Daily Papers

Recent advances in scene understanding benefit a lot from depth maps because of the 3D geometry information, especially in complex conditions (e.g., low light and overexposed). Existing approaches encode depth maps along with RGB images and perform feature fusion between them to enable more robust predictions. Taking into account that depth can be regarded as a geometry supplement for RGB images, a straightforward question arises: Do we really need to explicitly encode depth information with neural networks as done for RGB images? Based on this insight, in this paper, we investigate a new way to learn RGBD feature representations and present DFormerv2, a strong RGBD encoder that explicitly uses depth maps as geometry priors rather than encoding depth information with neural networks. Our goal is to extract the geometry clues from the depth and spatial distances among all the image patch tokens, which will then be used as geometry priors to allocate attention weights in self-attention. Extensive experiments demonstrate that DFormerv2 exhibits exceptional performance in various RGBD semantic segmentation benchmarks. Code is available at: https://github.com/VCIP-RGBD/DFormer.

Transformer first appears in the field of natural language processing and is later migrated to the computer vision domain, where it demonstrates excellent performance in vision tasks. However, recently, Retentive Network (RetNet) has emerged as an architecture with the potential to replace Transformer, attracting widespread attention in the NLP community. Therefore, we raise the question of whether transferring RetNet's idea to vision can also bring outstanding performance to vision tasks. To address this, we combine RetNet and Transformer to propose RMT. Inspired by RetNet, RMT introduces explicit decay into the vision backbone, bringing prior knowledge related to spatial distances to the vision model. This distance-related spatial prior allows for explicit control of the range of tokens that each token can attend to. Additionally, to reduce the computational cost of global modeling, we decompose this modeling process along the two coordinate axes of the image. Abundant experiments have demonstrated that our RMT exhibits exceptional performance across various computer vision tasks. For example, RMT achieves 84.1% Top1-acc on ImageNet-1k using merely 4.5G FLOPs. To the best of our knowledge, among all models, RMT achieves the highest Top1-acc when models are of similar size and trained with the same strategy. Moreover, RMT significantly outperforms existing vision backbones in downstream tasks such as object detection, instance segmentation, and semantic segmentation. Our work is still in progress.

In this work, we introduce a challenging image restoration task, referred to as SuperInpaint, which aims to reconstruct missing regions in low-resolution images and generate completed images with arbitrarily higher resolutions. We have found that this task cannot be effectively addressed by stacking state-of-the-art super-resolution and image inpainting methods as they amplify each other's flaws, leading to noticeable artifacts. To overcome these limitations, we propose the detail-enhanced attentional implicit representation (DEAR) that can achieve SuperInpaint with a single model, resulting in high-quality completed images with arbitrary resolutions. Specifically, we use a deep convolutional network to extract the latent embedding of an input image and then enhance the high-frequency components of the latent embedding via an adaptive high-pass filter. This leads to detail-enhanced semantic embedding. We further feed the semantic embedding into an unmask-attentional module that suppresses embeddings from ineffective masked pixels. Additionally, we extract a pixel-wise importance map that indicates which pixels should be used for image reconstruction. Given the coordinates of a pixel we want to reconstruct, we first collect its neighboring pixels in the input image and extract their detail-enhanced semantic embeddings, unmask-attentional semantic embeddings, importance values, and spatial distances to the desired pixel. Then, we feed all the above terms into an implicit representation and generate the color of the specified pixel. To evaluate our method, we extend three existing datasets for this new task and build 18 meaningful baselines using SOTA inpainting and super-resolution methods. Extensive experimental results demonstrate that our method outperforms all existing methods by a significant margin on four widely used metrics.

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

While recent years have witnessed great progress on using diffusion models for video generation, most of them are simple extensions of image generation frameworks, which fail to explicitly consider one of the key differences between videos and images, i.e., motion. In this paper, we propose a novel motion-aware video generation (MoVideo) framework that takes motion into consideration from two aspects: video depth and optical flow. The former regulates motion by per-frame object distances and spatial layouts, while the later describes motion by cross-frame correspondences that help in preserving fine details and improving temporal consistency. More specifically, given a key frame that exists or generated from text prompts, we first design a diffusion model with spatio-temporal modules to generate the video depth and the corresponding optical flows. Then, the video is generated in the latent space by another spatio-temporal diffusion model under the guidance of depth, optical flow-based warped latent video and the calculated occlusion mask. Lastly, we use optical flows again to align and refine different frames for better video decoding from the latent space to the pixel space. In experiments, MoVideo achieves state-of-the-art results in both text-to-video and image-to-video generation, showing promising prompt consistency, frame consistency and visual quality.

In this work, we propose a disruptively frugal LiDAR perception dataflow that generates rather than senses parts of the environment that are either predictable based on the extensive training of the environment or have limited consequence to the overall prediction accuracy. Therefore, the proposed methodology trades off sensing energy with training data for low-power robotics and autonomous navigation to operate frugally with sensors, extending their lifetime on a single battery charge. Our proposed generative pre-training strategy for this purpose, called as radially masked autoencoding (R-MAE), can also be readily implemented in a typical LiDAR system by selectively activating and controlling the laser power for randomly generated angular regions during on-field operations. Our extensive evaluations show that pre-training with R-MAE enables focusing on the radial segments of the data, thereby capturing spatial relationships and distances between objects more effectively than conventional procedures. Therefore, the proposed methodology not only reduces sensing energy but also improves prediction accuracy. For example, our extensive evaluations on Waymo, nuScenes, and KITTI datasets show that the approach achieves over a 5% average precision improvement in detection tasks across datasets and over a 4% accuracy improvement in transferring domains from Waymo and nuScenes to KITTI. In 3D object detection, it enhances small object detection by up to 4.37% in AP at moderate difficulty levels in the KITTI dataset. Even with 90% radial masking, it surpasses baseline models by up to 5.59% in mAP/mAPH across all object classes in the Waymo dataset. Additionally, our method achieves up to 3.17% and 2.31% improvements in mAP and NDS, respectively, on the nuScenes dataset, demonstrating its effectiveness with both single and fused LiDAR-camera modalities. https://github.com/sinatayebati/Radial_MAE.

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

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

Spatial 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.

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

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

Recent advancements in foundation models have enhanced AI systems' capabilities in autonomous tool usage and reasoning. However, their ability in location or map-based reasoning - which improves daily life by optimizing navigation, facilitating resource discovery, and streamlining logistics - has not been systematically studied. To bridge this gap, we introduce MapEval, a benchmark designed to assess diverse and complex map-based user queries with geo-spatial reasoning. MapEval features three task types (textual, API-based, and visual) that require collecting world information via map tools, processing heterogeneous geo-spatial contexts (e.g., named entities, travel distances, user reviews or ratings, images), and compositional reasoning, which all state-of-the-art foundation models find challenging. Comprising 700 unique multiple-choice questions about locations across 180 cities and 54 countries, MapEval evaluates foundation models' ability to handle spatial relationships, map infographics, travel planning, and navigation challenges. Using MapEval, we conducted a comprehensive evaluation of 28 prominent foundation models. While no single model excelled across all tasks, Claude-3.5-Sonnet, GPT-4o, and Gemini-1.5-Pro achieved competitive performance overall. However, substantial performance gaps emerged, particularly in MapEval, where agents with Claude-3.5-Sonnet outperformed GPT-4o and Gemini-1.5-Pro by 16% and 21%, respectively, and the gaps became even more amplified when compared to open-source LLMs. Our detailed analyses provide insights into the strengths and weaknesses of current models, though all models still fall short of human performance by more than 20% on average, struggling with complex map images and rigorous geo-spatial reasoning. This gap highlights MapEval's critical role in advancing general-purpose foundation models with stronger geo-spatial understanding.

