Daily Papers

In this work, we explore the technical feasibility of implementing end-to-end 3D object detection (3DOD) with surround-view fisheye camera system. Specifically, we first investigate the performance drop incurred when transferring classic pinhole-based 3D object detectors to fisheye imagery. To mitigate this, we then develop two methods that incorporate the unique geometry of fisheye images into mainstream detection frameworks: one based on the bird's-eye-view (BEV) paradigm, named FisheyeBEVDet, and the other on the query-based paradigm, named FisheyePETR. Both methods adopt spherical spatial representations to effectively capture fisheye geometry. In light of the lack of dedicated evaluation benchmarks, we release Fisheye3DOD, a new open dataset synthesized using CARLA and featuring both standard pinhole and fisheye camera arrays. Experiments on Fisheye3DOD show that our fisheye-compatible modeling improves accuracy by up to 6.2% over baseline methods.

Rotation estimation of high precision from an RGB-D object observation is a huge challenge in 6D object pose estimation, due to the difficulty of learning in the non-linear space of SO(3). In this paper, we propose a novel rotation estimation network, termed as VI-Net, to make the task easier by decoupling the rotation as the combination of a viewpoint rotation and an in-plane rotation. More specifically, VI-Net bases the feature learning on the sphere with two individual branches for the estimates of two factorized rotations, where a V-Branch is employed to learn the viewpoint rotation via binary classification on the spherical signals, while another I-Branch is used to estimate the in-plane rotation by transforming the signals to view from the zenith direction. To process the spherical signals, a Spherical Feature Pyramid Network is constructed based on a novel design of SPAtial Spherical Convolution (SPA-SConv), which settles the boundary problem of spherical signals via feature padding and realizesviewpoint-equivariant feature extraction by symmetric convolutional operations. We apply the proposed VI-Net to the challenging task of category-level 6D object pose estimation for predicting the poses of unknown objects without available CAD models; experiments on the benchmarking datasets confirm the efficacy of our method, which outperforms the existing ones with a large margin in the regime of high precision.

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

Point cloud segmentation is central to autonomous driving and 3D scene understanding. While voxel- and point-based methods dominate recent research due to their compatibility with deep architectures and ability to capture fine-grained geometry, they often incur high computational cost, irregular memory access, and limited real-time efficiency. In contrast, range-view methods, though relatively underexplored - can leverage mature 2D semantic segmentation techniques for fast and accurate predictions. Motivated by the rapid progress in Visual Foundation Models (VFMs) for captioning, zero-shot recognition, and multimodal tasks, we investigate whether SAM2, the current state-of-the-art VFM for segmentation tasks, can serve as a strong backbone for LiDAR point cloud segmentation in the range view. We present , to our knowledge, the first range-view framework that adapts SAM2 to 3D segmentation, coupling efficient 2D feature extraction with standard projection/back-projection to operate on point clouds. To optimize SAM2 for range-view representations, we implement several architectural modifications to the encoder: (1) a novel module that emphasizes horizontal spatial dependencies inherent in LiDAR range images, (2) a customized configuration of tailored to the geometric properties of spherical projections, and (3) an adapted mechanism in the encoder backbone specifically designed to capture the unique spatial patterns and discontinuities present in range-view pseudo-images. Our approach achieves competitive performance on SemanticKITTI while benefiting from the speed, scalability, and deployment simplicity of 2D-centric pipelines. This work highlights the viability of VFMs as general-purpose backbones for 3D perception and opens a path toward unified, foundation-model-driven LiDAR segmentation. Results lets us conclude that range-view segmentation methods using VFMs leads to promising results.

