Daily Papers

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.

We introduce Thinking with Spatial Code, a framework that transforms RGB video into explicit, temporally coherent 3D representations for physical-world visual question answering. We highlight the empirical finding that our proposed spatial encoder can parse videos into structured spatial code with explicit 3D oriented bounding boxes and semantic labels, enabling large language models (LLMs) to reason directly over explicit spatial variables. Specifically, we propose the spatial encoder that encodes image and geometric features by unifying 6D object parsing and tracking backbones with geometric prediction, and we further finetuning LLMs with reinforcement learning using a spatial rubric reward that encourages perspective-aware, geometrically grounded inference. As a result, our model outperforms proprietary vision-language models on VSI-Bench, setting a new state-of-the-art. Code is available at https://github.com/Beckschen/spatialcode.

A Milstein-type method is proposed for some highly non-linear non-autonomous time-changed stochastic differential equations (SDEs). The spatial variables in the coefficients of the time-changed SDEs satisfy the super-linear growth condition and the temporal variables obey some H\"older's continuity condition. The strong convergence in the finite time is studied and the convergence order is obtained.

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).

The extraction of invariant causal relationships from time series data with environmental attributes is critical for robust decision-making in domains such as climate science and environmental monitoring. However, existing methods either emphasize dynamic causal analysis without leveraging environmental contexts or focus on static invariant causal inference, leaving a gap in distributed temporal settings. In this paper, we propose Distributed Dynamic Invariant Causal Prediction in Time-series (DisDy-ICPT), a novel framework that learns dynamic causal relationships over time while mitigating spatial confounding variables without requiring data communication. We theoretically prove that DisDy-ICPT recovers stable causal predictors within a bounded number of communication rounds under standard sampling assumptions. Empirical evaluations on synthetic benchmarks and environment-segmented real-world datasets show that DisDy-ICPT achieves superior predictive stability and accuracy compared to baseline methods A and B. Our approach offers promising applications in carbon monitoring and weather forecasting. Future work will extend DisDy-ICPT to online learning scenarios.

We introduce Tadpole, a novel foundation model for three-dimensional partial differential equations (PDEs) that addresses key challenges in transferability, scalability to high dimensionality, and multi-functionality. Tadpole is pre-trained as an autoencoder on synthetic 3D PDE data generated by an efficient online data-generation framework. This enables large-scale, diverse training without storage or I/O overhead, demonstrated by scaling to an equivalent of hundreds of terabytes of training data. By autoencoding single-channel spatial crops, Tadpole learns rich and transferable representations across heterogeneous physical systems with varying numbers of state variables and spatial resolutions. Although pre-trained solely as an autoencoder, Tadpole can be efficiently applied for multiple downstream tasks beyond reconstruction, including dynamics learning and generative modeling. For dynamics learning, we propose a novel parameter-efficient fine-tuning strategy that integrates low-rank adaptation, latent-space transformations, and reintroduced skip connections, achieving accurate temporal modeling with a minimal number of trainable parameters. Tadpole demonstrates strong fine-tuning performance across various downstream tasks, highlighting its versatility and effectiveness as a foundation model for 3D PDE learning. Source code and pre-trained weights of Tadpole are available at https://github.com/tum-pbs/tadpole

Spatio-temporal video grounding (STVG) aims at localizing the spatio-temporal tube of a video, as specified by the input text query. In this paper, we utilize multimodal large language models (MLLMs) to explore a zero-shot solution in STVG. We reveal two key insights about MLLMs: (1) MLLMs tend to dynamically assign special tokens, referred to as grounding tokens, for grounding the text query; and (2) MLLMs often suffer from suboptimal grounding due to the inability to fully integrate the cues in the text query (e.g., attributes, actions) for inference. Based on these insights, we propose a MLLM-based zero-shot framework for STVG, which includes novel decomposed spatio-temporal highlighting (DSTH) and temporal-augmented assembling (TAS) strategies to unleash the reasoning ability of MLLMs. The DSTH strategy first decouples the original query into attribute and action sub-queries for inquiring the existence of the target both spatially and temporally. It then uses a novel logit-guided re-attention (LRA) module to learn latent variables as spatial and temporal prompts, by regularizing token predictions for each sub-query. These prompts highlight attribute and action cues, respectively, directing the model's attention to reliable spatial and temporal related visual regions. In addition, as the spatial grounding by the attribute sub-query should be temporally consistent, we introduce the TAS strategy to assemble the predictions using the original video frames and the temporal-augmented frames as inputs to help improve temporal consistency. We evaluate our method on various MLLMs, and show that it outperforms SOTA methods on three common STVG benchmarks. The code will be available at https://github.com/zaiquanyang/LLaVA_Next_STVG.

Predicting wildfire spread is critical for land management and disaster preparedness. To this end, we present `Next Day Wildfire Spread,' a curated, large-scale, multivariate data set of historical wildfires aggregating nearly a decade of remote-sensing data across the United States. In contrast to existing fire data sets based on Earth observation satellites, our data set combines 2D fire data with multiple explanatory variables (e.g., topography, vegetation, weather, drought index, population density) aligned over 2D regions, providing a feature-rich data set for machine learning. To demonstrate the usefulness of this data set, we implement a neural network that takes advantage of the spatial information of this data to predict wildfire spread. We compare the performance of the neural network with other machine learning models: logistic regression and random forest. This data set can be used as a benchmark for developing wildfire propagation models based on remote sensing data for a lead time of one day.

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

Accurate spatial-temporal traffic flow forecasting is crucial in aiding traffic managers in implementing control measures and assisting drivers in selecting optimal travel routes. Traditional deep-learning based methods for traffic flow forecasting typically rely on historical data to train their models, which are then used to make predictions on future data. However, the performance of the trained model usually degrades due to the temporal drift between the historical and future data. To make the model trained on historical data better adapt to future data in a fully online manner, this paper conducts the first study of the online test-time adaptation techniques for spatial-temporal traffic flow forecasting problems. To this end, we propose an Adaptive Double Correction by Series Decomposition (ADCSD) method, which first decomposes the output of the trained model into seasonal and trend-cyclical parts and then corrects them by two separate modules during the testing phase using the latest observed data entry by entry. In the proposed ADCSD method, instead of fine-tuning the whole trained model during the testing phase, a lite network is attached after the trained model, and only the lite network is fine-tuned in the testing process each time a data entry is observed. Moreover, to satisfy that different time series variables may have different levels of temporal drift, two adaptive vectors are adopted to provide different weights for different time series variables. Extensive experiments on four real-world traffic flow forecasting datasets demonstrate the effectiveness of the proposed ADCSD method. The code is available at https://github.com/Pengxin-Guo/ADCSD.

Feature engineering is required to obtain better results for time series forecasting, and decomposition is a crucial one. One decomposition approach often cannot be used for numerous forecasting tasks since the standard time series decomposition lacks flexibility and robustness. Traditional feature selection relies heavily on preexisting domain knowledge, has no generic methodology, and requires a lot of labor. However, most time series prediction models based on deep learning typically suffer from interpretability issue, so the "black box" results lead to a lack of confidence. To deal with the above issues forms the motivation of the thesis. In the paper we propose TSDFNet as a neural network with self-decomposition mechanism and an attentive feature fusion mechanism, It abandons feature engineering as a preprocessing convention and creatively integrates it as an internal module with the deep model. The self-decomposition mechanism empowers TSDFNet with extensible and adaptive decomposition capabilities for any time series, users can choose their own basis functions to decompose the sequence into temporal and generalized spatial dimensions. Attentive feature fusion mechanism has the ability to capture the importance of external variables and the causality with target variables. It can automatically suppress the unimportant features while enhancing the effective ones, so that users do not have to struggle with feature selection. Moreover, TSDFNet is easy to look into the "black box" of the deep neural network by feature visualization and analyze the prediction results. We demonstrate performance improvements over existing widely accepted models on more than a dozen datasets, and three experiments showcase the interpretability of TSDFNet.

The difficulty of monitoring biodiversity at fine scales and over large areas limits ecological knowledge and conservation efforts. To fill this gap, Species Distribution Models (SDMs) predict species across space from spatially explicit features. Yet, they face the challenge of integrating the rich but heterogeneous data made available over the past decade, notably millions of opportunistic species observations and standardized surveys, as well as multi-modal remote sensing data. In light of that, we have designed and developed a new European-scale dataset for SDMs at high spatial resolution (10-50 m), including more than 10k species (i.e., most of the European flora). The dataset comprises 5M heterogeneous Presence-Only records and 90k exhaustive Presence-Absence survey records, all accompanied by diverse environmental rasters (e.g., elevation, human footprint, and soil) that are traditionally used in SDMs. In addition, it provides Sentinel-2 RGB and NIR satellite images with 10 m resolution, a 20-year time-series of climatic variables, and satellite time-series from the Landsat program. In addition to the data, we provide an openly accessible SDM benchmark (hosted on Kaggle), which has already attracted an active community and a set of strong baselines for single predictor/modality and multimodal approaches. All resources, e.g., the dataset, pre-trained models, and baseline methods (in the form of notebooks), are available on Kaggle, allowing one to start with our dataset literally with two mouse clicks.