Attentional mechanisms are order-invariant. Positional encoding is a crucial component to allow attention-based deep model architectures such as Transformer to address sequences or images where the position of information matters. In this paper, we propose a novel positional encoding method based on learnable Fourier features. Instead of hard-coding each position as a token or a vector, we represent each position, which can be multi-dimensional, as a trainable encoding based on learnable Fourier feature mapping, modulated with a multi-layer perceptron. The representation is particularly advantageous for a spatial multi-dimensional position, e.g., pixel positions on an image, where L_2 distances or more complex positional relationships need to be captured. Our experiments based on several public benchmark tasks show that our learnable Fourier feature representation for multi-dimensional positional encoding outperforms existing methods by both improving the accuracy and allowing faster convergence.

We propose a self-supervised method for learning motion-focused video representations. Existing approaches minimize distances between temporally augmented videos, which maintain high spatial similarity. We instead propose to learn similarities between videos with identical local motion dynamics but an otherwise different appearance. We do so by adding synthetic motion trajectories to videos which we refer to as tubelets. By simulating different tubelet motions and applying transformations, such as scaling and rotation, we introduce motion patterns beyond what is present in the pretraining data. This allows us to learn a video representation that is remarkably data-efficient: our approach maintains performance when using only 25% of the pretraining videos. Experiments on 10 diverse downstream settings demonstrate our competitive performance and generalizability to new domains and fine-grained actions.

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.

Worldwide image geolocalization-the task of predicting GPS coordinates from images taken anywhere on Earth-poses a fundamental challenge due to the vast diversity in visual content across regions. While recent approaches adopt a two-stage pipeline of retrieving candidates and selecting the best match, they typically rely on simplistic similarity heuristics and point-wise supervision, failing to model spatial relationships among candidates. In this paper, we propose GeoRanker, a distance-aware ranking framework that leverages large vision-language models to jointly encode query-candidate interactions and predict geographic proximity. In addition, we introduce a multi-order distance loss that ranks both absolute and relative distances, enabling the model to reason over structured spatial relationships. To support this, we curate GeoRanking, the first dataset explicitly designed for geographic ranking tasks with multimodal candidate information. GeoRanker achieves state-of-the-art results on two well-established benchmarks (IM2GPS3K and YFCC4K), significantly outperforming current best methods.

Equation discovery from data is a core challenge in machine learning for science, requiring the recovery of concise symbolic expressions that govern complex physical and geometric phenomena. Recent approaches with large language models (LLMs) show promise in symbolic regression, but their success often hinges on memorized formulas or overly simplified functional forms. Existing benchmarks exacerbate this limitation: they focus on scalar functions, ignore domain grounding, and rely on brittle string-matching based metrics that fail to capture scientific equivalence. We introduce SurfaceBench, first comprehensive benchmark for symbolic surface discovery. SurfaceBench comprises 183 tasks across 15 categories of symbolic complexity, spanning explicit, implicit, and parametric equation representation forms. Each task includes ground-truth equations, variable semantics, and synthetically sampled three dimensional data. Unlike prior SR datasets, our tasks reflect surface-level structure, resist LLM memorization through novel symbolic compositions, and are grounded in scientific domains such as fluid dynamics, robotics, electromagnetics, and geometry. To evaluate equation discovery quality, we pair symbolic checks with geometry-aware metrics such as Chamfer and Hausdorff distances, capturing both algebraic fidelity and spatial reconstruction accuracy. Our experiments reveal that state-of-the-art frameworks, while occasionally successful on specific families, struggle to generalize across representation types and surface complexities. SurfaceBench thus establishes a challenging and diagnostic testbed that bridges symbolic reasoning with geometric reconstruction, enabling principled benchmarking of progress in compositional generalization, data-driven scientific induction, and geometry-aware reasoning with LLMs. We release the code here: https://github.com/Sanchit-404/surfacebench

Recently, Vision Language Models (VLMs) have experienced significant advancements, yet these models still face challenges in spatial hierarchical reasoning within indoor scenes. In this study, we introduce ROOT, a VLM-based system designed to enhance the analysis of indoor scenes. Specifically, we first develop an iterative object perception algorithm using GPT-4V to detect object entities within indoor scenes. This is followed by employing vision foundation models to acquire additional meta-information about the scene, such as bounding boxes. Building on this foundational data, we propose a specialized VLM, SceneVLM, which is capable of generating spatial hierarchical scene graphs and providing distance information for objects within indoor environments. This information enhances our understanding of the spatial arrangement of indoor scenes. To train our SceneVLM, we collect over 610,000 images from various public indoor datasets and implement a scene data generation pipeline with a semi-automated technique to establish relationships and estimate distances among indoor objects. By utilizing this enriched data, we conduct various training recipes and finish SceneVLM. Our experiments demonstrate that \rootname facilitates indoor scene understanding and proves effective in diverse downstream applications, such as 3D scene generation and embodied AI. The code will be released at https://github.com/harrytea/ROOT.

Understanding and reasoning about complex 3D environments requires structured scene representations that capture not only objects but also their semantic and spatial relationships. While recent works on 3D scene graph generation have leveraged pretrained VLMs without task-specific fine-tuning, they are largely confined to single-view settings, fail to support incremental updates as new observations arrive and lack explicit geometric grounding in 3D space, all of which are essential for embodied scenarios. In this paper, we propose, ZING-3D, a framework that leverages the vast knowledge of pretrained foundation models to enable open-vocabulary recognition and generate a rich semantic representation of the scene in a zero-shot manner while also enabling incremental updates and geometric grounding in 3D space, making it suitable for downstream robotics applications. Our approach leverages VLM reasoning to generate a rich 2D scene graph, which is grounded in 3D using depth information. Nodes represent open-vocabulary objects with features, 3D locations, and semantic context, while edges capture spatial and semantic relations with inter-object distances. Our experiments on scenes from the Replica and HM3D dataset show that ZING-3D is effective at capturing spatial and relational knowledge without the need of task-specific training.

Denoising Diffusion Probabilistic Models (DDPMs) achieve state-of-the-art performance in synthesizing new images from random noise, but they lack meaningful latent space that encodes data into features. Recent DDPM-based editing techniques try to mitigate this issue by inverting images back to their approximated staring noise. In this work, we study the relation between the initial Gaussian noise, the samples generated from it, and their corresponding latent encodings obtained through the inversion procedure. First, we interpret their spatial distance relations to show the inaccuracy of the DDIM inversion technique by localizing latent representations manifold between the initial noise and generated samples. Then, we demonstrate the peculiar relation between initial Gaussian noise and its corresponding generations during diffusion training, showing that the high-level features of generated images stabilize rapidly, keeping the spatial distance relationship between noises and generations consistent throughout the training.

