Daily Papers

Geometry is a fundamental branch of mathematics and plays a crucial role in evaluating the reasoning capabilities of multimodal large language models (MLLMs). However, existing multimodal mathematics benchmarks mainly focus on plane geometry and largely ignore solid geometry, which requires spatial reasoning and is more challenging than plane geometry. To address this critical gap, we introduce SolidGeo, the first large-scale benchmark specifically designed to evaluate the performance of MLLMs on mathematical reasoning tasks in solid geometry. SolidGeo consists of 3,113 real-world K-12 and competition-level problems, each paired with visual context and annotated with difficulty levels and fine-grained solid geometry categories. Our benchmark covers a wide range of 3D reasoning subjects such as projection, unfolding, spatial measurement, and spatial vector, offering a rigorous testbed for assessing solid geometry. Through extensive experiments, we observe that MLLMs encounter substantial challenges in solid geometry math tasks, with a considerable performance gap relative to human capabilities on SolidGeo. Moreover, we analyze the performance, inference efficiency and error patterns of various models, offering insights into the solid geometric mathematical reasoning capabilities of MLLMs. We hope SolidGeo serves as a catalyst for advancing MLLMs toward deeper geometric reasoning and spatial intelligence.

Recent advancements in 2D multimodal large language models (MLLMs) have significantly improved performance in vision-language tasks. However, extending these capabilities to 3D environments remains a distinct challenge due to the complexity of spatial reasoning. Nevertheless, existing 3D benchmarks often lack fine-grained numerical reasoning task annotations, limiting MLLMs' ability to perform precise spatial measurements and complex numerical reasoning. To address this gap, we introduce NUMINA, the first Natural Understanding benchmark for Multi-dimensional Intelligence and Numerical reasoning Abilities to enhance multimodal indoor perceptual understanding. NUMINA features multi-scale annotations and various question-answer pairs, generated using NUMINA-Flow, an automated annotation pipeline that integrates LLM rewriting and rule-based self-verification. We evaluate the performance of various state-of-the-art LLMs on NUMINA following the Chat-Scene framework, demonstrating that current LLMs struggle with multimodal numerical reasoning, particularly in performing precise computations such as distance and volume estimation, highlighting the need for further advancements in 3D models. The dataset and source codes can be obtained from https://github.com/fengshun124/NUMINA.

Correlative computational microscopy is accelerating the mapping of dynamic biological systems by integrating morphological and molecular measurements across spatial scales, from organelles to entire organisms. Visualization, measurement, and prediction of interactions among the components of biological systems can be accelerated by generalist computational imaging frameworks that relax the trade-offs imposed by multiplex dynamic imaging. This work reports a generalist framework for wave optical imaging of the architectural order (waveOrder) among biomolecules for encoding and decoding multiple specimen properties from a minimal set of acquired channels, with or without fluorescent labels. waveOrder expresses material properties in terms of elegant physically motivated basis vectors directly interpretable as phase, absorption, birefringence, diattenuation, and fluorophore density; and it expresses image data in terms of directly measurable Stokes parameters. We report a corresponding multi-channel reconstruction algorithm to recover specimen properties in multiple contrast modes. With this framework, we implement multiple 3D computational microscopy methods, including quantitative phase imaging, quantitative label-free imaging with phase and polarization, and fluorescence deconvolution imaging, across scales ranging from organelles to whole zebrafish. These advances are available via an extensible open-source computational imaging library, waveOrder, and a napari plugin, recOrder.

Spatial transcriptomics enables simultaneous measurement of gene expression and tissue morphology, offering unprecedented insights into cellular organization and disease mechanisms. However, the field lacks comprehensive benchmarks for evaluating multimodal learning methods that leverage both histology images and gene expression data. Here, we present HESCAPE, a large-scale benchmark for cross-modal contrastive pretraining in spatial transcriptomics, built on a curated pan-organ dataset spanning 6 different gene panels and 54 donors. We systematically evaluated state-of-the-art image and gene expression encoders across multiple pretraining strategies and assessed their effectiveness on two downstream tasks: gene mutation classification and gene expression prediction. Our benchmark demonstrates that gene expression encoders are the primary determinant of strong representational alignment, and that gene models pretrained on spatial transcriptomics data outperform both those trained without spatial data and simple baseline approaches. However, downstream task evaluation reveals a striking contradiction: while contrastive pretraining consistently improves gene mutation classification performance, it degrades direct gene expression prediction compared to baseline encoders trained without cross-modal objectives. We identify batch effects as a key factor that interferes with effective cross-modal alignment. Our findings highlight the critical need for batch-robust multimodal learning approaches in spatial transcriptomics. To accelerate progress in this direction, we release HESCAPE, providing standardized datasets, evaluation protocols, and benchmarking tools for the community

New era has unlocked exciting possibilities for extending Large Language Models (LLMs) to tackle 3D vision-language tasks. However, most existing 3D multimodal LLMs (MLLMs) rely on compressing holistic 3D scene information or segmenting independent objects to perform these tasks, which limits their spatial awareness due to insufficient representation of the richness inherent in 3D scenes. To overcome these limitations, we propose Spatial 3D-LLM, a 3D MLLM specifically designed to enhance spatial awareness for 3D vision-language tasks by enriching the spatial embeddings of 3D scenes. Spatial 3D-LLM integrates an LLM backbone with a progressive spatial awareness scheme that progressively captures spatial information as the perception field expands, generating location-enriched 3D scene embeddings to serve as visual prompts. Furthermore, we introduce two novel tasks: 3D object distance measurement and 3D layout editing, and construct a 3D instruction dataset, MODEL, to evaluate the model's spatial awareness capabilities. Experimental results demonstrate that Spatial 3D-LLM achieves state-of-the-art performance across a wide range of 3D vision-language tasks, revealing the improvements stemmed from our progressive spatial awareness scheme of mining more profound spatial information. Our code is available at https://github.com/bjshuyuan/Spatial-3D-LLM.

Non-contact video-based physiological measurement has many applications in health care and human-computer interaction. Practical applications require measurements to be accurate even in the presence of large head rotations. We propose the first end-to-end system for video-based measurement of heart and breathing rate using a deep convolutional network. The system features a new motion representation based on a skin reflection model and a new attention mechanism using appearance information to guide motion estimation, both of which enable robust measurement under heterogeneous lighting and major motions. Our approach significantly outperforms all current state-of-the-art methods on both RGB and infrared video datasets. Furthermore, it allows spatial-temporal distributions of physiological signals to be visualized via the attention mechanism.

Despite impressive high-level video comprehension, multimodal language models struggle with spatial reasoning across time and space. While current spatial training approaches rely on real-world video data, obtaining diverse footage with precise spatial annotations remains a bottleneck. To alleviate this bottleneck, we present SIMS-V -- a systematic data-generation framework that leverages the privileged information of 3D simulators to create spatially-rich video training data for multimodal language models. Using this framework, we investigate which properties of simulated data drive effective real-world transfer through systematic ablations of question types, mixes, and scales. We identify a minimal set of three question categories (metric measurement, perspective-dependent reasoning, and temporal tracking) that prove most effective for developing transferable spatial intelligence, outperforming comprehensive coverage despite using fewer question types. These insights enable highly efficient training: our 7B-parameter video LLM fine-tuned on just 25K simulated examples outperforms the larger 72B baseline and achieves competitive performance with proprietary models on rigorous real-world spatial reasoning benchmarks. Our approach demonstrates robust generalization, maintaining performance on general video understanding while showing substantial improvements on embodied and real-world spatial tasks.

We introduce FloorplanQA, a diagnostic benchmark for evaluating spatial reasoning in large-language models (LLMs). FloorplanQA is grounded in structured representations of indoor scenes, such as (e.g., kitchens, living rooms, bedrooms, bathrooms, and others), encoded symbolically in JSON or XML layouts. The benchmark covers core spatial tasks, including distance measurement, visibility, path finding, and object placement within constrained spaces. Our results across a variety of frontier open-source and commercial LLMs reveal that while models may succeed in shallow queries, they often fail to respect physical constraints, preserve spatial coherence, though they remain mostly robust to small spatial perturbations. FloorplanQA uncovers a blind spot in today's LLMs: inconsistent reasoning about indoor layouts. We hope this benchmark inspires new work on language models that can accurately infer and manipulate spatial and geometric properties in practical settings.