Storyboarding is a core skill in visual storytelling for film, animation, and games. However, automating this process requires a system to achieve two properties that current approaches rarely satisfy simultaneously: inter-shot consistency and explicit editability. While 2D diffusion-based generators produce vivid imagery, they often suffer from identity drift along with limited geometric control; conversely, traditional 3D animation workflows are consistent and editable but require expert-heavy, labor-intensive authoring. We present StoryBlender, a grounded 3D storyboard generation framework governed by a Story-centric Reflection Scheme. At its core, we propose the StoryBlender system, which is built on a three-stage pipeline: (1) Semantic-Spatial Grounding, to construct a continuity memory graph to decouple global assets from shot-specific variables for long-horizon consistency; (2) Canonical Asset Materialization, to instantiate entities in a unified coordinate space to maintain visual identity; and (3) Spatial-Temporal Dynamics, to achieve layout design and cinematic evolution through visual metrics. By orchestrating multiple agents in a hierarchical manner within a verification loop, StoryBlender iteratively self-corrects spatial hallucinations via engine-verified feedback. The resulting native 3D scenes support direct, precise editing of cameras and visual assets while preserving unwavering multi-shot continuity. Experiments demonstrate that StoryBlender significantly improves consistency and editability over both diffusion-based and 3D-grounded baselines. Code, data, and demonstration video will be available on https://engineeringai-lab.github.io/StoryBlender/

We present GeoGrid-Bench, a benchmark designed to evaluate the ability of foundation models to understand geo-spatial data in the grid structure. Geo-spatial datasets pose distinct challenges due to their dense numerical values, strong spatial and temporal dependencies, and unique multimodal representations including tabular data, heatmaps, and geographic visualizations. To assess how foundation models can support scientific research in this domain, GeoGrid-Bench features large-scale, real-world data covering 16 climate variables across 150 locations and extended time frames. The benchmark includes approximately 3,200 question-answer pairs, systematically generated from 8 domain expert-curated templates to reflect practical tasks encountered by human scientists. These range from basic queries at a single location and time to complex spatiotemporal comparisons across regions and periods. Our evaluation reveals that vision-language models perform best overall, and we provide a fine-grained analysis of the strengths and limitations of different foundation models in different geo-spatial tasks. This benchmark offers clearer insights into how foundation models can be effectively applied to geo-spatial data analysis and used to support scientific research.

Deploying robots in human-shared environments requires a deep understanding of how nearby agents and objects interact. Employing causal inference to model cause-and-effect relationships facilitates the prediction of human behaviours and enables the anticipation of robot interventions. However, a significant challenge arises due to the absence of implementation of existing causal discovery methods within the ROS ecosystem, the standard de-facto framework in robotics, hindering effective utilisation on real robots. To bridge this gap, in our previous work we proposed ROS-Causal, a ROS-based framework designed for onboard data collection and causal discovery in human-robot spatial interactions. In this work, we present an experimental evaluation of ROS-Causal both in simulation and on a new dataset of human-robot spatial interactions in a lab scenario, to assess its performance and effectiveness. Our analysis demonstrates the efficacy of this approach, showcasing how causal models can be extracted directly onboard by robots during data collection. The online causal models generated from the simulation are consistent with those from lab experiments. These findings can help researchers to enhance the performance of robotic systems in shared environments, firstly by studying the causal relations between variables in simulation without real people, and then facilitating the actual robot deployment in real human environments. ROS-Causal: https://lcastri.github.io/roscausal

We present a method for parametrizing sub-grid processes in the Shallow Water equations. We define coarse variables and local spatial averages and use a feed-forward neural network to learn sub-grid fluxes. Our method results in a local parametrization that uses a four-point computational stencil, which has several advantages over globally coupled parametrizations. We demonstrate numerically that our method improves energy balance in long-term turbulent simulations and also accurately reproduces individual solutions. The neural network parametrization can be easily combined with flux limiting to reduce oscillations near shocks. More importantly, our method provides reliable parametrizations, even in dynamical regimes that are not included in the training data.

Ensemble forecasting is crucial for improving weather predictions, especially for forecasts of extreme events. Constructing an ensemble prediction system (EPS) based on conventional NWP models is highly computationally expensive. ML models have emerged as valuable tools for deterministic weather forecasts, providing forecasts with significantly reduced computational requirements and even surpassing the forecast performance of traditional NWP models. However, challenges arise when applying ML models to ensemble forecasting. Recent ML models, such as GenCast and SEEDS model, rely on the ERA5 EDA or operational NWP ensemble members for forecast generation. Their spatial resolution is also considered too coarse for many applications. To overcome these limitations, we introduce FuXi-ENS, an advanced ML model designed to deliver 6-hourly global ensemble weather forecasts up to 15 days. This model runs at a significantly increased spatial resolution of 0.25\textdegree, incorporating 5 atmospheric variables at 13 pressure levels, along with 13 surface variables. By leveraging the inherent probabilistic nature of Variational AutoEncoder (VAE), FuXi-ENS optimizes a loss function that combines the CRPS and the KL divergence between the predicted and target distribution, facilitating the incorporation of flow-dependent perturbations in both initial conditions and forecast. This innovative approach makes FuXi-ENS an advancement over the traditional ones that use L1 loss combined with the KL loss in standard VAE models for ensemble weather forecasting. Results demonstrate that FuXi-ENS outperforms ensemble forecasts from the ECMWF, a world leading NWP model, in the CRPS of 98.1% of 360 variable and forecast lead time combinations. This achievement underscores the potential of the FuXi-ENS model to enhance ensemble weather forecasts, offering a promising direction for further development in this field.

Multivariate time series forecasting (MTSF) is crucial for decision-making to precisely forecast the future values/trends, based on the complex relationships identified from historical observations of multiple sequences. Recently, Spatial-Temporal Graph Neural Networks (STGNNs) have gradually become the theme of MTSF model as their powerful capability in mining spatial-temporal dependencies, but almost of them heavily rely on the assumption of historical data integrity. In reality, due to factors such as data collector failures and time-consuming repairment, it is extremely challenging to collect the whole historical observations without missing any variable. In this case, STGNNs can only utilize a subset of normal variables and easily suffer from the incorrect spatial-temporal dependency modeling issue, resulting in the degradation of their forecasting performance. To address the problem, in this paper, we propose a novel Graph Interpolation Attention Recursive Network (named GinAR) to precisely model the spatial-temporal dependencies over the limited collected data for forecasting. In GinAR, it consists of two key components, that is, interpolation attention and adaptive graph convolution to take place of the fully connected layer of simple recursive units, and thus are capable of recovering all missing variables and reconstructing the correct spatial-temporal dependencies for recursively modeling of multivariate time series data, respectively. Extensive experiments conducted on five real-world datasets demonstrate that GinAR outperforms 11 SOTA baselines, and even when 90% of variables are missing, it can still accurately predict the future values of all variables.

Reliably reconstructing physical fields from sparse sensor data is a challenge that frequently arises in many scientific domains. In practice, the process generating the data often is not understood to sufficient accuracy. Therefore, there is a growing interest in using the deep neural network route to address the problem. This work presents a novel approach that learns a continuous representation of the physical field using implicit neural representations (INRs). Specifically, after factorizing spatiotemporal variability into spatial and temporal components using the separation of variables technique, the method learns relevant basis functions from sparsely sampled irregular data points to develop a continuous representation of the data. In experimental evaluations, the proposed model outperforms recent INR methods, offering superior reconstruction quality on simulation data from a state-of-the-art climate model and a second dataset that comprises ultra-high resolution satellite-based sea surface temperature fields.

We introduce a new class of spatially stochastic physics and data informed deep latent models for parametric partial differential equations (PDEs) which operate through scalable variational neural processes. We achieve this by assigning probability measures to the spatial domain, which allows us to treat collocation grids probabilistically as random variables to be marginalised out. Adapting this spatial statistics view, we solve forward and inverse problems for parametric PDEs in a way that leads to the construction of Gaussian process models of solution fields. The implementation of these random grids poses a unique set of challenges for inverse physics informed deep learning frameworks and we propose a new architecture called Grid Invariant Convolutional Networks (GICNets) to overcome these challenges. We further show how to incorporate noisy data in a principled manner into our physics informed model to improve predictions for problems where data may be available but whose measurement location does not coincide with any fixed mesh or grid. The proposed method is tested on a nonlinear Poisson problem, Burgers equation, and Navier-Stokes equations, and we provide extensive numerical comparisons. We demonstrate significant computational advantages over current physics informed neural learning methods for parametric PDEs while improving the predictive capabilities and flexibility of these models.

Modeling multivariate time series has long been a subject that has attracted researchers from a diverse range of fields including economics, finance, and traffic. A basic assumption behind multivariate time series forecasting is that its variables depend on one another but, upon looking closely, it is fair to say that existing methods fail to fully exploit latent spatial dependencies between pairs of variables. In recent years, meanwhile, graph neural networks (GNNs) have shown high capability in handling relational dependencies. GNNs require well-defined graph structures for information propagation which means they cannot be applied directly for multivariate time series where the dependencies are not known in advance. In this paper, we propose a general graph neural network framework designed specifically for multivariate time series data. Our approach automatically extracts the uni-directed relations among variables through a graph learning module, into which external knowledge like variable attributes can be easily integrated. A novel mix-hop propagation layer and a dilated inception layer are further proposed to capture the spatial and temporal dependencies within the time series. The graph learning, graph convolution, and temporal convolution modules are jointly learned in an end-to-end framework. Experimental results show that our proposed model outperforms the state-of-the-art baseline methods on 3 of 4 benchmark datasets and achieves on-par performance with other approaches on two traffic datasets which provide extra structural information.

