. Our Experimental results indicate that, despite their size and power, general-purpose LLMs struggle to achieve satisfactory performance in these tasks. Compared to general-purpose LLMs, Xiangqi-R1 greatly advances with an 18% rise in move legality and a 22% boost in analysis accuracy. Our results point to a promising path for creating general strategic intelligence in spatially complex areas.

Recent advances in large language models(LLMs) enable compelling story generation, but connecting narrative text to playable visual environments remains an open challenge in procedural content generation(PCG). We present a lightweight pipeline that transforms short narrative prompts into a sequence of 2D tile-based game scenes, reflecting the temporal structure of stories. Given an LLM-generated narrative, our system identifies three key time frames, extracts spatial predicates in the form of "Object-Relation-Object" triples, and retrieves visual assets using affordance-aware semantic embeddings from the GameTileNet dataset. A layered terrain is generated using Cellular Automata, and objects are placed using spatial rules grounded in the predicate structure. We evaluated our system in ten diverse stories, analyzing tile-object matching, affordance-layer alignment, and spatial constraint satisfaction across frames. This prototype offers a scalable approach to narrative-driven scene generation and lays the foundation for future work on multi-frame continuity, symbolic tracking, and multi-agent coordination in story-centered PCG.

Dynamics of human body skeletons convey significant information for human action recognition. Conventional approaches for modeling skeletons usually rely on hand-crafted parts or traversal rules, thus resulting in limited expressive power and difficulties of generalization. In this work, we propose a novel model of dynamic skeletons called Spatial-Temporal Graph Convolutional Networks (ST-GCN), which moves beyond the limitations of previous methods by automatically learning both the spatial and temporal patterns from data. This formulation not only leads to greater expressive power but also stronger generalization capability. On two large datasets, Kinetics and NTU-RGBD, it achieves substantial improvements over mainstream methods.

Large Language Models (LLMs) have demonstrated remarkable capabilities across various tasks, yet they often struggle with spatial reasoning. This paper presents a novel neural-symbolic framework that enhances LLMs' spatial reasoning abilities through iterative feedback between LLMs and Answer Set Programming (ASP). We evaluate our approach on two benchmark datasets: StepGame and SparQA, implementing three distinct strategies: (1) direct prompting baseline, (2) Facts+Rules prompting, and (3) DSPy-based LLM+ASP pipeline with iterative refinement. Our experimental results demonstrate that the LLM+ASP pipeline significantly outperforms baseline methods, achieving an average 82% accuracy on StepGame and 69% on SparQA, marking improvements of 40-50% and 8-15% respectively over direct prompting. The success stems from three key innovations: (1) effective separation of semantic parsing and logical reasoning through a modular pipeline, (2) iterative feedback mechanism between LLMs and ASP solvers that improves program rate, and (3) robust error handling that addresses parsing, grounding, and solving failures. Additionally, we propose Facts+Rules as a lightweight alternative that achieves comparable performance on complex SparQA dataset, while reducing computational overhead.Our analysis across different LLM architectures (Deepseek, Llama3-70B, GPT-4.0 mini) demonstrates the framework's generalizability and provides insights into the trade-offs between implementation complexity and reasoning capability, contributing to the development of more interpretable and reliable AI systems.

This paper proposes a question-answering (QA) benchmark for spatial reasoning on natural language text which contains more realistic spatial phenomena not covered by prior work and is challenging for state-of-the-art language models (LM). We propose a distant supervision method to improve on this task. Specifically, we design grammar and reasoning rules to automatically generate a spatial description of visual scenes and corresponding QA pairs. Experiments show that further pretraining LMs on these automatically generated data significantly improves LMs' capability on spatial understanding, which in turn helps to better solve two external datasets, bAbI, and boolQ. We hope that this work can foster investigations into more sophisticated models for spatial reasoning over text.

For autonomous vehicles to safely share the road with human drivers, autonomous vehicles must abide by specific "road rules" that human drivers have agreed to follow. "Road rules" include rules that drivers are required to follow by law -- such as the requirement that vehicles stop at red lights -- as well as more subtle social rules -- such as the implicit designation of fast lanes on the highway. In this paper, we provide empirical evidence that suggests that -- instead of hard-coding road rules into self-driving algorithms -- a scalable alternative may be to design multi-agent environments in which road rules emerge as optimal solutions to the problem of maximizing traffic flow. We analyze what ingredients in driving environments cause the emergence of these road rules and find that two crucial factors are noisy perception and agents' spatial density. We provide qualitative and quantitative evidence of the emergence of seven social driving behaviors, ranging from obeying traffic signals to following lanes, all of which emerge from training agents to drive quickly to destinations without colliding. Our results add empirical support for the social road rules that countries worldwide have agreed on for safe, efficient driving.

Existing reasoning datasets saturate and fail to test abstract, multi-step problems, especially pathfinding and complex rule constraint satisfaction. We introduce SPaRC (Spatial Pathfinding Reasoning Challenge), a dataset of 1,000 2D grid pathfinding puzzles to evaluate spatial and symbolic reasoning, requiring step-by-step planning with arithmetic and geometric rules. Humans achieve near-perfect accuracy (98.0%; 94.5% on hard puzzles), while the best reasoning models, such as o4-mini, struggle (15.8%; 1.1% on hard puzzles). Models often generate invalid paths (>50% of puzzles for o4-mini), and reasoning tokens reveal they make errors in navigation and spatial logic. Unlike humans, who take longer on hard puzzles, models fail to scale test-time compute with difficulty. Allowing models to make multiple solution attempts improves accuracy, suggesting potential for better spatial reasoning with improved training and efficient test-time scaling methods. SPaRC can be used as a window into models' spatial reasoning limitations and drive research toward new methods that excel in abstract, multi-step problem-solving.

Recent advances in generative models have significantly impacted game generation. However, despite producing high-quality graphics and adequately receiving player input, existing models often fail to maintain fundamental game properties such as numerical and spatial consistency. Numerical consistency ensures gameplay mechanics correctly reflect score changes and other quantitative elements, while spatial consistency prevents jarring scene transitions, providing seamless player experiences. In this paper, we revisit the paradigm of generative games to explore what truly constitutes a Model as a Game (MaaG) with a well-developed mechanism. We begin with an empirical study on ``Traveler'', a 2D game created by an LLM featuring minimalist rules yet challenging generative models in maintaining consistency. Based on the DiT architecture, we design two specialized modules: (1) a numerical module that integrates a LogicNet to determine event triggers, with calculations processed externally as conditions for image generation; and (2) a spatial module that maintains a map of explored areas, retrieving location-specific information during generation and linking new observations to ensure continuity. Experiments across three games demonstrate that our integrated modules significantly enhance performance on consistency metrics compared to baselines, while incurring minimal time overhead during inference.

Recently, diffusion models have achieved great success in mono-channel audio generation. However, when it comes to stereo audio generation, the soundscapes often have a complex scene of multiple objects and directions. Controlling stereo audio with spatial contexts remains challenging due to high data costs and unstable generative models. To the best of our knowledge, this work represents the first attempt to address these issues. We first construct a large-scale, simulation-based, and GPT-assisted dataset, BEWO-1M, with abundant soundscapes and descriptions even including moving and multiple sources. Beyond text modality, we have also acquired a set of images and rationally paired stereo audios through retrieval to advance multimodal generation. Existing audio generation models tend to generate rather random and indistinct spatial audio. To provide accurate guidance for Latent Diffusion Models, we introduce the SpatialSonic model utilizing spatial-aware encoders and azimuth state matrices to reveal reasonable spatial guidance. By leveraging spatial guidance, our model not only achieves the objective of generating immersive and controllable spatial audio from text but also extends to other modalities as the pioneer attempt. Finally, under fair settings, we conduct subjective and objective evaluations on simulated and real-world data to compare our approach with prevailing methods. The results demonstrate the effectiveness of our method, highlighting its capability to generate spatial audio that adheres to physical rules.

Spatial reasoning is a crucial component of both biological and artificial intelligence. In this work, we present a comprehensive study of the capability of current state-of-the-art large language models (LLMs) on spatial reasoning. To support our study, we created and contribute a novel Spatial Reasoning Characterization (SpaRC) framework and Spatial Reasoning Paths (SpaRP) datasets, to enable an in-depth understanding of the spatial relations and compositions as well as the usefulness of spatial reasoning chains. We found that all the state-of-the-art LLMs do not perform well on the datasets -- their performances are consistently low across different setups. The spatial reasoning capability improves substantially as model sizes scale up. Finetuning both large language models (e.g., Llama-2-70B) and smaller ones (e.g., Llama-2-13B) can significantly improve their F1-scores by 7--32 absolute points. We also found that the top proprietary LLMs still significantly outperform their open-source counterparts in topological spatial understanding and reasoning.

The objective is the design of a Cellular Automata rule that can form patterns with 'touching' loops. A loop is defined as a closed path of 1-cells in a 2D grid on a zero background and with a zero border. A path cell is connected with two of its adjacent neighbors. In touching loops a path cell is also allowed to touch another on a diagonal. A CA rule was designed that can evolve stable touching loop patterns. The rule tries to cover the 2D space by overlapping tiles. The rule uses so-called templates, 5 x 5 matching patterns which are systematically derived from the given set of 3 x 3 tiles. The rule checks the pattern being evolved against a list of templates. If the outer neighbors of a template match, then the cell's state is set to the template's center value. Noise is injected if there is no matching template, or the tiles are not properly assembled. Thereby the evolution is driven to the desired loop patterns.

While many natural language inference (NLI) datasets target certain semantic phenomena, e.g., negation, tense & aspect, monotonicity, and presupposition, to the best of our knowledge, there is no NLI dataset that involves diverse types of spatial expressions and reasoning. We fill this gap by semi-automatically creating an NLI dataset for spatial reasoning, called SpaceNLI. The data samples are automatically generated from a curated set of reasoning patterns, where the patterns are annotated with inference labels by experts. We test several SOTA NLI systems on SpaceNLI to gauge the complexity of the dataset and the system's capacity for spatial reasoning. Moreover, we introduce a Pattern Accuracy and argue that it is a more reliable and stricter measure than the accuracy for evaluating a system's performance on pattern-based generated data samples. Based on the evaluation results we find that the systems obtain moderate results on the spatial NLI problems but lack consistency per inference pattern. The results also reveal that non-projective spatial inferences (especially due to the "between" preposition) are the most challenging ones.

Spatial reasoning is a key aspect of cognitive psychology and remains a major bottleneck for current vision-language models (VLMs). While extensive research has aimed to evaluate or improve VLMs' understanding of basic spatial relations, such as distinguishing left from right, near from far, and object counting, these tasks represent only the most fundamental level of spatial reasoning. In this work, we introduce OmniSpatial, a comprehensive and challenging benchmark for spatial reasoning, grounded in cognitive psychology. OmniSpatial covers four major categories: dynamic reasoning, complex spatial logic, spatial interaction, and perspective-taking, with 50 fine-grained subcategories. Through Internet data crawling and careful manual annotation, we construct over 1.5K question-answer pairs. Extensive experiments show that both open- and closed-source VLMs, as well as existing reasoning and spatial understanding models, exhibit significant limitations in comprehensive spatial understanding. We further analyze failure cases and propose potential directions for future research.

Over the past year, the development of large language models (LLMs) has brought spatial intelligence into focus, with much attention on vision-based embodied intelligence. However, spatial intelligence spans a broader range of disciplines and scales, from navigation and urban planning to remote sensing and earth science. What are the differences and connections between spatial intelligence across these fields? In this paper, we first review human spatial cognition and its implications for spatial intelligence in LLMs. We then examine spatial memory, knowledge representations, and abstract reasoning in LLMs, highlighting their roles and connections. Finally, we analyze spatial intelligence across scales -- from embodied to urban and global levels -- following a framework that progresses from spatial memory and understanding to spatial reasoning and intelligence. Through this survey, we aim to provide insights into interdisciplinary spatial intelligence research and inspire future studies.

If a Large Language Model (LLM) were to take a driving knowledge test today, would it pass? Beyond standard spatial and visual question-answering (QA) tasks on current autonomous driving benchmarks, driving knowledge tests require a complete understanding of all traffic rules, signage, and right-of-way principles. To pass this test, human drivers must discern various edge cases that rarely appear in real-world datasets. In this work, we present DriveQA, an extensive open-source text and vision-based benchmark that exhaustively covers traffic regulations and scenarios. Through our experiments using DriveQA, we show that (1) state-of-the-art LLMs and Multimodal LLMs (MLLMs) perform well on basic traffic rules but exhibit significant weaknesses in numerical reasoning and complex right-of-way scenarios, traffic sign variations, and spatial layouts, (2) fine-tuning on DriveQA improves accuracy across multiple categories, particularly in regulatory sign recognition and intersection decision-making, (3) controlled variations in DriveQA-V provide insights into model sensitivity to environmental factors such as lighting, perspective, distance, and weather conditions, and (4) pretraining on DriveQA enhances downstream driving task performance, leading to improved results on real-world datasets such as nuScenes and BDD, while also demonstrating that models can internalize text and synthetic traffic knowledge to generalize effectively across downstream QA tasks.

We propose SpatialLLM, a novel approach advancing spatial intelligence tasks in complex urban scenes. Unlike previous methods requiring geographic analysis tools or domain expertise, SpatialLLM is a unified language model directly addressing various spatial intelligence tasks without any training, fine-tuning, or expert intervention. The core of SpatialLLM lies in constructing detailed and structured scene descriptions from raw spatial data to prompt pre-trained LLMs for scene-based analysis. Extensive experiments show that, with our designs, pretrained LLMs can accurately perceive spatial distribution information and enable zero-shot execution of advanced spatial intelligence tasks, including urban planning, ecological analysis, traffic management, etc. We argue that multi-field knowledge, context length, and reasoning ability are key factors influencing LLM performances in urban analysis. We hope that SpatialLLM will provide a novel viable perspective for urban intelligent analysis and management. The code and dataset are available at https://github.com/WHU-USI3DV/SpatialLLM.

In this paper, we propose Bootstrapped Language-Image Pretraining-driven Fused State Representation in Proximal Policy Optimization (BLIP-FusePPO), a novel multimodal reinforcement learning (RL) framework for autonomous lane-keeping (LK), in which semantic embeddings generated by a vision-language model (VLM) are directly fused with geometric states, LiDAR observations, and Proportional-Integral-Derivative-based (PID) control feedback within the agent observation space. The proposed method lets the agent learn driving rules that are aware of their surroundings and easy to understand by combining high-level scene understanding from the VLM with low-level control and spatial signals. Our architecture brings together semantic, geometric, and control-aware representations to make policy learning more robust. A hybrid reward function that includes semantic alignment, LK accuracy, obstacle avoidance, and speed regulation helps learning to be more efficient and generalizable. Our method is different from the approaches that only use semantic models to shape rewards. Instead, it directly embeds semantic features into the state representation. This cuts down on expensive runtime inference and makes sure that semantic guidance is always available. The simulation results show that the proposed model is better at LK stability and adaptability than the best vision-based and multimodal RL baselines in a wide range of difficult driving situations. We make our code publicly available.