Spatial tracing, as a fundamental embodied interaction ability for robots, is inherently challenging as it requires multi-step metric-grounded reasoning compounded with complex spatial referring and real-world metric measurement. However, existing methods struggle with this compositional task. To this end, we propose RoboTracer, a 3D-aware VLM that first achieves both 3D spatial referring and measuring via a universal spatial encoder and a regression-supervised decoder to enhance scale awareness during supervised fine-tuning (SFT). Moreover, RoboTracer advances multi-step metric-grounded reasoning via reinforcement fine-tuning (RFT) with metric-sensitive process rewards, supervising key intermediate perceptual cues to accurately generate spatial traces. To support SFT and RFT training, we introduce TraceSpatial, a large-scale dataset of 30M QA pairs, spanning outdoor/indoor/tabletop scenes and supporting complex reasoning processes (up to 9 steps). We further present TraceSpatial-Bench, a challenging benchmark filling the gap to evaluate spatial tracing. Experimental results show that RoboTracer surpasses baselines in spatial understanding, measuring, and referring, with an average success rate of 79.1%, and also achieves SOTA performance on TraceSpatial-Bench by a large margin, exceeding Gemini-2.5-Pro by 36% accuracy. Notably, RoboTracer can be integrated with various control policies to execute long-horizon, dynamic tasks across diverse robots (UR5, G1 humanoid) in cluttered real-world scenes.

Reading measurement instruments is effortless for humans and requires relatively little domain expertise, yet it remains surprisingly challenging for current vision-language models (VLMs) as we find in preliminary evaluation. In this work, we introduce MeasureBench, a benchmark on visual measurement reading covering both real-world and synthesized images of various types of measurements, along with an extensible pipeline for data synthesis. Our pipeline procedurally generates a specified type of gauge with controllable visual appearance, enabling scalable variation in key details such as pointers, scales, fonts, lighting, and clutter. Evaluation on popular proprietary and open-weight VLMs shows that even the strongest frontier VLMs struggle measurement reading in general. A consistent failure mode is indicator localization: models can read digits or labels but misidentify the key positions of pointers or alignments, leading to big numeric errors despite plausible textual reasoning. We have also conducted preliminary experiments with reinforcement learning over synthetic data, and find encouraging results on in-domain synthetic subset but less promising for real-world images. Our analysis highlights a fundamental limitation of current VLMs in fine-grained spatial grounding. We hope this resource can help future advances on visually grounded numeracy and precise spatial perception of VLMs, bridging the gap between recognizing numbers and measuring the world.

Existing state-of-the-art disparity estimation works mostly leverage the 4D concatenation volume and construct a very deep 3D convolution neural network (CNN) for disparity regression, which is inefficient due to the high memory consumption and slow inference speed. In this paper, we propose a network named EDNet for efficient disparity estimation. Firstly, we construct a combined volume which incorporates contextual information from the squeezed concatenation volume and feature similarity measurement from the correlation volume. The combined volume can be next aggregated by 2D convolutions which are faster and require less memory than 3D convolutions. Secondly, we propose an attention-based spatial residual module to generate attention-aware residual features. The attention mechanism is applied to provide intuitive spatial evidence about inaccurate regions with the help of error maps at multiple scales and thus improve the residual learning efficiency. Extensive experiments on the Scene Flow and KITTI datasets show that EDNet outperforms the previous 3D CNN based works and achieves state-of-the-art performance with significantly faster speed and less memory consumption.

The ability to measure and track the speed and trajectory of a community's post-disaster recovery is essential to inform resource allocation and prioritization. The current survey-based approaches to examining community recovery, however, have significant lags and put the burden of data collection on affected people. Also, the existing literature lacks quantitative measures for important milestones to inform the assessment of recovery trajectory. Recognizing these gaps, this study uses location-based data related to visitation patterns and credit card transactions to specify critical recovery milestones related to population activity recovery. Using data from 2017 Hurricane Harvey in Harris County (Texas), the study specifies four critical post-disaster recovery milestones and calculates quantitative measurements of the length of time between the end of a hazard event and when the spatial areas (census tracts) reached these milestones based on fluctuations in visits to essential and non-essential facilities, and essential and non-essential credit card transactions. Accordingly, an integrated recovery metric is created for an overall measurement of each spatial area's recovery progression. Exploratory statistical analyses were conducted to examine whether variations in community recovery progression in achieving the critical milestones is correlated to its flood status, socioeconomic characteristics, and demographic composition. Finally, the extent of spatial inequality is examined. The results show the presence of moderate spatial inequality in population activity recovery in Hurricane Harvey, based upon which the inequality of recovery is measured. Results of this study can benefit post-disaster recovery resource allocation as well as improve community resilience towards future natural hazards.

Urban transformations have profound societal impact on both individuals and communities at large. Accurately assessing these shifts is essential for understanding their underlying causes and ensuring sustainable urban planning. Traditional measurements often encounter constraints in spatial and temporal granularity, failing to capture real-time physical changes. While street view imagery, capturing the heartbeat of urban spaces from a pedestrian point of view, can add as a high-definition, up-to-date, and on-the-ground visual proxy of urban change. We curate the largest street view time series dataset to date, and propose an end-to-end change detection model to effectively capture physical alterations in the built environment at scale. We demonstrate the effectiveness of our proposed method by benchmark comparisons with previous literature and implementing it at the city-wide level. Our approach has the potential to supplement existing dataset and serve as a fine-grained and accurate assessment of urban change.

Spectro-astrometry is used to investigate the low velocity component (LVC) of the optical forbidden emission from the T Tauri stars RU Lupi and AS 205 N. Both stars also have high velocity forbidden emission (HVC) which is tracing a jet. For AS 205 N, analysis reveals a complicated outflow system. For RU Lupi, the [O I] 6300 and [S II] 6716, 6731 LV narrow component (NC) is offset along the same position angle (PA) as the HVC but with a different velocity gradient than the jet, in that displacement from the stellar position along the rotation axis is decreasing with increasing velocity. From the LVC NC PA and velocity gradient, it is inferred that the NC is tracing a wide angled MHD disk wind. A photoevaporative wind is ruled out. This is supported by a comparison with a previous spectro-astrometric study of the CO fundamental line. The decrease in offset with increasing velocity is interpreted as tracing an increase in the height of the wind with increasing disk radius. This is one of the first measurements of the spatial extent of the forbidden emission line LVC NC (~ 40 au, 8 au for RU~Lupi in the [S II] 6731 and [O I] 6300 lines) and the first direct confirmation that the LVC narrow component can trace an MHD disk wind.

Air pollution constitutes a global problem of paramount importance that affects not only human health, but also the environment. The existence of spatial and temporal data regarding the concentrations of pollutants is crucial for performing air pollution studies and monitor emissions. However, although observation data presents great temporal coverage, the number of stations is very limited and they are usually built in more populated areas. The main objective of this work is to create models capable of inferring pollutant concentrations in locations where no observation data exists. A machine learning model, more specifically the random forest model, was developed for predicting concentrations in the Iberian Peninsula in 2019 for five selected pollutants: NO_2, O_3 SO_2, PM10, and PM2.5. Model features include satellite measurements, meteorological variables, land use classification, temporal variables (month, day of year), and spatial variables (latitude, longitude, altitude). The models were evaluated using various methods, including station 10-fold cross-validation, in which in each fold observations from 10\% of the stations are used as testing data and the rest as training data. The R^2, RMSE and mean bias were determined for each model. The NO_2 and O_3 models presented good values of R^2, 0.5524 and 0.7462, respectively. However, the SO_2, PM10, and PM2.5 models performed very poorly in this regard, with R^2 values of -0.0231, 0.3722, and 0.3303, respectively. All models slightly overestimated the ground concentrations, except the O_3 model. All models presented acceptable cross-validation RMSE, except the O_3 and PM10 models where the mean value was a little higher (12.5934 mu g/m^3 and 10.4737 mu g/m^3, respectively).

We present RadarGen, a diffusion model for synthesizing realistic automotive radar point clouds from multi-view camera imagery. RadarGen adapts efficient image-latent diffusion to the radar domain by representing radar measurements in bird's-eye-view form that encodes spatial structure together with radar cross section (RCS) and Doppler attributes. A lightweight recovery step reconstructs point clouds from the generated maps. To better align generation with the visual scene, RadarGen incorporates BEV-aligned depth, semantic, and motion cues extracted from pretrained foundation models, which guide the stochastic generation process toward physically plausible radar patterns. Conditioning on images makes the approach broadly compatible, in principle, with existing visual datasets and simulation frameworks, offering a scalable direction for multimodal generative simulation. Evaluations on large-scale driving data show that RadarGen captures characteristic radar measurement distributions and reduces the gap to perception models trained on real data, marking a step toward unified generative simulation across sensing modalities.