Accurate prediction of traffic accident severity is critical for improving road safety, optimizing emergency response strategies, and informing the design of safer transportation infrastructure. However, existing approaches often struggle to effectively model the intricate interdependencies among spatial, temporal, and contextual variables that govern accident outcomes. In this study, we introduce STARN-GAT, a Multi-Modal Spatio-Temporal Graph Attention Network, which leverages adaptive graph construction and modality-aware attention mechanisms to capture these complex relationships. Unlike conventional methods, STARN-GAT integrates road network topology, temporal traffic patterns, and environmental context within a unified attention-based framework. The model is evaluated on the Fatality Analysis Reporting System (FARS) dataset, achieving a Macro F1-score of 85 percent, ROC-AUC of 0.91, and recall of 81 percent for severe incidents. To ensure generalizability within the South Asian context, STARN-GAT is further validated on the ARI-BUET traffic accident dataset, where it attains a Macro F1-score of 0.84, recall of 0.78, and ROC-AUC of 0.89. These results demonstrate the model's effectiveness in identifying high-risk cases and its potential for deployment in real-time, safety-critical traffic management systems. Furthermore, the attention-based architecture enhances interpretability, offering insights into contributing factors and supporting trust in AI-assisted decision-making. Overall, STARN-GAT bridges the gap between advanced graph neural network techniques and practical applications in road safety analytics.

Perception is often viewed as a process that transforms physical variables, external to an observer, into internal psychological variables. Such a process can be modeled by a function coined perceptual scale. The perceptual scale can be deduced from psychophysical measurements that consist in comparing the relative differences between stimuli (i.e. difference scaling experiments). However, this approach is often overlooked by the modeling and experimentation communities. Here, we demonstrate the value of measuring the perceptual scale of classical (spatial frequency, orientation) and less classical physical variables (interpolation between textures) by embedding it in recent probabilistic modeling of perception. First, we show that the assumption that an observer has an internal representation of univariate parameters such as spatial frequency or orientation while stimuli are high-dimensional does not lead to contradictory predictions when following the theoretical framework. Second, we show that the measured perceptual scale corresponds to the transduction function hypothesized in this framework. In particular, we demonstrate that it is related to the Fisher information of the generative model that underlies perception and we test the predictions given by the generative model of different stimuli in a set a of difference scaling experiments. Our main conclusion is that the perceptual scale is mostly driven by the stimulus power spectrum. Finally, we propose that this measure of perceptual scale is a way to push further the notion of perceptual distances by estimating the perceptual geometry of images i.e. the path between images instead of simply the distance between those.

Spatiotemporal reasoning plays a key role in Cyber-Physical Systems (CPS). Despite advances in Large Language Models (LLMs) and Large Reasoning Models (LRMs), their capacity to reason about complex spatiotemporal signals remains underexplored. This paper proposes a hierarchical SpatioTemporal reAsoning benchmaRK, STARK, to systematically evaluate LLMs across three levels of reasoning complexity: state estimation (e.g., predicting field variables, localizing and tracking events in space and time), spatiotemporal reasoning over states (e.g., inferring spatial-temporal relationships), and world-knowledge-aware reasoning that integrates contextual and domain knowledge (e.g., intent prediction, landmark-aware navigation). We curate 26 distinct spatiotemporal tasks with diverse sensor modalities, comprising 14,552 challenges where models answer directly or by Python Code Interpreter. Evaluating 3 LRMs and 8 LLMs, we find LLMs achieve limited success in tasks requiring geometric reasoning (e.g., multilateration or triangulation), particularly as complexity increases. Surprisingly, LRMs show robust performance across tasks with various levels of difficulty, often competing or surpassing traditional first-principle-based methods. Our results show that in reasoning tasks requiring world knowledge, the performance gap between LLMs and LRMs narrows, with some LLMs even surpassing LRMs. However, the LRM o3 model continues to achieve leading performance across all evaluated tasks, a result attributed primarily to the larger size of the reasoning models. STARK motivates future innovations in model architectures and reasoning paradigms for intelligent CPS by providing a structured framework to identify limitations in the spatiotemporal reasoning of LLMs and LRMs.

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.

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.

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.

Spatial competence is the quality of maintaining a consistent internal representation of an environment and using it to infer discrete structure and plan actions under constraints. Prevailing spatial evaluations for large models are limited to probing isolated primitives through 3D transformations or visual question answering. We introduce the Spatial Competence Benchmark (SCBench), spanning three hierarchical capability buckets whose tasks require executable outputs verified by deterministic checkers or simulator-based evaluators. On SCBench, three frontier models exhibit monotonically decreasing accuracy up the capability ladder. Sweeping output-token caps shows that accuracy gains concentrate at low budgets and saturate quickly, and failures are dominated by locally plausible geometry that breaks global constraints. We release the task generators, verifiers, and visualisation tooling.

This article studies the change in the prediction accuracy of a response variable when the number of predictors increases, and all variables follow a multivariate normal distribution. Assuming that the correlations between variables are independently drawn, I show that adding variables leads to globally increasing returns to scale when the mean of the correlation distribution is zero. The speed of learning depends positively on the variance of the correlation distribution. I use simulations to study the more complex case of correlation distributions with a non-zero mean and find a pattern of decreasing returns followed by increasing returns to scale - as long as the variance of correlations is not degenerate, in which case globally decreasing returns emerge. I train a collaborative filtering algorithm using the MovieLens 1M dataset to analyze returns from adding variables in a more realistic setting and find globally increasing returns to scale across 2,000 variables. The results suggest significant scale advantages from additional variables in prediction tasks.

Modelling individual decision-making during infectious disease outbreaks is crucial for understanding behavioural dynamics and informing effective public health interventions. Prior work has shown that large language models can simulate realistic human behaviour by generating agent decisions based on demographic prompts and situational context. We build on this foundation with a spatially grounded, agent-based simulation framework that integrates LLM-generated decisions about self-reported influenza-like illness into a census-based synthetic population of agents. Location is treated as a central feature: agents are assigned to spatial units within cities, capturing the spatial distributions of different demographic groups using real-world census data and enabling geographically diverse behavioural modelling. We implement and compare three decision scenarios, independent reasoning, household influence, and message framing, and simulate self-reporting outcomes in San Francisco and Atlanta. Results reveal that income and education are the dominant drivers of reporting rate variation, with smaller but consistent effects from geography, LLM model choice, and message framing. Our framework generates synthetic data that captures both social and geographic heterogeneity, supporting spatial epidemiological modelling and bias-aware behavioural analysis.

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.

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.

Existing self-supervised learning (SSL) methods primarily learn object-invariant representations but often neglect the spatial structure and relationships among object parts. To address this limitation, we introduce Spatial Prediction (SP), a spatially aware pretext regression task that predicts the relative position and scale between a pair of disentangled local views from the same image. By modeling part-to-part relationships in a continuous geometric space, SP encourages representations to capture fine-grained spatial dependencies beyond invariant categorical semantics, thereby learning the compositional structure of visual scenes. SP is implemented as a decoupled plug-in and can be seamlessly integrated into diverse SSL frameworks. Extensive experiments show consistent improvements across image recognition, fine-grained classification, semantic segmentation, and depth estimation, as well as substantial gains in out-of-distribution robustness for object recognition. To evaluate spatial reasoning, we introduce (1) a position and scale prediction task on image patch pairs and (2) a jigsaw understanding task requiring patch reordering and recognition after reconstruction. Strong performance on these tasks indicates improved spatial structure and geometric awareness. Overall, explicitly modeling spatial information provides an effective inductive bias for SSL, leading to more structured representations and better generalization. Code and models will be released.

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

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.

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

Spatial visualization is the mental ability to imagine, transform, and manipulate the spatial characteristics of objects and actions. This intelligence is a part of human cognition where actions and perception are connected on a mental level. To explore whether state-of-the-art Vision-Language Models (VLMs) exhibit this ability, we develop MentalBlackboard, an open-ended spatial visualization benchmark for Paper Folding and Hole Punching tests within two core tasks: prediction and planning. Our prediction experiments reveal that models struggle with applying symmetrical transformations, even when they predict the sequence of unfolding steps correctly. Also, rotations introduce a significant challenge to the physical situational awareness for models. The planning task reveals limitations of models in analyzing symmetrical relationships and in implementing the multi-stage symmetry process, with Claude Opus 4.1 achieving the highest planning score at an accuracy of 10\%. The top-performing model, o3, attains a peak performance of 71.6\% on the generalization task, which does not require spatial visualization but transfers spatial data; however, it achieves only 25\% accuracy on text-based prediction tasks.

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.

Text-to-image (T2I) models have achieved remarkable success in generating high-fidelity images, but they often fail in handling complex spatial relationships, e.g., spatial perception, reasoning, or interaction. These critical aspects are largely overlooked by current benchmarks due to their short or information-sparse prompt design. In this paper, we introduce SpatialGenEval, a new benchmark designed to systematically evaluate the spatial intelligence of T2I models, covering two key aspects: (1) SpatialGenEval involves 1,230 long, information-dense prompts across 25 real-world scenes. Each prompt integrates 10 spatial sub-domains and corresponding 10 multi-choice question-answer pairs, ranging from object position and layout to occlusion and causality. Our extensive evaluation of 21 state-of-the-art models reveals that higher-order spatial reasoning remains a primary bottleneck. (2) To demonstrate that the utility of our information-dense design goes beyond simple evaluation, we also construct the SpatialT2I dataset. It contains 15,400 text-image pairs with rewritten prompts to ensure image consistency while preserving information density. Fine-tuned results on current foundation models (i.e., Stable Diffusion-XL, Uniworld-V1, OmniGen2) yield consistent performance gains (+4.2%, +5.7%, +4.4%) and more realistic effects in spatial relations, highlighting a data-centric paradigm to achieve spatial intelligence in T2I models.