Inferring spatial relations in natural language is a crucial ability an intelligent system should possess. The bAbI dataset tries to capture tasks relevant to this domain (task 17 and 19). However, these tasks have several limitations. Most importantly, they are limited to fixed expressions, they are limited in the number of reasoning steps required to solve them, and they fail to test the robustness of models to input that contains irrelevant or redundant information. In this paper, we present a new Question-Answering dataset called StepGame for robust multi-hop spatial reasoning in texts. Our experiments demonstrate that state-of-the-art models on the bAbI dataset struggle on the StepGame dataset. Moreover, we propose a Tensor-Product based Memory-Augmented Neural Network (TP-MANN) specialized for spatial reasoning tasks. Experimental results on both datasets show that our model outperforms all the baselines with superior generalization and robustness performance.

Although Vision Language Models (VLMs) exhibit strong perceptual abilities and impressive visual reasoning, they struggle with attention to detail and precise action planning in complex, dynamic environments, leading to subpar performance. Real-world tasks typically require complex interactions, advanced spatial reasoning, long-term planning, and continuous strategy refinement, usually necessitating understanding the physics rules of the target scenario. However, evaluating these capabilities in real-world scenarios is often prohibitively expensive. To bridge this gap, we introduce DeepPHY, a novel benchmark framework designed to systematically evaluate VLMs' understanding and reasoning about fundamental physical principles through a series of challenging simulated environments. DeepPHY integrates multiple physical reasoning environments of varying difficulty levels and incorporates fine-grained evaluation metrics. Our evaluation finds that even state-of-the-art VLMs struggle to translate descriptive physical knowledge into precise, predictive control.

Various methods have been proposed for utilizing Large Language Models (LLMs) in autonomous driving. One strategy of using LLMs for autonomous driving involves inputting surrounding objects as text prompts to the LLMs, along with their coordinate and velocity information, and then outputting the subsequent movements of the vehicle. When using LLMs for such purposes, capabilities such as spatial recognition and planning are essential. In particular, two foundational capabilities are required: (1) spatial-aware decision making, which is the ability to recognize space from coordinate information and make decisions to avoid collisions, and (2) the ability to adhere to traffic rules. However, quantitative research has not been conducted on how accurately different types of LLMs can handle these problems. In this study, we quantitatively evaluated these two abilities of LLMs in the context of autonomous driving. Furthermore, to conduct a Proof of Concept (POC) for the feasibility of implementing these abilities in actual vehicles, we developed a system that uses LLMs to drive a vehicle.

We present APT, an advanced Large Language Model (LLM)-driven framework that enables autonomous agents to construct complex and creative structures within the Minecraft environment. Unlike previous approaches that primarily concentrate on skill-based open-world tasks or rely on image-based diffusion models for generating voxel-based structures, our method leverages the intrinsic spatial reasoning capabilities of LLMs. By employing chain-of-thought decomposition along with multimodal inputs, the framework generates detailed architectural layouts and blueprints that the agent can execute under zero-shot or few-shot learning scenarios. Our agent incorporates both memory and reflection modules to facilitate lifelong learning, adaptive refinement, and error correction throughout the building process. To rigorously evaluate the agent's performance in this emerging research area, we introduce a comprehensive benchmark consisting of diverse construction tasks designed to test creativity, spatial reasoning, adherence to in-game rules, and the effective integration of multimodal instructions. Experimental results using various GPT-based LLM backends and agent configurations demonstrate the agent's capacity to accurately interpret extensive instructions involving numerous items, their positions, and orientations. The agent successfully produces complex structures complete with internal functionalities such as Redstone-powered systems. A/B testing indicates that the inclusion of a memory module leads to a significant increase in performance, emphasizing its role in enabling continuous learning and the reuse of accumulated experience. Additionally, the agent's unexpected emergence of scaffolding behavior highlights the potential of future LLM-driven agents to utilize subroutine planning and leverage the emergence ability of LLMs to autonomously develop human-like problem-solving techniques.

Creating large-scale interactive 3D environments is essential for the development of Robotics and Embodied AI research. Current methods, including manual design, procedural generation, diffusion-based scene generation, and large language model (LLM) guided scene design, are hindered by limitations such as excessive human effort, reliance on predefined rules or training datasets, and limited 3D spatial reasoning ability. Since pre-trained 2D image generative models better capture scene and object configuration than LLMs, we address these challenges by introducing Architect, a generative framework that creates complex and realistic 3D embodied environments leveraging diffusion-based 2D image inpainting. In detail, we utilize foundation visual perception models to obtain each generated object from the image and leverage pre-trained depth estimation models to lift the generated 2D image to 3D space. Our pipeline is further extended to a hierarchical and iterative inpainting process to continuously generate placement of large furniture and small objects to enrich the scene. This iterative structure brings the flexibility for our method to generate or refine scenes from various starting points, such as text, floor plans, or pre-arranged environments.

Spatial reasoning ability is crucial for Vision Language Models (VLMs) to support real-world applications in diverse domains including robotics, augmented reality, and autonomous navigation. Unfortunately, existing benchmarks are inadequate in assessing spatial reasoning ability, especially the intrinsic-dynamic spatial reasoning which is a fundamental aspect of human spatial cognition. In this paper, we propose a unified benchmark, Spatial-DISE, based on a cognitively grounded taxonomy that categorizes tasks into four fundamental quadrants: Intrinsic-Static, Intrinsic-Dynamic, Extrinsic-Static, and Extrinsic-Dynamic spatial reasoning. Moreover, to address the issue of data scarcity, we develop a scalable and automated pipeline to generate diverse and verifiable spatial reasoning questions, resulting in a new Spatial-DISE dataset that includes Spatial-DISE Bench (559 evaluation VQA pairs) and Spatial-DISE-12K (12K+ training VQA pairs). Our comprehensive evaluation across 28 state-of-the-art VLMs reveals that, current VLMs have a large and consistent gap to human competence, especially on multi-step multi-view spatial reasoning. Spatial-DISE offers a robust framework, valuable dataset, and clear direction for future research toward human-like spatial intelligence. Benchmark, dataset, and code will be publicly released.

Humans possess spatial reasoning abilities that enable them to understand spaces through multimodal observations, such as vision and sound. Large multimodal reasoning models extend these abilities by learning to perceive and reason, showing promising performance across diverse spatial tasks. However, systematic reviews and publicly available benchmarks for these models remain limited. In this survey, we provide a comprehensive review of multimodal spatial reasoning tasks with large models, categorizing recent progress in multimodal large language models (MLLMs) and introducing open benchmarks for evaluation. We begin by outlining general spatial reasoning, focusing on post-training techniques, explainability, and architecture. Beyond classical 2D tasks, we examine spatial relationship reasoning, scene and layout understanding, as well as visual question answering and grounding in 3D space. We also review advances in embodied AI, including vision-language navigation and action models. Additionally, we consider emerging modalities such as audio and egocentric video, which contribute to novel spatial understanding through new sensors. We believe this survey establishes a solid foundation and offers insights into the growing field of multimodal spatial reasoning. Updated information about this survey, codes and implementation of the open benchmarks can be found at https://github.com/zhengxuJosh/Awesome-Spatial-Reasoning.

Vision language models (VLMs) have demonstrated impressive performance across a wide range of downstream tasks. However, their proficiency in spatial reasoning remains limited, despite its crucial role in tasks involving navigation and interaction with physical environments. Specifically, most of these tasks rely on the core spatial reasoning capabilities in two-dimensional (2D) environments, and our evaluation reveals that state-of-the-art VLMs frequently generate implausible and incorrect responses to composite spatial reasoning problems, including simple pathfinding tasks that humans can solve effortlessly at a glance. To address this, we explore an effective approach to enhance 2D spatial reasoning within VLMs by training the model solely on basic spatial capabilities. We begin by disentangling the key components of 2D spatial reasoning: direction comprehension, distance estimation, and localization. Our central hypothesis is that mastering these basic spatial capabilities can significantly enhance a model's performance on composite spatial tasks requiring advanced spatial understanding and combinatorial problem-solving, with generalized improvements in visual-spatial tasks. To investigate this hypothesis, we introduce Sparkle, a framework that fine-tunes VLMs on these three basic spatial capabilities by synthetic data generation and targeted supervision to form an instruction dataset for each capability. Our experiments demonstrate that VLMs fine-tuned with Sparkle achieve significant performance gains, not only in the basic tasks themselves but also in generalizing to composite and out-of-distribution spatial reasoning tasks. These findings underscore the effectiveness of mastering basic spatial capabilities in enhancing composite spatial problem-solving, offering insights into systematic strategies for improving VLMs' spatial reasoning capabilities.

Spatial reasoning remains a critical yet underdeveloped capability in existing vision-language models (VLMs), especially for Spatial Visual Question Answering (Spatial VQA) tasks that require understanding relative positions, distances, and object configurations. Inspired by the R1 paradigm introduced in DeepSeek-R1, which enhances reasoning in language models through rule-based reinforcement learning (RL), we propose SVQA-R1, the first framework to extend R1-style training to spatial VQA. In particular, we introduce Spatial-GRPO, a novel group-wise RL strategy that constructs view-consistent rewards by perturbing spatial relations between objects, e.g., mirror flipping, thereby encouraging the model to develop a consistent and grounded understanding of space. Our model, SVQA-R1, not only achieves dramatically improved accuracy on spatial VQA benchmarks but also exhibits interpretable reasoning paths even without using supervised fine-tuning (SFT) data. Extensive experiments and visualization demonstrate the effectiveness of SVQA-R1 across multiple spatial reasoning benchmarks.

Spatial reasoning plays a vital role in both human cognition and machine intelligence, prompting new research into language models' (LMs) capabilities in this regard. However, existing benchmarks reveal shortcomings in evaluating qualitative spatial reasoning (QSR). These benchmarks typically present oversimplified scenarios or unclear natural language descriptions, hindering effective evaluation. We present a novel benchmark for assessing QSR in LMs, which is grounded in realistic 3D simulation data, offering a series of diverse room layouts with various objects and their spatial relationships. This approach provides a more detailed and context-rich narrative for spatial reasoning evaluation, diverging from traditional, toy-task-oriented scenarios. Our benchmark encompasses a broad spectrum of qualitative spatial relationships, including topological, directional, and distance relations. These are presented with different viewing points, varied granularities, and density of relation constraints to mimic real-world complexities. A key contribution is our logic-based consistency-checking tool, which enables the assessment of multiple plausible solutions, aligning with real-world scenarios where spatial relationships are often open to interpretation. Our benchmark evaluation of advanced LMs reveals their strengths and limitations in spatial reasoning. They face difficulties with multi-hop spatial reasoning and interpreting a mix of different view descriptions, pointing to areas for future improvement.

Reasoning about motion and space is a fundamental cognitive capability that is required by multiple real-world applications. While many studies highlight that large multimodal language models (MLMs) struggle to reason about space, they only focus on static spatial relationships, and not dynamic awareness of motion and space, i.e., reasoning about the effect of egocentric and object motions on spatial relationships. Manually annotating such object and camera movements is expensive. Hence, we introduce SAT, a simulated spatial aptitude training dataset comprising both static and dynamic spatial reasoning across 175K question-answer (QA) pairs and 20K scenes. Complementing this, we also construct a small (150 image-QAs) yet challenging dynamic spatial test set using real-world images. Leveraging our SAT datasets and 6 existing static spatial benchmarks, we systematically investigate what improves both static and dynamic spatial awareness. Our results reveal that simulations are surprisingly effective at imparting spatial aptitude to MLMs that translate to real images. We show that perfect annotations in simulation are more effective than existing approaches of pseudo-annotating real images. For instance, SAT training improves a LLaVA-13B model by an average 11% and a LLaVA-Video-7B model by an average 8% on multiple spatial benchmarks, including our real-image dynamic test set and spatial reasoning on long videos -- even outperforming some large proprietary models. While reasoning over static relationships improves with synthetic training data, there is still considerable room for improvement for dynamic reasoning questions.

Spatial intelligence (SI) represents a cognitive ability encompassing the visualization, manipulation, and reasoning about spatial relationships, underpinning disciplines from neuroscience to robotics. We introduce SITE, a benchmark dataset towards SI Thorough Evaluation in a standardized format of multi-choice visual question-answering, designed to assess large vision-language models' spatial intelligence across diverse visual modalities (single-image, multi-image, and video) and SI factors (figural to environmental scales, spatial visualization and orientation, intrinsic and extrinsic, static and dynamic). Our approach to curating the benchmark combines a bottom-up survey about 31 existing datasets and a top-down strategy drawing upon three classification systems in cognitive science, which prompt us to design two novel types of tasks about view-taking and dynamic scenes. Extensive experiments reveal that leading models fall behind human experts especially in spatial orientation, a fundamental SI factor. Moreover, we demonstrate a positive correlation between a model's spatial reasoning proficiency and its performance on an embodied AI task.

Large Language Models (LLMs) have demonstrated unprecedented capabilities across various natural language processing tasks. Their ability to process and generate viable text and code has made them ubiquitous in many fields, while their deployment as knowledge bases and "reasoning" tools remains an area of ongoing research. In geography, a growing body of literature has been focusing on evaluating LLMs' geographical knowledge and their ability to perform spatial reasoning. However, very little is still known about the internal functioning of these models, especially about how they process geographical information. In this chapter, we establish a novel framework for the study of geospatial mechanistic interpretability - using spatial analysis to reverse engineer how LLMs handle geographical information. Our aim is to advance our understanding of the internal representations that these complex models generate while processing geographical information - what one might call "how LLMs think about geographic information" if such phrasing was not an undue anthropomorphism. We first outline the use of probing in revealing internal structures within LLMs. We then introduce the field of mechanistic interpretability, discussing the superposition hypothesis and the role of sparse autoencoders in disentangling polysemantic internal representations of LLMs into more interpretable, monosemantic features. In our experiments, we use spatial autocorrelation to show how features obtained for placenames display spatial patterns related to their geographic location and can thus be interpreted geospatially, providing insights into how these models process geographical information. We conclude by discussing how our framework can help shape the study and use of foundation models in geography.

3D spatial reasoning is the ability to analyze and interpret the positions, orientations, and spatial relationships of objects within the 3D space. This allows models to develop a comprehensive understanding of the 3D scene, enabling their applicability to a broader range of areas, such as autonomous navigation, robotics, and AR/VR. While large multi-modal models (LMMs) have achieved remarkable progress in a wide range of image and video understanding tasks, their capabilities to perform 3D spatial reasoning on diverse natural images are less studied. In this work we present the first comprehensive 3D spatial reasoning benchmark, 3DSRBench, with 2,772 manually annotated visual question-answer pairs across 12 question types. We conduct robust and thorough evaluation of 3D spatial reasoning capabilities by balancing the data distribution and adopting a novel FlipEval strategy. To further study the robustness of 3D spatial reasoning w.r.t. camera 3D viewpoints, our 3DSRBench includes two subsets with 3D spatial reasoning questions on paired images with common and uncommon viewpoints. We benchmark a wide range of open-sourced and proprietary LMMs, uncovering their limitations in various aspects of 3D awareness, such as height, orientation, location, and multi-object reasoning, as well as their degraded performance on images with uncommon camera viewpoints. Our 3DSRBench provide valuable findings and insights about the future development of LMMs with strong 3D reasoning capabilities. Our project page and dataset is available https://3dsrbench.github.io.