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

Learning 3D representations that generalize well to arbitrarily oriented inputs is a challenge of practical importance in applications varying from computer vision to physics and chemistry. We propose a novel multi-resolution convolutional architecture for learning over concentric spherical feature maps, of which the single sphere representation is a special case. Our hierarchical architecture is based on alternatively learning to incorporate both intra-sphere and inter-sphere information. We show the applicability of our method for two different types of 3D inputs, mesh objects, which can be regularly sampled, and point clouds, which are irregularly distributed. We also propose an efficient mapping of point clouds to concentric spherical images, thereby bridging spherical convolutions on grids with general point clouds. We demonstrate the effectiveness of our approach in improving state-of-the-art performance on 3D classification tasks with rotated data.

We introduce a generalized attention mechanism for spherical domains, enabling Transformer architectures to natively process data defined on the two-dimensional sphere - a critical need in fields such as atmospheric physics, cosmology, and robotics, where preserving spherical symmetries and topology is essential for physical accuracy. By integrating numerical quadrature weights into the attention mechanism, we obtain a geometrically faithful spherical attention that is approximately rotationally equivariant, providing strong inductive biases and leading to better performance than Cartesian approaches. To further enhance both scalability and model performance, we propose neighborhood attention on the sphere, which confines interactions to geodesic neighborhoods. This approach reduces computational complexity and introduces the additional inductive bias for locality, while retaining the symmetry properties of our method. We provide optimized CUDA kernels and memory-efficient implementations to ensure practical applicability. The method is validated on three diverse tasks: simulating shallow water equations on the rotating sphere, spherical image segmentation, and spherical depth estimation. Across all tasks, our spherical Transformers consistently outperform their planar counterparts, highlighting the advantage of geometric priors for learning on spherical domains.

Multimodal large laboratory models (MLLMs) still struggle with spatial understanding under the dominant perspective-image paradigm, which inherits the narrow field of view of human-like perception. For navigation, robotic search, and 3D scene understanding, 360-degree panoramic sensing offers a form of supersensing by capturing the entire surrounding environment at once. However, existing MLLM pipelines typically decompose panoramas into multiple perspective views, leaving the spherical structure of equirectangular projection (ERP) largely implicit. In this paper, we study pano-native understanding, which requires an MLLM to reason over an ERP panorama as a continuous, observer-centered space. To this end, we first define the key abilities for pano-native understanding, including semantic anchoring, spherical localization, reference-frame transformation, and depth-aware 3D spatial reasoning. We then build a large-scale metadata construction pipeline that converts mixed-source ERP panoramas into geometry-aware, language-grounded, and depth-aware supervision, and instantiate these signals as capability-aligned instruction tuning data. On the model side, we introduce PanoWorld with Spherical Spatial Cross-Attention, which injects spherical geometry into the visual stream. We further construct PanoSpace-Bench, a diagnostic benchmark for evaluating ERP-native spatial reasoning. Experiments show that PanoWorld substantially outperforms both proprietary and open-source baselines on PanoSpace-Bench, H* Bench, and R2R-CE Val-Unseen benchmarks. These results demonstrate that robust panoramic reasoning requires dedicated pano-native supervision and geometry-aware model adaptation. All source code and proposed data will be publicly released.

Emerging from low-level vision theory, steerable filters found their counterpart in prior work on steerable convolutional neural networks equivariant to rigid transformations. In our work, we propose a steerable feed-forward learning-based approach that consists of neurons with spherical decision surfaces and operates on point clouds. Such spherical neurons are obtained by conformal embedding of Euclidean space and have recently been revisited in the context of learning representations of point sets. Focusing on 3D geometry, we exploit the isometry property of spherical neurons and derive a 3D steerability constraint. After training spherical neurons to classify point clouds in a canonical orientation, we use a tetrahedron basis to quadruplicate the neurons and construct rotation-equivariant spherical filter banks. We then apply the derived constraint to interpolate the filter bank outputs and, thus, obtain a rotation-invariant network. Finally, we use a synthetic point set and real-world 3D skeleton data to verify our theoretical findings. The code is available at https://github.com/pavlo-melnyk/steerable-3d-neurons.

Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges, such as handling thin structures and non-watertight geometries, which limit their flexibility and accuracy. In contrast, we propose a novel geometric data representation that models geometry as distributions-a powerful representation that makes no assumptions about surface genus, connectivity, or boundary conditions. Our approach uses diffusion models with a novel network architecture to learn surface point distributions, capturing fine-grained geometric details. We evaluate our representation qualitatively and quantitatively across various object types, demonstrating its effectiveness in achieving high geometric fidelity. Additionally, we explore applications using our representation, such as textured mesh representation, neural surface compression, dynamic object modeling, and rendering, highlighting its potential to advance 3D geometric learning.

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.

Spherical CNNs generalize CNNs to functions on the sphere, by using spherical convolutions as the main linear operation. The most accurate and efficient way to compute spherical convolutions is in the spectral domain (via the convolution theorem), which is still costlier than the usual planar convolutions. For this reason, applications of spherical CNNs have so far been limited to small problems that can be approached with low model capacity. In this work, we show how spherical CNNs can be scaled for much larger problems. To achieve this, we make critical improvements including novel variants of common model components, an implementation of core operations to exploit hardware accelerator characteristics, and application-specific input representations that exploit the properties of our model. Experiments show our larger spherical CNNs reach state-of-the-art on several targets of the QM9 molecular benchmark, which was previously dominated by equivariant graph neural networks, and achieve competitive performance on multiple weather forecasting tasks. Our code is available at https://github.com/google-research/spherical-cnn.

The increasing demand for AR/VR applications has highlighted the need for high-quality 360-degree panoramic content. However, generating high-quality 360-degree panoramic images and videos remains a challenging task due to the severe distortions introduced by equirectangular projection (ERP). Existing approaches either fine-tune pretrained diffusion models on limited ERP datasets or attempt tuning-free methods that still rely on ERP latent representations, leading to discontinuities near the poles. In this paper, we introduce SphereDiff, a novel approach for seamless 360-degree panoramic image and video generation using state-of-the-art diffusion models without additional tuning. We define a spherical latent representation that ensures uniform distribution across all perspectives, mitigating the distortions inherent in ERP. We extend MultiDiffusion to spherical latent space and propose a spherical latent sampling method to enable direct use of pretrained diffusion models. Moreover, we introduce distortion-aware weighted averaging to further improve the generation quality in the projection process. Our method outperforms existing approaches in generating 360-degree panoramic content while maintaining high fidelity, making it a robust solution for immersive AR/VR applications. The code is available here. https://github.com/pmh9960/SphereDiff

We propose a spherical kernel for efficient graph convolution of 3D point clouds. Our metric-based kernels systematically quantize the local 3D space to identify distinctive geometric relationships in the data. Similar to the regular grid CNN kernels, the spherical kernel maintains translation-invariance and asymmetry properties, where the former guarantees weight sharing among similar local structures in the data and the latter facilitates fine geometric learning. The proposed kernel is applied to graph neural networks without edge-dependent filter generation, making it computationally attractive for large point clouds. In our graph networks, each vertex is associated with a single point location and edges connect the neighborhood points within a defined range. The graph gets coarsened in the network with farthest point sampling. Analogous to the standard CNNs, we define pooling and unpooling operations for our network. We demonstrate the effectiveness of the proposed spherical kernel with graph neural networks for point cloud classification and semantic segmentation using ModelNet, ShapeNet, RueMonge2014, ScanNet and S3DIS datasets. The source code and the trained models can be downloaded from https://github.com/hlei-ziyan/SPH3D-GCN.