Humans perceive and understand real-world spaces through a stream of visual observations. Therefore, the ability to streamingly maintain and update spatial evidence from potentially unbounded video streams is essential for spatial intelligence. The core challenge is not simply longer context windows but how spatial information is selected, organized, and retained over time. In this paper, we propose Spatial-TTT towards streaming visual-based spatial intelligence with test-time training (TTT), which adapts a subset of parameters (fast weights) to capture and organize spatial evidence over long-horizon scene videos. Specifically, we design a hybrid architecture and adopt large-chunk updates parallel with sliding-window attention for efficient spatial video processing. To further promote spatial awareness, we introduce a spatial-predictive mechanism applied to TTT layers with 3D spatiotemporal convolution, which encourages the model to capture geometric correspondence and temporal continuity across frames. Beyond architecture design, we construct a dataset with dense 3D spatial descriptions, which guides the model to update its fast weights to memorize and organize global 3D spatial signals in a structured manner. Extensive experiments demonstrate that Spatial-TTT improves long-horizon spatial understanding and achieves state-of-the-art performance on video spatial benchmarks. Project page: https://liuff19.github.io/Spatial-TTT.

The increasing availability of large-scale global datasets has generated a demand for scalable spatial prediction methods defined on spherical domains. Classical spatial models that rely on Euclidean distance representations are inappropriate for spherical data because planar projections distort geodesic distances and spatial neighborhood structures, while traditional kriging-based prediction methods are often computationally prohibitive for massive datasets. To address these challenges, we propose a Spherical DeepKriging framework for spatial prediction on S^2. The proposed approach constructs a flexible prediction model by integrating thin-plate spline (TPS) basis functions defined intrinsically on the sphere. Simulation studies and real data analyses are presented to demonstrate the superior predictive performance of the proposed method.

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.

Debates about whether development projects improve living conditions persist, partly because observational estimates can be biased by incomplete adjustment and because reliable outcome data are scarce at the neighborhood level. We address both issues in a continent-scale, sector-specific evaluation of Chinese and World Bank projects across 9,899 neighborhoods in 36 African countries (2002 to 2013), representative of 88% of the population. First, we use a recent dataset that measures living conditions with a machine-learned wealth index derived from contemporaneous satellite imagery, yielding a consistent panel of 6.7 km square mosaics. Second, to strengthen identification, we proxy officials' map-based placement criteria using pre-treatment daytime satellite images and fuse these with rich tabular covariates to estimate funder- and sector-specific ATEs via inverse-probability weighting. Incorporating imagery systematically shrinks effects relative to tabular-only models, indicating prior work likely overstated benefits. On average, both donors raise wealth, with larger gains for China; sector extremes in our sample include Trade and Tourism for the World Bank (+6.27 IWI points), and Emergency Response for China (+14.32). Assignment-mechanism analyses show World Bank placement is generally more predictable from imagery alone, as well as from tabular covariates. This suggests that Chinese project placements are more driven by non-visible, political, or event-driven factors than World Bank placements. To probe residual concerns about selection on observables, we also estimate within-neighborhood (unit) fixed-effects models at a spatial resolution about 450 times finer than prior fixed effects analyses, leveraging the computer-vision-imputed IWI panels; these deliver smaller but directionally consistent effects.

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.

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.

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.

Conditional visual generation has witnessed remarkable progress with the advent of diffusion models (DMs), especially in tasks like control-to-image generation. However, challenges such as expensive computational cost, high inference latency, and difficulties of integration with large language models (LLMs) have necessitated exploring alternatives to DMs. This paper introduces ControlVAR, a novel framework that explores pixel-level controls in visual autoregressive (VAR) modeling for flexible and efficient conditional generation. In contrast to traditional conditional models that learn the conditional distribution, ControlVAR jointly models the distribution of image and pixel-level conditions during training and imposes conditional controls during testing. To enhance the joint modeling, we adopt the next-scale AR prediction paradigm and unify control and image representations. A teacher-forcing guidance strategy is proposed to further facilitate controllable generation with joint modeling. Extensive experiments demonstrate the superior efficacy and flexibility of ControlVAR across various conditional generation tasks against popular conditional DMs, \eg, ControlNet and T2I-Adaptor. Code: https://github.com/lxa9867/ControlVAR.

Despite advancements in Multi-modal Large Language Models (MLLMs) for scene understanding, their performance on complex spatial reasoning tasks requiring mental simulation remains significantly limited. Current methods often rely on passive observation of spatial data, failing to internalize an active mental imagery process. To bridge this gap, we propose SpatialDreamer, a reinforcement learning framework that enables spatial reasoning through a closedloop process of active exploration, visual imagination via a world model, and evidence-grounded reasoning. To address the lack of fine-grained reward supervision in longhorizontal reasoning tasks, we propose Geometric Policy Optimization (GeoPO), which introduces tree-structured sampling and step-level reward estimation with geometric consistency constraints. Extensive experiments demonstrate that SpatialDreamer delivers highly competitive results across multiple challenging benchmarks, signifying a critical advancement in human-like active spatial mental simulation for MLLMs.

Spatial intelligence refers to the ability to perceive, reason about, and describe objects and their relationships within three-dimensional environments, forming a foundation for embodied perception and scene understanding. 3D captioning aims to describe 3D scenes in natural language; however, it remains challenging due to the sparsity and irregularity of point clouds and, more critically, the weak grounding and limited out-of-distribution (OOD) generalization of existing captioners across drastically different environments, including indoor and outdoor 3D scenes. To address this challenge, we propose 3D CoCa v2, a generalizable 3D captioning framework that unifies contrastive vision-language learning with 3D caption generation and further improves robustness via test-time search (TTS) without updating the captioner parameters. 3D CoCa v2 builds on a frozen CLIP-based semantic prior, a spatially-aware 3D scene encoder for geometry, and a multimodal decoder jointly optimized with contrastive and captioning objectives, avoiding external detectors or handcrafted proposals. At inference, TTS produces diverse caption candidates and performs reward-guided selection using a compact scene summary. Experiments show improvements over 3D CoCa of +1.50 CIDEr@0.5IoU on ScanRefer and +1.61 CIDEr@0.5IoU on Nr3D, and +3.8 CIDEr@0.25 in zero-shot OOD evaluation on TOD3Cap. Code will be released at https://github.com/AIGeeksGroup/3DCoCav2.

Learning feature representations of geographical space is vital for any machine learning model that integrates geolocated data, spanning application domains such as remote sensing, ecology, or epidemiology. Recent work mostly embeds coordinates using sine and cosine projections based on Double Fourier Sphere (DFS) features -- these embeddings assume a rectangular data domain even on global data, which can lead to artifacts, especially at the poles. At the same time, relatively little attention has been paid to the exact design of the neural network architectures these functional embeddings are combined with. This work proposes a novel location encoder for globally distributed geographic data that combines spherical harmonic basis functions, natively defined on spherical surfaces, with sinusoidal representation networks (SirenNets) that can be interpreted as learned Double Fourier Sphere embedding. We systematically evaluate the cross-product of positional embeddings and neural network architectures across various classification and regression benchmarks and synthetic evaluation datasets. In contrast to previous approaches that require the combination of both positional encoding and neural networks to learn meaningful representations, we show that both spherical harmonics and sinusoidal representation networks are competitive on their own but set state-of-the-art performances across tasks when combined. We provide source code at www.github.com/marccoru/locationencoder

Observational studies of causal effects require adjustment for confounding factors. In the tabular setting, where these factors are well-defined, separate random variables, the effect of confounding is well understood. However, in public policy, ecology, and in medicine, decisions are often made in non-tabular settings, informed by patterns or objects detected in images (e.g., maps, satellite or tomography imagery). Using such imagery for causal inference presents an opportunity because objects in the image may be related to the treatment and outcome of interest. In these cases, we rely on the images to adjust for confounding but observed data do not directly label the existence of the important objects. Motivated by real-world applications, we formalize this challenge, how it can be handled, and what conditions are sufficient to identify and estimate causal effects. We analyze finite-sample performance using simulation experiments, estimating effects using a propensity adjustment algorithm that employs a machine learning model to estimate the image confounding. Our experiments also examine sensitivity to misspecification of the image pattern mechanism. Finally, we use our methodology to estimate the effects of policy interventions on poverty in African communities from satellite imagery.

Spatial reasoning is a foundational capability for multimodal large language models (MLLMs) to perceive and operate within the physical world. However, existing benchmarks predominantly rely on passive evaluation (e.g., static VQA) or simulator-specific pipelines, failing to assess general interactive spatial understanding. We introduce SpatialWorld, a unified benchmark designed specifically for evaluating the interactive spatial understanding of multimodal agents in complex real-world tasks. Integrating eight heterogeneous simulation backends under a shared, simulator-agnostic protocol, SpatialWorld features 760 human-annotated tasks across diverse domains (e.g., household routines, travel, social collaboration). Agents must solve tasks under vision-only partial observability, actively gathering egocentric visual evidence and expressing decisions via a unified, text-based action interface native to MLLMs. For reliable evaluation, each task includes a human-validated initial state, a reference trajectory, and a terminal-state verifier. Evaluating 15 advanced agents reveals that robust spatial task solving remains challenging: the strongest model, GPT-5, achieves an average task success rate (TSR) of only 17.4%, while the leading open-source model, Qwen-3.5, reaches 14.1%. Further analysis exposes a clear mismatch between task success and execution efficiency, alongside substantial domain-specific performance variations. These bottlenecks in active exploration and long-horizon planning position SpatialWorld as a rigorous testbed for future spatial agents.

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.