We present Depth Anything at Any Condition (DepthAnything-AC), a foundation monocular depth estimation (MDE) model capable of handling diverse environmental conditions. Previous foundation MDE models achieve impressive performance across general scenes but not perform well in complex open-world environments that involve challenging conditions, such as illumination variations, adverse weather, and sensor-induced distortions. To overcome the challenges of data scarcity and the inability of generating high-quality pseudo-labels from corrupted images, we propose an unsupervised consistency regularization finetuning paradigm that requires only a relatively small amount of unlabeled data. Furthermore, we propose the Spatial Distance Constraint to explicitly enforce the model to learn patch-level relative relationships, resulting in clearer semantic boundaries and more accurate details. Experimental results demonstrate the zero-shot capabilities of DepthAnything-AC across diverse benchmarks, including real-world adverse weather benchmarks, synthetic corruption benchmarks, and general benchmarks. Project Page: https://ghost233lism.github.io/depthanything-AC-page Code: https://github.com/HVision-NKU/DepthAnythingAC

Neural architectures that learn potential energy surfaces from molecular data have undergone fast improvement in recent years. A key driver of this success is the Message Passing Neural Network (MPNN) paradigm. Its favorable scaling with system size partly relies upon a spatial distance limit on messages. While this focus on locality is a useful inductive bias, it also impedes the learning of long-range interactions such as electrostatics and van der Waals forces. To address this drawback, we propose Ewald message passing: a nonlocal Fourier space scheme which limits interactions via a cutoff on frequency instead of distance, and is theoretically well-founded in the Ewald summation method. It can serve as an augmentation on top of existing MPNN architectures as it is computationally inexpensive and agnostic to architectural details. We test the approach with four baseline models and two datasets containing diverse periodic (OC20) and aperiodic structures (OE62). We observe robust improvements in energy mean absolute errors across all models and datasets, averaging 10% on OC20 and 16% on OE62. Our analysis shows an outsize impact of these improvements on structures with high long-range contributions to the ground truth energy.

Humans possess the visual-spatial intelligence to remember spaces from sequential visual observations. However, can Multimodal Large Language Models (MLLMs) trained on million-scale video datasets also ``think in space'' from videos? We present a novel video-based visual-spatial intelligence benchmark (VSI-Bench) of over 5,000 question-answer pairs, and find that MLLMs exhibit competitive - though subhuman - visual-spatial intelligence. We probe models to express how they think in space both linguistically and visually and find that while spatial reasoning capabilities remain the primary bottleneck for MLLMs to reach higher benchmark performance, local world models and spatial awareness do emerge within these models. Notably, prevailing linguistic reasoning techniques (e.g., chain-of-thought, self-consistency, tree-of-thoughts) fail to improve performance, whereas explicitly generating cognitive maps during question-answering enhances MLLMs' spatial distance ability.

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.

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

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 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.

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.

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.

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

We present a new regular grid search algorithm for quick fixed-radius nearest-neighbor lookup developed in Python. This module indexes a set of k-dimensional points in a regular grid, with optional periodic conditions, providing a fast approach for nearest neighbors queries. In this first installment we provide three types of queries: bubble, shell and the nth-nearest; as well as three different metrics of interest in astronomy: the euclidean and two distance functions in spherical coordinates of varying precision, haversine and Vincenty; and the possibility of providing a custom distance function. This package results particularly useful for large datasets where a brute-force search turns impractical.

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.

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.

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

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

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

Next point-of-interest (POI) recommendation predicts a user's next destination from historical movements. Traditional models require intensive training, while LLMs offer flexible and generalizable zero-shot solutions but often generate generic or geographically irrelevant results due to missing trajectory and spatial context. To address these issues, we propose RALLM-POI, a framework that couples LLMs with retrieval-augmented generation and self-rectification. We first propose a Historical Trajectory Retriever (HTR) that retrieves relevant past trajectories to serve as contextual references, which are then reranked by a Geographical Distance Reranker (GDR) for prioritizing spatially relevant trajectories. Lastly, an Agentic LLM Rectifier (ALR) is designed to refine outputs through self-reflection. Without additional training, RALLM-POI achieves substantial accuracy gains across three real-world Foursquare datasets, outperforming both conventional and LLM-based baselines. Code is released at https://github.com/LKRcrocodile/RALLM-POI.

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.

Finding meaningful representations and distances of hierarchical data is important in many fields. This paper presents a new method for hierarchical data embedding and distance. Our method relies on combining diffusion geometry, a central approach to manifold learning, and hyperbolic geometry. Specifically, using diffusion geometry, we build multi-scale densities on the data, aimed to reveal their hierarchical structure, and then embed them into a product of hyperbolic spaces. We show theoretically that our embedding and distance recover the underlying hierarchical structure. In addition, we demonstrate the efficacy of the proposed method and its advantages compared to existing methods on graph embedding benchmarks and hierarchical datasets.

Estimating the geographical range of a species from sparse observations is a challenging and important geospatial prediction problem. Given a set of locations where a species has been observed, the goal is to build a model to predict whether the species is present or absent at any location. This problem has a long history in ecology, but traditional methods struggle to take advantage of emerging large-scale crowdsourced datasets which can include tens of millions of records for hundreds of thousands of species. In this work, we use Spatial Implicit Neural Representations (SINRs) to jointly estimate the geographical range of 47k species simultaneously. We find that our approach scales gracefully, making increasingly better predictions as we increase the number of species and the amount of data per species when training. To make this problem accessible to machine learning researchers, we provide four new benchmarks that measure different aspects of species range estimation and spatial representation learning. Using these benchmarks, we demonstrate that noisy and biased crowdsourced data can be combined with implicit neural representations to approximate expert-developed range maps for many species.

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

We focus on the problem of species distribution modeling using global-scale presence-only data. Most previous studies have mapped the range of a given species using geographical and environmental features alone. To capture a stronger implicit relationship between species, we encode the taxonomic hierarchy of species using a large language model. This enables range mapping for any taxonomic rank and unseen species without additional supervision. Further, we propose a novel proximity-aware evaluation metric that enables evaluating species distribution models using any pixel-level representation of ground-truth species range map. The proposed metric penalizes the predictions of a model based on its proximity to the ground truth. We describe the effectiveness of our model by systematically evaluating on the task of species range prediction, zero-shot prediction and geo-feature regression against the state-of-the-art. Results show our model outperforms the strong baselines when trained with a variety of multi-label learning losses.