Personalized Head-Related Transfer Functions (HRTFs) are starting to be introduced in many commercial immersive audio applications and are crucial for realistic spatial audio rendering. However, one of the main hesitations regarding their introduction is that creating personalized HRTFs is impractical at scale due to the complexities of the HRTF measurement process. To mitigate this drawback, HRTF spatial upsampling has been proposed with the aim of reducing measurements required. While prior work has seen success with different machine learning (ML) approaches, these models often struggle with long-range spatial consistency and generalization at high upsampling factors. In this paper, we propose a novel transformer-based architecture for HRTF upsampling, leveraging the attention mechanism to better capture spatial correlations across the HRTF sphere. Working in the spherical harmonic (SH) domain, our model learns to reconstruct high-resolution HRTFs from sparse input measurements with significantly improved accuracy. To enhance spatial coherence, we introduce a neighbor dissimilarity loss that promotes magnitude smoothness, yielding more realistic upsampling. We evaluate our method using both perceptual localization models and objective spectral distortion metrics. Experiments show that our model surpasses leading methods by a substantial margin in generating realistic, high-fidelity HRTFs.

Ambient air pollution remains a critical issue in the United Kingdom, where data on air pollution concentrations form the foundation for interventions aimed at improving air quality. However, the current air pollution monitoring station network in the UK is characterized by spatial sparsity, heterogeneous placement, and frequent temporal data gaps, often due to issues such as power outages. We introduce a scalable data-driven supervised machine learning model framework designed to address temporal and spatial data gaps by filling missing measurements. This approach provides a comprehensive dataset for England throughout 2018 at a 1kmx1km hourly resolution. Leveraging machine learning techniques and real-world data from the sparsely distributed monitoring stations, we generate 355,827 synthetic monitoring stations across the study area, yielding data valued at approximately \pounds70 billion. Validation was conducted to assess the model's performance in forecasting, estimating missing locations, and capturing peak concentrations. The resulting dataset is of particular interest to a diverse range of stakeholders engaged in downstream assessments supported by outdoor air pollution concentration data for NO2, O3, PM10, PM2.5, and SO2. This resource empowers stakeholders to conduct studies at a higher resolution than was previously possible.

Unprecedented volumes of Earth observation data are continually collected around the world, but high-quality labels remain scarce given the effort required to make physical measurements and observations. This has led to considerable investment in bespoke modeling efforts translating sparse labels into maps. Here we introduce AlphaEarth Foundations, an embedding field model yielding a highly general, geospatial representation that assimilates spatial, temporal, and measurement contexts across multiple sources, enabling accurate and efficient production of maps and monitoring systems from local to global scales. The embeddings generated by AlphaEarth Foundations are the only to consistently outperform all previous featurization approaches tested on a diverse set of mapping evaluations without re-training. We will release a dataset of global, annual, analysis-ready embedding field layers from 2017 through 2024.

We present Spatial Region 3D (SR-3D) aware vision-language model that connects single-view 2D images and multi-view 3D data through a shared visual token space. SR-3D supports flexible region prompting, allowing users to annotate regions with bounding boxes, segmentation masks on any frame, or directly in 3D, without the need for exhaustive multi-frame labeling. We achieve this by enriching 2D visual features with 3D positional embeddings, which allows the 3D model to draw upon strong 2D priors for more accurate spatial reasoning across frames, even when objects of interest do not co-occur within the same view. Extensive experiments on both general 2D vision language and specialized 3D spatial benchmarks demonstrate that SR-3D achieves state-of-the-art performance, underscoring its effectiveness for unifying 2D and 3D representation space on scene understanding. Moreover, we observe applicability to in-the-wild videos without sensory 3D inputs or ground-truth 3D annotations, where SR-3D accurately infers spatial relationships and metric measurements.

The modeling of industrial scenes is essential for simulations in industrial manufacturing. While large language models (LLMs) have shown significant progress in generating general 3D scenes from textual descriptions, generating industrial scenes with LLMs poses a unique challenge due to their demand for precise measurements and positioning, requiring complex planning over spatial arrangement. To address this challenge, we introduce SceneGenAgent, an LLM-based agent for generating industrial scenes through C# code. SceneGenAgent ensures precise layout planning through a structured and calculable format, layout verification, and iterative refinement to meet the quantitative requirements of industrial scenarios. Experiment results demonstrate that LLMs powered by SceneGenAgent exceed their original performance, reaching up to 81.0% success rate in real-world industrial scene generation tasks and effectively meeting most scene generation requirements. To further enhance accessibility, we construct SceneInstruct, a dataset designed for fine-tuning open-source LLMs to integrate into SceneGenAgent. Experiments show that fine-tuning open-source LLMs on SceneInstruct yields significant performance improvements, with Llama3.1-70B approaching the capabilities of GPT-4o. Our code and data are available at https://github.com/THUDM/SceneGenAgent .

Recent advances in the theory of Neural Operators (NOs) have enabled fast and accurate computation of the solutions to complex systems described by partial differential equations (PDEs). Despite their great success, current NO-based solutions face important challenges when dealing with spatio-temporal PDEs over long time scales. Specifically, the current theory of NOs does not present a systematic framework to perform data assimilation and efficiently correct the evolution of PDE solutions over time based on sparsely sampled noisy measurements. In this paper, we propose a learning-based state-space approach to compute the solution operators to infinite-dimensional semilinear PDEs. Exploiting the structure of semilinear PDEs and the theory of nonlinear observers in function spaces, we develop a flexible recursive method that allows for both prediction and data assimilation by combining prediction and correction operations. The proposed framework is capable of producing fast and accurate predictions over long time horizons, dealing with irregularly sampled noisy measurements to correct the solution, and benefits from the decoupling between the spatial and temporal dynamics of this class of PDEs. We show through experiments on the Kuramoto-Sivashinsky, Navier-Stokes and Korteweg-de Vries equations that the proposed model is robust to noise and can leverage arbitrary amounts of measurements to correct its prediction over a long time horizon with little computational overhead.

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.

We identify the task of measuring data to quantitatively characterize the composition of machine learning data and datasets. Similar to an object's height, width, and volume, data measurements quantify different attributes of data along common dimensions that support comparison. Several lines of research have proposed what we refer to as measurements, with differing terminology; we bring some of this work together, particularly in fields of computer vision and language, and build from it to motivate measuring data as a critical component of responsible AI development. Measuring data aids in systematically building and analyzing machine learning (ML) data towards specific goals and gaining better control of what modern ML systems will learn. We conclude with a discussion of the many avenues of future work, the limitations of data measurements, and how to leverage these measurement approaches in research and practice.

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.

Flying Triangulation sensors enable a free-hand and motion-robust 3D data acquisition of complex shaped objects. The measurement principle is based on a multi-line light-sectioning approach and uses sophisticated algorithms for real-time registration (S. Ettl et al., Appl. Opt. 51 (2012) 281-289). As "single-shot principle", light sectioning enables the option to get surface data from one single camera exposure. But there is a drawback: A pixel-dense measurement is not possible because of fundamental information-theoretical reasons. By "pixel-dense" we understand that each pixel displays individually measured distance information, neither interpolated from its neighbour pixels nor using lateral context information. Hence, for monomodal single-shot principles, the 3D data generated from one 2D raw image display a significantly lower space-bandwidth than the camera permits. This is the price one must pay for motion robustness. Currently, our sensors project about 10 lines (each with 1000 pixels), reaching an considerable lower data efficiency than theoretically possible for a single-shot sensor. Our aim is to push Flying Triangulation to its information-theoretical limits. Therefore, the line density as well as the measurement depth needs to be significantly increased. This causes serious indexing ambiguities. On the road to a single-shot 3D movie camera, we are working on solutions to overcome the problem of false line indexing by utilizing yet unexploited information. We will present several approaches and will discuss profound information-theoretical questions about the information efficiency of 3D sensors.

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.

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.

Geolocating images of a ground-level scene entails estimating the location on Earth where the picture was taken, in absence of GPS or other location metadata. Typically, methods are evaluated by measuring the Great Circle Distance (GCD) between a predicted location and ground truth. However, this measurement is limited because it only evaluates a single point, not estimates of regions or score heatmaps. This is especially important in applications to rural, wilderness and under-sampled areas, where finding the exact location may not be possible, and when used in aggregate systems that progressively narrow down locations. In this paper, we introduce a novel metric, Recall vs Area (RvA), which measures the accuracy of estimated distributions of locations. RvA treats image geolocation results similarly to document retrieval, measuring recall as a function of area: For a ranked list of (possibly non-contiguous) predicted regions, we measure the accumulated area required for the region to contain the ground truth coordinate. This produces a curve similar to a precision-recall curve, where "precision" is replaced by square kilometers area, allowing evaluation of performance for different downstream search area budgets. Following directly from this view of the problem, we then examine a simple ensembling approach to global-scale image geolocation, which incorporates information from multiple sources to help address domain shift, and can readily incorporate multiple models, attribute predictors, and data sources. We study its effectiveness by combining the geolocation models GeoEstimation and the current SOTA GeoCLIP, with attribute predictors based on ORNL LandScan and ESA-CCI Land Cover. We find significant improvements in image geolocation for areas that are under-represented in the training set, particularly non-urban areas, on both Im2GPS3k and Street View images.