Partial correlations quantify linear association between two variables adjusting for the influence of the remaining variables. They form the backbone for graphical models and are readily obtained from the inverse of the covariance matrix. For compositional data, the covariance structure is specified from log ratios of variables, so unless we try to "open" the data via a normalization, this implies changes in the definition and interpretation of partial correlations. In the present work, we elucidate how results derived by Aitchison (1986) lead to a natural definition of partial correlation that has a number of advantages over current measures of association. For this, we show that the residuals of log-ratios between a variable with a reference, when adjusting for all remaining variables including the reference, are reference-independent. Since the reference itself can be controlled for, correlations between residuals are defined for the variables directly without the necessity to recur to ratios except when specifying which variables are partialled out. Thus, perhaps surprisingly, partial correlations do not have the problems commonly found with measures of pairwise association on compositional data. They are well-defined between two variables, are properly scaled, and allow for negative association. By design, they are subcompositionally incoherent, but they share this property with conventional partial correlations (where results change when adjusting for the influence of fewer variables). We discuss the equivalence with normalization-based approaches whenever the normalizing variables are controlled for. We also discuss the partial variances and correlations we obtain from a previously studied data set of Roman glass cups.

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.

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

The pursuit of spatial intelligence fundamentally relies on access to large-scale, fine-grained 3D data. However, existing approaches predominantly construct spatial understanding benchmarks by generating question-answer (QA) pairs from a limited number of manually annotated datasets, rather than systematically annotating new large-scale 3D scenes from raw web data. As a result, their scalability is severely constrained, and model performance is further hindered by domain gaps inherent in these narrowly curated datasets. In this work, we propose Holi-Spatial, the first fully automated, large-scale, spatially-aware multimodal dataset, constructed from raw video inputs without human intervention, using the proposed data curation pipeline. Holi-Spatial supports multi-level spatial supervision, ranging from geometrically accurate 3D Gaussian Splatting (3DGS) reconstructions with rendered depth maps to object-level and relational semantic annotations, together with corresponding spatial Question-Answer (QA) pairs. Following a principled and systematic pipeline, we further construct Holi-Spatial-4M, the first large-scale, high-quality 3D semantic dataset, containing 12K optimized 3DGS scenes, 1.3M 2D masks, 320K 3D bounding boxes, 320K instance captions, 1.2M 3D grounding instances, and 1.2M spatial QA pairs spanning diverse geometric, relational, and semantic reasoning tasks. Holi-Spatial demonstrates exceptional performance in data curation quality, significantly outperforming existing feed-forward and per-scene optimized methods on datasets such as ScanNet, ScanNet++, and DL3DV. Furthermore, fine-tuning Vision-Language Models (VLMs) on spatial reasoning tasks using this dataset has also led to substantial improvements in model performance.

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.

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.

The spatio-temporal relations of impacts of extreme events and their drivers in climate data are not fully understood and there is a need of machine learning approaches to identify such spatio-temporal relations from data. The task, however, is very challenging since there are time delays between extremes and their drivers, and the spatial response of such drivers is inhomogeneous. In this work, we propose a first approach and benchmarks to tackle this challenge. Our approach is trained end-to-end to predict spatio-temporally extremes and spatio-temporally drivers in the physical input variables jointly. By enforcing the network to predict extremes from spatio-temporal binary masks of identified drivers, the network successfully identifies drivers that are correlated with extremes. We evaluate our approach on three newly created synthetic benchmarks, where two of them are based on remote sensing or reanalysis climate data, and on two real-world reanalysis datasets. The source code and datasets are publicly available at the project page https://hakamshams.github.io/IDE.

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.

Many social and environmental phenomena are associated with macroscopic changes in the built environment, captured by satellite imagery on a global scale and with daily temporal resolution. While widely used for prediction, these images and especially image sequences remain underutilized for causal inference, especially in the context of randomized controlled trials (RCTs), where causal identification is established by design. In this paper, we develop and compare a set of general tools for analyzing Conditional Average Treatment Effects (CATEs) from temporal satellite data that can be applied to any RCT where geographical identifiers are available. Through a simulation study, we analyze different modeling strategies for estimating CATE in sequences of satellite images. We find that image sequence representation models with more parameters generally yield a greater ability to detect heterogeneity. To explore the role of model and data choice in practice, we apply the approaches to two influential RCTs -- Banerjee et al. (2015), a poverty study in Cusco, Peru, and Bolsen et al. (2014), a water conservation experiment in Georgia, USA. We benchmark our image sequence models against image-only, tabular-only, and combined image-tabular data sources, summarizing practical implications for investigators in a multivariate analysis. Land cover classifications over satellite images facilitate interpretation of what image features drive heterogeneity. We also show robustness to data and model choice of satellite-based generalization of the RCT results to larger geographical areas outside the original. Overall, this paper shows how satellite sequence data can be incorporated into the analysis of RCTs, and provides evidence about the implications of data, model, and evaluation metric choice for causal analysis.

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

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.

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.

We introduce a novel machine learning model for credit risk by combining tree-boosting with a latent spatio-temporal Gaussian process model accounting for frailty correlation. This allows for modeling non-linearities and interactions among predictor variables in a flexible data-driven manner and for accounting for spatio-temporal variation that is not explained by observable predictor variables. We also show how estimation and prediction can be done in a computationally efficient manner. In an application to a large U.S. mortgage credit risk data set, we find that both predictive default probabilities for individual loans and predictive loan portfolio loss distributions obtained with our novel approach are more accurate compared to conventional independent linear hazard models and also linear spatio-temporal models. Using interpretability tools for machine learning models, we find that the likely reasons for this outperformance are strong interaction and non-linear effects in the predictor variables and the presence of large spatio-temporal frailty effects.

Observational studies require adjustment for confounding factors that are correlated with both the treatment and outcome. In the setting where the observed variables are tabular quantities such as average income in a neighborhood, tools have been developed for addressing such confounding. However, in many parts of the developing world, features about local communities may be scarce. In this context, satellite imagery can play an important role, serving as a proxy for the confounding variables otherwise unobserved. In this paper, we study confounder adjustment in this non-tabular setting, where patterns or objects found in satellite images contribute to the confounder bias. Using the evaluation of anti-poverty aid programs in Africa as our running example, we formalize the challenge of performing causal adjustment with such unstructured data -- what conditions are sufficient to identify causal effects, how to perform estimation, and how to quantify the ways in which certain aspects of the unstructured image object are most predictive of the treatment decision. Via simulation, we also explore the sensitivity of satellite image-based observational inference to image resolution and to misspecification of the image-associated confounder. Finally, we apply these tools in estimating the effect of anti-poverty interventions in African communities from satellite imagery.

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 intelligence is essential for multimodal large language models, yet current benchmarks largely assess it only from an understanding perspective. We ask whether modern generative or unified multimodal models also possess generative spatial intelligence (GSI), the ability to respect and manipulate 3D spatial constraints during image generation, and whether such capability can be measured or improved. We introduce GSI-Bench, the first benchmark designed to quantify GSI through spatially grounded image editing. It consists of two complementary components: GSI-Real, a high-quality real-world dataset built via a 3D-prior-guided generation and filtering pipeline, and GSI-Syn, a large-scale synthetic benchmark with controllable spatial operations and fully automated labeling. Together with a unified evaluation protocol, GSI-Bench enables scalable, model-agnostic assessment of spatial compliance and editing fidelity. Experiments show that fine-tuning unified multimodal models on GSI-Syn yields substantial gains on both synthetic and real tasks and, strikingly, also improves downstream spatial understanding. This provides the first clear evidence that generative training can tangibly strengthen spatial reasoning, establishing a new pathway for advancing spatial intelligence in multimodal models.

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

The choice of representation for geographic location significantly impacts the accuracy of models for a broad range of geospatial tasks, including fine-grained species classification, population density estimation, and biome classification. Recent works like SatCLIP and GeoCLIP learn such representations by contrastively aligning geolocation with co-located images. While these methods work exceptionally well, in this paper, we posit that the current training strategies fail to fully capture the important visual features. We provide an information-theoretic perspective on why the resulting embeddings from these methods discard crucial visual information that is important for many downstream tasks. To solve this problem, we propose a novel retrieval-augmented strategy called RANGE. We build our method on the intuition that the visual features of a location can be estimated by combining the visual features from multiple similar-looking locations. We evaluate our method across a wide variety of tasks. Our results show that RANGE outperforms the existing state-of-the-art models with significant margins in most tasks. We show gains of up to 13.1% on classification tasks and 0.145 R^2 on regression tasks. All our code and models will be made available at: https://github.com/mvrl/RANGE.

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.

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.

Conventional supervised learning methods typically assume i.i.d samples and are found to be sensitive to out-of-distribution (OOD) data. We propose Generative Causal Representation Learning (GCRL) which leverages causality to facilitate knowledge transfer under distribution shifts. While we evaluate the effectiveness of our proposed method in human trajectory prediction models, GCRL can be applied to other domains as well. First, we propose a novel causal model that explains the generative factors in motion forecasting datasets using features that are common across all environments and with features that are specific to each environment. Selection variables are used to determine which parts of the model can be directly transferred to a new environment without fine-tuning. Second, we propose an end-to-end variational learning paradigm to learn the causal mechanisms that generate observations from features. GCRL is supported by strong theoretical results that imply identifiability of the causal model under certain assumptions. Experimental results on synthetic and real-world motion forecasting datasets show the robustness and effectiveness of our proposed method for knowledge transfer under zero-shot and low-shot settings by substantially outperforming the prior motion forecasting models on out-of-distribution prediction. Our code is available at https://github.com/sshirahmad/GCRL.