In high dimension, low sample size (HDLSS) settings, classifiers based on Euclidean distances like the nearest neighbor classifier and the average distance classifier perform quite poorly if differences between locations of the underlying populations get masked by scale differences. To rectify this problem, several modifications of these classifiers have been proposed in the literature. However, existing methods are confined to location and scale differences only, and often fail to discriminate among populations differing outside of the first two moments. In this article, we propose some simple transformations of these classifiers resulting into improved performance even when the underlying populations have the same location and scale. We further propose a generalization of these classifiers based on the idea of grouping of variables. The high-dimensional behavior of the proposed classifiers is studied theoretically. Numerical experiments with a variety of simulated examples as well as an extensive analysis of real data sets exhibit advantages of the proposed methods.

Many mobile robots rely on 2D laser scanners for localization, mapping, and navigation. However, those sensors are unable to correctly provide distance to obstacles such as glass panels and tables whose actual occupancy is invisible at the height the sensor is measuring. In this work, instead of estimating the distance to obstacles from richer sensor readings such as 3D lasers or RGBD sensors, we present a method to estimate the distance directly from raw 2D laser data. To learn a mapping from raw 2D laser distances to obstacle distances we frame the problem as a learning task and train a neural network formed as an autoencoder. A novel configuration of network hyperparameters is proposed for the task at hand and is quantitatively validated on a test set. Finally, we qualitatively demonstrate in real time on a Care-O-bot 4 that the trained network can successfully infer obstacle distances from partial 2D laser readings.

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

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.

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.

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

Next generations of radio surveys are expected to identify tens of millions of new sources, and identifying and classifying their morphologies will require novel and more efficient methods. Self-Organising Maps (SOMs), a type of unsupervised machine learning, can be used to address this problem. We map 251,259 multi-Gaussian sources from Rapid ASKAP Continuum Survey (RACS) onto a SOM with discrete neurons. Similarity metrics, such as Euclidean distances, can be used to identify the best-matching neuron or unit (BMU) for each input image. We establish a reliability threshold by visually inspecting a subset of input images and their corresponding BMU. We label the individual neurons based on observed morphologies and these labels are included in our value-added catalogue of RACS sources. Sources for which the Euclidean distance to their BMU is lesssim 5 (accounting for approximately 79% of sources) have an estimated >90% reliability for their SOM-derived morphological labels. This reliability falls to less than 70% at Euclidean distances gtrsim 7. Beyond this threshold it is unlikely that the morphological label will accurately describe a given source. Our catalogue of complex radio sources from RACS with their SOM-derived morphological labels from this work will be made publicly available.

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

English. This document aims to study the best algorithms to verify the belonging of a specific document to a related domain by comparing different methods for calculating the distance between two vectors. This study has been made possible with the help of the structures made available by the Apache Spark framework. Starting from the study illustrated in the publication "New frontier of textual classification: Big data and distributed calculus" by Massimiliano Morrelli et al., We wanted to carry out a study on the possible implementation of a solution capable of calculating the Similarity of a sentence using the distributed environment. Italiano. Il presente documento persegue l'obiettivo di studiare gli algoritmi migliori per verificare l'appartenenza di un determinato documento a un relativo dominio tramite un confronto di diversi metodi per il calcolo della distanza fra due vettori. Tale studio \`e stato condotto con l'ausilio delle strutture messe a disposizione dal framework Apache Spark. Partendo dallo studio illustrato nella pubblicazione "Nuova frontiera della classificazione testuale: Big data e calcolo distribuito" di Massimiliano Morrelli et al., si \`e voluto realizzare uno studio sulla possibile implementazione di una soluzione in grado di calcolare la Similarit\`a di una frase sfruttando l'ambiente distribuito.

Humans subconsciously engage in geospatial reasoning when reading articles. We recognize place names and their spatial relations in text and mentally associate them with their physical locations on Earth. Although pretrained language models can mimic this cognitive process using linguistic context, they do not utilize valuable geospatial information in large, widely available geographical databases, e.g., OpenStreetMap. This paper introduces GeoLM, a geospatially grounded language model that enhances the understanding of geo-entities in natural language. GeoLM leverages geo-entity mentions as anchors to connect linguistic information in text corpora with geospatial information extracted from geographical databases. GeoLM connects the two types of context through contrastive learning and masked language modeling. It also incorporates a spatial coordinate embedding mechanism to encode distance and direction relations to capture geospatial context. In the experiment, we demonstrate that GeoLM exhibits promising capabilities in supporting toponym recognition, toponym linking, relation extraction, and geo-entity typing, which bridge the gap between natural language processing and geospatial sciences. The code is publicly available at https://github.com/knowledge-computing/geolm.

We present a new approach for the approximate K-nearest neighbor search based on navigable small world graphs with controllable hierarchy (Hierarchical NSW, HNSW). The proposed solution is fully graph-based, without any need for additional search structures, which are typically used at the coarse search stage of the most proximity graph techniques. Hierarchical NSW incrementally builds a multi-layer structure consisting from hierarchical set of proximity graphs (layers) for nested subsets of the stored elements. The maximum layer in which an element is present is selected randomly with an exponentially decaying probability distribution. This allows producing graphs similar to the previously studied Navigable Small World (NSW) structures while additionally having the links separated by their characteristic distance scales. Starting search from the upper layer together with utilizing the scale separation boosts the performance compared to NSW and allows a logarithmic complexity scaling. Additional employment of a heuristic for selecting proximity graph neighbors significantly increases performance at high recall and in case of highly clustered data. Performance evaluation has demonstrated that the proposed general metric space search index is able to strongly outperform previous opensource state-of-the-art vector-only approaches. Similarity of the algorithm to the skip list structure allows straightforward balanced distributed implementation.

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.

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

Cross-modal metric learning is a prominent research topic that bridges the semantic heterogeneity between vision and language. Existing methods frequently utilize simple cosine or complex distance metrics to transform the pairwise features into a similarity score, which suffers from an inadequate or inefficient capability for distance measurements. Consequently, we propose a Generalized Structural Sparse Function to dynamically capture thorough and powerful relationships across modalities for pair-wise similarity learning while remaining concise but efficient. Specifically, the distance metric delicately encapsulates two formats of diagonal and block-diagonal terms, automatically distinguishing and highlighting the cross-channel relevancy and dependency inside a structured and organized topology. Hence, it thereby empowers itself to adapt to the optimal matching patterns between the paired features and reaches a sweet spot between model complexity and capability. Extensive experiments on cross-modal and two extra uni-modal retrieval tasks (image-text retrieval, person re-identification, fine-grained image retrieval) have validated its superiority and flexibility over various popular retrieval frameworks. More importantly, we further discover that it can be seamlessly incorporated into multiple application scenarios, and demonstrates promising prospects from Attention Mechanism to Knowledge Distillation in a plug-and-play manner. Our code is publicly available at: https://github.com/Paranioar/GSSF.

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

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

We show the existence of a Locality-Sensitive Hashing (LSH) family for the angular distance that yields an approximate Near Neighbor Search algorithm with the asymptotically optimal running time exponent. Unlike earlier algorithms with this property (e.g., Spherical LSH [Andoni, Indyk, Nguyen, Razenshteyn 2014], [Andoni, Razenshteyn 2015]), our algorithm is also practical, improving upon the well-studied hyperplane LSH [Charikar, 2002] in practice. We also introduce a multiprobe version of this algorithm, and conduct experimental evaluation on real and synthetic data sets. We complement the above positive results with a fine-grained lower bound for the quality of any LSH family for angular distance. Our lower bound implies that the above LSH family exhibits a trade-off between evaluation time and quality that is close to optimal for a natural class of LSH functions.