Most real-world 3D measurements from depth sensors are incomplete, and to address this issue the point cloud completion task aims to predict the complete shapes of objects from partial observations. Previous works often adapt an encoder-decoder architecture, where the encoder is trained to extract embeddings that are used as inputs to generate predictions from the decoder. However, the learned embeddings have sparse distribution in the feature space, which leads to worse generalization results during testing. To address these problems, this paper proposes a hyperspherical module, which transforms and normalizes embeddings from the encoder to be on a unit hypersphere. With the proposed module, the magnitude and direction of the output hyperspherical embedding are decoupled and only the directional information is optimized. We theoretically analyze the hyperspherical embedding and show that it enables more stable training with a wider range of learning rates and more compact embedding distributions. Experiment results show consistent improvement of point cloud completion in both single-task and multi-task learning, which demonstrates the effectiveness of the proposed method.

We present a new and general framework for convolutional neural network operations on spherical (or omnidirectional) images. Our approach represents the surface as a graph of connected points that doesn't rely on a particular sampling strategy. Additionally, by using an interpolated version of SelectionConv, we can operate on the sphere while using existing 2D CNNs and their weights. Since our method leverages existing graph implementations, it is also fast and can be fine-tuned efficiently. Our method is also general enough to be applied to any surface type, even those that are topologically non-simple. We demonstrate the effectiveness of our technique on the tasks of style transfer and segmentation for spheres as well as stylization for 3D meshes. We provide a thorough ablation study of the performance of various spherical sampling strategies.

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

Comprehensive panoramic scene understanding is critical for immersive applications, yet it remains challenging due to the scarcity of high-resolution, multi-task annotations. While perspective foundation models have achieved success through data scaling, directly adapting them to the panoramic domain often fails due to severe geometric distortions and coordinate system discrepancies. Furthermore, the underlying relations between diverse dense prediction tasks in spherical spaces are underexplored. To address these challenges, we propose MTPano, a robust multi-task panoramic foundation model established by a label-free training pipeline. First, to circumvent data scarcity, we leverage powerful perspective dense priors. We project panoramic images into perspective patches to generate accurate, domain-gap-free pseudo-labels using off-the-shelf foundation models, which are then re-projected to serve as patch-wise supervision. Second, to tackle the interference between task types, we categorize tasks into rotation-invariant (e.g., depth, segmentation) and rotation-variant (e.g., surface normals) groups. We introduce the Panoramic Dual BridgeNet, which disentangles these feature streams via geometry-aware modulation layers that inject absolute position and ray direction priors. To handle the distortion from equirectangular projections (ERP), we incorporate ERP token mixers followed by a dual-branch BridgeNet for interactions with gradient truncation, facilitating beneficial cross-task information sharing while blocking conflicting gradients from incompatible task attributes. Additionally, we introduce auxiliary tasks (image gradient, point map, etc.) to fertilize the cross-task learning process. Extensive experiments demonstrate that MTPano achieves state-of-the-art performance on multiple benchmarks and delivers competitive results against task-specific panoramic specialist foundation models.

Recent advances in generative models highlight the power of geometry-aware modeling in manifold-constrained settings. Yet, for natural images, the field remains confined to Euclidean assumptions, failing to exploit the potential of intrinsic geometric structures within the data. In this work, we investigate the geometry of natural images and observe that semantic information is predominantly encoded in directional components, while norm components can be approximated by the global average. This property holds across both RGB and latent spaces, suggesting that natural images can be effectively modeled on a hypersphere. Building on this finding, we introduce Spherical Optimal Transport Flow Matching (SOT-CFM), which utilizes angular distance, and Spherical Flow Matching (SFM), which constrains dynamics directly on the manifold. Our experiments demonstrate that these geometry-aware methods achieve superior performance against Euclidean baselines. Ultimately, this work provides a novel perspective that bridges the gap between Riemannian manifold-based modeling and natural image generation.