Large climate-model ensembles are computationally expensive; yet many downstream analyses would benefit from additional, statistically consistent realizations of spatiotemporal climate variables. We study a generative modeling approach for producing new realizations from a limited set of available runs by transferring structure learned across an ensemble. Using monthly near-surface temperature time series from ten independent reanalysis realizations (ERA5), we find that a vanilla conditional variational autoencoder (CVAE) trained jointly across realizations yields a fragmented latent space that fails to generalize to unseen ensemble members. To address this, we introduce a latent-constrained CVAE (LC-CVAE) that enforces cross-realization homogeneity of latent embeddings at a small set of shared geographic 'anchor' locations. We then use multi-output Gaussian process regression in the latent space to predict latent coordinates at unsampled locations in a new realization, followed by decoding to generate full time series fields. Experiments and ablations demonstrate (i) instability when training on a single realization, (ii) diminishing returns after incorporating roughly five realizations, and (iii) a trade-off between spatial coverage and reconstruction quality that is closely linked to the average neighbor distance in latent space.

We show that there is a general, informative and reliable procedure for discovering causal relations when, for all the investigator knows, both latent variables and selection bias may be at work. Given information about conditional independence and dependence relations between measured variables, even when latent variables and selection bias may be present, there are sufficient conditions for reliably concluding that there is a causal path from one variable to another, and sufficient conditions for reliably concluding when no such causal path exists.

Recent progress in text-to-image generation has greatly advanced visual fidelity and creativity, but it has also imposed higher demands on prompt complexity-particularly in encoding intricate spatial relationships. In such cases, achieving satisfactory results often requires multiple sampling attempts. To address this challenge, we introduce a novel method that strengthens the spatial understanding of current image generation models. We first construct the SpatialReward-Dataset with over 80k preference pairs. Building on this dataset, we build SpatialScore, a reward model designed to evaluate the accuracy of spatial relationships in text-to-image generation, achieving performance that even surpasses leading proprietary models on spatial evaluation. We further demonstrate that this reward model effectively enables online reinforcement learning for the complex spatial generation. Extensive experiments across multiple benchmarks show that our specialized reward model yields significant and consistent gains in spatial understanding for image generation.

Recent advancements in Large Vision-Language Models (VLMs) have demonstrated exceptional semantic understanding, yet these models consistently struggle with spatial reasoning, often failing at fundamental geometric tasks such as depth ordering and precise coordinate grounding. Recent efforts introduce spatial supervision from scene-centric datasets (e.g., multi-view scans or indoor video), but are constrained by the limited number of underlying scenes. As a result, the scale and diversity of such data remain significantly smaller than those of web-scale 2D image collections. To address this limitation, we propose SpatialForge, a scalable data synthesis pipeline that transforms in-the-wild 2D images into spatial reasoning supervision. Our approach decomposes spatial reasoning into perception and relation, and constructs structured supervision signals covering depth, layout, and viewpoint-dependent reasoning, with automatic verification to ensure data quality. Based on this pipeline, we build SpatialForge-10M, a large-scale dataset containing 10 million spatial QA pairs. Extensive experiments across multiple spatial reasoning benchmarks demonstrate that training on SpatialForge-10M significantly improves the spatial reasoning ability of standard VLMs, highlighting the effectiveness of scaling 2D data for 3D-aware spatial reasoning.

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.

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/.

While large language models have become the prevailing approach for agentic reasoning and planning, their success in symbolic domains does not readily translate to the physical world. Spatial intelligence, the ability to perceive 3D structure, reason about object relationships, and act under physical constraints, is an orthogonal capability that proves important for embodied agents. Existing surveys address either agentic architectures or spatial domains in isolation. None provide a unified framework connecting these complementary capabilities. This paper bridges that gap. Through a thorough review of over 2,000 papers, citing 742 works from top-tier venues, we introduce a unified three-axis taxonomy connecting agentic capabilities with spatial tasks across scales. Crucially, we distinguish spatial grounding (metric understanding of geometry and physics) from symbolic grounding (associating images with text), arguing that perception alone does not confer agency. Our analysis reveals three key findings mapped to these axes: (1) hierarchical memory systems (Capability axis) are important for long-horizon spatial tasks. (2) GNN-LLM integration (Task axis) is a promising approach for structured spatial reasoning. (3) World models (Scale axis) are essential for safe deployment across micro-to-macro spatial scales. We conclude by identifying six grand challenges and outlining directions for future research, including the need for unified evaluation frameworks to standardize cross-domain assessment. This taxonomy provides a foundation for unifying fragmented research efforts and enabling the next generation of spatially-aware autonomous systems in robotics, autonomous vehicles, and geospatial intelligence.

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.

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/.

Covariates provide valuable information on external factors that influence time series and are critical in many real-world time series forecasting tasks. For example, in retail, covariates may indicate promotions or peak dates such as holiday seasons that heavily influence demand forecasts. Recent advances in pretraining large language model architectures for time series forecasting have led to highly accurate forecasters. However, the majority of these models do not readily use covariates as they are often specific to a certain task or domain. This paper introduces a new method to incorporate covariates into pretrained time series forecasting models. Our proposed approach incorporates covariate information into pretrained forecasting models through modular blocks that inject past and future covariate information, without necessarily modifying the pretrained model in consideration. In order to evaluate our approach, we introduce a benchmark composed of 32 different synthetic datasets with varying dynamics to evaluate the effectivity of forecasting models with covariates. Extensive evaluations on both synthetic and real datasets show that our approach effectively incorporates covariate information into pretrained models, outperforming existing baselines.

Spatial reasoning is a fundamental aspect of human cognition, yet it remains a major challenge for contemporary vision-language models (VLMs). Prior work largely relied on synthetic or LLM-generated environments with limited task designs and puzzle-like setups, failing to capture the real-world complexity, visual noise, and diverse spatial relationships that VLMs encounter. To address this, we introduce SpatiaLab, a comprehensive benchmark for evaluating VLMs' spatial reasoning in realistic, unconstrained contexts. SpatiaLab comprises 1,400 visual question-answer pairs across six major categories: Relative Positioning, Depth & Occlusion, Orientation, Size & Scale, Spatial Navigation, and 3D Geometry, each with five subcategories, yielding 30 distinct task types. Each subcategory contains at least 25 questions, and each main category includes at least 200 questions, supporting both multiple-choice and open-ended evaluation. Experiments across diverse state-of-the-art VLMs, including open- and closed-source models, reasoning-focused, and specialized spatial reasoning models, reveal a substantial gap in spatial reasoning capabilities compared with humans. In the multiple-choice setup, InternVL3.5-72B achieves 54.93% accuracy versus 87.57% for humans. In the open-ended setting, all models show a performance drop of around 10-25%, with GPT-5-mini scoring highest at 40.93% versus 64.93% for humans. These results highlight key limitations in handling complex spatial relationships, depth perception, navigation, and 3D geometry. By providing a diverse, real-world evaluation framework, SpatiaLab exposes critical challenges and opportunities for advancing VLMs' spatial reasoning, offering a benchmark to guide future research toward robust, human-aligned spatial understanding. SpatiaLab is available at: https://spatialab-reasoning.github.io/.

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.

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.

This paper proposes a method for the automatic creation of variables (in the case of regression) that complement the information contained in the initial input vector. The method works as a pre-processing step in which the continuous values of the variable to be regressed are discretized into a set of intervals which are then used to define value thresholds. Then classifiers are trained to predict whether the value to be regressed is less than or equal to each of these thresholds. The different outputs of the classifiers are then concatenated in the form of an additional vector of variables that enriches the initial vector of the regression problem. The implemented system can thus be considered as a generic pre-processing tool. We tested the proposed enrichment method with 5 types of regressors and evaluated it in 33 regression datasets. Our experimental results confirm the interest of the approach.

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 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.

Spatial embodied intelligence requires agents to act to acquire information under partial observability. While multimodal foundation models excel at passive perception, their capacity for active, self-directed exploration remains understudied. We propose Theory of Space, defined as an agent's ability to actively acquire information through self-directed, active exploration and to construct, revise, and exploit a spatial belief from sequential, partial observations. We evaluate this through a benchmark where the goal is curiosity-driven exploration to build an accurate cognitive map. A key innovation is spatial belief probing, which prompts models to reveal their internal spatial representations at each step. Our evaluation of state-of-the-art models reveals several critical bottlenecks. First, we identify an Active-Passive Gap, where performance drops significantly when agents must autonomously gather information. Second, we find high inefficiency, as models explore unsystematically compared to program-based proxies. Through belief probing, we diagnose that while perception is an initial bottleneck, global beliefs suffer from instability that causes spatial knowledge to degrade over time. Finally, using a false belief paradigm, we uncover Belief Inertia, where agents fail to update obsolete priors with new evidence. This issue is present in text-based agents but is particularly severe in vision-based models. Our findings suggest that current foundation models struggle to maintain coherent, revisable spatial beliefs during active exploration.