Magnitude of a finite metric space and the related notion of magnitude functions on metric spaces is an active area of research in algebraic topology. Magnitude originally arose in the context of biology, where it represents the number of effective species in an environment; when applied to a one-parameter family of metric spaces tX with scale parameter t, the magnitude captures much of the underlying geometry of the space. Prior work has mostly focussed on properties of magnitude in a global sense; in this paper we restrict the sets to finite subsets of Euclidean space and investigate its individual components. We give an explicit formula for the corrected inclusion-exclusion principle, and define a quantity associated with each point, called the moment which gives an intrinsic ordering to the points. We exploit this in order to form an algorithm which approximates the convex hull.

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.

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

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

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

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

Metric space magnitude, an active field of research in algebraic topology, is a scalar quantity that summarizes the effective number of distinct points that live in a general metric space. The {\em weighting vector} is a closely-related concept that captures, in a nontrivial way, much of the underlying geometry of the original metric space. Recent work has demonstrated that when the metric space is Euclidean, the weighting vector serves as an effective tool for boundary detection. We recast this result and show the weighting vector may be viewed as a solution to a kernelized SVM. As one consequence, we apply this new insight to the task of outlier detection, and we demonstrate performance that is competitive or exceeds performance of state-of-the-art techniques on benchmark data sets. Under mild assumptions, we show the weighting vector, which has computational cost of matrix inversion, can be efficiently approximated in linear time. We show how nearest neighbor methods can approximate solutions to the minimization problems defined by SVMs.

Machine learning models -- including prominent zero-shot models -- are often trained on datasets whose labels are only a small proportion of a larger label space. Such spaces are commonly equipped with a metric that relates the labels via distances between them. We propose a simple approach to exploit this information to adapt the trained model to reliably predict new classes -- or, in the case of zero-shot prediction, to improve its performance -- without any additional training. Our technique is a drop-in replacement of the standard prediction rule, swapping argmax with the Fr\'echet mean. We provide a comprehensive theoretical analysis for this approach, studying (i) learning-theoretic results trading off label space diameter, sample complexity, and model dimension, (ii) characterizations of the full range of scenarios in which it is possible to predict any unobserved class, and (iii) an optimal active learning-like next class selection procedure to obtain optimal training classes for when it is not possible to predict the entire range of unobserved classes. Empirically, using easily-available external metrics, our proposed approach, Loki, gains up to 29.7% relative improvement over SimCLR on ImageNet and scales to hundreds of thousands of classes. When no such metric is available, Loki can use self-derived metrics from class embeddings and obtains a 10.5% improvement on pretrained zero-shot models such as CLIP.

Incorporating domain-specific priors in search and navigation tasks has shown promising results in improving generalization and sample complexity over end-to-end trained policies. In this work, we study how object embeddings that capture spatial semantic priors can guide search and navigation tasks in a structured environment. We know that humans can search for an object like a book, or a plate in an unseen house, based on the spatial semantics of bigger objects detected. For example, a book is likely to be on a bookshelf or a table, whereas a plate is likely to be in a cupboard or dishwasher. We propose a method to incorporate such spatial semantic awareness in robots by leveraging pre-trained language models and multi-relational knowledge bases as object embeddings. We demonstrate using these object embeddings to search a query object in an unseen indoor environment. We measure the performance of these embeddings in an indoor simulator (AI2Thor). We further evaluate different pre-trained embedding onSuccess Rate(SR) and success weighted by Path Length(SPL).

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

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.

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

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.

We introduce a flexible framework that produces high-quality almost-exact matches for causal inference. Most prior work in matching uses ad-hoc distance metrics, often leading to poor quality matches, particularly when there are irrelevant covariates. In this work, we learn an interpretable distance metric for matching, which leads to substantially higher quality matches. The learned distance metric stretches the covariate space according to each covariate's contribution to outcome prediction: this stretching means that mismatches on important covariates carry a larger penalty than mismatches on irrelevant covariates. Our ability to learn flexible distance metrics leads to matches that are interpretable and useful for the estimation of conditional average treatment effects.

Given a set of dissimilarity measurements amongst data points, determining what metric representation is most "consistent" with the input measurements or the metric that best captures the relevant geometric features of the data is a key step in many machine learning algorithms. Existing methods are restricted to specific kinds of metrics or small problem sizes because of the large number of metric constraints in such problems. In this paper, we provide an active set algorithm, Project and Forget, that uses Bregman projections, to solve metric constrained problems with many (possibly exponentially) inequality constraints. We provide a theoretical analysis of Project and Forget and prove that our algorithm converges to the global optimal solution and that the L_2 distance of the current iterate to the optimal solution decays asymptotically at an exponential rate. We demonstrate that using our method we can solve large problem instances of three types of metric constrained problems: general weight correlation clustering, metric nearness, and metric learning; in each case, out-performing the state of the art methods with respect to CPU times and problem sizes.

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

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

Hyperbolic embeddings offer excellent quality with few dimensions when embedding hierarchical data structures like synonym or type hierarchies. Given a tree, we give a combinatorial construction that embeds the tree in hyperbolic space with arbitrarily low distortion without using optimization. On WordNet, our combinatorial embedding obtains a mean-average-precision of 0.989 with only two dimensions, while Nickel et al.'s recent construction obtains 0.87 using 200 dimensions. We provide upper and lower bounds that allow us to characterize the precision-dimensionality tradeoff inherent in any hyperbolic embedding. To embed general metric spaces, we propose a hyperbolic generalization of multidimensional scaling (h-MDS). We show how to perform exact recovery of hyperbolic points from distances, provide a perturbation analysis, and give a recovery result that allows us to reduce dimensionality. The h-MDS approach offers consistently low distortion even with few dimensions across several datasets. Finally, we extract lessons from the algorithms and theory above to design a PyTorch-based implementation that can handle incomplete information and is scalable.

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/.

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.

Most text-based information retrieval (IR) systems index objects by words or phrases. These discrete systems have been augmented by models that use embeddings to measure similarity in continuous space. But continuous-space models are typically used just to re-rank the top candidates. We consider the problem of end-to-end continuous retrieval, where standard approximate nearest neighbor (ANN) search replaces the usual discrete inverted index, and rely entirely on distances between learned embeddings. By training simple models specifically for retrieval, with an appropriate model architecture, we improve on a discrete baseline by 8% and 26% (MAP) on two similar-question retrieval tasks. We also discuss the problem of evaluation for retrieval systems, and show how to modify existing pairwise similarity datasets for this purpose.