Spatial reasoning is an important component of human intelligence. We can imagine the shapes of 3D objects and reason about their spatial relations by merely looking at their three-view line drawings in 2D, with different levels of competence. Can deep networks be trained to perform spatial reasoning tasks? How can we measure their "spatial intelligence"? To answer these questions, we present the SPARE3D dataset. Based on cognitive science and psychometrics, SPARE3D contains three types of 2D-3D reasoning tasks on view consistency, camera pose, and shape generation, with increasing difficulty. We then design a method to automatically generate a large number of challenging questions with ground truth answers for each task. They are used to provide supervision for training our baseline models using state-of-the-art architectures like ResNet. Our experiments show that although convolutional networks have achieved superhuman performance in many visual learning tasks, their spatial reasoning performance on SPARE3D tasks is either lower than average human performance or even close to random guesses. We hope SPARE3D can stimulate new problem formulations and network designs for spatial reasoning to empower intelligent robots to operate effectively in the 3D world via 2D sensors. The dataset and code are available at https://ai4ce.github.io/SPARE3D.

Multi-modal models have achieved remarkable progress in recent years. Nevertheless, they continue to exhibit notable limitations in spatial understanding and reasoning, which are fundamental capabilities to achieving artificial general intelligence. With the recent release of GPT-5, allegedly the most powerful AI model to date, it is timely to examine where the leading models stand on the path toward spatial intelligence. First, we propose a comprehensive taxonomy of spatial tasks that unifies existing benchmarks and discuss the challenges in ensuring fair evaluation. We then evaluate state-of-the-art proprietary and open-source models on eight key benchmarks, at a cost exceeding one billion total tokens. Our empirical study reveals that (1) GPT-5 demonstrates unprecedented strength in spatial intelligence, yet (2) still falls short of human performance across a broad spectrum of tasks. Moreover, we (3) identify the more challenging spatial intelligence problems for multi-modal models, and (4) proprietary models do not exhibit a decisive advantage when facing the most difficult problems. In addition, we conduct a qualitative evaluation across a diverse set of scenarios that are intuitive for humans yet fail even the most advanced multi-modal models.

Incorporating spatial information, particularly those influenced by climate, weather, and demographic factors, is crucial for improving underwriting precision and enhancing risk management in insurance. However, spatial data are often unstructured, high-dimensional, and difficult to integrate into predictive models. Embedding methods are needed to convert spatial data into meaningful representations for modelling tasks. We propose a novel multi-view contrastive learning framework for generating spatial embeddings that combine information from multiple spatial data sources. To train the model, we construct a spatial dataset that merges satellite imagery and OpenStreetMap features across Europe. The framework aligns these spatial views with coordinate-based encodings, producing low-dimensional embeddings that capture both spatial structure and contextual similarity. Once trained, the model generates embeddings directly from latitude-longitude pairs, enabling any dataset with coordinates to be enriched with meaningful spatial features without requiring access to the original spatial inputs. In a case study on French real estate prices, we compare models trained on raw coordinates against those using our spatial embeddings as inputs. The embeddings consistently improve predictive accuracy across generalised linear, additive, and boosting models, while providing interpretable spatial effects and demonstrating transferability to unseen regions.

Spatial relations are a basic part of human cognition. However, they are expressed in natural language in a variety of ways, and previous work has suggested that current vision-and-language models (VLMs) struggle to capture relational information. In this paper, we present Visual Spatial Reasoning (VSR), a dataset containing more than 10k natural text-image pairs with 65 types of spatial relations in English (such as: under, in front of, and facing). While using a seemingly simple annotation format, we show how the dataset includes challenging linguistic phenomena, such as varying reference frames. We demonstrate a large gap between human and model performance: the human ceiling is above 95%, while state-of-the-art models only achieve around 70%. We observe that VLMs' by-relation performances have little correlation with the number of training examples and the tested models are in general incapable of recognising relations concerning the orientations of objects.

Spatial confounding poses a significant challenge in scientific studies involving spatial data, where unobserved spatial variables can influence both treatment and outcome, possibly leading to spurious associations. To address this problem, we introduce SpaCE: The Spatial Confounding Environment, the first toolkit to provide realistic benchmark datasets and tools for systematically evaluating causal inference methods designed to alleviate spatial confounding. Each dataset includes training data, true counterfactuals, a spatial graph with coordinates, and smoothness and confounding scores characterizing the effect of a missing spatial confounder. It also includes realistic semi-synthetic outcomes and counterfactuals, generated using state-of-the-art machine learning ensembles, following best practices for causal inference benchmarks. The datasets cover real treatment and covariates from diverse domains, including climate, health and social sciences. SpaCE facilitates an automated end-to-end pipeline, simplifying data loading, experimental setup, and evaluating machine learning and causal inference models. The SpaCE project provides several dozens of datasets of diverse sizes and spatial complexity. It is publicly available as a Python package, encouraging community feedback and contributions.

Vision Language Models (VLMs) have demonstrated remarkable performance in 2D vision and language tasks. However, their ability to reason about spatial arrangements remains limited. In this work, we introduce Spatial Region GPT (SpatialRGPT) to enhance VLMs' spatial perception and reasoning capabilities. SpatialRGPT advances VLMs' spatial understanding through two key innovations: (1) a data curation pipeline that enables effective learning of regional representation from 3D scene graphs, and (2) a flexible plugin module for integrating depth information into the visual encoder of existing VLMs. During inference, when provided with user-specified region proposals, SpatialRGPT can accurately perceive their relative directions and distances. Additionally, we propose SpatialRGBT-Bench, a benchmark with ground-truth 3D annotations encompassing indoor, outdoor, and simulated environments, for evaluating 3D spatial cognition in VLMs. Our results demonstrate that SpatialRGPT significantly enhances performance in spatial reasoning tasks, both with and without local region prompts. The model also exhibits strong generalization capabilities, effectively reasoning about complex spatial relations and functioning as a region-aware dense reward annotator for robotic tasks. Code, dataset, and benchmark are released at https://www.anjiecheng.me/SpatialRGPT

Current vision-language models may incorporate single-dimensional spatial cues, such as depth, object boundary, and basic spatial directions (e.g. left, right, front, back), yet often lack the multi-dimensional spatial reasoning necessary for human-like understanding and real-world applications. To address this gap, we develop SPHERE (Spatial Perception and Hierarchical Evaluation of REasoning), a hierarchical evaluation framework with a new human-annotated dataset to pinpoint model strengths and weaknesses, advancing from single-skill tasks to multi-skill tasks, and ultimately to complex reasoning tasks that require the integration of multiple spatial and visual cues with logical reasoning. Benchmark evaluation of state-of-the-art open-source models reveal significant shortcomings, especially in the abilities to understand distance and proximity, to reason from both allocentric and egocentric viewpoints, and to perform complex reasoning in a physical context. This work underscores the need for more advanced approaches to spatial understanding and reasoning, paving the way for improvements in vision-language models and their alignment with human-like spatial capabilities. The dataset will be open-sourced upon publication.

Spatial reasoning is an essential problem in embodied AI research. Efforts to enhance spatial reasoning abilities through supplementary spatial data and fine-tuning have proven limited and ineffective when addressing complex embodied tasks, largely due to their dependence on language-based outputs. While some approaches have introduced a point-based action space to mitigate this issue, they fall short in managing more intricate tasks within complex environments. This deficiency arises from their failure to fully exploit the inherent thinking and reasoning capabilities that are fundamental strengths of Vision-Language Models (VLMs). To address these limitations, we propose a novel approach named SpatialCoT, specifically designed to bolster the spatial reasoning capabilities of VLMs. Our approach comprises two stages: spatial coordinate bi-directional alignment, which aligns vision-language inputs with spatial coordinates, and chain-of-thought spatial grounding, which harnesses the reasoning capabilities of language models for advanced spatial reasoning. We evaluate SpatialCoT on challenging navigation and manipulation tasks, both in simulation and real-world settings. Experimental results demonstrate that our method significantly outperforms previous state-of-the-art approaches in both tasks.

Not yet. We present SPACE, a benchmark that systematically evaluates spatial cognition in frontier models. Our benchmark builds on decades of research in cognitive science. It evaluates large-scale mapping abilities that are brought to bear when an organism traverses physical environments, smaller-scale reasoning about object shapes and layouts, and cognitive infrastructure such as spatial attention and memory. For many tasks, we instantiate parallel presentations via text and images, allowing us to benchmark both large language models and large multimodal models. Results suggest that contemporary frontier models fall short of the spatial intelligence of animals, performing near chance level on a number of classic tests of animal cognition.

Spatial reasoning is a core component of human cognition, enabling individuals to perceive, comprehend, and interact with the physical world. It relies on a nuanced understanding of spatial structures and inter-object relationships, serving as the foundation for complex reasoning and decision-making. To investigate whether current vision-language models (VLMs) exhibit similar capability, we introduce Jigsaw-Puzzles, a novel benchmark consisting of 1,100 carefully curated real-world images with high spatial complexity. Based on this dataset, we design five tasks to rigorously evaluate VLMs' spatial perception, structural understanding, and reasoning capabilities, while deliberately minimizing reliance on domain-specific knowledge to better isolate and assess the general spatial reasoning capability. We conduct a comprehensive evaluation across 24 state-of-the-art VLMs. The results show that even the strongest model, Gemini-2.5-Pro, achieves only 77.14% overall accuracy and performs particularly poorly on the Order Generation task, with only 30.00% accuracy, far below the performance exceeding 90% achieved by human participants. This persistent gap underscores the need for continued progress, positioning Jigsaw-Puzzles as a challenging and diagnostic benchmark for advancing spatial reasoning research in VLMs.

Spatial computing is a technological advancement that facilitates the seamless integration of devices into the physical environment, resulting in a more natural and intuitive digital world user experience. Spatial computing has the potential to become a significant advancement in the field of computing. From GPS and location-based services to healthcare, spatial computing technologies have influenced and improved our interactions with the digital world. The use of spatial computing in creating interactive digital environments has become increasingly popular and effective. This is explained by its increasing significance among researchers and industrial organisations, which motivated us to conduct this review. This review provides a detailed overview of spatial computing, including its enabling technologies and its impact on various applications. Projects related to spatial computing are also discussed. In this review, we also explored the potential challenges and limitations of spatial computing. Furthermore, we discuss potential solutions and future directions. Overall, this paper aims to provide a comprehensive understanding of spatial computing, its enabling technologies, their impact on various applications, emerging challenges, and potential solutions.

Understanding the spatial relations between objects in images is a surprisingly challenging task. A chair may be "behind" a person even if it appears to the left of the person in the image (depending on which way the person is facing). Two students that appear close to each other in the image may not in fact be "next to" each other if there is a third student between them. We introduce SpatialSense, a dataset specializing in spatial relation recognition which captures a broad spectrum of such challenges, allowing for proper benchmarking of computer vision techniques. SpatialSense is constructed through adversarial crowdsourcing, in which human annotators are tasked with finding spatial relations that are difficult to predict using simple cues such as 2D spatial configuration or language priors. Adversarial crowdsourcing significantly reduces dataset bias and samples more interesting relations in the long tail compared to existing datasets. On SpatialSense, state-of-the-art recognition models perform comparably to simple baselines, suggesting that they rely on straightforward cues instead of fully reasoning about this complex task. The SpatialSense benchmark provides a path forward to advancing the spatial reasoning capabilities of computer vision systems. The dataset and code are available at https://github.com/princeton-vl/SpatialSense.

Spatial understanding is a crucial capability for robots to make grounded decisions based on their environment. This foundational skill enables robots not only to perceive their surroundings but also to reason about and interact meaningfully within the world. In modern robotics, these capabilities are taken on by visual language models, and they face significant challenges when applied to spatial reasoning context due to their training data sources. These sources utilize general-purpose image datasets, and they often lack sophisticated spatial scene understanding capabilities. For example, the datasets do not address reference frame comprehension - spatial relationships require clear contextual understanding, whether from an ego-centric, object-centric, or world-centric perspective, which allow for effective real-world interaction. To address this issue, we introduce RoboSpatial, a large-scale spatial understanding dataset consisting of real indoor and tabletop scenes captured as 3D scans and egocentric images, annotated with rich spatial information relevant to robotics. The dataset includes 1M images, 5K 3D scans, and 3M annotated spatial relationships, with paired 2D egocentric images and 3D scans to make it both 2D and 3D ready. Our experiments show that models trained with RoboSpatial outperform baselines on downstream tasks such as spatial affordance prediction, spatial relationship prediction, and robotics manipulation.

Artificial intelligence (AI) has made remarkable progress across various domains, with large language models like ChatGPT gaining substantial attention for their human-like text-generation capabilities. Despite these achievements, spatial reasoning remains a significant challenge for these models. Benchmarks like StepGame evaluate AI spatial reasoning, where ChatGPT has shown unsatisfactory performance. However, the presence of template errors in the benchmark has an impact on the evaluation results. Thus there is potential for ChatGPT to perform better if these template errors are addressed, leading to more accurate assessments of its spatial reasoning capabilities. In this study, we refine the StepGame benchmark, providing a more accurate dataset for model evaluation. We analyze GPT's spatial reasoning performance on the rectified benchmark, identifying proficiency in mapping natural language text to spatial relations but limitations in multi-hop reasoning. We provide a flawless solution to the benchmark by combining template-to-relation mapping with logic-based reasoning. This combination demonstrates proficiency in performing qualitative reasoning on StepGame without encountering any errors. We then address the limitations of GPT models in spatial reasoning. We deploy Chain-of-thought and Tree-of-thoughts prompting strategies, offering insights into GPT's ``cognitive process", and achieving remarkable improvements in accuracy. Our investigation not only sheds light on model deficiencies but also proposes enhancements, contributing to the advancement of AI with more robust spatial reasoning capabilities.

Large language models (LLMs) show remarkable capabilities across a variety of tasks. Despite the models only seeing text in training, several recent studies suggest that LLM representations implicitly capture aspects of the underlying grounded concepts. Here, we explore LLM representations of a particularly salient kind of grounded knowledge -- spatial relationships. We design natural-language navigation tasks and evaluate the ability of LLMs, in particular GPT-3.5-turbo, GPT-4, and Llama2 series models, to represent and reason about spatial structures. These tasks reveal substantial variability in LLM performance across different spatial structures, including square, hexagonal, and triangular grids, rings, and trees. In extensive error analysis, we find that LLMs' mistakes reflect both spatial and non-spatial factors. These findings suggest that LLMs appear to capture certain aspects of spatial structure implicitly, but room for improvement remains.