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.

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.

Reconstructing medical images from partial measurements is an important inverse problem in Computed Tomography (CT) and Magnetic Resonance Imaging (MRI). Existing solutions based on machine learning typically train a model to directly map measurements to medical images, leveraging a training dataset of paired images and measurements. These measurements are typically synthesized from images using a fixed physical model of the measurement process, which hinders the generalization capability of models to unknown measurement processes. To address this issue, we propose a fully unsupervised technique for inverse problem solving, leveraging the recently introduced score-based generative models. Specifically, we first train a score-based generative model on medical images to capture their prior distribution. Given measurements and a physical model of the measurement process at test time, we introduce a sampling method to reconstruct an image consistent with both the prior and the observed measurements. Our method does not assume a fixed measurement process during training, and can thus be flexibly adapted to different measurement processes at test time. Empirically, we observe comparable or better performance to supervised learning techniques in several medical imaging tasks in CT and MRI, while demonstrating significantly better generalization to unknown measurement processes.

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/

Reconstructing 4D spatial intelligence from visual observations has long been a central yet challenging task in computer vision, with broad real-world applications. These range from entertainment domains like movies, where the focus is often on reconstructing fundamental visual elements, to embodied AI, which emphasizes interaction modeling and physical realism. Fueled by rapid advances in 3D representations and deep learning architectures, the field has evolved quickly, outpacing the scope of previous surveys. Additionally, existing surveys rarely offer a comprehensive analysis of the hierarchical structure of 4D scene reconstruction. To address this gap, we present a new perspective that organizes existing methods into five progressive levels of 4D spatial intelligence: (1) Level 1 -- reconstruction of low-level 3D attributes (e.g., depth, pose, and point maps); (2) Level 2 -- reconstruction of 3D scene components (e.g., objects, humans, structures); (3) Level 3 -- reconstruction of 4D dynamic scenes; (4) Level 4 -- modeling of interactions among scene components; and (5) Level 5 -- incorporation of physical laws and constraints. We conclude the survey by discussing the key challenges at each level and highlighting promising directions for advancing toward even richer levels of 4D spatial intelligence. To track ongoing developments, we maintain an up-to-date project page: https://github.com/yukangcao/Awesome-4D-Spatial-Intelligence.

With the rapid development of spatial audio technologies today, applications in AR, VR, and other scenarios have garnered extensive attention. Unlike traditional mono sound, spatial audio offers a more realistic and immersive auditory experience. Despite notable progress in the field, there remains a lack of comprehensive surveys that systematically organize and analyze these methods and their underlying technologies. In this paper, we provide a comprehensive overview of spatial audio and systematically review recent literature in the area. To address this, we chronologically outlining existing work related to spatial audio and categorize these studies based on input-output representations, as well as generation and understanding tasks, thereby summarizing various research aspects of spatial audio. In addition, we review related datasets, evaluation metrics, and benchmarks, offering insights from both training and evaluation perspectives. Related materials are available at https://github.com/dieKarotte/ASAudio.

Humans can directly imagine and manipulate visual images in their minds, a capability known as spatial visualization. While multi-modal Large Language Models (MLLMs) support imagination-based reasoning, spatial visualization remains insufficiently evaluated, typically embedded within broader mathematical and logical assessments. Existing evaluations often rely on IQ tests or math competitions that may overlap with training data, compromising assessment reliability. To this end, we introduce SpatialViz-Bench, a comprehensive multi-modal benchmark for spatial visualization with 12 tasks across 4 sub-abilities, comprising 1,180 automatically generated problems. Our evaluation of 33 state-of-the-art MLLMs not only reveals wide performance variations and demonstrates the benchmark's strong discriminative power, but also uncovers counter-intuitive findings: models exhibit unexpected behaviors by showing difficulty perception that misaligns with human intuition, displaying dramatic 2D-to-3D performance cliffs, and defaulting to formula derivation despite spatial tasks requiring visualization alone. SpatialVizBench empirically demonstrates that state-of-the-art MLLMs continue to exhibit deficiencies in spatial visualization tasks, thereby addressing a significant lacuna in the field. The benchmark is publicly available.

Given a stationary state-space model that relates a sequence of hidden states and corresponding measurements or observations, Bayesian filtering provides a principled statistical framework for inferring the posterior distribution of the current state given all measurements up to the present time. For example, the Apollo lunar module implemented a Kalman filter to infer its location from a sequence of earth-based radar measurements and land safely on the moon. To perform Bayesian filtering, we require a measurement model that describes the conditional distribution of each observation given state. The Kalman filter takes this measurement model to be linear, Gaussian. Here we show how a nonlinear, Gaussian approximation to the distribution of state given observation can be used in conjunction with Bayes' rule to build a nonlinear, non-Gaussian measurement model. The resulting approach, called the Discriminative Kalman Filter (DKF), retains fast closed-form updates for the posterior. We argue there are many cases where the distribution of state given measurement is better-approximated as Gaussian, especially when the dimensionality of measurements far exceeds that of states and the Bernstein-von Mises theorem applies. Online neural decoding for brain-computer interfaces provides a motivating example, where filtering incorporates increasingly detailed measurements of neural activity to provide users control over external devices. Within the BrainGate2 clinical trial, the DKF successfully enabled three volunteers with quadriplegia to control an on-screen cursor in real-time using mental imagery alone. Participant "T9" used the DKF to type out messages on a tablet PC.

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.

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.

Multimodal large language models (MLLMs) have achieved impressive success in question-answering tasks, yet their capabilities for spatial understanding are less explored. This work investigates a critical question: do existing MLLMs possess 3D spatial perception and understanding abilities? Concretely, we make the following contributions in this paper: (i) we introduce VGBench, a benchmark specifically designed to assess MLLMs for visual geometry perception, e.g., camera pose and motion estimation; (ii) we propose SpatialScore, the most comprehensive and diverse multimodal spatial understanding benchmark to date, integrating VGBench with relevant data from the other 11 existing datasets. This benchmark comprises 28K samples across various spatial understanding tasks, modalities, and QA formats, along with a carefully curated challenging subset, SpatialScore-Hard; (iii) we develop SpatialAgent, a novel multi-agent system incorporating 9 specialized tools for spatial understanding, supporting both Plan-Execute and ReAct reasoning paradigms; (iv) we conduct extensive evaluations to reveal persistent challenges in spatial reasoning while demonstrating the effectiveness of SpatialAgent. We believe SpatialScore will offer valuable insights and serve as a rigorous benchmark for the next evolution of MLLMs.

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

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.

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.

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.

Reasoning about spatial audio with large language models requires a spatial audio encoder as an acoustic front-end to obtain audio embeddings for further processing. Such an encoder needs to capture all information required to detect the type of sound events, as well as the direction and distance of their corresponding sources. Accomplishing this with a single audio encoder is demanding as the information required for each of these tasks is mostly independent of each other. As a result, the performance obtained with a single encoder is often worse than when using task-specific audio encoders. In this work, we present DSpAST, a novel audio encoder based on SpatialAST that learns disentangled representations of spatial audio while having only 0.2% additional parameters. Experiments on SpatialSoundQA with the spatial audio reasoning system BAT demonstrate that DSpAST significantly outperforms SpatialAST.

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.

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.

In a recent paper Juodis and Reese (2022) (JR) show that the application of the CD test proposed by Pesaran (2004) to residuals from panels with latent factors results in over-rejection. They propose a randomized test statistic to correct for over-rejection, and add a screening component to achieve power. This paper considers the same problem but from a different perspective, and shows that the standard CD test remains valid if the latent factors are weak in the sense the strength is less than half. In the case where latent factors are strong, we propose a bias-corrected version, CD*, which is shown to be asymptotically standard normal under the null of error cross-sectional independence and have power against network type alternatives. This result is shown to hold for pure latent factor models as well as for panel regression models with latent factors. The case where the errors are serially correlated is also considered. Small sample properties of the CD* test are investigated by Monte Carlo experiments and are shown to have the correct size for strong and weak factors as well as for Gaussian and non-Gaussian errors. In contrast, it is found that JR's test tends to over-reject in the case of panels with non-Gaussian errors, and has low power against spatial network alternatives. In an empirical application, using the CD* test, it is shown that there remains spatial error dependence in a panel data model for real house price changes across 377 Metropolitan Statistical Areas in the U.S., even after the effects of latent factors are filtered out.