Quantifying similarity between neural representations -- e.g. hidden layer activation vectors -- is a perennial problem in deep learning and neuroscience research. Existing methods compare deterministic responses (e.g. artificial networks that lack stochastic layers) or averaged responses (e.g., trial-averaged firing rates in biological data). However, these measures of _deterministic_ representational similarity ignore the scale and geometric structure of noise, both of which play important roles in neural computation. To rectify this, we generalize previously proposed shape metrics (Williams et al. 2021) to quantify differences in _stochastic_ representations. These new distances satisfy the triangle inequality, and thus can be used as a rigorous basis for many supervised and unsupervised analyses. Leveraging this novel framework, we find that the stochastic geometries of neurobiological representations of oriented visual gratings and naturalistic scenes respectively resemble untrained and trained deep network representations. Further, we are able to more accurately predict certain network attributes (e.g. training hyperparameters) from its position in stochastic (versus deterministic) shape space.

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.

We present two new classes of algorithms for efficient field integration on graphs encoding point clouds. The first class, SeparatorFactorization(SF), leverages the bounded genus of point cloud mesh graphs, while the second class, RFDiffusion(RFD), uses popular epsilon-nearest-neighbor graph representations for point clouds. Both can be viewed as providing the functionality of Fast Multipole Methods (FMMs), which have had a tremendous impact on efficient integration, but for non-Euclidean spaces. We focus on geometries induced by distributions of walk lengths between points (e.g., shortest-path distance). We provide an extensive theoretical analysis of our algorithms, obtaining new results in structural graph theory as a byproduct. We also perform exhaustive empirical evaluation, including on-surface interpolation for rigid and deformable objects (particularly for mesh-dynamics modeling), Wasserstein distance computations for point clouds, and the Gromov-Wasserstein variant.

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.

To characterize the location (mean, median) of a set of graphs, one needs a notion of centrality that is adapted to metric spaces, since graph sets are not Euclidean spaces. A standard approach is to consider the Frechet mean. In this work, we equip a set of graphs with the pseudometric defined by the norm between the eigenvalues of their respective adjacency matrix. Unlike the edit distance, this pseudometric reveals structural changes at multiple scales, and is well adapted to studying various statistical problems for graph-valued data. We describe an algorithm to compute an approximation to the sample Frechet mean of a set of undirected unweighted graphs with a fixed size using this pseudometric.

The shadow of an abstract simplicial complex K with vertices in R^N is a subset of R^N defined as the union of the convex hulls of simplices of K. The Vietoris--Rips complex of a metric space (S,d) at scale β is an abstract simplicial complex whose each k-simplex corresponds to (k+1) points of S within diameter β. In case Ssubsetmathbb R^2 and d(a,b)=|a-b| the standard Euclidean metric, the natural shadow projection of the Vietoris--Rips complex is already proved by Chambers et al. to induce isomorphisms on π_0 and π_1. We extend the result beyond the standard Euclidean distance on Ssubsetmathbb R^N to a family of path-based metrics, d^varepsilon_{S}. From the pairwise Euclidean distances of points in S, we introduce a family (parametrized by varepsilon) of path-based Vietoris--Rips complexes R^varepsilon_β(S) for a scale β>0. If SsubsetR^2 is Hausdorff-close to a planar Euclidean graph G, we provide quantitative bounds on scales β,varepsilon for the shadow projection map of the Vietoris--Rips complex of (S,d^varepsilon_S) at scale β to induce π_1-isomorphism. This paper first studies the homotopy-type recovery of Gsubsetmathbb R^N using the abstract Vietoris--Rips complex of a Hausdorff-close sample S under the d^varepsilon_S metric. Then, our result on the π_1-isomorphism induced by the shadow projection lends itself to providing also a geometrically close embedding for the reconstruction. Based on the length of the shortest loop and large-scale distortion of the embedding of G, we quantify the choice of a suitable sample density varepsilon and a scale β at which the shadow of R^varepsilon_β(S) is homotopy-equivalent and Hausdorff-close to G.

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.

Given a database of bit strings A_1,ldots,A_min {0,1}^n, a fundamental data structure task is to estimate the distances between a given query Bin {0,1}^n with all the strings in the database. In addition, one might further want to ensure the integrity of the database by releasing these distance statistics in a secure manner. In this work, we propose differentially private (DP) data structures for this type of tasks, with a focus on Hamming and edit distance. On top of the strong privacy guarantees, our data structures are also time- and space-efficient. In particular, our data structure is epsilon-DP against any sequence of queries of arbitrary length, and for any query B such that the maximum distance to any string in the database is at most k, we output m distance estimates. Moreover, - For Hamming distance, our data structure answers any query in widetilde O(mk+n) time and each estimate deviates from the true distance by at most widetilde O(k/e^{epsilon/log k}); - For edit distance, our data structure answers any query in widetilde O(mk^2+n) time and each estimate deviates from the true distance by at most widetilde O(k/e^{epsilon/(log k log n)}). For moderate k, both data structures support sublinear query operations. We obtain these results via a novel adaptation of the randomized response technique as a bit flipping procedure, applied to the sketched strings.

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.

The application of machine learning (ML) in a range of geospatial tasks is increasingly common but often relies on globally available covariates such as satellite imagery that can either be expensive or lack predictive power. Here we explore the question of whether the vast amounts of knowledge found in Internet language corpora, now compressed within large language models (LLMs), can be leveraged for geospatial prediction tasks. We first demonstrate that LLMs embed remarkable spatial information about locations, but naively querying LLMs using geographic coordinates alone is ineffective in predicting key indicators like population density. We then present GeoLLM, a novel method that can effectively extract geospatial knowledge from LLMs with auxiliary map data from OpenStreetMap. We demonstrate the utility of our approach across multiple tasks of central interest to the international community, including the measurement of population density and economic livelihoods. Across these tasks, our method demonstrates a 70% improvement in performance (measured using Pearson's r^2) relative to baselines that use nearest neighbors or use information directly from the prompt, and performance equal to or exceeding satellite-based benchmarks in the literature. With GeoLLM, we observe that GPT-3.5 outperforms Llama 2 and RoBERTa by 19% and 51% respectively, suggesting that the performance of our method scales well with the size of the model and its pretraining dataset. Our experiments reveal that LLMs are remarkably sample-efficient, rich in geospatial information, and robust across the globe. Crucially, GeoLLM shows promise in mitigating the limitations of existing geospatial covariates and complementing them well. Code is available on the project website: https://rohinmanvi.github.io/GeoLLM

In this work, we show that it is possible to extract significant amounts of alignment training data from a post-trained model -- useful to steer the model to improve certain capabilities such as long-context reasoning, safety, instruction following, and maths. While the majority of related work on memorisation has focused on measuring success of training data extraction through string matching, we argue that embedding models are better suited for our specific goals. Distances measured through a high quality embedding model can identify semantic similarities between strings that a different metric such as edit distance will struggle to capture. In fact, in our investigation, approximate string matching would have severely undercounted (by a conservative estimate of 10times) the amount of data that can be extracted due to trivial artifacts that deflate the metric. Interestingly, we find that models readily regurgitate training data that was used in post-training phases such as SFT or RL. We show that this data can be then used to train a base model, recovering a meaningful amount of the original performance. We believe our work exposes a possibly overlooked risk towards extracting alignment data. Finally, our work opens up an interesting discussion on the downstream effects of distillation practices: since models seem to be regurgitating aspects of their training set, distillation can therefore be thought of as indirectly training on the model's original dataset.