Visual Spatial Reasoning (VSR) is a core human cognitive ability and a critical requirement for advancing embodied intelligence and autonomous systems. Despite recent progress in Vision-Language Models (VLMs), achieving human-level VSR remains highly challenging due to the complexity of representing and reasoning over three-dimensional space. In this paper, we present a systematic investigation of VSR in VLMs, encompassing a review of existing methodologies across input modalities, model architectures, training strategies, and reasoning mechanisms. Furthermore, we categorize spatial intelligence into three levels of capability, ie, basic perception, spatial understanding, spatial planning, and curate SIBench, a spatial intelligence benchmark encompassing nearly 20 open-source datasets across 23 task settings. Experiments with state-of-the-art VLMs reveal a pronounced gap between perception and reasoning, as models show competence in basic perceptual tasks but consistently underperform in understanding and planning tasks, particularly in numerical estimation, multi-view reasoning, temporal dynamics, and spatial imagination. These findings underscore the substantial challenges that remain in achieving spatial intelligence, while providing both a systematic roadmap and a comprehensive benchmark to drive future research in the field. The related resources of this study are accessible at https://sibench.github.io/Awesome-Visual-Spatial-Reasoning/.

Spatial reasoning is a fundamental capability of embodied agents and has garnered widespread attention in the field of multimodal large language models (MLLMs). In this work, we propose a novel benchmark, Open3DVQA, to comprehensively evaluate the spatial reasoning capacities of current state-of-the-art (SOTA) foundation models in open 3D space. Open3DVQA consists of 9k VQA samples, collected using an efficient semi-automated tool in a high-fidelity urban simulator. We evaluate several SOTA MLLMs across various aspects of spatial reasoning, such as relative and absolute spatial relationships, situational reasoning, and object-centric spatial attributes. Our results reveal that: 1) MLLMs perform better at answering questions regarding relative spatial relationships than absolute spatial relationships, 2) MLLMs demonstrate similar spatial reasoning abilities for both egocentric and allocentric perspectives, and 3) Fine-tuning large models significantly improves their performance across different spatial reasoning tasks. We believe that our open-source data collection tools and in-depth analyses will inspire further research on MLLM spatial reasoning capabilities. The benchmark is available at https://github.com/WeichenZh/Open3DVQA.

Spatial reasoning tasks in multi-agent environments such as event prediction, agent type identification, or missing data imputation are important for multiple applications (e.g., autonomous surveillance over sensor networks and subtasks for reinforcement learning (RL)). StarCraft II game replays encode intelligent (and adversarial) multi-agent behavior and could provide a testbed for these tasks; however, extracting simple and standardized representations for prototyping these tasks is laborious and hinders reproducibility. In contrast, MNIST and CIFAR10, despite their extreme simplicity, have enabled rapid prototyping and reproducibility of ML methods. Following the simplicity of these datasets, we construct a benchmark spatial reasoning dataset based on StarCraft II replays that exhibit complex multi-agent behaviors, while still being as easy to use as MNIST and CIFAR10. Specifically, we carefully summarize a window of 255 consecutive game states to create 3.6 million summary images from 60,000 replays, including all relevant metadata such as game outcome and player races. We develop three formats of decreasing complexity: Hyperspectral images that include one channel for every unit type (similar to multispectral geospatial images), RGB images that mimic CIFAR10, and grayscale images that mimic MNIST. We show how this dataset can be used for prototyping spatial reasoning methods. All datasets, code for extraction, and code for dataset loading can be found at https://starcraftdata.davidinouye.com

Many data have an underlying dependence on spatial location; it may be weather on the Earth, a simulation on a mesh, or a registered image. Yet this feature is rarely taken advantage of, and violates common assumptions made by many neural network layers, such as translation equivariance. Further, many works that do incorporate locality fail to capture fine-grained structure. To address this, we introduce the Spatial Mixture-of-Experts (SMoE) layer, a sparsely-gated layer that learns spatial structure in the input domain and routes experts at a fine-grained level to utilize it. We also develop new techniques to train SMoEs, including a self-supervised routing loss and damping expert errors. Finally, we show strong results for SMoEs on numerous tasks, and set new state-of-the-art results for medium-range weather prediction and post-processing ensemble weather forecasts.

Spatial intelligence is a critical frontier for Multimodal Large Language Models (MLLMs), empowering them to comprehend the physical world. Drawing inspiration from human perception mechanisms, existing studies attempt to construct a coherent spatial understanding via grid-based cognitive maps from multi-frame visual inputs. However, current grid-based map methods rely on discretized raster representations, which limit the model's ability in fine-grained spatial reasoning. To overcome this limitation, we propose Video2Layout, a framework for reconstructing metric-grounded spatial layouts from video. The framework employs continuous object boundary coordinates to quantify inter-object physical distances and object size. This empowers the model with quantitative spatial computation capabilities, effectively alleviating the inherent ambiguity when describing spatial relationships in natural language. Specifically, our method comprises two core stages. First, in supervised fine-tuning stage, we construct a high-quality dataset from the AI2THOR simulator, which enables the model to learn the mapping from visual inputs to precise boundary coordinates. Subsequently, a reinforcement fine-tuning stage further enhances the model's real-world generalization capabilities. To systematically evaluate the correlation between cognitive map accuracy and image quantity, as well as how the quantity of image inputs affects spatial reasoning accuracy, we introduce QVS-Bench, a diagnostic benchmark designed to analyze the relevant mechanisms. Evaluated on QVS-Bench and mainstream spatial reasoning benchmarks, our model, V2LO-7B achieves an average improvement of 4.92% over the model trained on grid maps, validating the superiority of our method. Our code is available at https://github.com/ybrrraway/Video2Layout.

We study the problem of jointly reasoning about language and vision through a navigation and spatial reasoning task. We introduce the Touchdown task and dataset, where an agent must first follow navigation instructions in a real-life visual urban environment, and then identify a location described in natural language to find a hidden object at the goal position. The data contains 9,326 examples of English instructions and spatial descriptions paired with demonstrations. Empirical analysis shows the data presents an open challenge to existing methods, and qualitative linguistic analysis shows that the data displays richer use of spatial reasoning compared to related resources.

How can a robot efficiently extract a desired object from a shelf when it is fully occluded by other objects? Prior works propose geometric approaches for this problem but do not consider object semantics. Shelves in pharmacies, restaurant kitchens, and grocery stores are often organized such that semantically similar objects are placed close to one another. Can large language models (LLMs) serve as semantic knowledge sources to accelerate robotic mechanical search in semantically arranged environments? With Semantic Spatial Search on Shelves (S^4), we use LLMs to generate affinity matrices, where entries correspond to semantic likelihood of physical proximity between objects. We derive semantic spatial distributions by synthesizing semantics with learned geometric constraints. S^4 incorporates Optical Character Recognition (OCR) and semantic refinement with predictions from ViLD, an open-vocabulary object detection model. Simulation experiments suggest that semantic spatial search reduces the search time relative to pure spatial search by an average of 24% across three domains: pharmacy, kitchen, and office shelves. A manually collected dataset of 100 semantic scenes suggests that OCR and semantic refinement improve object detection accuracy by 35%. Lastly, physical experiments in a pharmacy shelf suggest 47.1% improvement over pure spatial search. Supplementary material can be found at https://sites.google.com/view/s4-rss/home.

Spatial reasoning is a core aspect of human intelligence that allows perception, inference and planning in 3D environments. However, current vision-language models (VLMs) struggle to maintain geometric coherence and cross-view consistency for spatial reasoning in multi-view settings. We attribute this gap to the lack of fine-grained benchmarks that isolate multi-view reasoning from single-view perception and temporal factors. To address this, we present ReMindView-Bench, a cognitively grounded benchmark for evaluating how VLMs construct, align and maintain spatial mental models across complementary viewpoints. ReMindView-Bench systematically varies viewpoint spatial pattern and query type to probe key factors of spatial cognition. Evaluations of 15 current VLMs reveals consistent failures in cross-view alignment and perspective-taking in multi-view spatial reasoning, motivating deeper analysis on the reasoning process. Explicit phase-wise analysis using LLM-as-a-judge and self-consistency prompting shows that VLMs perform well on in-frame perception but degrade sharply when integrating information across views. Implicit analysis, including linear probing and entropy dynamics, further show progressive loss of task-relevant information and uncertainty separation between correct and incorrect trajectories. These results provide a cognitively grounded diagnosis of VLM spatial reasoning and reveal how multi-view spatial mental models are formed, degraded and destabilized across reasoning phases. The ReMindView-Bench benchmark is available at https://huggingface.co/datasets/Xue0823/ReMindView-Bench, and the source codes of benchmark construction and VLM reasoning analysis are available at https://github.com/pittisl/ReMindView-Bench.

Driving on roads is restricted by various traffic rules, aiming to ensure safety for all traffic participants. However, human road users usually do not adhere to these rules strictly, resulting in varying degrees of rule conformity. Such deviations from given rules are key components of today's road traffic. In autonomous driving, robotic agents can disturb traffic flow, when rule deviations are not taken into account. In this paper, we present an approach to derive the distribution of degrees of rule conformity from human driving data. We demonstrate our method with the Waymo Open Motion dataset and Safety Distance and Speed Limit rules.

Spatial reasoning remains a fundamental challenge for Vision-Language Models (VLMs), with current approaches struggling to achieve robust performance despite recent advances. We identify that this limitation stems from a critical gap: existing methods attempt to learn spatial reasoning directly without establishing the hierarchical foundations of perception and understanding. To address this challenge, we present a comprehensive methodology for building spatial intelligence progressively. We introduce SpatialLadder-26k, a multimodal dataset containing 26,610 samples spanning object localization, single image, multi-view, and video spatial reasoning tasks, constructed through a standardized pipeline that ensures systematic coverage across modalities. Building on this dataset, we design a three-stage progressive training framework that (1) establishes spatial perception through object localization, (2) develops spatial understanding through multi-dimensional spatial tasks, and (3) strengthens complex reasoning via reinforcement learning with verifiable rewards. This approach yields SpatialLadder, a 3B-parameter model that achieves state-of-the-art performance on spatial reasoning benchmarks, with 23.4% average improvement over the base model, surpassing GPT-4o by 20.8% and Gemini-2.0-Flash by 10.1%. Notably, SpatialLadder maintains strong generalization with 7.2% improvement on out-of-domain benchmarks, demonstrating that progressive training from perception to reasoning is essential for robust spatial intelligence.

Vision Language Models (VLMs) exhibit a fundamental semantic-to-geometric gap in spatial reasoning: they excel at qualitative semantic inference but their reasoning operates within a lossy semantic space, misaligned with high-fidelity geometry. Current paradigms fail to bridge this gap. Training-based methods suffer from an ``oracle paradox,'' learning flawed spatial logic from imperfect oracles. Tool-integrated methods constrain the final computation but critically leave the VLM's planning process unconstrained, resulting in geometrically flawed plans. In this work, we propose Geometrically-Constrained Agent (GCA), a training-free agentic paradigm that resolves this gap by introducing a formal task constraint. Specifically, we strategically decouples the VLM's role into two stages. First, acting as a semantic analyst, the VLM translates the user's ambiguous query into the formal, verifiable task constraint, which defines the reference frame and objective. Second, acting as a task solver, the VLM generates and executes tool calls strictly within the deterministic bounds defined by the constraint. This geometrically-constrained reasoning strategy successfully resolve the semantic-to-geometric gap, yielding a robust and verifiable reasoning pathway for spatial reasoning. Comprehensive experiments demonstrate that GCA achieves SOTA performance on multiple spatial reasoning benchmarks, surpassing existing training-based and tool-integrated methods by ~27%. Please see our homepage at https://gca-spatial-reasoning.github.io.

The integration of language and 3D perception is critical for embodied AI and robotic systems to perceive, understand, and interact with the physical world. Spatial reasoning, a key capability for understanding spatial relationships between objects, remains underexplored in current 3D vision-language research. Existing datasets often mix semantic cues (e.g., object name) with spatial context, leading models to rely on superficial shortcuts rather than genuinely interpreting spatial relationships. To address this gap, we introduce Surprise3D, a novel dataset designed to evaluate language-guided spatial reasoning segmentation in complex 3D scenes. Surprise3D consists of more than 200k vision language pairs across 900+ detailed indoor scenes from ScanNet++ v2, including more than 2.8k unique object classes. The dataset contains 89k+ human-annotated spatial queries deliberately crafted without object name, thereby mitigating shortcut biases in spatial understanding. These queries comprehensively cover various spatial reasoning skills, such as relative position, narrative perspective, parametric perspective, and absolute distance reasoning. Initial benchmarks demonstrate significant challenges for current state-of-the-art expert 3D visual grounding methods and 3D-LLMs, underscoring the necessity of our dataset and the accompanying 3D Spatial Reasoning Segmentation (3D-SRS) benchmark suite. Surprise3D and 3D-SRS aim to facilitate advancements in spatially aware AI, paving the way for effective embodied interaction and robotic planning. The code and datasets can be found in https://github.com/liziwennba/SUPRISE.

Earthquakes are evaluated among the most destructive disasters for human beings, as also experienced for Turkiye region. Data science has the property of discovering hidden patterns in case a sufficient volume of data is supplied. Time dependency of events, specifically being defined by co-occurrence in a specific time window, may be handled as an associate rule mining task such as a market-basket analysis application. In this regard, we assumed each day's seismic activity as a single basket of events, leading to discovering the association patterns between these events. Consequently, this study presents the most prominent association rules for the earthquakes recorded in Turkiye region in the last 5 years, each year presented separately. Results indicate statistical inference with events recorded from regions of various distances, which could be further verified with geologic evidence from the field. As a result, we believe that the current study may form a statistical basis for the future works with the aid of machine learning algorithm performed for associate rule mining.

We introduce Cosmos-Transfer, a conditional world generation model that can generate world simulations based on multiple spatial control inputs of various modalities such as segmentation, depth, and edge. In the design, the spatial conditional scheme is adaptive and customizable. It allows weighting different conditional inputs differently at different spatial locations. This enables highly controllable world generation and finds use in various world-to-world transfer use cases, including Sim2Real. We conduct extensive evaluations to analyze the proposed model and demonstrate its applications for Physical AI, including robotics Sim2Real and autonomous vehicle data enrichment. We further demonstrate an inference scaling strategy to achieve real-time world generation with an NVIDIA GB200 NVL72 rack. To help accelerate research development in the field, we open-source our models and code at https://github.com/nvidia-cosmos/cosmos-transfer1.

Planning the layout of bicycle-sharing stations is a complex process, especially in cities where bicycle sharing systems are just being implemented. Urban planners often have to make a lot of estimates based on both publicly available data and privately provided data from the administration and then use the Location-Allocation model popular in the field. Many municipalities in smaller cities may have difficulty hiring specialists to carry out such planning. This thesis proposes a new solution to streamline and facilitate the process of such planning by using spatial embedding methods. Based only on publicly available data from OpenStreetMap, and station layouts from 34 cities in Europe, a method has been developed to divide cities into micro-regions using the Uber H3 discrete global grid system and to indicate regions where it is worth placing a station based on existing systems in different cities using transfer learning. The result of the work is a mechanism to support planners in their decision making when planning a station layout with a choice of reference cities.