Spatial reasoning is a fundamental capability for vision-language models (VLMs) deployed in real-world environments. However, visual observations are inherently limited representations of a 3D world: occlusion can render objects invisible, and perspective can make geometric properties misleading. Despite this, existing spatial reasoning benchmarks typically assume that observations are sufficient and reliable, focusing on whether models produce correct answers rather than whether they recognize when a question cannot be answered and what additional observations would be needed. In this work, we challenge this assumption by constructing a controlled evaluation framework, SpatialUncertain, and introducing two types of observation challenges: (1) occlusion, which hides target information, and (2) perspective ambiguity, which produces misleading visual cues. For each configuration, we design spatial questions that are answerable under clean observations but require abstention under the introduced challenges. We further evaluate whether models can identify which additional viewpoints would resolve perspective ambiguity. Our results across a diverse set of frontier open- and closed-source VLMs reveal two consistent failure modes. First, models are prone to overconfident answering, attempting to solve spatial reasoning tasks even when visual evidence is incomplete or misleading, with average accuracy around 30\% under occlusion and below 10\% under perspective ambiguity. Second, even when additional views are available, some models perform near random chance in identifying which would provide reliable evidence. Together, our findings call for moving beyond answer correctness toward evaluating whether models know when to abstain and how to seek reliable evidence.

The presence of distribution shifts poses a significant challenge for deploying modern machine learning models in real-world applications. This work focuses on the target shift problem in a regression setting (Zhang et al., 2013; Nguyen et al., 2016). More specifically, the target variable y (also known as the response variable), which is continuous, has different marginal distributions in the training source and testing domain, while the conditional distribution of features x given y remains the same. While most literature focuses on classification tasks with finite target space, the regression problem has an infinite dimensional target space, which makes many of the existing methods inapplicable. In this work, we show that the continuous target shift problem can be addressed by estimating the importance weight function from an ill-posed integral equation. We propose a nonparametric regularized approach named ReTaSA to solve the ill-posed integral equation and provide theoretical justification for the estimated importance weight function. The effectiveness of the proposed method has been demonstrated with extensive numerical studies on synthetic and real-world datasets.

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.

Vision-language models (VLMs) achieve strong performance on spatial reasoning benchmarks, yet it remains unclear whether this reflects structured 3D understanding or reliance on statistical shortcuts in natural images. We introduce a representation-level analysis framework that constructs minimal contrastive pairs to measure how spatial axes are organized and disentangled within VLM embeddings. Our analysis across multiple model families reveals a consistent vertical-distance entanglement: models conflate vertical image position with distance, mirroring the perspective bias of natural photographs. This bias produces a significant accuracy gap between perspective-consistent and counter-heuristic examples, and intensifies under data scaling even as overall benchmark accuracy improves. We further show that models with similar benchmark scores can exhibit different internal representations, and that these differences predict accuracy and robustness across diverse spatial reasoning benchmarks. To isolate this bias from evaluation-set skew, we introduce SpatialTunnel, a synthetic benchmark designed to expose spatial shortcut biases by removing common correlations present in natural images. Experiments confirm that the entanglement is model-intrinsic, and that models with well-separated spatial axes exhibit greater robustness, suggesting that well-structured spatial representations lead to more reliable spatial reasoning across diverse benchmarks. Code and benchmark are available on the project page: https://cheolhong0916.github.io/whyfarlooksup.github.io/.

Autoregressive video diffusion models have proved effective for world modeling and interactive scene generation, with Minecraft gameplay as a representative application. To faithfully simulate play, a model must generate natural content while exploring new scenes and preserve spatial consistency when revisiting explored areas. Under limited computation budgets, it must compress and exploit historical cues within a finite context window, which exposes a trade-off: Temporal-only memory lacks long-term spatial consistency, whereas adding spatial memory strengthens consistency but may degrade new scene generation quality when the model over-relies on insufficient spatial context. We present Memory Forcing, a learning framework that pairs training protocols with a geometry-indexed spatial memory. Hybrid Training exposes distinct gameplay regimes, guiding the model to rely on temporal memory during exploration and incorporate spatial memory for revisits. Chained Forward Training extends autoregressive training with model rollouts, where chained predictions create larger pose variations and encourage reliance on spatial memory for maintaining consistency. Point-to-Frame Retrieval efficiently retrieves history by mapping currently visible points to their source frames, while Incremental 3D Reconstruction maintains and updates an explicit 3D cache. Extensive experiments demonstrate that Memory Forcing achieves superior long-term spatial consistency and generative quality across diverse environments, while maintaining computational efficiency for extended sequences.

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.

Spatial reasoning (SR), the ability to infer 3D spatial information from 2D inputs, is essential for real-world applications such as embodied AI and autonomous driving. However, existing research primarily focuses on indoor environments and typically relies on multi-view observations, which limits their generalizability to outdoor scenarios and constrains their applicability to monocular images, the most common real-world setting. In this work, we propose MonoSR, a large-scale monocular spatial reasoning dataset that spans diverse scenarios including indoor, outdoor, and object-centric settings, and supports multiple question types. MonoSR provides a path toward open-world monocular spatial reasoning. Beyond introducing the dataset, we evaluate advanced vision-language models to reveal their limitations on this challenging task. We further analyze whether auxiliary information is crucial for monocular spatial reasoning and offer practical guidance for designing future models. These contributions collectively establish a foundation for advancing monocular spatial reasoning in real-world, open-world environments.

Spatial understanding is a fundamental cornerstone of human-level intelligence. Nonetheless, current research predominantly focuses on domain-specific data production, leaving a critical void: the absence of a principled, open-source engine capable of fully unleashing the potential of high-quality spatial data. To bridge this gap, we elucidate the design principles of a robust data generation system and introduce OpenSpatial -- an open-source data engine engineered for high quality, extensive scalability, broad task diversity, and optimized efficiency. OpenSpatial adopts 3D bounding boxes as the fundamental primitive to construct a comprehensive data hierarchy across five foundational tasks: Spatial Measurement (SM), Spatial Relationship (SR), Camera Perception (CP), Multi-view Consistency (MC), and Scene-Aware Reasoning (SAR). Leveraging this scalable infrastructure, we curate OpenSpatial-3M, a large-scale dataset comprising 3 million high-fidelity samples. Extensive evaluations demonstrate that versatile models trained on our dataset achieve state-of-the-art performance across a wide spectrum of spatial reasoning benchmarks. Notably, the best-performing model exhibits a substantial average improvement of 19 percent, relatively. Furthermore, we provide a systematic analysis of how data attributes influence spatial perception. By open-sourcing both the engine and the 3M-scale dataset, we provide a robust foundation to accelerate future research in spatial intelligence.

As of writing this paper, COVID-19 (Coronavirus disease 2019) has spread to more than 220 countries and territories. Following the outbreak, the pandemic's seriousness has made people more active on social media, especially on the microblogging platforms such as Twitter and Weibo. The pandemic-specific discourse has remained on-trend on these platforms for months now. Previous studies have confirmed the contributions of such socially generated conversations towards situational awareness of crisis events. The early forecasts of cases are essential to authorities to estimate the requirements of resources needed to cope with the outgrowths of the virus. Therefore, this study attempts to incorporate the public discourse in the design of forecasting models particularly targeted for the steep-hill region of an ongoing wave. We propose a sentiment-involved topic-based latent variables search methodology for designing forecasting models from publicly available Twitter conversations. As a use case, we implement the proposed methodology on Australian COVID-19 daily cases and Twitter conversations generated within the country. Experimental results: (i) show the presence of latent social media variables that Granger-cause the daily COVID-19 confirmed cases, and (ii) confirm that those variables offer additional prediction capability to forecasting models. Further, the results show that the inclusion of social media variables introduces 48.83--51.38% improvements on RMSE over the baseline models. We also release the large-scale COVID-19 specific geotagged global tweets dataset, MegaGeoCOV, to the public anticipating that the geotagged data of this scale would aid in understanding the conversational dynamics of the pandemic through other spatial and temporal contexts.

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.

Researchers are usually interested in examining the impact of covariates when separating heterogeneous samples into latent classes that are more homogeneous. The majority of theoretical and empirical studies with such aims have focused on identifying covariates as predictors of class membership in the structural equation modeling framework. In other words, the covariates only indirectly affect the sample heterogeneity. However, the covariates' influence on between-individual differences can also be direct. This article presents a mixture model that investigates covariates to explain within-cluster and between-cluster heterogeneity simultaneously, known as a mixture-of-experts (MoE) model. This study aims to extend the MoE framework to investigate heterogeneity in nonlinear trajectories: to identify latent classes, covariates as predictors to clusters, and covariates that explain within-cluster differences in change patterns over time. Our simulation studies demonstrate that the proposed model generally estimates the parameters unbiasedly, precisely and exhibits appropriate empirical coverage for a nominal 95% confidence interval. This study also proposes implementing structural equation model forests to shrink the covariate space of the proposed mixture model. We illustrate how to select covariates and construct the proposed model with longitudinal mathematics achievement data. Additionally, we demonstrate that the proposed mixture model can be further extended in the structural equation modeling framework by allowing the covariates that have direct effects to be time-varying.

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.

Knowledge about the hidden factors that determine particular system dynamics is crucial for both explaining them and pursuing goal-directed interventions. Inferring these factors from time series data without supervision remains an open challenge. Here, we focus on spatiotemporal processes, including wave propagation and weather dynamics, for which we assume that universal causes (e.g. physics) apply throughout space and time. A recently introduced DIstributed SpatioTemporal graph Artificial Neural network Architecture (DISTANA) is used and enhanced to learn such processes, requiring fewer parameters and achieving significantly more accurate predictions compared to temporal convolutional neural networks and other related approaches. We show that DISTANA, when combined with a retrospective latent state inference principle called active tuning, can reliably derive location-respective hidden causal factors. In a current weather prediction benchmark, DISTANA infers our planet's land-sea mask solely by observing temperature dynamics and, meanwhile, uses the self inferred information to improve its own future temperature predictions.