Earth observation data such as satellite imagery can, when combined with machine learning, have profound impacts on our understanding of the geography of poverty through the prediction of living conditions, especially where government-derived economic indicators are either unavailable or potentially untrustworthy. Recent work has progressed in using EO data not only to predict spatial economic outcomes, but also to explore cause and effect, an understanding which is critical for downstream policy analysis. In this review, we first document the growth of interest in EO-ML analyses in the causal space. We then trace the relationship between spatial statistics and EO-ML methods before discussing the four ways in which EO data has been used in causal ML pipelines -- (1.) poverty outcome imputation for downstream causal analysis, (2.) EO image deconfounding, (3.) EO-based treatment effect heterogeneity, and (4.) EO-based transportability analysis. We conclude by providing a workflow for how researchers can incorporate EO data in causal ML analysis going forward.

End-to-end learning of robot control policies, structured as neural networks, has emerged as a promising approach to robotic manipulation. To complete many common tasks, relevant objects are required to pass in and out of a robot's field of view. In these settings, spatial memory - the ability to remember the spatial composition of the scene - is an important competency. However, building such mechanisms into robot learning systems remains an open research problem. We introduce mindmap (Spatial Memory in Deep Feature Maps for 3D Action Policies), a 3D diffusion policy that generates robot trajectories based on a semantic 3D reconstruction of the environment. We show in simulation experiments that our approach is effective at solving tasks where state-of-the-art approaches without memory mechanisms struggle. We release our reconstruction system, training code, and evaluation tasks to spur research in this direction.

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.

Significant progress has been made in spatial intelligence, spanning both spatial reconstruction and world exploration. However, the scalability and real-world fidelity of current models remain severely constrained by the scarcity of large-scale, high-quality training data. While several datasets provide camera pose information, they are typically limited in scale, diversity, and annotation richness, particularly for real-world dynamic scenes with ground-truth camera motion. To this end, we collect SpatialVID, a dataset consists of a large corpus of in-the-wild videos with diverse scenes, camera movements and dense 3D annotations such as per-frame camera poses, depth, and motion instructions. Specifically, we collect more than 21,000 hours of raw video, and process them into 2.7 million clips through a hierarchical filtering pipeline, totaling 7,089 hours of dynamic content. A subsequent annotation pipeline enriches these clips with detailed spatial and semantic information, including camera poses, depth maps, dynamic masks, structured captions, and serialized motion instructions. Analysis of SpatialVID's data statistics reveals a richness and diversity that directly foster improved model generalization and performance, establishing it as a key asset for the video and 3D vision research community.

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/.

Computer-aided design (CAD) significantly enhances the efficiency, accuracy, and innovation of design processes by enabling precise 2D and 3D modeling, extensive analysis, and optimization. Existing methods for creating CAD models rely on latent vectors or point clouds, which are difficult to obtain and costly to store. Recent advances in Multimodal Large Language Models (MLLMs) have inspired researchers to use natural language instructions and images for CAD model construction. However, these models still struggle with inferring accurate 3D spatial location and orientation, leading to inaccuracies in determining the spatial 3D starting points and extrusion directions for constructing geometries. This work introduces CAD-GPT, a CAD synthesis method with spatial reasoning-enhanced MLLM that takes either a single image or a textual description as input. To achieve precise spatial inference, our approach introduces a 3D Modeling Spatial Mechanism. This method maps 3D spatial positions and 3D sketch plane rotation angles into a 1D linguistic feature space using a specialized spatial unfolding mechanism, while discretizing 2D sketch coordinates into an appropriate planar space to enable precise determination of spatial starting position, sketch orientation, and 2D sketch coordinate translations. Extensive experiments demonstrate that CAD-GPT consistently outperforms existing state-of-the-art methods in CAD model synthesis, both quantitatively and qualitatively.

Humans rely on multisensory integration to perceive spatial environments, where auditory cues enable sound source localization in three-dimensional space. Despite the critical role of spatial audio in immersive technologies such as VR/AR, most existing multimodal datasets provide only monaural audio, which limits the development of spatial audio generation and understanding. To address these challenges, we introduce MRSAudio, a large-scale multimodal spatial audio dataset designed to advance research in spatial audio understanding and generation. MRSAudio spans four distinct components: MRSLife, MRSSpeech, MRSMusic, and MRSSing, covering diverse real-world scenarios. The dataset includes synchronized binaural and ambisonic audio, exocentric and egocentric video, motion trajectories, and fine-grained annotations such as transcripts, phoneme boundaries, lyrics, scores, and prompts. To demonstrate the utility and versatility of MRSAudio, we establish five foundational tasks: audio spatialization, and spatial text to speech, spatial singing voice synthesis, spatial music generation and sound event localization and detection. Results show that MRSAudio enables high-quality spatial modeling and supports a broad range of spatial audio research. Demos and dataset access are available at https://mrsaudio.github.io.

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.

We present LASER, an image-based Monte Carlo Localization (MCL) framework for 2D floor maps. LASER introduces the concept of latent space rendering, where 2D pose hypotheses on the floor map are directly rendered into a geometrically-structured latent space by aggregating viewing ray features. Through a tightly coupled rendering codebook scheme, the viewing ray features are dynamically determined at rendering-time based on their geometries (i.e. length, incident-angle), endowing our representation with view-dependent fine-grain variability. Our codebook scheme effectively disentangles feature encoding from rendering, allowing the latent space rendering to run at speeds above 10KHz. Moreover, through metric learning, our geometrically-structured latent space is common to both pose hypotheses and query images with arbitrary field of views. As a result, LASER achieves state-of-the-art performance on large-scale indoor localization datasets (i.e. ZInD and Structured3D) for both panorama and perspective image queries, while significantly outperforming existing learning-based methods in speed.

Spatial intelligence is essential for multimodal large language models (MLLMs) operating in the complex physical world. Existing benchmarks, however, probe only single-image relations and thus fail to assess the multi-image spatial reasoning that real-world deployments demand. We introduce MMSI-Bench, a VQA benchmark dedicated to multi-image spatial intelligence. Six 3D-vision researchers spent more than 300 hours meticulously crafting 1,000 challenging, unambiguous multiple-choice questions from over 120,000 images, each paired with carefully designed distractors and a step-by-step reasoning process. We conduct extensive experiments and thoroughly evaluate 34 open-source and proprietary MLLMs, observing a wide gap: the strongest open-source model attains roughly 30% accuracy and OpenAI's o3 reasoning model reaches 40%, while humans score 97%. These results underscore the challenging nature of MMSI-Bench and the substantial headroom for future research. Leveraging the annotated reasoning processes, we also provide an automated error analysis pipeline that diagnoses four dominant failure modes, including (1) grounding errors, (2) overlap-matching and scene-reconstruction errors, (3) situation-transformation reasoning errors, and (4) spatial-logic errors, offering valuable insights for advancing multi-image spatial intelligence. Project page: https://runsenxu.com/projects/MMSI_Bench .

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.

Imitation learning method has shown immense promise for robotic manipulation, yet its practical deployment is fundamentally constrained by the data scarcity. Despite prior work on collecting large-scale datasets, there still remains a significant gap to robust spatial generalization. We identify a key limitation: individual trajectories, regardless of their length, are typically collected from a single, static spatial configuration of the environment. This includes fixed object and target spatial positions as well as unchanging camera viewpoints, which significantly restricts the diversity of spatial information available for learning. To address this critical bottleneck in data efficiency, we propose MOtion-Based Variability Enhancement (MOVE), a simple yet effective data collection paradigm that enables the acquisition of richer spatial information from dynamic demonstrations. Our core contribution is an augmentation strategy that injects motion into any movable objects within the environment for each demonstration. This process implicitly generates a dense and diverse set of spatial configurations within a single trajectory. We conduct extensive experiments in both simulation and real-world environments to validate our approach. For example, in simulation tasks requiring strong spatial generalization, MOVE achieves an average success rate of 39.1\%, a 76.1\% relative improvement over the static data collection paradigm (22.2\%), and yields up to 2--5times gains in data efficiency on certain tasks. Our code is available at https://github.com/lucywang720/MOVE.