Multi-step spatial reasoning entails understanding and reasoning about spatial relationships across multiple sequential steps, which is crucial for tackling complex real-world applications, such as robotic manipulation, autonomous navigation, and automated assembly. To assess how well current Multimodal Large Language Models (MLLMs) have acquired this fundamental capability, we introduce LEGO-Puzzles, a scalable benchmark designed to evaluate both spatial understanding and sequential reasoning in MLLMs through LEGO-based tasks. LEGO-Puzzles consists of 1,100 carefully curated visual question-answering (VQA) samples spanning 11 distinct tasks, ranging from basic spatial understanding to complex multi-step reasoning. Based on LEGO-Puzzles, we conduct a comprehensive evaluation of state-of-the-art MLLMs and uncover significant limitations in their spatial reasoning capabilities: even the most powerful MLLMs can answer only about half of the test cases, whereas human participants achieve over 90\% accuracy. In addition to VQA tasks, we evaluate MLLMs' abilities to generate LEGO images following assembly illustrations. Our experiments show that only Gemini-2.0-Flash and GPT-4o exhibit a limited ability to follow these instructions, while other MLLMs either replicate the input image or generate completely irrelevant outputs. Overall, LEGO-Puzzles exposes critical deficiencies in existing MLLMs' spatial understanding and sequential reasoning capabilities, and underscores the need for further advancements in multimodal spatial reasoning.

Spatial cognition is fundamental to real-world multimodal intelligence, allowing models to effectively interact with the physical environment. While multimodal large language models (MLLMs) have made significant strides, existing benchmarks often oversimplify spatial cognition, reducing it to a single-dimensional metric, which fails to capture the hierarchical structure and interdependence of spatial abilities. To address this gap, we propose a hierarchical spatial cognition framework that decomposes spatial intelligence into five progressively complex levels from basic observation to high-level planning. Building upon this taxonomy, we construct SpatialBench, a large-scale, fine-grained benchmark covering 15 tasks aligned with these cognitive levels. To provide a unified evaluation across heterogeneous tasks, we further introduce a high-level capability-oriented metric that reliably assesses a model's overall spatial reasoning ability. Extensive experiments over massive MLLMs reveal distinct performance stratification across cognitive levels: models exhibit strong perceptual grounding yet remain limited in symbolic reasoning, causal inference, and planning. Additional human tests demonstrate that humans perform selective, goal-directed abstraction, while MLLMs tend to over-attend to surface details without coherent spatial intent. Our work establishes the first systematic framework for measuring hierarchical spatial cognition in MLLMs, laying the foundation for future spatially intelligent systems.

Large Multimodal Models (LMMs) have achieved strong performance across a range of vision and language tasks. However, their spatial reasoning capabilities are under-investigated. In this paper, we construct a novel VQA dataset, Spatial-MM, to comprehensively study LMMs' spatial understanding and reasoning capabilities. Our analyses on object-relationship and multi-hop reasoning reveal several important findings. Firstly, bounding boxes and scene graphs, even synthetic ones, can significantly enhance LMMs' spatial reasoning. Secondly, LMMs struggle more with questions posed from the human perspective than the camera perspective about the image. Thirdly, chain of thought (CoT) prompting does not improve model performance on complex multi-hop questions involving spatial relations. % Moreover, spatial reasoning steps are much less accurate than non-spatial ones across MLLMs. Lastly, our perturbation analysis on GQA-spatial reveals that LMMs are much stronger at basic object detection than complex spatial reasoning. We believe our benchmark dataset and in-depth analyses can spark further research on LMMs spatial reasoning. Spatial-MM benchmark is available at: https://github.com/FatemehShiri/Spatial-MM

Spatial relation reasoning is a crucial task for multimodal large language models (MLLMs) to understand the objective world. However, current benchmarks have issues like relying on bounding boxes, ignoring perspective substitutions, or allowing questions to be answered using only the model's prior knowledge without image understanding. To address these issues, we introduce SpatialMQA, a human-annotated spatial relation reasoning benchmark based on COCO2017, which enables MLLMs to focus more on understanding images in the objective world. To ensure data quality, we design a well-tailored annotation procedure, resulting in SpatialMQA consisting of 5,392 samples. Based on this benchmark, a series of closed- and open-source MLLMs are implemented and the results indicate that the current state-of-the-art MLLM achieves only 48.14% accuracy, far below the human-level accuracy of 98.40%. Extensive experimental analyses are also conducted, suggesting the future research directions. The benchmark and codes are available at https://github.com/ziyan-xiaoyu/SpatialMQA.git.

This study investigates the spatial reasoning capabilities of vision-language models (VLMs) through Chain-of-Thought (CoT) prompting and reinforcement learning. We begin by evaluating the impact of different prompting strategies and find that simple CoT formats, where the model generates a reasoning step before the answer, not only fail to help, but can even harm the model's original performance. In contrast, structured multi-stage prompting based on scene graphs (SceneGraph CoT) significantly improves spatial reasoning accuracy. Furthermore, to improve spatial reasoning ability, we fine-tune models using Group Relative Policy Optimization (GRPO) on the SAT dataset and evaluate their performance on CVBench. Compared to supervised fine-tuning (SFT), GRPO achieves higher accuracy on Pass@1 evaluations and demonstrates superior robustness under out-of-distribution (OOD) conditions. In particular, we find that SFT overfits to surface-level linguistic patterns and may degrade performance when test-time phrasing changes (e.g., from "closer to" to "farther from"). GRPO, on the other hand, generalizes more reliably and maintains stable performance under such shifts. Our findings provide insights into how reinforcement learning and structured prompting improve the spatial reasoning capabilities and generalization behavior of modern VLMs. All code is open source at: https://github.com/Yvonne511/spatial-vlm-investigator

Recent vision-language (VL) models are powerful, but can they reliably distinguish "right" from "left"? We curate three new corpora to quantify model comprehension of such basic spatial relations. These tests isolate spatial reasoning more precisely than existing datasets like VQAv2, e.g., our What'sUp benchmark contains sets of photographs varying only the spatial relations of objects, keeping their identity fixed (see Figure 1: models must comprehend not only the usual case of a dog under a table, but also, the same dog on top of the same table). We evaluate 18 VL models, finding that all perform poorly, e.g., BLIP finetuned on VQAv2, which nears human parity on VQAv2, achieves 56% accuracy on our benchmarks vs. humans at 99%. We conclude by studying causes of this surprising behavior, finding: 1) that popular vision-language pretraining corpora like LAION-2B contain little reliable data for learning spatial relationships; and 2) that basic modeling interventions like up-weighting preposition-containing instances or fine-tuning on our corpora are not sufficient to address the challenges our benchmarks pose. We are hopeful that these corpora will facilitate further research, and we release our data and code at https://github.com/amitakamath/whatsup_vlms.

With the current surge in spatial reasoning explorations, researchers have made significant progress in understanding indoor scenes, but still struggle with diverse applications such as robotics and autonomous driving. This paper aims to advance all-scale spatial reasoning across diverse scenarios by tackling two key challenges: 1) the heavy reliance on indoor 3D scans and labor-intensive manual annotations for dataset curation; 2) the absence of effective all-scale scene modeling, which often leads to overfitting to individual scenes. In this paper, we introduce a holistic solution that integrates a structured spatial reasoning knowledge system, scale-aware modeling, and a progressive training paradigm, as the first attempt to broaden the all-scale spatial intelligence of MLLMs to the best of our knowledge. Using a task-specific, specialist-driven automated pipeline, we curate over 38K video scenes across 5 spatial scales to create SpaceVista-1M, a dataset comprising approximately 1M spatial QA pairs spanning 19 diverse task types. While specialist models can inject useful domain knowledge, they are not reliable for evaluation. We then build an all-scale benchmark with precise annotations by manually recording, retrieving, and assembling video-based data. However, naive training with SpaceVista-1M often yields suboptimal results due to the potential knowledge conflict. Accordingly, we introduce SpaceVista-7B, a spatial reasoning model that accepts dense inputs beyond semantics and uses scale as an anchor for scale-aware experts and progressive rewards. Finally, extensive evaluations across 5 benchmarks, including our SpaceVista-Bench, demonstrate competitive performance, showcasing strong generalization across all scales and scenarios. Our dataset, model, and benchmark will be released on https://peiwensun2000.github.io/mm2km .

Spatial understanding is a fundamental aspect of computer vision and integral for human-level reasoning about images, making it an important component for grounded language understanding. While recent text-to-image synthesis (T2I) models have shown unprecedented improvements in photorealism, it is unclear whether they have reliable spatial understanding capabilities. We investigate the ability of T2I models to generate correct spatial relationships among objects and present VISOR, an evaluation metric that captures how accurately the spatial relationship described in text is generated in the image. To benchmark existing models, we introduce a dataset, SR_{2D}, that contains sentences describing two or more objects and the spatial relationships between them. We construct an automated evaluation pipeline to recognize objects and their spatial relationships, and employ it in a large-scale evaluation of T2I models. Our experiments reveal a surprising finding that, although state-of-the-art T2I models exhibit high image quality, they are severely limited in their ability to generate multiple objects or the specified spatial relations between them. Our analyses demonstrate several biases and artifacts of T2I models such as the difficulty with generating multiple objects, a bias towards generating the first object mentioned, spatially inconsistent outputs for equivalent relationships, and a correlation between object co-occurrence and spatial understanding capabilities. We conduct a human study that shows the alignment between VISOR and human judgement about spatial understanding. We offer the SR_{2D} dataset and the VISOR metric to the community in support of T2I reasoning research.

Understanding and reasoning about spatial relationships is a fundamental capability for Visual Question Answering (VQA) and robotics. While Vision Language Models (VLM) have demonstrated remarkable performance in certain VQA benchmarks, they still lack capabilities in 3D spatial reasoning, such as recognizing quantitative relationships of physical objects like distances or size differences. We hypothesize that VLMs' limited spatial reasoning capability is due to the lack of 3D spatial knowledge in training data and aim to solve this problem by training VLMs with Internet-scale spatial reasoning data. To this end, we present a system to facilitate this approach. We first develop an automatic 3D spatial VQA data generation framework that scales up to 2 billion VQA examples on 10 million real-world images. We then investigate various factors in the training recipe, including data quality, training pipeline, and VLM architecture. Our work features the first internet-scale 3D spatial reasoning dataset in metric space. By training a VLM on such data, we significantly enhance its ability on both qualitative and quantitative spatial VQA. Finally, we demonstrate that this VLM unlocks novel downstream applications in chain-of-thought spatial reasoning and robotics due to its quantitative estimation capability. Project website: https://spatial-vlm.github.io/

Our goal is to synthesize 3D human motions given textual inputs describing simultaneous actions, for example 'waving hand' while 'walking' at the same time. We refer to generating such simultaneous movements as performing 'spatial compositions'. In contrast to temporal compositions that seek to transition from one action to another, spatial compositing requires understanding which body parts are involved in which action, to be able to move them simultaneously. Motivated by the observation that the correspondence between actions and body parts is encoded in powerful language models, we extract this knowledge by prompting GPT-3 with text such as "what are the body parts involved in the action <action name>?", while also providing the parts list and few-shot examples. Given this action-part mapping, we combine body parts from two motions together and establish the first automated method to spatially compose two actions. However, training data with compositional actions is always limited by the combinatorics. Hence, we further create synthetic data with this approach, and use it to train a new state-of-the-art text-to-motion generation model, called SINC ("SImultaneous actioN Compositions for 3D human motions"). In our experiments, that training with such GPT-guided synthetic data improves spatial composition generation over baselines. Our code is publicly available at https://sinc.is.tue.mpg.de/.

Spatial intelligence is a critical component of embodied AI, promoting robots to understand and interact with their environments. While recent advances have enhanced the ability of VLMs to perceive object locations and positional relationships, they still lack the capability to precisely understand object orientations-a key requirement for tasks involving fine-grained manipulations. Addressing this limitation not only requires geometric reasoning but also an expressive and intuitive way to represent orientation. In this context, we propose that natural language offers a more flexible representation space than canonical frames, making it particularly suitable for instruction-following robotic systems. In this paper, we introduce the concept of semantic orientation, which defines object orientations using natural language in a reference-frame-free manner (e.g., the ''plug-in'' direction of a USB or the ''handle'' direction of a knife). To support this, we construct OrienText300K, a large-scale dataset of 3D models annotated with semantic orientations that link geometric understanding to functional semantics. By integrating semantic orientation into a VLM system, we enable robots to generate manipulation actions with both positional and orientational constraints. Extensive experiments in simulation and real world demonstrate that our approach significantly enhances robotic manipulation capabilities, e.g., 48.7% accuracy on Open6DOR and 74.9% accuracy on SIMPLER.

Rule-based reasoning, a fundamental type of legal reasoning, enables us to draw conclusions by accurately applying a rule to a set of facts. We explore causal language models as rule-based reasoners, specifically with respect to compositional rules - rules consisting of multiple elements which form a complex logical expression. Reasoning about compositional rules is challenging because it requires multiple reasoning steps, and attending to the logical relationships between elements. We introduce a new prompting method, Chain of Logic, which elicits rule-based reasoning through decomposition (solving elements as independent threads of logic), and recomposition (recombining these sub-answers to resolve the underlying logical expression). This method was inspired by the IRAC (Issue, Rule, Application, Conclusion) framework, a sequential reasoning approach used by lawyers. We evaluate chain of logic across eight rule-based reasoning tasks involving three distinct compositional rules from the LegalBench benchmark and demonstrate it consistently outperforms other prompting methods, including chain of thought and self-ask, using open-source and commercial language models.

Recent advancements in Multimodal Large Language Models (MLLMs) have significantly enhanced performance on 2D visual tasks. However, improving their spatial intelligence remains a challenge. Existing 3D MLLMs always rely on additional 3D or 2.5D data to incorporate spatial awareness, restricting their utility in scenarios with only 2D inputs, such as images or videos. In this paper, we present Spatial-MLLM, a novel framework for visual-based spatial reasoning from purely 2D observations. Unlike conventional video MLLMs which rely on CLIP-based visual encoders optimized for semantic understanding, our key insight is to unleash the strong structure prior from the feed-forward visual geometry foundation model. Specifically, we propose a dual-encoder architecture: a pretrained 2D visual encoder to extract semantic features, and a spatial encoder-initialized from the backbone of the visual geometry model-to extract 3D structure features. A connector then integrates both features into unified visual tokens for enhanced spatial understanding. Furthermore, we propose a space-aware frame sampling strategy at inference time, which selects the spatially informative frames of a video sequence, ensuring that even under limited token length, the model focuses on frames critical for spatial reasoning. Beyond architecture improvements, we construct the Spatial-MLLM-120k dataset and train the model on it using supervised fine-tuning and GRPO. Extensive experiments on various real-world datasets demonstrate that our spatial-MLLM achieves state-of-the-art performance in a wide range of visual-based spatial understanding and reasoning tasks. Project page: https://diankun-wu.github.io/Spatial-MLLM/.

Large language models (LLMs) have exhibited impressive performance in language comprehension and various reasoning tasks. However, their abilities in spatial reasoning, a crucial aspect of human cognition, remain relatively unexplored. Human possess a remarkable ability to create mental images of unseen objects and actions through a process known as the Mind's Eye, enabling the imagination of the unseen world. Inspired by this cognitive capacity, we propose Visualization-of-Thought (VoT) prompting. VoT aims to elicit spatial reasoning of LLMs by visualizing their reasoning traces, thereby guiding subsequent reasoning steps. We employed VoT for multi-hop spatial reasoning tasks, including natural language navigation, visual navigation, and visual tiling in 2D grid worlds. Experimental results demonstrated that VoT significantly enhances the spatial reasoning abilities of LLMs. Notably, VoT outperformed existing multimodal large language models (MLLMs) in these tasks. While VoT works surprisingly well on LLMs, the ability to generate mental images to facilitate spatial reasoning resembles the mind's eye process, suggesting its potential viability in MLLMs.