While spatial foundation models have demonstrated impressive performance on standard datasets, a critical question remains: are they truly all-round players capable of generalizing robustly across diverse downstream tasks, arbitrary viewpoints, shifting scene domains, varying input densities, and specific hardware constraints? Answering this overarching question requires a holistic assessment, yet current models are mainly evaluated on specific domains for which they were specifically designed or trained. Such evaluations are intrinsically limited by narrow paradigm coverage, limited scene domains, and arbitrary frame sampling, making it fundamentally difficult to assess their true generalization capabilities. To address this gap, we present SpatialBench, a cross-paradigm, domain-diverse benchmark for spatial foundation models with deterministic sampling. SpatialBench features unprecedented scale and rigorous deterministic design, comprising 19 datasets and 546 scenes across 5 diverse spatial domains. It comprehensively evaluates 41 models across 6 paradigms on 5 task suites under 4 different input density settings. Our extensive evaluation reveals that current models are not yet all-round players, and uncovers crucial insights for future advancement. Specifically, we demonstrate that full-context attention maximizes accuracy while bounded-memory strategies unlock long-sequence scalability. Moreover, our empirical evaluations in challenging embodied and egocentric tasks demonstrate that strict domain alignment and high data quality are far more critical to performance than simple dataset scaling. Furthermore, to address the largest data gap identified in our analysis, we go beyond evaluation by introducing a large-scale dataset, DA-Next-5M, and a strong baseline model, DA-Next, pushing the boundaries of spatial representation learning.

The capabilities of large language models (LLMs) have sparked debate over whether such systems just learn an enormous collection of superficial statistics or a coherent model of the data generating process -- a world model. We find evidence for the latter by analyzing the learned representations of three spatial datasets (world, US, NYC places) and three temporal datasets (historical figures, artworks, news headlines) in the Llama-2 family of models. We discover that LLMs learn linear representations of space and time across multiple scales. These representations are robust to prompting variations and unified across different entity types (e.g. cities and landmarks). In addition, we identify individual ``space neurons'' and ``time neurons'' that reliably encode spatial and temporal coordinates. Our analysis demonstrates that modern LLMs acquire structured knowledge about fundamental dimensions such as space and time, supporting the view that they learn not merely superficial statistics, but literal world models.

Designing a convolution for a spherical neural network requires a delicate tradeoff between efficiency and rotation equivariance. DeepSphere, a method based on a graph representation of the sampled sphere, strikes a controllable balance between these two desiderata. This contribution is twofold. First, we study both theoretically and empirically how equivariance is affected by the underlying graph with respect to the number of vertices and neighbors. Second, we evaluate DeepSphere on relevant problems. Experiments show state-of-the-art performance and demonstrates the efficiency and flexibility of this formulation. Perhaps surprisingly, comparison with previous work suggests that anisotropic filters might be an unnecessary price to pay. Our code is available at https://github.com/deepsphere

As the most common representation for 3D shapes, mesh is often stored discretely with arrays of vertices and faces. However, 3D shapes in the real world are presented continuously. In this paper, we propose to learn a continuous representation for meshes with fixed topology, a common and practical setting in many faces-, hand-, and body-related applications. First, we split the template into multiple closed manifold genus-0 meshes so that each genus-0 mesh can be parameterized onto the unit sphere. Then we learn spherical implicit surface (SIS), which takes a spherical coordinate and a global feature or a set of local features around the coordinate as inputs, predicting the vertex corresponding to the coordinate as an output. Since the spherical coordinates are continuous, SIS can depict a mesh in an arbitrary resolution. SIS representation builds a bridge between discrete and continuous representation in 3D shapes. Specifically, we train SIS networks in a self-supervised manner for two tasks: a reconstruction task and a super-resolution task. Experiments show that our SIS representation is comparable with state-of-the-art methods that are specifically designed for meshes with a fixed resolution and significantly outperforms methods that work in arbitrary resolutions.