Vision-Language Models (VLMs) are increasingly deployed in embodied environments, where they need produce numerical outputs such as action magnitudes and spatial coordinates. Although these numbers appear meaningful, it remains unclear whether these numerical outputs are genuinely grounded in spatial perception. Therefore, in this work, we revisit spatial numerical understanding through SpaceNum, a unified framework that captures two complementary settings: numbers as dynamic transitions during spatial exploration, and numbers as static layouts in spatial reasoning. We formulate two bidirectional tasks, Num2Space and Space2Num, to evaluate how well VLMs map between vision-side spatial structure and language-side numerical representations. We systematically study whether current VLMs truly understand numerical values in spatial settings. Across dynamic transitions and static layouts, we find that models largely fail to ground numbers in spatial meaning and often perform close to random guess. Through error analysis, reasoning trace analysis, and controlled interventions, we show that current VLMs rely heavily on shallow spatial cues, struggle to build stable coordinate-aware representations, and fail to abstract structured spatial layouts from visual observations. We further show that explicit reasoning provides only marginal gains, while tuning can partially improve spatial numerical understanding and transfer to external spatial reasoning benchmarks.

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.

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.

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.

Recent studies have extended the application of large language models (LLMs) to geographic problems, revealing surprising geospatial competence even without explicit spatial supervision. However, LLMs still face challenges in spatial consistency, multi-hop reasoning, and geographic bias. To address these issues, we propose GeoSR, a self-refining agentic reasoning framework that embeds core geographic principles -- most notably Tobler's First Law of Geography -- into an iterative prediction loop. In GeoSR, the reasoning process is decomposed into three collaborating agents: (1) a variable-selection agent that selects relevant covariates from the same location; (2) a point-selection agent that chooses reference predictions at nearby locations generated by the LLM in previous rounds; and (3) a refine agent that coordinates the iterative refinement process by evaluating prediction quality and triggering further rounds when necessary. This agentic loop progressively improves prediction quality by leveraging both spatial dependencies and inter-variable relationships. We validate GeoSR on tasks ranging from physical-world property estimation to socioeconomic prediction. Experimental results show consistent improvements over standard prompting strategies, demonstrating that incorporating geostatistical priors and spatially structured reasoning into LLMs leads to more accurate and equitable geospatial predictions. The code of GeoSR is available at https://github.com/JinfanTang/GeoSR.

Mediated by today's visual displays, information space allows users to discover, access and interact with a wide range of digital and physical information. The information presented in this space may be digital, physical or a blend of both, and appear across different dimensions - such as texts, images, 3D content and physical objects embedded within real-world environment. Navigating within the information space often involves interacting with mixed-dimensional entities, visually represented in both 2D and 3D. At times, interactions also involve transitioning among entities represented in different dimensions. We introduce the concept of mixed-dimensional information space, encompassing entities represented in both 2D and 3D. Interactions within the mixed-dimensional information space should be seamless and efficient: users should be able to focus on their primary tasks without being distracted by interactions with or transitions between entities. While incorporating 3D representations into the mixed-dimensional information space offers intuitive and immersive ways to interact with complex information, it is important to address potential seams and inefficiencies that arise while interacting with both 2D and 3D entities. This dissertation introduces new interactive techniques and systems to realize seamless and efficient interactions within the mixed-dimensional information space. This dissertation introduces three interactive systems: MemoVis which aims to use emergent generative AI to help users create reference images for 3D design feedback; PaperToPlace which demonstrates how paper-based instruction documents can be transformed and spatialized into a context-aware MR experience; and VRContour which explores how contour delineation workflow can be brought into VR.

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

Small sample sizes are common in many disciplines, which necessitates pooling roughly similar datasets across multiple institutions to study weak but relevant associations between images and disease outcomes. Such data often manifest shift/imbalance in covariates (i.e., secondary non-imaging data). Controlling for such nuisance variables is common within standard statistical analysis, but the ideas do not directly apply to overparameterized models. Consequently, recent work has shown how strategies from invariant representation learning provides a meaningful starting point, but the current repertoire of methods is limited to accounting for shifts/imbalances in just a couple of covariates at a time. In this paper, we show how viewing this problem from the perspective of Category theory provides a simple and effective solution that completely avoids elaborate multi-stage training pipelines that would otherwise be needed. We show the effectiveness of this approach via extensive experiments on real datasets. Further, we discuss how this style of formulation offers a unified perspective on at least 5+ distinct problem settings, from self-supervised learning to matching problems in 3D reconstruction.

Precise spatial understanding in Earth Observation is essential for translating raw aerial imagery into actionable insights for critical applications like urban planning, environmental monitoring and disaster management. However, Multimodal Large Language Models exhibit critical deficiencies in fine-grained spatial understanding within Remote Sensing, primarily due to a reliance on limited or repurposed legacy datasets. To bridge this gap, we introduce a large-scale dataset grounded in verifiable cadastral vector data, comprising 3.8 million annotated objects across 510k high-resolution images with 135 granular semantic categories. We validate this resource through a comprehensive instruction-tuning benchmark spanning seven spatial reasoning tasks. Our evaluation establishes a robust baseline using a standard LLaVA architecture. We show that while current RS-specialized and commercial models (e.g., Gemini) struggle in zero-shot settings, high-fidelity supervision effectively bridges this gap, enabling standard architectures to master fine-grained spatial grounding without complex architectural modifications.

We develop a method to generate predictive regions that cover a multivariate response variable with a user-specified probability. Our work is composed of two components. First, we use a deep generative model to learn a representation of the response that has a unimodal distribution. Existing multiple-output quantile regression approaches are effective in such cases, so we apply them on the learned representation, and then transform the solution to the original space of the response. This process results in a flexible and informative region that can have an arbitrary shape, a property that existing methods lack. Second, we propose an extension of conformal prediction to the multivariate response setting that modifies any method to return sets with a pre-specified coverage level. The desired coverage is theoretically guaranteed in the finite-sample case for any distribution. Experiments conducted on both real and synthetic data show that our method constructs regions that are significantly smaller compared to existing techniques.

Multimodal Large Language Models (MLLMs) have demonstrated impressive performance in general vision-language tasks. However, recent studies have exposed critical limitations in their spatial reasoning capabilities. This deficiency in spatial reasoning significantly constrains MLLMs' ability to interact effectively with the physical world, thereby limiting their broader applications. We argue that spatial reasoning capabilities will not naturally emerge from merely scaling existing architectures and training methodologies. Instead, this challenge demands dedicated attention to fundamental modifications in the current MLLM development approach. In this position paper, we first establish a comprehensive framework for spatial reasoning within the context of MLLMs. We then elaborate on its pivotal role in real-world applications. Through systematic analysis, we examine how individual components of the current methodology, from training data to reasoning mechanisms, influence spatial reasoning capabilities. This examination reveals critical limitations while simultaneously identifying promising avenues for advancement. Our work aims to direct the AI research community's attention toward these crucial yet underexplored aspects. By highlighting these challenges and opportunities, we seek to catalyze progress toward achieving human-like spatial reasoning capabilities in MLLMs.

A ubiquitous feature of data of our era is their extra-large sizes and dimensions. Analyzing such high-dimensional data poses significant challenges, since the feature dimension is often much larger than the sample size. This thesis introduces robust and computationally efficient methods to address several common challenges associated with high-dimensional data. In my first manuscript, I propose a coherent approach to variable screening that accommodates nonlinear associations. I develop a novel variable screening method that transcends traditional linear assumptions by leveraging mutual information, with an intended application in neuroimaging data. This approach allows for accurate identification of important variables by capturing nonlinear as well as linear relationships between the outcome and covariates. Building on this foundation, I develop new optimization methods for sparse estimation using nonconvex penalties in my second manuscript. These methods address notable challenges in current statistical computing practices, facilitating computationally efficient and robust analyses of complex datasets. The proposed method can be applied to a general class of optimization problems. In my third manuscript, I contribute to robust modeling of high-dimensional correlated observations by developing a mixed-effects model based on Tsallis power-law entropy maximization and discussed the theoretical properties of such distribution. This model surpasses the constraints of conventional Gaussian models by accommodating a broader class of distributions with enhanced robustness to outliers. Additionally, I develop a proximal nonlinear conjugate gradient algorithm that accelerates convergence while maintaining numerical stability, along with rigorous statistical properties for the proposed framework.

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

While Vision-Language Models (VLMs) exhibit exceptional 2D visual understanding, their ability to comprehend and reason about 3D space--a cornerstone of spatial intelligence--remains superficial. Current methodologies attempt to bridge this domain gap either by relying on explicit 3D modalities or by augmenting VLMs with partial, view-conditioned geometric priors. However, such approaches hinder scalability and ultimately burden the language model with the ill-posed task of implicitly reconstructing holistic 3D geometry from sparse cues. In this paper, we argue that spatial intelligence can emerge inherently from 2D vision alone, rather than being imposed via explicit spatial instruction tuning. To this end, we introduce Spa3R, a self-supervised framework that learns a unified, view-invariant spatial representation directly from unposed multi-view images. Spa3R is built upon the proposed Predictive Spatial Field Modeling (PSFM) paradigm, where Spa3R learns to synthesize feature fields for arbitrary unseen views conditioned on a compact latent representation, thereby internalizing a holistic and coherent understanding of the underlying 3D scene. We further integrate the pre-trained Spa3R Encoder into existing VLMs via a lightweight adapter to form Spa3-VLM, effectively grounding language reasoning in a global spatial context. Experiments on the challenging VSI-Bench demonstrate that Spa3-VLM achieves state-of-the-art accuracy of 58.6% on 3D VQA, significantly outperforming prior methods. These results highlight PSFM as a scalable path toward advancing spatial intelligence. Code is available at https://github.com/hustvl/Spa3R.

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