Spatial relationships between objects represent key scene information for humans to understand and interact with the world. To study the capability of current computer vision systems to recognize physically grounded spatial relations, we start by proposing precise relation definitions that permit consistently annotating a benchmark dataset. Despite the apparent simplicity of this task relative to others in the recognition literature, we observe that existing approaches perform poorly on this benchmark. We propose new approaches exploiting the long-range attention capabilities of transformers for this task, and evaluating key design principles. We identify a simple "RelatiViT" architecture and demonstrate that it outperforms all current approaches. To our knowledge, this is the first method to convincingly outperform naive baselines on spatial relation prediction in in-the-wild settings. The code and datasets are available in https://sites.google.com/view/spatial-relation.

We present GeoSynth, a model for synthesizing satellite images with global style and image-driven layout control. The global style control is via textual prompts or geographic location. These enable the specification of scene semantics or regional appearance respectively, and can be used together. We train our model on a large dataset of paired satellite imagery, with automatically generated captions, and OpenStreetMap data. We evaluate various combinations of control inputs, including different types of layout controls. Results demonstrate that our model can generate diverse, high-quality images and exhibits excellent zero-shot generalization. The code and model checkpoints are available at https://github.com/mvrl/GeoSynth.

The next Point-of-Interest (POI) recommendation task aims to predict users' next destinations based on their historical movement data and plays a key role in location-based services and personalized applications. Accurate next POI recommendation depends on effectively modeling geographic information and POI transition relations, which are crucial for capturing spatial dependencies and user movement patterns. While Large Language Models (LLMs) exhibit strong capabilities in semantic understanding and contextual reasoning, applying them to spatial tasks like next POI recommendation remains challenging. First, the infrequent nature of specific GPS coordinates makes it difficult for LLMs to model precise spatial contexts. Second, the lack of knowledge about POI transitions limits their ability to capture potential POI-POI relationships. To address these issues, we propose GA-LLM (Geography-Aware Large Language Model), a novel framework that enhances LLMs with two specialized components. The Geographic Coordinate Injection Module (GCIM) transforms GPS coordinates into spatial representations using hierarchical and Fourier-based positional encoding, enabling the model to understand geographic features from multiple perspectives. The POI Alignment Module (PAM) incorporates POI transition relations into the LLM's semantic space, allowing it to infer global POI relationships and generalize to unseen POIs. Experiments on three real-world datasets demonstrate the state-of-the-art performance of GA-LLM.

Vision-centric hierarchical embodied models have demonstrated strong potential for long-horizon robotic control. However, existing methods lack spatial awareness capabilities, limiting their effectiveness in bridging visual plans to actionable control in complex environments. To address this problem, we propose Spatial Policy (SP), a unified spatial-aware visuomotor robotic manipulation framework via explicit spatial modeling and reasoning. Specifically, we first design a spatial-conditioned embodied video generation module to model spatially guided predictions through a spatial plan table. Then, we propose a spatial-based action prediction module to infer executable actions with coordination. Finally, we propose a spatial reasoning feedback policy to refine the spatial plan table via dual-stage replanning. Extensive experiments show that SP significantly outperforms state-of-the-art baselines, achieving a 33.0% average improvement over the best baseline. With an 86.7% average success rate across 11 diverse tasks, SP substantially enhances the practicality of embodied models for robotic control applications. Code and checkpoints are maintained at https://plantpotatoonmoon.github.io/SpatialPolicy/.

Although planning is a crucial component of the autonomous driving stack, researchers have yet to develop robust planning algorithms that are capable of safely handling the diverse range of possible driving scenarios. Learning-based planners suffer from overfitting and poor long-tail performance. On the other hand, rule-based planners generalize well, but might fail to handle scenarios that require complex driving maneuvers. To address these limitations, we investigate the possibility of leveraging the common-sense reasoning capabilities of Large Language Models (LLMs) such as GPT4 and Llama2 to generate plans for self-driving vehicles. In particular, we develop a novel hybrid planner that leverages a conventional rule-based planner in conjunction with an LLM-based planner. Guided by commonsense reasoning abilities of LLMs, our approach navigates complex scenarios which existing planners struggle with, produces well-reasoned outputs while also remaining grounded through working alongside the rule-based approach. Through extensive evaluation on the nuPlan benchmark, we achieve state-of-the-art performance, outperforming all existing pure learning- and rule-based methods across most metrics. Our code will be available at https://llmassist.github.io.

Despite impressive advancements in Visual-Language Models (VLMs) for multi-modal tasks, their reliance on RGB inputs limits precise spatial understanding. Existing methods for integrating spatial cues, such as point clouds or depth, either require specialized sensors or fail to effectively exploit depth information for higher-order reasoning. To this end, we propose a novel Spatial Sense and Reasoning method, dubbed SSR, a novel framework that transforms raw depth data into structured, interpretable textual rationales. These textual rationales serve as meaningful intermediate representations to significantly enhance spatial reasoning capabilities. Additionally, we leverage knowledge distillation to compress the generated rationales into compact latent embeddings, which facilitate resource-efficient and plug-and-play integration into existing VLMs without retraining. To enable comprehensive evaluation, we introduce a new dataset named SSR-CoT, a million-scale visual-language reasoning dataset enriched with intermediate spatial reasoning annotations, and present SSRBench, a comprehensive multi-task benchmark. Extensive experiments on multiple benchmarks demonstrate SSR substantially improves depth utilization and enhances spatial reasoning, thereby advancing VLMs toward more human-like multi-modal understanding. Our project page is at https://yliu-cs.github.io/SSR.

The Theory of Multiple Intelligences underscores the hierarchical nature of cognitive capabilities. To advance Spatial Artificial Intelligence, we pioneer a psychometric framework defining five Basic Spatial Abilities (BSAs) in Visual Language Models (VLMs): Spatial Perception, Spatial Relation, Spatial Orientation, Mental Rotation, and Spatial Visualization. Benchmarking 13 mainstream VLMs through nine validated psychometric experiments reveals significant gaps versus humans (average score 24.95 vs. 68.38), with three key findings: 1) VLMs mirror human hierarchies (strongest in 2D orientation, weakest in 3D rotation) with independent BSAs (Pearson's r<0.4); 2) Smaller models such as Qwen2-VL-7B surpass larger counterparts, with Qwen leading (30.82) and InternVL2 lagging (19.6); 3) Interventions like chain-of-thought (0.100 accuracy gain) and 5-shot training (0.259 improvement) show limits from architectural constraints. Identified barriers include weak geometry encoding and missing dynamic simulation. By linking psychometric BSAs to VLM capabilities, we provide a diagnostic toolkit for spatial intelligence evaluation, methodological foundations for embodied AI development, and a cognitive science-informed roadmap for achieving human-like spatial intelligence.

The Airbnb search system grapples with many unique challenges as it continues to evolve. We oversee a marketplace that is nuanced by geography, diversity of homes, and guests with a variety of preferences. Crafting an efficient search system that can accommodate diverse guest needs, while showcasing relevant homes lies at the heart of Airbnb's success. Airbnb search has many challenges that parallel other recommendation and search systems but it has a unique information retrieval problem, upstream of ranking, called location retrieval. It requires defining a topological map area that is relevant to the searched query for homes listing retrieval. The purpose of this paper is to demonstrate the methodology, challenges, and impact of building a machine learning based location retrieval product from the ground up. Despite the lack of suitable, prevalent machine learning based approaches, we tackle cold start, generalization, differentiation and algorithmic bias. We detail the efficacy of heuristics, statistics, machine learning, and reinforcement learning approaches to solve these challenges, particularly for systems that are often unexplored by current literature.

Recent advances in LVLMs have improved vision-language understanding, but they still struggle with spatial perception, limiting their ability to reason about complex 3D scenes. Unlike previous approaches that incorporate 3D representations into models to improve spatial understanding, we aim to unlock the potential of VLMs by leveraging spatially relevant image data. To this end, we introduce a novel 2D spatial data generation and annotation pipeline built upon scene data with 3D ground-truth. This pipeline enables the creation of a diverse set of spatial tasks, ranging from basic perception tasks to more complex reasoning tasks. Leveraging this pipeline, we construct SPAR-7M, a large-scale dataset generated from thousands of scenes across multiple public datasets. In addition, we introduce SPAR-Bench, a benchmark designed to offer a more comprehensive evaluation of spatial capabilities compared to existing spatial benchmarks, supporting both single-view and multi-view inputs. Training on both SPAR-7M and large-scale 2D datasets enables our models to achieve state-of-the-art performance on 2D spatial benchmarks. Further fine-tuning on 3D task-specific datasets yields competitive results, underscoring the effectiveness of our dataset in enhancing spatial reasoning.

Instruction generation is a vital and multidisciplinary research area with broad applications. Existing instruction generation models are limited to generating instructions in a single style from a particular dataset, and the style and content of generated instructions cannot be controlled. Moreover, most existing instruction generation methods also disregard the spatial modeling of the navigation environment. Leveraging the capabilities of Large Language Models (LLMs), we propose C-Instructor, which utilizes the chain-of-thought-style prompt for style-controllable and content-controllable instruction generation. Firstly, we propose a Chain of Thought with Landmarks (CoTL) mechanism, which guides the LLM to identify key landmarks and then generate complete instructions. CoTL renders generated instructions more accessible to follow and offers greater controllability over the manipulation of landmark objects. Furthermore, we present a Spatial Topology Modeling Task to facilitate the understanding of the spatial structure of the environment. Finally, we introduce a Style-Mixed Training policy, harnessing the prior knowledge of LLMs to enable style control for instruction generation based on different prompts within a single model instance. Extensive experiments demonstrate that instructions generated by C-Instructor outperform those generated by previous methods in text metrics, navigation guidance evaluation, and user studies.

Humans have a natural ability to perform semantic associations with the surrounding objects in the environment. This allows them to create a mental map of the environment, allowing them to navigate on-demand when given linguistic instructions. A natural goal in Vision Language Navigation (VLN) research is to impart autonomous agents with similar capabilities. Recent works take a step towards this goal by creating a semantic spatial map representation of the environment without any labeled data. However, their representations are limited for practical applicability as they do not distinguish between different instances of the same object. In this work, we address this limitation by integrating instance-level information into spatial map representation using a community detection algorithm and utilizing word ontology learned by large language models (LLMs) to perform open-set semantic associations in the mapping representation. The resulting map representation improves the navigation performance by two-fold (233%) on realistic language commands with instance-specific descriptions compared to the baseline. We validate the practicality and effectiveness of our approach through extensive qualitative and quantitative experiments.

Spatial audio quality is a highly multifaceted concept, with many interactions between environmental, geometrical, anatomical, psychological, and contextual considerations. Methods for characterization or evaluation of the geometrical components of spatial audio quality, however, remain scarce, despite being perhaps the least subjective aspect of spatial audio quality to quantify. By considering interchannel time and level differences relative to a reference signal, it is possible to construct a signal model to isolate some of the spatial distortion. By using a combination of least-square optimization and heuristics, we propose a signal decomposition method to isolate the spatial error from a processed signal, in terms of interchannel gain leakages and changes in relative delays. This allows the computation of simple energy-ratio metrics, providing objective measures of spatial and non-spatial signal qualities, with minimal assumptions and no dataset dependency. Experiments demonstrate the robustness of the method against common spatial signal degradation introduced by, e.g., audio compression and music source separation. Implementation is available at https://github.com/karnwatcharasupat/spauq.

One of the key shortcomings in current text-to-image (T2I) models is their inability to consistently generate images which faithfully follow the spatial relationships specified in the text prompt. In this paper, we offer a comprehensive investigation of this limitation, while also developing datasets and methods that achieve state-of-the-art performance. First, we find that current vision-language datasets do not represent spatial relationships well enough; to alleviate this bottleneck, we create SPRIGHT, the first spatially-focused, large scale dataset, by re-captioning 6 million images from 4 widely used vision datasets. Through a 3-fold evaluation and analysis pipeline, we find that SPRIGHT largely improves upon existing datasets in capturing spatial relationships. To demonstrate its efficacy, we leverage only ~0.25% of SPRIGHT and achieve a 22% improvement in generating spatially accurate images while also improving the FID and CMMD scores. Secondly, we find that training on images containing a large number of objects results in substantial improvements in spatial consistency. Notably, we attain state-of-the-art on T2I-CompBench with a spatial score of 0.2133, by fine-tuning on <500 images. Finally, through a set of controlled experiments and ablations, we document multiple findings that we believe will enhance the understanding of factors that affect spatial consistency in text-to-image models. We publicly release our dataset and model to foster further research in this area.

Learning optimal policies in sparse rewards settings is difficult as the learning agent has little to no feedback on the quality of its actions. In these situations, a good strategy is to focus on exploration, hopefully leading to the discovery of a reward signal to improve on. A learning algorithm capable of dealing with this kind of settings has to be able to (1) explore possible agent behaviors and (2) exploit any possible discovered reward. Efficient exploration algorithms have been proposed that require to define a behavior space, that associates to an agent its resulting behavior in a space that is known to be worth exploring. The need to define this space is a limitation of these algorithms. In this work, we introduce STAX, an algorithm designed to learn a behavior space on-the-fly and to explore it while efficiently optimizing any reward discovered. It does so by separating the exploration and learning of the behavior space from the exploitation of the reward through an alternating two-steps process. In the first step, STAX builds a repertoire of diverse policies while learning a low-dimensional representation of the high-dimensional observations generated during the policies evaluation. In the exploitation step, emitters are used to optimize the performance of the discovered rewarding solutions. Experiments conducted on three different sparse reward environments show that STAX performs comparably to existing baselines while requiring much less prior information about the task as it autonomously builds the behavior space.

Despite recent advances in multimodal content generation enabled by vision-language models (VLMs), their ability to reason about and generate structured 3D scenes remains largely underexplored. This limitation constrains their utility in spatially grounded tasks such as embodied AI, immersive simulations, and interactive 3D applications. We introduce a new paradigm that enables VLMs to generate, understand, and edit complex 3D environments by injecting a continually evolving spatial context. Constructed from multimodal input, this context consists of three components: a scene portrait that provides a high-level semantic blueprint, a semantically labeled point cloud capturing object-level geometry, and a scene hypergraph that encodes rich spatial relationships, including unary, binary, and higher-order constraints. Together, these components provide the VLM with a structured, geometry-aware working memory that integrates its inherent multimodal reasoning capabilities with structured 3D understanding for effective spatial reasoning. Building on this foundation, we develop an agentic 3D scene generation pipeline in which the VLM iteratively reads from and updates the spatial context. The pipeline features high-quality asset generation with geometric restoration, environment setup with automatic verification, and ergonomic adjustment guided by the scene hypergraph. Experiments show that our framework can handle diverse and challenging inputs, achieving a level of generalization not observed in prior work. Further results demonstrate that injecting spatial context enables VLMs to perform downstream tasks such as interactive scene editing and path planning, suggesting strong potential for spatially intelligent systems in computer graphics, 3D vision, and embodied applications.