The growing availability of co-located geospatial data spanning aerial imagery, street-level views, elevation models, text, and geographic coordinates offers a unique opportunity for multimodal representation learning. We introduce UNIGEOCLIP, a massively multimodal contrastive framework to jointly align five complementary geospatial modalities in a single unified embedding space. Unlike prior approaches that fuse modalities or rely on a central pivot representation, our method performs all-to-all contrastive alignment, enabling seamless comparison, retrieval, and reasoning across arbitrary combinations of modalities. We further propose a scaled latitude-longitude encoder that improves spatial representation by capturing multi-scale geographic structure. Extensive experiments across downstream geospatial tasks demonstrate that UNIGEOCLIP consistently outperforms single-modality contrastive models and coordinate-only baselines, highlighting the benefits of holistic multimodal geospatial alignment. A reference implementation is available at https://gastruc.github.io/unigeoclip.

We propose a new class of linear-time attention mechanisms based on a relaxed and computationally efficient formulation of the recently introduced E-Product, often referred to as the Yat-kernel (Bouhsine, 2025). The resulting interactions are geometry-aware and inspired by inverse-square interactions in physics. Our method, Spherical Linearized Attention with Yat Kernels (SLAY), constrains queries and keys to the unit sphere so that attention depends only on angular alignment. Using Bernstein's theorem, we express the spherical Yat-kernel as a nonnegative mixture of polynomial-exponential product kernels and derive a strictly positive random-feature approximation enabling linear-time O(L) attention. We establish positive definiteness and boundedness on the sphere and show that the estimator yields well-defined, nonnegative attention scores. Empirically, SLAY achieves performance that is nearly indistinguishable from standard softmax attention while retaining linear time and memory scaling, and consistently outperforms prior linear-time attention mechanisms such as Performers and Cosformers. To the best of our knowledge, SLAY represents the closest linear-time approximation to softmax attention reported to date, enabling scalable Transformers without the typical performance trade-offs of attention linearization.

Panoramic imagery offers a full 360° field of view and is increasingly common in consumer devices. However, it introduces non-pinhole distortions that challenge joint pose estimation and 3D reconstruction. Existing feed-forward models, built for perspective cameras, generalize poorly to this setting. We propose PanoVGGT, a permutation-equivariant Transformer framework that jointly predicts camera poses, depth maps, and 3D point clouds from one or multiple panoramas in a single forward pass. The model incorporates spherical-aware positional embeddings and a panorama-specific three-axis SO(3) rotation augmentation, enabling effective geometric reasoning in the spherical domain. To resolve inherent global-frame ambiguity, we further introduce a stochastic anchoring strategy during training. In addition, we contribute PanoCity, a large-scale outdoor panoramic dataset with dense depth and 6-DoF pose annotations. Extensive experiments on PanoCity and standard benchmarks demonstrate that PanoVGGT achieves competitive accuracy, strong robustness, and improved cross-domain generalization. Code and dataset will be released.

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

We present a novel type of neural fields that uses general radial bases for signal representation. State-of-the-art neural fields typically rely on grid-based representations for storing local neural features and N-dimensional linear kernels for interpolating features at continuous query points. The spatial positions of their neural features are fixed on grid nodes and cannot well adapt to target signals. Our method instead builds upon general radial bases with flexible kernel position and shape, which have higher spatial adaptivity and can more closely fit target signals. To further improve the channel-wise capacity of radial basis functions, we propose to compose them with multi-frequency sinusoid functions. This technique extends a radial basis to multiple Fourier radial bases of different frequency bands without requiring extra parameters, facilitating the representation of details. Moreover, by marrying adaptive radial bases with grid-based ones, our hybrid combination inherits both adaptivity and interpolation smoothness. We carefully designed weighting schemes to let radial bases adapt to different types of signals effectively. Our experiments on 2D image and 3D signed distance field representation demonstrate the higher accuracy and compactness of our method than prior arts. When applied to neural radiance field reconstruction, our method achieves state-of-the-art rendering quality, with small model size and comparable training speed.

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.

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.