While vision language models (VLMs) excel in 2D semantic visual understanding, their ability to quantitatively reason about 3D spatial relationships remains under-explored, due to the deficiency of 2D images' spatial representation ability. In this paper, we analyze the problem hindering VLMs' spatial understanding abilities and propose SD-VLM, a novel framework that significantly enhances fundamental spatial perception abilities of VLMs through two key contributions: (1) propose Massive Spatial Measuring and Understanding (MSMU) dataset with precise spatial annotations, and (2) introduce a simple depth positional encoding method strengthening VLMs' spatial awareness. MSMU dataset covers massive quantitative spatial tasks with 700K QA pairs, 2.5M physical numerical annotations, and 10K chain-of-thought augmented samples. We have trained SD-VLM, a strong generalist VLM which shows superior quantitative spatial measuring and understanding capability. SD-VLM not only achieves state-of-the-art performance on our proposed MSMU-Bench, but also shows spatial generalization abilities on other spatial understanding benchmarks including Q-Spatial and SpatialRGPT-Bench. Extensive experiments demonstrate that SD-VLM outperforms GPT-4o and Intern-VL3-78B by 26.91% and 25.56% respectively on MSMU-Bench. Code and models are released at https://github.com/cpystan/SD-VLM.

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.

Full quantum tomography of high-dimensional quantum systems is experimentally infeasible due to the exponential scaling of the number of required measurements on the number of qubits in the system. However, several ideas were proposed recently for predicting the limited number of features for these states, or estimating the expectation values of operators, without the need for full state reconstruction. These ideas go under the general name of shadow tomography. Here we provide an experimental demonstration of property estimation based on classical shadows proposed in [H.-Y. Huang, R. Kueng, J. Preskill. Nat. Phys. https://doi.org/10.1038/s41567-020-0932-7 (2020)] and study its performance in the quantum optical experiment with high-dimensional spatial states of photons. We show on experimental data how this procedure outperforms conventional state reconstruction in fidelity estimation from a limited number of measurements.

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.

Multimodal Large Language Models (MLLMs) have achieved remarkable progress in various multimodal tasks. To pursue higher intelligence in space, MLLMs require integrating multiple atomic spatial capabilities to handle complex and dynamic tasks. However, existing benchmarks struggle to comprehensively evaluate the spatial intelligence of common MLLMs from the atomic level to the compositional level. To fill this gap, we present SpaCE-10, a comprehensive benchmark for compositional spatial evaluations. In SpaCE-10, we define 10 atomic spatial capabilities, which are combined to form 8 compositional capabilities. Based on these definitions, we propose a novel hierarchical annotation pipeline to generate high-quality and diverse question-answer (QA) pairs. With over 150+ hours of human expert effort, we obtain over 5k QA pairs for 811 real indoor scenes in SpaCE-10, which covers various evaluation settings like point cloud input and multi-choice QA. We conduct an extensive evaluation of common MLLMs on SpaCE-10 and find that even the most advanced MLLM still lags behind humans by large margins. Through our careful study, we also draw several significant findings that benefit the MLLM community. For example, we reveal that the shortcoming of counting capability greatly limits the compositional spatial capabilities of existing MLLMs. The evaluation code and benchmark datasets are available at https://github.com/Cuzyoung/SpaCE-10.

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/.

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.

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.

We obtain the multiple-parameter quantum Cram\'er-Rao bound for estimating the transverse Cartesian components of the centroid and separation of two incoherent optical point sources using an imaging system with finite spatial bandwidth. Under quite general and realistic assumptions on the point-spread function of the imaging system, and for weak source strengths, we show that the Cram\'er-Rao bounds for the x and y components of the separation are independent of the values of those components, which may be well below the conventional Rayleigh resolution limit. We also propose two linear optics-based measurement methods that approach the quantum bound for the estimation of the Cartesian components of the separation once the centroid has been located. One of the methods is an interferometric scheme that approaches the quantum bound for sub-Rayleigh separations. The other method using fiber coupling can in principle attain the bound regardless of the distance between the two sources.

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.

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.

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

Quantifying and assessing urban greenery is consequential for planning and development, reflecting the everlasting importance of green spaces for multiple climate and well-being dimensions of cities. Evaluation can be broadly grouped into objective (e.g., measuring the amount of greenery) and subjective (e.g., polling the perception of people) approaches, which may differ -- what people see and feel about how green a place is might not match the measurements of the actual amount of vegetation. In this work, we advance the state of the art by measuring such differences and explaining them through human, geographic, and spatial dimensions. The experiments rely on contextual information extracted from street view imagery and a comprehensive urban visual perception survey collected from 1,000 people across five countries with their extensive demographic and personality information. We analyze the discrepancies between objective measures (e.g., Green View Index (GVI)) and subjective scores (e.g., pairwise ratings), examining whether they can be explained by a variety of human and visual factors such as age group and spatial variation of greenery in the scene. The findings reveal that such discrepancies are comparable around the world and that demographics and personality do not play a significant role in perception. Further, while perceived and measured greenery correlate consistently across geographies (both where people and where imagery are from), where people live plays a significant role in explaining perceptual differences, with these two, as the top among seven, features that influences perceived greenery the most. This location influence suggests that cultural, environmental, and experiential factors substantially shape how individuals observe greenery in cities.

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.

Earth observation (EO) data spans a wide range of spatial, spectral, and temporal resolutions, from high-resolution optical imagery to low resolution multispectral products or radar time series. While recent foundation models have improved multimodal integration for learning meaningful representations, they often expect fixed input resolutions or are based on sensor-specific encoders limiting generalization across heterogeneous EO modalities. To overcome these limitations we introduce RAMEN, a resolution-adjustable multimodal encoder that learns a shared visual representation across EO data in a fully sensor-agnostic manner. RAMEN treats the modality and spatial and temporal resolutions as key input data features, enabling coherent analysis across modalities within a unified latent space. Its main methodological contribution is to define spatial resolution as a controllable output parameter, giving users direct control over the desired level of detail at inference and allowing explicit trade-offs between spatial precision and computational cost. We train a single, unified transformer encoder reconstructing masked multimodal EO data drawn from diverse sources, ensuring generalization across sensors and resolutions. Once pretrained, RAMEN transfers effectively to both known and unseen sensor configurations and outperforms larger state-of-the-art models on the community-standard PANGAEA benchmark, containing various multi-sensor and multi-resolution downstream tasks. Our code and pretrained model are available at https://github.com/nicolashoudre/RAMEN.

Understanding geometric properties of natural language processing models' latent spaces allows the manipulation of these properties for improved performance on downstream tasks. One such property is the amount of data spread in a model's latent space, or how fully the available latent space is being used. In this work, we define data spread and demonstrate that the commonly used measures of data spread, Average Cosine Similarity and a partition function min/max ratio I(V), do not provide reliable metrics to compare the use of latent space across models. We propose and examine eight alternative measures of data spread, all but one of which improve over these current metrics when applied to seven synthetic data distributions. Of our proposed measures, we recommend one principal component-based measure and one entropy-based measure that provide reliable, relative measures of spread and can be used to compare models of different sizes and dimensionalities.

Standard methods for detecting discontinuities in conditional means are not applicable to outcomes that are complex, non-Euclidean objects like distributions, networks, or covariance matrices. This article develops a nonparametric test for jumps in conditional means when outcomes lie in a non-Euclidean metric space. Using local Fr\'echet regressionx2014which generalizes standard regression to metric-space valued datax2014the method estimates a mean path on either side of a candidate cutoff, extending existing k-sample tests to a flexible regression setting. Key theoretical contributions include a central limit theorem for the local estimator of the conditional Fr\'echet variance and the asymptotic validity and consistency of the proposed test. Simulations confirm nominal size control and robust power in finite samples. Two applications demonstrate the method's value by revealing effects invisible to scalar-based tests. First, I detect a sharp change in work-from-home compositions at Washington State's income threshold for non-compete enforceability during COVID-19, highlighting remote work's role as a bargaining margin. Second, I find that countries restructure their input-output networks after losing preferential US trade access. These findings underscore that analyzing regression functions within their native metric spaces can reveal structural discontinuities that scalar summaries would miss.

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.

Metric space magnitude, an active subject of research in algebraic topology, originally arose in the context of biology, where it was used to represent the effective number of distinct species in an environment. In a more general setting, the magnitude of a metric space is a real number that aims to quantify the effective number of distinct points in the space. The contribution of each point to a metric space's global magnitude, which is encoded by the {\em weighting vector}, captures much of the underlying geometry of the original metric space. Surprisingly, when the metric space is Euclidean, the weighting vector also serves as an effective tool for boundary detection. This allows the weighting vector to serve as the foundation of novel algorithms for classic machine learning tasks such as classification, outlier detection and active learning. We demonstrate, using experiments and comparisons on classic benchmark datasets, the promise of the proposed magnitude and weighting vector-based approaches.

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.

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.