As textual reasoning with large language models (LLMs) has advanced significantly, there has been growing interest in enhancing the multimodal reasoning capabilities of large vision-language models (LVLMs). However, existing methods primarily approach multimodal reasoning in a straightforward, text-centric manner, where both reasoning and answer derivation are conducted purely through text, with the only difference being the presence of multimodal input. As a result, these methods often encounter fundamental limitations in spatial reasoning tasks that demand precise geometric understanding and continuous spatial tracking-capabilities that humans achieve through mental visualization and manipulation. To address the limitations, we propose drawing to reason in space, a novel paradigm that enables LVLMs to reason through elementary drawing operations in the visual space. By equipping models with basic drawing operations, including annotating bounding boxes and drawing auxiliary lines, we empower them to express and analyze spatial relationships through direct visual manipulation, meanwhile avoiding the performance ceiling imposed by specialized perception tools in previous tool-integrated reasoning approaches. To cultivate this capability, we develop a three-stage training framework: cold-start training with synthetic data to establish basic drawing abilities, reflective rejection sampling to enhance self-reflection behaviors, and reinforcement learning to directly optimize for target rewards. Extensive experiments demonstrate that our model, named VILASR, consistently outperforms existing methods across diverse spatial reasoning benchmarks, involving maze navigation, static spatial reasoning, video-based reasoning, and multi-view-based reasoning tasks, with an average improvement of 18.4%.

We address the problem of detecting human-object interactions in images using graphical neural networks. Unlike conventional methods, where nodes send scaled but otherwise identical messages to each of their neighbours, we propose to condition messages between pairs of nodes on their spatial relationships, resulting in different messages going to neighbours of the same node. To this end, we explore various ways of applying spatial conditioning under a multi-branch structure. Through extensive experimentation we demonstrate the advantages of spatial conditioning for the computation of the adjacency structure, messages and the refined graph features. In particular, we empirically show that as the quality of the bounding boxes increases, their coarse appearance features contribute relatively less to the disambiguation of interactions compared to the spatial information. Our method achieves an mAP of 31.33% on HICO-DET and 54.2% on V-COCO, significantly outperforming state-of-the-art on fine-tuned detections.

Enhancing the spatial reasoning capabilities of Multi-modal Large Language Models (MLLMs) for video understanding is crucial yet challenging. We present Spatial-R1, a targeted approach involving two key contributions: the curation of SR, a new video spatial reasoning dataset from ScanNet with automatically generated QA pairs across seven task types, and the application of Task-Specific Group Relative Policy Optimization (GRPO) for fine-tuning. By training the Qwen2.5-VL-7B-Instruct model on SR using GRPO, Spatial-R1 significantly advances performance on the VSI-Bench benchmark, achieving a 7.4\% gain over the baseline and outperforming strong contemporary models. This work validates the effectiveness of specialized data curation and optimization techniques for improving complex spatial reasoning in video MLLMs.

Large Vision Language Models (VLMs) have long struggled with spatial reasoning tasks. Surprisingly, even simple spatial reasoning tasks, such as recognizing "under" or "behind" relationships between only two objects, pose significant challenges for current VLMs. In this work, we study the spatial reasoning challenge from the lens of mechanistic interpretability, diving into the model's internal states to examine the interactions between image and text tokens. By tracing attention distribution over the image through out intermediate layers, we observe that successful spatial reasoning correlates strongly with the model's ability to align its attention distribution with actual object locations, particularly differing between familiar and unfamiliar spatial relationships. Motivated by these findings, we propose ADAPTVIS based on inference-time confidence scores to sharpen the attention on highly relevant regions when confident, while smoothing and broadening the attention window to consider a wider context when confidence is lower. This training-free decoding method shows significant improvement (e.g., up to a 50 absolute point improvement) on spatial reasoning benchmarks such as WhatsUp and VSR with negligible cost. We make code and data publicly available for research purposes at https://github.com/shiqichen17/AdaptVis.

Visual environments are structured, consisting of distinct objects or entities. These entities have properties -- both visible and latent -- that determine the manner in which they interact with one another. To partition images into entities, deep-learning researchers have proposed structural inductive biases such as slot-based architectures. To model interactions among entities, equivariant graph neural nets (GNNs) are used, but these are not particularly well suited to the task for two reasons. First, GNNs do not predispose interactions to be sparse, as relationships among independent entities are likely to be. Second, GNNs do not factorize knowledge about interactions in an entity-conditional manner. As an alternative, we take inspiration from cognitive science and resurrect a classic approach, production systems, which consist of a set of rule templates that are applied by binding placeholder variables in the rules to specific entities. Rules are scored on their match to entities, and the best fitting rules are applied to update entity properties. In a series of experiments, we demonstrate that this architecture achieves a flexible, dynamic flow of control and serves to factorize entity-specific and rule-based information. This disentangling of knowledge achieves robust future-state prediction in rich visual environments, outperforming state-of-the-art methods using GNNs, and allows for the extrapolation from simple (few object) environments to more complex environments.

By employing large language models (LLMs) to retrieve documents and generate natural language responses, Generative Engines, such as Google AI overview and ChatGPT, provide significantly enhanced user experiences and have rapidly become the new form of search. Their rapid adoption also drives the needs of Generative Engine Optimization (GEO), as content providers are eager to gain more traction from them. In this paper, we introduce AutoGEO, a framework to automatically learn generative engine preferences when using retrieved contents for response generation, and rewrite web contents for more such traction. AutoGEO first prompts frontier LLMs to explain generative engine preferences and extract meaningful preference rules from these explanations. Then it uses preference rules as context engineering for AutoGEO_API, a prompt-based GEO system, and as rule-based rewards to train AutoGEO_Mini, a cost-effective GEO model. Experiments on the standard GEO-Bench and two newly constructed benchmarks using real user queries demonstrate the effectiveness of AutoGEO in enhancing content traction while preserving search utility. Analyses confirm the learned rules' robustness and abilities to capture unique preferences in variant domains, and AutoGEO systems' ability to embed them in content optimization. The code is released at https://github.com/cxcscmu/AutoGEO.

In Marius von Senden's Space and Sight, a newly sighted blind patient describes the experience of a corner as lemon-like, because corners "prick" sight like lemons prick the tongue. Prickliness, here, is a dimension in the feature space of sensory experience, an effect of the perceived on the perceiver that arises where the two interact. In the account of the newly sighted, an effect familiar from one interaction translates to a novel context. Perception serves as the vehicle for generalization, in that an effect shared across different experiences produces a concrete abstraction grounded in those experiences. Cezanne and the post-impressionists, fluent in the language of experience translation, realized that the way to paint a concrete form that best reflected reality was to paint not what they saw, but what it was like to see. We envision a future of creation using AI where what it is like to see is replicable, transferrable, manipulable - part of the artist's palette that is both grounded in a particular context, and generalizable beyond it. An active line of research maps human-interpretable features onto directions in GAN latent space. Supervised and self-supervised approaches that search for anticipated directions or use off-the-shelf classifiers to drive image manipulation in embedding space are limited in the variety of features they can uncover. Unsupervised approaches that discover useful new directions show that the space of perceptually meaningful directions is nowhere close to being fully mapped. As this space is broad and full of creative potential, we want tools for direction discovery that capture the richness and generalizability of human perception. Our approach puts creators in the discovery loop during real-time tool use, in order to identify directions that are perceptually meaningful to them, and generate interpretable image translations along those directions.

Spatial cognition enables adaptive goal-directed behavior by constructing internal models of space. Robust biological systems consolidate spatial knowledge into three interconnected forms: landmarks for salient cues, route knowledge for movement trajectories, and survey knowledge for map-like representations. While recent advances in multi-modal large language models (MLLMs) have enabled visual-language reasoning in embodied agents, these efforts lack structured spatial memory and instead operate reactively, limiting their generalization and adaptability in complex real-world environments. Here we present Brain-inspired Spatial Cognition for Navigation (BSC-Nav), a unified framework for constructing and leveraging structured spatial memory in embodied agents. BSC-Nav builds allocentric cognitive maps from egocentric trajectories and contextual cues, and dynamically retrieves spatial knowledge aligned with semantic goals. Integrated with powerful MLLMs, BSC-Nav achieves state-of-the-art efficacy and efficiency across diverse navigation tasks, demonstrates strong zero-shot generalization, and supports versatile embodied behaviors in the real physical world, offering a scalable and biologically grounded path toward general-purpose spatial intelligence.

Starting with early successes in computer vision tasks, deep learning based techniques have since overtaken state of the art approaches in a multitude of domains. However, it has been demonstrated time and again that these techniques fail to capture semantic context and logical constraints, instead often relying on spurious correlations to arrive at the answer. Since application of deep learning techniques to critical scenarios are dependent on adherence to domain specific constraints, several attempts have been made to address this issue. One limitation holding back a thorough exploration of this area, is a lack of suitable datasets which feature a rich set of rules. In order to address this, we present the ChessVision Dataset, consisting of 200,000+ images of annotated chess games in progress, requiring recreation of the game state from its corresponding image. This is accompanied by a curated set of rules which constrains the set of predictions to "reasonable" game states, and are designed to probe key semantic abilities like localization and enumeration. Alongside standard metrics, additional metrics to measure performance with regards to logical consistency is presented. We analyze several popular and state of the art vision models on this task, and show that, although their performance on standard metrics are laudable, they produce a plethora of incoherent results, indicating that this dataset presents a significant challenge for future works.

Text-to-image diffusion models excel at generating photorealistic images, but commonly struggle to render accurate spatial relationships described in text prompts. We identify two core issues underlying this common failure: 1) the ambiguous nature of spatial-related data in existing datasets, and 2) the inability of current text encoders to accurately interpret the spatial semantics of input descriptions. We address these issues with CoMPaSS, a versatile training framework that enhances spatial understanding of any T2I diffusion model. CoMPaSS solves the ambiguity of spatial-related data with the Spatial Constraints-Oriented Pairing (SCOP) data engine, which curates spatially-accurate training data through a set of principled spatial constraints. To better exploit the curated high-quality spatial priors, CoMPaSS further introduces a Token ENcoding ORdering (TENOR) module to allow better exploitation of high-quality spatial priors, effectively compensating for the shortcoming of text encoders. Extensive experiments on four popular open-weight T2I diffusion models covering both UNet- and MMDiT-based architectures demonstrate the effectiveness of CoMPaSS by setting new state-of-the-arts with substantial relative gains across well-known benchmarks on spatial relationships generation, including VISOR (+98%), T2I-CompBench Spatial (+67%), and GenEval Position (+131%). Code will be available at https://github.com/blurgyy/CoMPaSS.

The rapid advancement of multimodal large language models (LLMs) has opened new frontiers in artificial intelligence, enabling the integration of diverse large-scale data types such as text, images, and spatial information. In this paper, we explore the potential of multimodal LLMs (MLLM) for geospatial artificial intelligence (GeoAI), a field that leverages spatial data to address challenges in domains including Geospatial Semantics, Health Geography, Urban Geography, Urban Perception, and Remote Sensing. We propose a MLLM (OmniGeo) tailored to geospatial applications, capable of processing and analyzing heterogeneous data sources, including satellite imagery, geospatial metadata, and textual descriptions. By combining the strengths of natural language understanding and spatial reasoning, our model enhances the ability of instruction following and the accuracy of GeoAI systems. Results demonstrate that our model outperforms task-specific models and existing LLMs on diverse geospatial tasks, effectively addressing the multimodality nature while achieving competitive results on the zero-shot geospatial tasks. Our code will be released after publication.

Language models now constitute essential tools for improving efficiency for many professional tasks such as writing, coding, or learning. For this reason, it is imperative to identify inherent biases. In the field of Natural Language Processing, five sources of bias are well-identified: data, annotation, representation, models, and research design. This study focuses on biases related to geographical knowledge. We explore the connection between geography and language models by highlighting their tendency to misrepresent spatial information, thus leading to distortions in the representation of geographical distances. This study introduces four indicators to assess these distortions, by comparing geographical and semantic distances. Experiments are conducted from these four indicators with ten widely used language models. Results underscore the critical necessity of inspecting and rectifying spatial biases in language models to ensure accurate and equitable representations.

Multimodal large language models (MLLMs) have achieved remarkable progress in vision-language tasks, but they continue to struggle with spatial understanding. Existing spatial MLLMs often rely on explicit 3D inputs or architecture-specific modifications, and remain constrained by large-scale datasets or sparse supervision. To address these limitations, we introduce SpatialThinker, a 3D-aware MLLM trained with RL to integrate structured spatial grounding with multi-step reasoning. The model simulates human-like spatial perception by constructing a scene graph of task-relevant objects and spatial relations, and reasoning towards an answer via dense spatial rewards. SpatialThinker consists of two key contributions: (1) a data synthesis pipeline that generates STVQA-7K, a high-quality spatial VQA dataset, and (2) online RL with a multi-objective dense spatial reward enforcing spatial grounding. SpatialThinker-7B outperforms supervised fine-tuning and the sparse RL baseline on spatial understanding and real-world VQA benchmarks, nearly doubling the base-model gain compared to sparse RL, and surpassing GPT-4o. These results showcase the effectiveness of combining spatial supervision with reward-aligned reasoning in enabling robust 3D spatial understanding with limited data and advancing MLLMs towards human-level visual reasoning.

Geometric methods for solving open-world off-road navigation tasks, by learning occupancy and metric maps, provide good generalization but can be brittle in outdoor environments that violate their assumptions (e.g., tall grass). Learning-based methods can directly learn collision-free behavior from raw observations, but are difficult to integrate with standard geometry-based pipelines. This creates an unfortunate conflict -- either use learning and lose out on well-understood geometric navigational components, or do not use it, in favor of extensively hand-tuned geometry-based cost maps. In this work, we reject this dichotomy by designing the learning and non-learning-based components in a way such that they can be effectively combined in a self-supervised manner. Both components contribute to a planning criterion: the learned component contributes predicted traversability as rewards, while the geometric component contributes obstacle cost information. We instantiate and comparatively evaluate our system in both in-distribution and out-of-distribution environments, showing that this approach inherits complementary gains from the learned and geometric components and significantly outperforms either of them. Videos of our results are hosted at https://sites.google.com/view/hybrid-imitative-planning

Visual spatial description (VSD) aims to generate texts that describe the spatial relations of the given objects within images. Existing VSD work merely models the 2D geometrical vision features, thus inevitably falling prey to the problem of skewed spatial understanding of target objects. In this work, we investigate the incorporation of 3D scene features for VSD. With an external 3D scene extractor, we obtain the 3D objects and scene features for input images, based on which we construct a target object-centered 3D spatial scene graph (Go3D-S2G), such that we model the spatial semantics of target objects within the holistic 3D scenes. Besides, we propose a scene subgraph selecting mechanism, sampling topologically-diverse subgraphs from Go3D-S2G, where the diverse local structure features are navigated to yield spatially-diversified text generation. Experimental results on two VSD datasets demonstrate that our framework outperforms the baselines significantly, especially improving on the cases with complex visual spatial relations. Meanwhile, our method can produce more spatially-diversified generation. Code is available at https://github.com/zhaoyucs/VSD.