We introduce 3DShape2VecSet, a novel shape representation for neural fields designed for generative diffusion models. Our shape representation can encode 3D shapes given as surface models or point clouds, and represents them as neural fields. The concept of neural fields has previously been combined with a global latent vector, a regular grid of latent vectors, or an irregular grid of latent vectors. Our new representation encodes neural fields on top of a set of vectors. We draw from multiple concepts, such as the radial basis function representation and the cross attention and self-attention function, to design a learnable representation that is especially suitable for processing with transformers. Our results show improved performance in 3D shape encoding and 3D shape generative modeling tasks. We demonstrate a wide variety of generative applications: unconditioned generation, category-conditioned generation, text-conditioned generation, point-cloud completion, and image-conditioned generation.

We present a simple yet powerful neural network that implicitly represents and renders 3D objects and scenes only from 2D observations. The network models 3D geometries as a general radiance field, which takes a set of 2D images with camera poses and intrinsics as input, constructs an internal representation for each point of the 3D space, and then renders the corresponding appearance and geometry of that point viewed from an arbitrary position. The key to our approach is to learn local features for each pixel in 2D images and to then project these features to 3D points, thus yielding general and rich point representations. We additionally integrate an attention mechanism to aggregate pixel features from multiple 2D views, such that visual occlusions are implicitly taken into account. Extensive experiments demonstrate that our method can generate high-quality and realistic novel views for novel objects, unseen categories and challenging real-world scenes.

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

The reliance on Deep Neural Network (DNN)-based classifiers in safety-critical and real-world applications necessitates Open-Set Recognition (OSR). OSR enables the identification of input data from classes unknown during training as unknown, as opposed to misclassifying them as belonging to a known class. DNNs consist of a feature extraction backbone and classifier head; however, most OSR methods typically train both components jointly, often yielding feature representations that adapt poorly to unknown data. Other approaches employ off-the-shelf objectives, such as supervised contrastive learning, which are not specifically designed for OSR. To address these limitations, we propose SpHOR, which explicitly shapes the feature space via supervised representation learning, before training a classifier. Instead of relying on generic feature learning, SpHOR custom-designs representation learning for OSR through three key innovations: (1) enforcing discriminative class-specific features via orthogonal label embeddings, ensuring clearer separation between classes. (2) imposing a spherical constraint, modeling representations as a mixture of von Mises-Fisher distributions. (3) integrating Mixup and Label Smoothing (LS) directly into the representation learning stage. To quantify how these techniques enhance representations for OSR, we introduce two metrics: the Angular Separability (AS) and Norm Separability (NS). Combining all three innovations, SpHOR achieves state-of-the-art results (in AUROC and OSCR) across various coarse-grained and fine-grained open-set benchmarks, particularly excelling on the Semantic Shift Benchmark with improvements up to 5.1\%. Code at https://github.com/nadarasarbahavan/SpHOR

Spatial intelligence requires visual representations that capture both semantic objects and geometric structure in the physical world. To support this, two major pre-training schemes are now widely used as foundation backbones: Vision-Language Models (VLMs), which use language supervision to align visual observations with semantic concepts, and Video Generation Models (VGMs), which learn from temporally evolving visual worlds. However, it still remains unclear which pre-training scheme provides a better representation substrate for spatial intelligence. In this paper, we present the first systematic frozen-feature probing study of VLMs and VGMs across three representative axes of spatial intelligence: semantic tagging, instance grouping, and 3D geometry prediction. Using the lightweight probe, our framework enables a controlled comparison of what information is already encoded in frozen representations from two model families. Experimental results reveal a clear complementarity: VLMs are stronger at semantic tagging and instance grouping, while VGMs provide more accessible signals for dense geometry and camera motion. Moreover, a naive fusion of the two already yields a representation that excels at both geometry and semantics, suggesting a promising direction for building stronger spatial-intelligence backbones by effectively integrating features from both model families. Our code is available at https://github.com/om-ai-lab/Probing-VLM-VGM{https://github.com/om-ai-lab/Probing-VLM-VGM}.

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

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.

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.