Precise spatial modeling in the operating room (OR) is foundational to many clinical tasks, supporting intraoperative awareness, hazard avoidance, and surgical decision-making. While existing approaches leverage large-scale multimodal datasets for latent-space alignment to implicitly learn spatial relationships, they overlook the 3D capabilities of MLLMs. However, this approach raises two issues: (1) Operating rooms typically lack multiple video and audio sensors, making multimodal 3D data difficult to obtain; (2) Training solely on readily available 2D data fails to capture fine-grained details in complex scenes. To address this gap, we introduce Spatial-ORMLLM, the first large vision-language model for 3D spatial reasoning in operating rooms using only RGB modality to infer volumetric and semantic cues, enabling downstream medical tasks with detailed and holistic spatial context. Spatial-ORMLLM incorporates a Spatial-Enhanced Feature Fusion Block, which integrates 2D modality inputs with rich 3D spatial knowledge extracted by the estimation algorithm and then feeds the combined features into the visual tower. By employing a unified end-to-end MLLM framework, it combines powerful spatial features with textual features to deliver robust 3D scene reasoning without any additional expert annotations or sensor inputs. Experiments on multiple benchmark clinical datasets demonstrate that Spatial-ORMLLM achieves state-of-the-art performance and generalizes robustly to previously unseen surgical scenarios and downstream tasks.

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.

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.

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.

From a single image, visual cues can help deduce intrinsic and extrinsic camera parameters like the focal length and the gravity direction. This single-image calibration can benefit various downstream applications like image editing and 3D mapping. Current approaches to this problem are based on either classical geometry with lines and vanishing points or on deep neural networks trained end-to-end. The learned approaches are more robust but struggle to generalize to new environments and are less accurate than their classical counterparts. We hypothesize that they lack the constraints that 3D geometry provides. In this work, we introduce GeoCalib, a deep neural network that leverages universal rules of 3D geometry through an optimization process. GeoCalib is trained end-to-end to estimate camera parameters and learns to find useful visual cues from the data. Experiments on various benchmarks show that GeoCalib is more robust and more accurate than existing classical and learned approaches. Its internal optimization estimates uncertainties, which help flag failure cases and benefit downstream applications like visual localization. The code and trained models are publicly available at https://github.com/cvg/GeoCalib.

Radio interferometric imaging aims to estimate an unknown sky intensity image from degraded observations, acquired through an antenna array. In the theoretical case of a perfectly calibrated array, it has been shown that solving the corresponding imaging problem by iterative algorithms based on convex optimization and compressive sensing theory can be competitive with classical algorithms such as CLEAN. However, in practice, antenna-based gains are unknown and have to be calibrated. Future radio telescopes, such as the SKA, aim at improving imaging resolution and sensitivity by orders of magnitude. At this precision level, the direction-dependency of the gains must be accounted for, and radio interferometric imaging can be understood as a blind deconvolution problem. In this context, the underlying minimization problem is non-convex, and adapted techniques have to be designed. In this work, leveraging recent developments in non-convex optimization, we propose the first joint calibration and imaging method in radio interferometry, with proven convergence guarantees. Our approach, based on a block-coordinate forward-backward algorithm, jointly accounts for visibilities and suitable priors on both the image and the direction-dependent effects (DDEs). As demonstrated in recent works, sparsity remains the prior of choice for the image, while DDEs are modelled as smooth functions of the sky, i.e. spatially band-limited. Finally, we show through simulations the efficiency of our method, for the reconstruction of both images of point sources and complex extended sources. MATLAB code is available on GitHub.

Selective state space models (SSMs), such as Mamba, highly excel at capturing long-range dependencies in 1D sequential data, while their applications to 2D vision tasks still face challenges. Current visual SSMs often convert images into 1D sequences and employ various scanning patterns to incorporate local spatial dependencies. However, these methods are limited in effectively capturing the complex image spatial structures and the increased computational cost caused by the lengthened scanning paths. To address these limitations, we propose Spatial-Mamba, a novel approach that establishes neighborhood connectivity directly in the state space. Instead of relying solely on sequential state transitions, we introduce a structure-aware state fusion equation, which leverages dilated convolutions to capture image spatial structural dependencies, significantly enhancing the flow of visual contextual information. Spatial-Mamba proceeds in three stages: initial state computation in a unidirectional scan, spatial context acquisition through structure-aware state fusion, and final state computation using the observation equation. Our theoretical analysis shows that Spatial-Mamba unifies the original Mamba and linear attention under the same matrix multiplication framework, providing a deeper understanding of our method. Experimental results demonstrate that Spatial-Mamba, even with a single scan, attains or surpasses the state-of-the-art SSM-based models in image classification, detection and segmentation. Source codes and trained models can be found at https://github.com/EdwardChasel/Spatial-Mamba.

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.

Graph measures that express closeness or distance between nodes can be employed for graph nodes clustering using metric clustering algorithms. There are numerous measures applicable to this task, and which one performs better is an open question. We study the performance of 25 graph measures on generated graphs with different parameters. While usually measure comparisons are limited to general measure ranking on a particular dataset, we aim to explore the performance of various measures depending on graph features. Using an LFR graph generator, we create a dataset of 11780 graphs covering the whole LFR parameter space. For each graph, we assess the quality of clustering with k-means algorithm for each considered measure. Based on this, we determine the best measure for each area of the parameter space. We find that the parameter space consists of distinct zones where one particular measure is the best. We analyze the geometry of the resulting zones and describe it with simple criteria. Given particular graph parameters, this allows us to recommend a particular measure to use for clustering.

When retrieval-augmented generation (RAG) systems hallucinate, what geometric trace does this leave in embedding space? We introduce the Semantic Grounding Index (SGI), defined as the ratio of angular distances from the response to the question versus the context on the unit hypersphere S^{d-1}.Our central finding is semantic laziness: hallucinated responses remain angularly proximate to questions rather than departing toward retrieved contexts. On HaluEval (n=5,000), we observe large effect sizes (Cohen's d ranging from 0.92 to 1.28) across five embedding models with mean cross-model correlation r=0.85. Crucially, we derive from the spherical triangle inequality that SGI's discriminative power should increase with question-context angular separation θ(q,c)-a theoretical prediction confirmed empirically: effect size rises monotonically from d=0.61 -low θ(q,c), to d=1.27 -high θ(q,c), with AUC improving from 0.72 to 0.83. Subgroup analysis reveals that SGI excels on long responses (d=2.05) and short questions (d=1.22), while remaining robust across context lengths. Calibration analysis yields ECE=0.10, indicating SGI scores can serve as probability estimates, not merely rankings. A critical negative result on TruthfulQA (AUC=0.478) establishes that angular geometry measures topical engagement rather than factual accuracy. SGI provides computationally efficient, theoretically grounded infrastructure for identifying responses that warrant verification in production RAG deployments.

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 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.

Despite recent advances demonstrating vision-language models' (VLMs) abilities to describe complex relationships in images using natural language, their capability to quantitatively reason about object sizes and distances remains underexplored. In this work, we introduce a manually annotated benchmark, Q-Spatial Bench, with 271 questions across five categories designed for quantitative spatial reasoning and systematically investigate the performance of state-of-the-art VLMs on this task. Our analysis reveals that reasoning about distances between objects is particularly challenging for SoTA VLMs; however, some VLMs significantly outperform others, with an over 40-point gap between the two best performing models. We also make the surprising observation that the success rate of the top-performing VLM increases by 19 points when a reasoning path using a reference object emerges naturally in the response. Inspired by this observation, we develop a zero-shot prompting technique, SpatialPrompt, that encourages VLMs to answer quantitative spatial questions using reference objects as visual cues. By instructing VLMs to use reference objects in their reasoning paths via SpatialPrompt, Gemini 1.5 Pro, Gemini 1.5 Flash, and GPT-4V improve their success rates by over 40, 20, and 30 points, respectively. We emphasize that these significant improvements are obtained without needing more data, model architectural modifications, or fine-tuning.

Priorities in multi-criteria decision-making (MCDM) convey the relevance preference of one criterion over another, which is usually reflected by imposing the non-negativity and unit-sum constraints. The processing of such priorities is different than other unconstrained data, but this point is often neglected by researchers, which results in fallacious statistical analysis. This article studies three prevalent fallacies in group MCDM along with solutions based on compositional data analysis to avoid misusing statistical operations. First, we use a compositional approach to aggregate the priorities of a group of DMs and show that the outcome of the compositional analysis is identical to the normalized geometric mean, meaning that the arithmetic mean should be avoided. Furthermore, a new aggregation method is developed, which is a robust surrogate for the geometric mean. We also discuss the errors in computing measures of dispersion, including standard deviation and distance functions. Discussing the fallacies in computing the standard deviation, we provide a probabilistic criteria ranking by developing proper Bayesian tests, where we calculate the extent to which a criterion is more important than another. Finally, we explain the errors in computing the distance between priorities, and a clustering algorithm is specially tailored based on proper distance metrics.