Unlocking spatial reasoning in Large Multimodal Models (LMMs) is crucial for enabling intelligent interaction with 3D environments. While prior efforts often rely on explicit 3D inputs or specialized model architectures, we ask: can LMMs reason about 3D space using only structured 2D representations derived from perception? We introduce Struct2D, a perception-guided prompting framework that combines bird's-eye-view (BEV) images with object marks and object-centric metadata, optionally incorporating egocentric keyframes when needed. Using Struct2D, we conduct an in-depth zero-shot analysis of closed-source LMMs (e.g., GPT-o3) and find that they exhibit surprisingly strong spatial reasoning abilities when provided with structured 2D inputs, effectively handling tasks such as relative direction estimation and route planning. Building on these insights, we construct Struct2D-Set, a large-scale instruction tuning dataset with 200K fine-grained QA pairs across eight spatial reasoning categories, generated automatically from 3D indoor scenes. We fine-tune an open-source LMM (Qwen2.5VL) on Struct2D-Set, achieving competitive performance on multiple benchmarks, including 3D question answering, dense captioning, and object grounding. Our approach demonstrates that structured 2D inputs can effectively bridge perception and language reasoning in LMMs-without requiring explicit 3D representations as input. We will release both our code and dataset to support future research.

Recent advances in multimodal large language models (MLLMs) have significantly enhanced their capabilities; however, their spatial perception abilities remain a notable limitation. To address this challenge, multimodal data synthesis offers a promising solution. Yet, ensuring that synthesized data adhere to spatial common sense is a non-trivial task. In this work, we introduce SKG2Data, a novel multimodal synthesis approach guided by spatial knowledge graphs, grounded in the concept of knowledge-to-data generation. SKG2Data automatically constructs a Spatial Knowledge Graph (SKG) to emulate human-like perception of spatial directions and distances, which is subsequently utilized to guide multimodal data synthesis. Extensive experiments demonstrate that data synthesized from diverse types of spatial knowledge, including direction and distance, not only enhance the spatial perception and reasoning abilities of MLLMs but also exhibit strong generalization capabilities. We hope that the idea of knowledge-based data synthesis can advance the development of spatial intelligence.

We present a central-peripheral vision-inspired framework (CVP), a simple yet effective multimodal model for spatial reasoning that draws inspiration from the two types of human visual fields -- central vision and peripheral vision. Existing approaches primarily rely on unstructured representations, such as point clouds, voxels, or patch features, and inject scene context implicitly via coordinate embeddings. However, this often results in limited spatial reasoning capabilities due to the lack of explicit, high-level structural understanding. To address this limitation, we introduce two complementary components into a Large Multimodal Model-based architecture: target-affinity token, analogous to central vision, that guides the model's attention toward query-relevant objects; and allocentric grid, akin to peripheral vision, that captures global scene context and spatial arrangements. These components work in tandem to enable structured, context-aware understanding of complex 3D environments. Experiments show that CVP achieves state-of-the-art performance across a range of 3D scene understanding benchmarks.

As deep learning technology advances and more urban spatial-temporal data accumulates, an increasing number of deep learning models are being proposed to solve urban spatial-temporal prediction problems. However, there are limitations in the existing field, including open-source data being in various formats and difficult to use, few papers making their code and data openly available, and open-source models often using different frameworks and platforms, making comparisons challenging. A standardized framework is urgently needed to implement and evaluate these methods. To address these issues, we propose LibCity, an open-source library that offers researchers a credible experimental tool and a convenient development framework. In this library, we have reproduced 65 spatial-temporal prediction models and collected 55 spatial-temporal datasets, allowing researchers to conduct comprehensive experiments conveniently. By enabling fair model comparisons, designing a unified data storage format, and simplifying the process of developing new models, LibCity is poised to make significant contributions to the spatial-temporal prediction field.

Spatial understanding is essential for Multimodal Large Language Models (MLLMs) to support perception, reasoning, and planning in embodied environments. Despite recent progress, existing studies reveal that MLLMs still struggle with spatial understanding. However, existing research lacks a comprehensive and systematic evaluation of these limitations, often restricted to isolated scenarios, such as single-view or video. In this work, we present a systematic analysis of spatial understanding from both data and architectural perspectives across three representative scenarios: single-view, multi-view, and video. We propose a benchmark named MulSeT (Multi-view Spatial Understanding Tasks), and design a series of experiments to analyze the spatial reasoning capabilities of MLLMs. From the data perspective, the performance of spatial understanding converges quickly as the training data increases, and the upper bound is relatively low, especially for tasks that require spatial imagination. This indicates that merely expanding training data is insufficient to achieve satisfactory performance. From the architectural perspective, we find that spatial understanding relies more heavily on the positional encoding within the visual encoder than within the language model, in both cascaded and native MLLMs. Moreover, we explore reasoning injection and envision future improvements through architectural design to optimize spatial understanding. These insights shed light on the limitations of current MLLMs and suggest new directions for improving spatial reasoning capabilities through data scaling and architectural tuning.

Goal representation affects the performance of Hierarchical Reinforcement Learning (HRL) algorithms by decomposing the complex learning problem into easier subtasks. Recent studies show that representations that preserve temporally abstract environment dynamics are successful in solving difficult problems and provide theoretical guarantees for optimality. These methods however cannot scale to tasks where environment dynamics increase in complexity i.e. the temporally abstract transition relations depend on larger number of variables. On the other hand, other efforts have tried to use spatial abstraction to mitigate the previous issues. Their limitations include scalability to high dimensional environments and dependency on prior knowledge. In this paper, we propose a novel three-layer HRL algorithm that introduces, at different levels of the hierarchy, both a spatial and a temporal goal abstraction. We provide a theoretical study of the regret bounds of the learned policies. We evaluate the approach on complex continuous control tasks, demonstrating the effectiveness of spatial and temporal abstractions learned by this approach.

Despite recent advances on multi-modal models, 3D spatial reasoning remains a challenging task for state-of-the-art open-source and proprietary models. Recent studies explore data-driven approaches and achieve enhanced spatial reasoning performance by fine-tuning models on 3D-related visual question-answering data. However, these methods typically perform spatial reasoning in an implicit manner and often fail on questions that are trivial to humans, even with long chain-of-thought reasoning. In this work, we introduce SpatialReasoner, a novel large vision-language model (LVLM) that addresses 3D spatial reasoning with explicit 3D representations shared between multiple stages--3D perception, computation, and reasoning. Explicit 3D representations provide a coherent interface that supports advanced 3D spatial reasoning and improves the generalization ability to novel question types. Furthermore, by analyzing the explicit 3D representations in multi-step reasoning traces of SpatialReasoner, we study the factual errors and identify key shortcomings of current LVLMs. Results show that our SpatialReasoner achieves improved performance on a variety of spatial reasoning benchmarks, outperforming Gemini 2.0 by 9.2% on 3DSRBench, and generalizes better when evaluating on novel 3D spatial reasoning questions. Our study bridges the 3D parsing capabilities of prior visual foundation models with the powerful reasoning abilities of large language models, opening new directions for 3D spatial reasoning.

Spatial understanding remains a weakness of Large Vision-Language Models (LVLMs). Existing supervised fine-tuning (SFT) and recent reinforcement learning with verifiable rewards (RLVR) pipelines depend on costly supervision, specialized tools, or constrained environments that limit scale. We introduce Spatial-SSRL, a self-supervised RL paradigm that derives verifiable signals directly from ordinary RGB or RGB-D images. Spatial-SSRL automatically formulates five pretext tasks that capture 2D and 3D spatial structure: shuffled patch reordering, flipped patch recognition, cropped patch inpainting, regional depth ordering, and relative 3D position prediction. These tasks provide ground-truth answers that are easy to verify and require no human or LVLM annotation. Training on our tasks substantially improves spatial reasoning while preserving general visual capabilities. On seven spatial understanding benchmarks in both image and video settings, Spatial-SSRL delivers average accuracy gains of 4.63% (3B) and 3.89% (7B) over the Qwen2.5-VL baselines. Our results show that simple, intrinsic supervision enables RLVR at scale and provides a practical route to stronger spatial intelligence in LVLMs.

This document presents the Center for Robot Assisted Search And Rescue - Uncrewed Aerial Systems - Disaster Response Overhead Inspection Dataset (CRASAR-U-DROIDs) for building damage assessment and spatial alignment collected from small uncrewed aerial systems (sUAS) geospatial imagery. This dataset is motivated by the increasing use of sUAS in disaster response and the lack of previous work in utilizing high-resolution geospatial sUAS imagery for machine learning and computer vision models, the lack of alignment with operational use cases, and with hopes of enabling further investigations between sUAS and satellite imagery. The CRASAR-U-DRIODs dataset consists of fifty-two (52) orthomosaics from ten (10) federally declared disasters (Hurricane Ian, Hurricane Ida, Hurricane Harvey, Hurricane Idalia, Hurricane Laura, Hurricane Michael, Musset Bayou Fire, Mayfield Tornado, Kilauea Eruption, and Champlain Towers Collapse) spanning 67.98 square kilometers (26.245 square miles), containing 21,716 building polygons and damage labels, and 7,880 adjustment annotations. The imagery was tiled and presented in conjunction with overlaid building polygons to a pool of 130 annotators who provided human judgments of damage according to the Joint Damage Scale. These annotations were then reviewed via a two-stage review process in which building polygon damage labels were first reviewed individually and then again by committee. Additionally, the building polygons have been aligned spatially to precisely overlap with the imagery to enable more performant machine learning models to be trained. It appears that CRASAR-U-DRIODs is the largest labeled dataset of sUAS orthomosaic imagery.

We study the impact on mechanisms for facility location of moving from one dimension to two (or more) dimensions and Euclidean or Manhattan distances. We consider three fundamental axiomatic properties: anonymity which is a basic fairness property, Pareto optimality which is one of the most important efficiency properties, and strategy proofness which ensures agents do not have an incentive to mis-report. We also consider how well such mechanisms can approximate the optimal welfare. Our results are somewhat negative. Moving from one dimension to two (or more) dimensions often makes these axiomatic properties more difficult to achieve. For example, with two facilities in Euclidean space or with just a single facility in Manhattan space, no mechanism is anonymous, Pareto optimal and strategy proof. By contrast, mechanisms on the line exist with all three properties.We also show that approximation ratios may increase when moving to two (or more) dimensions. All our impossibility results are minimal. If we drop one of the three axioms (anonymity, Pareto optimality or strategy proofness) multiple mechanisms satisfy the other two axioms.

Open-vocabulary 3D visual grounding aims to localize target objects based on free-form language queries, which is crucial for embodied AI applications such as autonomous navigation, robotics, and augmented reality. Learning 3D language fields through neural representations enables accurate understanding of 3D scenes from limited viewpoints and facilitates the localization of target objects in complex environments. However, existing language field methods struggle to accurately localize instances using spatial relations in language queries, such as ``the book on the chair.'' This limitation mainly arises from inadequate reasoning about spatial relations in both language queries and 3D scenes. In this work, we propose SpatialReasoner, a novel neural representation-based framework with large language model (LLM)-driven spatial reasoning that constructs a visual properties-enhanced hierarchical feature field for open-vocabulary 3D visual grounding. To enable spatial reasoning in language queries, SpatialReasoner fine-tunes an LLM to capture spatial relations and explicitly infer instructions for the target, anchor, and spatial relation. To enable spatial reasoning in 3D scenes, SpatialReasoner incorporates visual properties (opacity and color) to construct a hierarchical feature field. This field represents language and instance features using distilled CLIP features and masks extracted via the Segment Anything Model (SAM). The field is then queried using the inferred instructions in a hierarchical manner to localize the target 3D instance based on the spatial relation in the language query. Extensive experiments show that our framework can be seamlessly integrated into different neural representations, outperforming baseline models in 3D visual grounding while empowering their spatial reasoning capability.

Spatial intelligence spans a rich suite of abilities, including visualising and transforming shapes, mentally rotating objects, judging relational positions and containment, and estimating numerosity. However, it still remains a critical unresolved challenge for Multimodal Large Language Models (MLLMs).To fill this gap, we propose to treat Euclidean geometry problem-solving as a surrogate task. Specifically, we meticulously constructed a curated multimodal dataset, called Euclid30K, comprising approximately 30K plane and solid geometry problems. To enable the model to acquire and apply Euclidean principles from these geometry problems, we employed Group Relative Policy Optimization (GRPO) to finetune the Qwen2.5VL family and RoboBrain2.0 family, inspiring the models to identify shapes, count, and relate entities, and perform multi-step deductive reasoning using Euclidean principles. Our experiments demonstrate that the resulting models achieve substantial zero-shot gains across four spatial reasoning benchmarks (Super-CLEVR, Omni3DBench, VSI-Bench, and MindCube) without any task-specific adaptations. Notably, after training on the Euclid30K, the mean VSI-Bench accuracy of all evaluated models rose from 34.5% to 40.5%, improving by 5.5 percentage points. Among them, RoboBrain2.0-Euclid-7B achieves 49.6\% accuracy, surpassing the previous state-of-the-art model, Spatial-MLLM.To our knowledge, this is the first systematic study showing that geometry-centric fine-tuning can confer vision-language models with broadly transferable spatial skills. Code and Euclid30K dataset can be found in https://zgca-ai4edu.github.io/Euclids_Gift.

Capturing spatial relationships from visual inputs is a cornerstone of human-like general intelligence. Several previous studies have tried to enhance the spatial awareness of Vision-Language Models (VLMs) by adding extra expert encoders, which brings extra overhead and usually harms general capabilities. To enhance the spatial ability in general architectures, we introduce Visual Spatial Tuning (VST), a comprehensive framework to cultivate VLMs with human-like visuospatial abilities, from spatial perception to reasoning. We first attempt to enhance spatial perception in VLMs by constructing a large-scale dataset termed VST-P, which comprises 4.1 million samples spanning 19 skills across single views, multiple images, and videos. Then, we present VST-R, a curated dataset with 135K samples that instruct models to reason in space. In particular, we adopt a progressive training pipeline: supervised fine-tuning to build foundational spatial knowledge, followed by reinforcement learning to further improve spatial reasoning abilities. Without the side-effect to general capabilities, the proposed VST consistently achieves state-of-the-art results on several spatial benchmarks, including 34.8% on MMSI-Bench and 61.2% on VSIBench. It turns out that the Vision-Language-Action models can be significantly enhanced with the proposed spatial tuning paradigm, paving the way for more physically grounded AI.

Most existing spatial reasoning benchmarks focus on static or globally observable environments, failing to capture the challenges of long-horizon reasoning and memory utilization under partial observability and dynamic changes. We introduce two dynamic spatial benchmarks, locally observable maze navigation and match-2 elimination that systematically evaluate models' abilities in spatial understanding and adaptive planning when local perception, environment feedback, and global objectives are tightly coupled. Each action triggers structural changes in the environment, requiring continuous update of cognition and strategy. We further propose a subjective experience-based memory mechanism for cross-task experience transfer and validation. Experiments show that our benchmarks reveal key limitations of mainstream models in dynamic spatial reasoning and long-term memory, providing a comprehensive platform for future methodological advances. Our code and data are available at https://anonymous.4open.science/r/EvoEmpirBench-143C/.