Few prior works study deep learning on point sets. PointNet by Qi et al. is a pioneer in this direction. However, by design PointNet does not capture local structures induced by the metric space points live in, limiting its ability to recognize fine-grained patterns and generalizability to complex scenes. In this work, we introduce a hierarchical neural network that applies PointNet recursively on a nested partitioning of the input point set. By exploiting metric space distances, our network is able to learn local features with increasing contextual scales. With further observation that point sets are usually sampled with varying densities, which results in greatly decreased performance for networks trained on uniform densities, we propose novel set learning layers to adaptively combine features from multiple scales. Experiments show that our network called PointNet++ is able to learn deep point set features efficiently and robustly. In particular, results significantly better than state-of-the-art have been obtained on challenging benchmarks of 3D point clouds.

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

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.

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

Spatio-temporal reasoning is essential in understanding real-world environments in various fields, eg, autonomous driving and sports analytics. Recent advances have improved the spatial reasoning ability of Vision-Language Models (VLMs) by introducing large-scale data, but these models still struggle to analyze kinematic elements like traveled distance and speed of moving objects. To bridge this gap, we construct a spatio-temporal reasoning dataset and benchmark involving kinematic instruction tuning, referred to as STKit and STKit-Bench. They consist of real-world videos with 3D annotations, detailing object motion dynamics: traveled distance, speed, movement direction, inter-object distance comparisons, and relative movement direction. To further scale such data construction to videos without 3D labels, we propose an automatic pipeline to generate pseudo-labels using 4D reconstruction in real-world scale. With our kinematic instruction tuning data for spatio-temporal reasoning, we present ST-VLM, a VLM enhanced for spatio-temporal reasoning, which exhibits outstanding performance on STKit-Bench. Furthermore, we show that ST-VLM generalizes robustly across diverse domains and tasks, outperforming baselines on other spatio-temporal benchmarks (eg, ActivityNet, TVQA+). Finally, by integrating learned spatio-temporal reasoning with existing abilities, ST-VLM enables complex multi-step reasoning. Project page: https://ikodoh.github.io/ST-VLM.

Accurate spatial reasoning in outdoor environments - covering geometry, object pose, and inter-object relationships - is fundamental to downstream tasks such as mapping, motion forecasting, and high-level planning in autonomous driving. We introduce SURDS, a large-scale benchmark designed to systematically evaluate the spatial reasoning capabilities of vision language models (VLMs). Built on the nuScenes dataset, SURDS comprises 41,080 vision-question-answer training instances and 9,250 evaluation samples, spanning six spatial categories: orientation, depth estimation, pixel-level localization, pairwise distance, lateral ordering, and front-behind relations. We benchmark leading general-purpose VLMs, including GPT, Gemini, and Qwen, revealing persistent limitations in fine-grained spatial understanding. To address these deficiencies, we go beyond static evaluation and explore whether alignment techniques can improve spatial reasoning performance. Specifically, we propose a reinforcement learning-based alignment scheme leveraging spatially grounded reward signals - capturing both perception-level accuracy (location) and reasoning consistency (logic). We further incorporate final-answer correctness and output-format rewards to guide fine-grained policy adaptation. Our GRPO-aligned variant achieves an overall score of 40.80 in the SURDS benchmark. Notably, it outperforms proprietary systems such as GPT-4o (13.30) and Gemini-2.0-flash (35.71). To our best knowledge, this is the first study to demonstrate that reinforcement learning-based alignment can significantly and consistently enhance the spatial reasoning capabilities of VLMs in real-world driving contexts. We release the SURDS benchmark, evaluation toolkit, and GRPO alignment code through: https://github.com/XiandaGuo/Drive-MLLM.

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

Existing deep learning-based cross-view geo-localization methods primarily focus on improving the accuracy of cross-domain image matching, rather than enabling models to comprehensively capture contextual information around the target and minimize the cost of localization errors. To support systematic research into this Distance-Aware Cross-View Geo-Localization (DACVGL) problem, we construct Distance-Aware Campus (DA-Campus), the first benchmark that pairs multi-view imagery with precise distance annotations across three spatial resolutions. Based on DA-Campus, we formulate DACVGL as a hierarchical retrieval problem across different domains. Our study further reveals that, due to the inherent complexity of spatial relationships among buildings, this problem can only be addressed via a contrastive learning paradigm, rather than conventional metric learning. To tackle this challenge, we propose Dynamic Contrastive Learning (DyCL), a novel framework that progressively aligns feature representations according to hierarchical spatial margins. Extensive experiments demonstrate that DyCL is highly complementary to existing multi-scale metric learning methods and yields substantial improvements in both hierarchical retrieval performance and overall cross-view geo-localization accuracy. Our code and benchmark are publicly available at https://github.com/anocodetest1/DyCL.

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

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

The magnitude of a finite metric space has recently emerged as a novel invariant quantity, allowing to measure the effective size of a metric space. Despite encouraging first results demonstrating the descriptive abilities of the magnitude, such as being able to detect the boundary of a metric space, the potential use cases of magnitude remain under-explored. In this work, we investigate the properties of the magnitude on images, an important data modality in many machine learning applications. By endowing each individual images with its own metric space, we are able to define the concept of magnitude on images and analyse the individual contribution of each pixel with the magnitude vector. In particular, we theoretically show that the previously known properties of boundary detection translate to edge detection abilities in images. Furthermore, we demonstrate practical use cases of magnitude for machine learning applications and propose a novel magnitude model that consists of a computationally efficient magnitude computation and a learnable metric. By doing so, we address the computational hurdle that used to make magnitude impractical for many applications and open the way for the adoption of magnitude in machine learning research.

Neural signed distance functions (SDFs) have been a vital representation to represent 3D shapes or scenes with neural networks. An SDF is an implicit function that can query signed distances at specific coordinates for recovering a 3D surface. Although implicit functions work well on a single shape or scene, they pose obstacles when analyzing multiple SDFs with high-fidelity geometry details, due to the limited information encoded in the latent space for SDFs and the loss of geometry details. To overcome these obstacles, we introduce a method to represent multiple SDFs in a common space, aiming to recover more high-fidelity geometry details with more compact latent representations. Our key idea is to take full advantage of the benefits of generalization-based and overfitting-based learning strategies, which manage to preserve high-fidelity geometry details with compact latent codes. Based on this framework, we also introduce a novel sampling strategy to sample training queries. The sampling can improve the training efficiency and eliminate artifacts caused by the influence of other SDFs. We report numerical and visual evaluations on widely used benchmarks to validate our designs and show advantages over the latest methods in terms of the representative ability and compactness.

Image ranking is to rank images based on some known ranked images. In this paper, we propose an improved linear ordinal distance metric learning approach based on the linear distance metric learning model. By decomposing the distance metric A as L^TL, the problem can be cast as looking for a linear map between two sets of points in different spaces, meanwhile maintaining some data structures. The ordinal relation of the labels can be maintained via classical multidimensional scaling, a popular tool for dimension reduction in statistics. A least squares fitting term is then introduced to the cost function, which can also maintain the local data structure. The resulting model is an unconstrained problem, and can better fit the data structure. Extensive numerical results demonstrate the improvement of the new approach over the linear distance metric learning model both in speed and ranking performance.