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.

Episodic memory plays a crucial role in various cognitive processes, such as the ability to mentally recall past events. While cognitive science emphasizes the significance of spatial context in the formation and retrieval of episodic memory, the current primary approach to implementing episodic memory in AI systems is through transformers that store temporally ordered experiences, which overlooks the spatial dimension. As a result, it is unclear how the underlying structure could be extended to incorporate the spatial axis beyond temporal order alone and thereby what benefits can be obtained. To address this, this paper explores the use of Spatially-Aware Transformer models that incorporate spatial information. These models enable the creation of place-centric episodic memory that considers both temporal and spatial dimensions. Adopting this approach, we demonstrate that memory utilization efficiency can be improved, leading to enhanced accuracy in various place-centric downstream tasks. Additionally, we propose the Adaptive Memory Allocator, a memory management method based on reinforcement learning that aims to optimize efficiency of memory utilization. Our experiments demonstrate the advantages of our proposed model in various environments and across multiple downstream tasks, including prediction, generation, reasoning, and reinforcement learning. The source code for our models and experiments will be available at https://github.com/junmokane/spatially-aware-transformer.

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.

Virtual sensing techniques allow for inferring signals at new unmonitored locations by exploiting spatio-temporal measurements coming from physical sensors at different locations. However, as the sensor coverage becomes sparse due to costs or other constraints, physical proximity cannot be used to support interpolation. In this paper, we overcome this challenge by leveraging dependencies between the target variable and a set of correlated variables (covariates) that can frequently be associated with each location of interest. From this viewpoint, covariates provide partial observability, and the problem consists of inferring values for unobserved channels by exploiting observations at other locations to learn how such variables can correlate. We introduce a novel graph-based methodology to exploit such relationships and design a graph deep learning architecture, named GgNet, implementing the framework. The proposed approach relies on propagating information over a nested graph structure that is used to learn dependencies between variables as well as locations. GgNet is extensively evaluated under different virtual sensing scenarios, demonstrating higher reconstruction accuracy compared to the state-of-the-art.

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.

Current evaluation paradigms for large language models (LLMs) represent a critical blind spot in AI research--relying on opaque numerical metrics that conceal fundamental limitations in spatial reasoning while providing no intuitive understanding of model capabilities. This deficiency creates a dangerous disconnect between reported performance and practical abilities, particularly for applications requiring physical world understanding. We introduce LTD-Bench, a breakthrough benchmark that transforms LLM evaluation from abstract scores to directly observable visual outputs by requiring models to generate drawings through dot matrices or executable code. This approach makes spatial reasoning limitations immediately apparent even to non-experts, bridging the fundamental gap between statistical performance and intuitive assessment. LTD-Bench implements a comprehensive methodology with complementary generation tasks (testing spatial imagination) and recognition tasks (assessing spatial perception) across three progressively challenging difficulty levels, methodically evaluating both directions of the critical language-spatial mapping. Our extensive experiments with state-of-the-art models expose an alarming capability gap: even LLMs achieving impressive results on traditional benchmarks demonstrate profound deficiencies in establishing bidirectional mappings between language and spatial concept--a fundamental limitation that undermines their potential as genuine world models. Furthermore, LTD-Bench's visual outputs enable powerful diagnostic analysis, offering a potential approach to investigate model similarity.

Existing autonomous driving systems rely on onboard sensors (cameras, LiDAR, IMU, etc) for environmental perception. However, this paradigm is limited by the drive-time perception horizon and often fails under limited view scope, occlusion or extreme conditions such as darkness and rain. In contrast, human drivers are able to recall road structure even under poor visibility. To endow models with this ``recall" ability, we propose the spatial retrieval paradigm, introducing offline retrieved geographic images as an additional input. These images are easy to obtain from offline caches (e.g, Google Maps or stored autonomous driving datasets) without requiring additional sensors, making it a plug-and-play extension for existing AD tasks. For experiments, we first extend the nuScenes dataset with geographic images retrieved via Google Maps APIs and align the new data with ego-vehicle trajectories. We establish baselines across five core autonomous driving tasks: object detection, online mapping, occupancy prediction, end-to-end planning, and generative world modeling. Extensive experiments show that the extended modality could enhance the performance of certain tasks. We will open-source dataset curation code, data, and benchmarks for further study of this new autonomous driving paradigm.

Existing indoor SLAM datasets primarily focus on robot sensing, often lacking building architectures. To address this gap, we design and construct the first dataset to couple the SLAM and BIM, named SLABIM. This dataset provides BIM and SLAM-oriented sensor data, both modeling a university building at HKUST. The as-designed BIM is decomposed and converted for ease of use. We employ a multi-sensor suite for multi-session data collection and mapping to obtain the as-built model. All the related data are timestamped and organized, enabling users to deploy and test effectively. Furthermore, we deploy advanced methods and report the experimental results on three tasks: registration, localization and semantic mapping, demonstrating the effectiveness and practicality of SLABIM. We make our dataset open-source at https://github.com/HKUST-Aerial-Robotics/SLABIM.

As unmanned aerial systems (UASs) increasingly integrate into the US national airspace system, there is an increasing need to characterize how commercial and recreational UASs may encounter each other. To inform the development and evaluation of safety critical technologies, we demonstrate a methodology to analytically calculate all potential relative geometries between different UAS operations performing inspection missions. This method is based on a previously demonstrated technique that leverages open source geospatial information to generate representative unmanned aircraft trajectories. Using open source data and parallel processing techniques, we performed trillions of calculations to estimate the relative horizontal distance between geospatial points across sixteen locations.

By interpreting the product of the Principal Component Analysis, that is the covariance matrix, as a sequence of nested subspaces naturally coming with weights according to the level of approximation they provide, we are able to embed all d--dimensional Grassmannians into a stratified space of covariance matrices. We observe that Grassmannians constitute the lowest dimensional skeleton of the stratification while it is possible to define a Riemaniann metric on the highest dimensional and dense stratum, such a metric being compatible with the global stratification. With such a Riemaniann metric at hand, it is possible to look for geodesics between two linear subspaces of different dimensions that do not go through higher dimensional linear subspaces as would euclidean geodesics. Building upon the proposed embedding of Grassmannians into the stratified space of covariance matrices, we generalize the concept of varifolds to what we call flagfolds in order to model multi-dimensional shapes.

3D spatial understanding is essential in real-world applications such as robotics, autonomous vehicles, virtual reality, and medical imaging. Recently, Large Language Models (LLMs), having demonstrated remarkable success across various domains, have been leveraged to enhance 3D understanding tasks, showing potential to surpass traditional computer vision methods. In this survey, we present a comprehensive review of methods integrating LLMs with 3D spatial understanding. We propose a taxonomy that categorizes existing methods into three branches: image-based methods deriving 3D understanding from 2D visual data, point cloud-based methods working directly with 3D representations, and hybrid modality-based methods combining multiple data streams. We systematically review representative methods along these categories, covering data representations, architectural modifications, and training strategies that bridge textual and 3D modalities. Finally, we discuss current limitations, including dataset scarcity and computational challenges, while highlighting promising research directions in spatial perception, multi-modal fusion, and real-world applications.

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.

Image geolocalization, in which, traditionally, an AI model predicts the precise GPS coordinates of an image is a challenging task with many downstream applications. However, the user cannot utilize the model to further their knowledge other than the GPS coordinate; the model lacks an understanding of the location and the conversational ability to communicate with the user. In recent days, with tremendous progress of large multimodal models (LMMs) proprietary and open-source researchers have attempted to geolocalize images via LMMs. However, the issues remain unaddressed; beyond general tasks, for more specialized downstream tasks, one of which is geolocalization, LMMs struggle. In this work, we propose to solve this problem by introducing a conversational model GAEA that can provide information regarding the location of an image, as required by a user. No large-scale dataset enabling the training of such a model exists. Thus we propose a comprehensive dataset GAEA with 800K images and around 1.6M question answer pairs constructed by leveraging OpenStreetMap (OSM) attributes and geographical context clues. For quantitative evaluation, we propose a diverse benchmark comprising 4K image-text pairs to evaluate conversational capabilities equipped with diverse question types. We consider 11 state-of-the-art open-source and proprietary LMMs and demonstrate that GAEA significantly outperforms the best open-source model, LLaVA-OneVision by 25.69% and the best proprietary model, GPT-4o by 8.28%. Our dataset, model and codes are available