Spatial sound reasoning is a fundamental human skill, enabling us to navigate and interpret our surroundings based on sound. In this paper we present BAT, which combines the spatial sound perception ability of a binaural acoustic scene analysis model with the natural language reasoning capabilities of a large language model (LLM) to replicate this innate ability. To address the lack of existing datasets of in-the-wild spatial sounds, we synthesized a binaural audio dataset using AudioSet and SoundSpaces 2.0. Next, we developed SpatialSoundQA, a spatial sound-based question-answering dataset, offering a range of QA tasks that train BAT in various aspects of spatial sound perception and reasoning. The acoustic front end encoder of BAT is a novel spatial audio encoder named Spatial Audio Spectrogram Transformer, or Spatial-AST, which by itself achieves strong performance across sound event detection, spatial localization, and distance estimation. By integrating Spatial-AST with LLaMA-2 7B model, BAT transcends standard Sound Event Localization and Detection (SELD) tasks, enabling the model to reason about the relationships between the sounds in its environment. Our experiments demonstrate BAT's superior performance on both spatial sound perception and reasoning, showcasing the immense potential of LLMs in navigating and interpreting complex spatial audio environments.

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.

The recent success of distributed word representations has led to an increased interest in analyzing the properties of their spatial distribution. Several studies have suggested that contextualized word embedding models do not isotropically project tokens into vector space. However, current methods designed to measure isotropy, such as average random cosine similarity and the partition score, have not been thoroughly analyzed and are not appropriate for measuring isotropy. We propose IsoScore: a novel tool that quantifies the degree to which a point cloud uniformly utilizes the ambient vector space. Using rigorously designed tests, we demonstrate that IsoScore is the only tool available in the literature that accurately measures how uniformly distributed variance is across dimensions in vector space. Additionally, we use IsoScore to challenge a number of recent conclusions in the NLP literature that have been derived using brittle metrics of isotropy. We caution future studies from using existing tools to measure isotropy in contextualized embedding space as resulting conclusions will be misleading or altogether inaccurate.

This research is aimed to solve the tweet/user geolocation prediction task and provide a flexible methodology for the geotagging of textual big data. The suggested approach implements neural networks for natural language processing (NLP) to estimate the location as coordinate pairs (longitude, latitude) and two-dimensional Gaussian Mixture Models (GMMs). The scope of proposed models has been finetuned on a Twitter dataset using pretrained Bidirectional Encoder Representations from Transformers (BERT) as base models. Performance metrics show a median error of fewer than 30 km on a worldwide-level, and fewer than 15 km on the US-level datasets for the models trained and evaluated on text features of tweets' content and metadata context.

A growing literature in computational neuroscience leverages gradient descent and learning algorithms that approximate it to study synaptic plasticity in the brain. However, the vast majority of this work ignores a critical underlying assumption: the choice of distance for synaptic changes - i.e. the geometry of synaptic plasticity. Gradient descent assumes that the distance is Euclidean, but many other distances are possible, and there is no reason that biology necessarily uses Euclidean geometry. Here, using the theoretical tools provided by mirror descent, we show that the distribution of synaptic weights will depend on the geometry of synaptic plasticity. We use these results to show that experimentally-observed log-normal weight distributions found in several brain areas are not consistent with standard gradient descent (i.e. a Euclidean geometry), but rather with non-Euclidean distances. Finally, we show that it should be possible to experimentally test for different synaptic geometries by comparing synaptic weight distributions before and after learning. Overall, our work shows that the current paradigm in theoretical work on synaptic plasticity that assumes Euclidean synaptic geometry may be misguided and that it should be possible to experimentally determine the true geometry of synaptic plasticity in the brain.

Place recognition is a key module for long-term SLAM systems. Current LiDAR-based place recognition methods usually use representations of point clouds such as unordered points or range images. These methods achieve high recall rates of retrieval, but their performance may degrade in the case of view variation or scene changes. In this work, we explore the potential of a different representation in place recognition, i.e. bird's eye view (BEV) images. We observe that the structural contents of BEV images are less influenced by rotations and translations of point clouds. We validate that, without any delicate design, a simple VGGNet trained on BEV images achieves comparable performance with the state-of-the-art place recognition methods in scenes of slight viewpoint changes. For more robust place recognition, we design a rotation-invariant network called BEVPlace. We use group convolution to extract rotation-equivariant local features from the images and NetVLAD for global feature aggregation. In addition, we observe that the distance between BEV features is correlated with the geometry distance of point clouds. Based on the observation, we develop a method to estimate the position of the query cloud, extending the usage of place recognition. The experiments conducted on large-scale public datasets show that our method 1) achieves state-of-the-art performance in terms of recall rates, 2) is robust to view changes, 3) shows strong generalization ability, and 4) can estimate the positions of query point clouds. Source codes are publicly available at https://github.com/zjuluolun/BEVPlace.

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.

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.

Navigating drones through natural language commands remains challenging due to the dearth of accessible multi-modal datasets and the stringent precision requirements for aligning visual and textual data. To address this pressing need, we introduce GeoText-1652, a new natural language-guided geo-localization benchmark. This dataset is systematically constructed through an interactive human-computer process leveraging Large Language Model (LLM) driven annotation techniques in conjunction with pre-trained vision models. GeoText-1652 extends the established University-1652 image dataset with spatial-aware text annotations, thereby establishing one-to-one correspondences between image, text, and bounding box elements. We further introduce a new optimization objective to leverage fine-grained spatial associations, called blending spatial matching, for region-level spatial relation matching. Extensive experiments reveal that our approach maintains a competitive recall rate comparing other prevailing cross-modality methods. This underscores the promising potential of our approach in elevating drone control and navigation through the seamless integration of natural language commands in real-world scenarios.

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.

This study introduces SpatialPrompting, a novel framework that harnesses the emergent reasoning capabilities of off-the-shelf multimodal large language models to achieve zero-shot spatial reasoning in three-dimensional (3D) environments. Unlike existing methods that rely on expensive 3D-specific fine-tuning with specialized 3D inputs such as point clouds or voxel-based features, SpatialPrompting employs a keyframe-driven prompt generation strategy. This framework uses metrics such as vision-language similarity, Mahalanobis distance, field of view, and image sharpness to select a diverse and informative set of keyframes from image sequences and then integrates them with corresponding camera pose data to effectively abstract spatial relationships and infer complex 3D structures. The proposed framework not only establishes a new paradigm for flexible spatial reasoning that utilizes intuitive visual and positional cues but also achieves state-of-the-art zero-shot performance on benchmark datasets, such as ScanQA and SQA3D, across several metrics. The proposed method effectively eliminates the need for specialized 3D inputs and fine-tuning, offering a simpler and more scalable alternative to conventional approaches.

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.

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

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.

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

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