Achieving human-like spatial intelligence for vision-language models (VLMs) requires inferring 3D structures from 2D observations, recognizing object properties and relations in 3D space, and performing high-level spatial reasoning. In this paper, we propose a principled hierarchical framework that decomposes the learning of 3D spatial understanding in VLMs into four progressively complex levels, from geometric perception to abstract spatial reasoning. Guided by this framework, we construct an automated pipeline that processes approximately 5M images with over 45M objects to generate 3D spatial VQA pairs across diverse tasks and scenes for VLM supervised fine-tuning. We also develop an RGB-D VLM incorporating metric-scale point maps as auxiliary inputs to further enhance spatial understanding. Extensive experiments demonstrate that our approach achieves state-of-the-art performance on multiple spatial understanding and reasoning benchmarks, surpassing specialized spatial models and large proprietary systems such as Gemini-2.5-pro and GPT-5. Moreover, our analysis reveals clear dependencies among hierarchical task levels, offering new insights into how multi-level task design facilitates the emergence of 3D spatial intelligence.

Convolutional Neural Networks define an exceptionally powerful class of models, but are still limited by the lack of ability to be spatially invariant to the input data in a computationally and parameter efficient manner. In this work we introduce a new learnable module, the Spatial Transformer, which explicitly allows the spatial manipulation of data within the network. This differentiable module can be inserted into existing convolutional architectures, giving neural networks the ability to actively spatially transform feature maps, conditional on the feature map itself, without any extra training supervision or modification to the optimisation process. We show that the use of spatial transformers results in models which learn invariance to translation, scale, rotation and more generic warping, resulting in state-of-the-art performance on several benchmarks, and for a number of classes of transformations.

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

We introduce an inference-time scene optimization algorithm utilizing triangle soup, a collection of disconnected translucent triangle primitives, as the representation for the geometry and appearance of a scene. Unlike full-rank Gaussian kernels, triangles are a natural, locally-flat proxy for surfaces that can be connected to achieve highly complex geometry. When coupled with per-vertex Spherical Harmonics (SH), triangles provide a rich visual representation without incurring an expensive increase in primitives. We leverage our new representation to incorporate optimization objectives and enforce spatial regularization directly on the underlying primitives. The main differentiator of our approach is the definition and enforcement of soft connectivity forces between triangles during optimization, encouraging explicit, but soft, surface continuity in 3D. Experiments on representative 3D reconstruction and novel view synthesis datasets show improvements in geometric accuracy compared to current state-of-the-art algorithms without sacrificing visual fidelity.

Sparse autoencoders have recently produced dictionaries of high-dimensional vectors corresponding to the universe of concepts represented by large language models. We find that this concept universe has interesting structure at three levels: 1) The "atomic" small-scale structure contains "crystals" whose faces are parallelograms or trapezoids, generalizing well-known examples such as (man-woman-king-queen). We find that the quality of such parallelograms and associated function vectors improves greatly when projecting out global distractor directions such as word length, which is efficiently done with linear discriminant analysis. 2) The "brain" intermediate-scale structure has significant spatial modularity; for example, math and code features form a "lobe" akin to functional lobes seen in neural fMRI images. We quantify the spatial locality of these lobes with multiple metrics and find that clusters of co-occurring features, at coarse enough scale, also cluster together spatially far more than one would expect if feature geometry were random. 3) The "galaxy" scale large-scale structure of the feature point cloud is not isotropic, but instead has a power law of eigenvalues with steepest slope in middle layers. We also quantify how the clustering entropy depends on the layer.

Existing neural field representations for 3D object reconstruction either (1) utilize object-level representations, but suffer from low-quality details due to conditioning on a global latent code, or (2) are able to perfectly reconstruct the observations, but fail to utilize object-level prior knowledge to infer unobserved regions. We present SimNP, a method to learn category-level self-similarities, which combines the advantages of both worlds by connecting neural point radiance fields with a category-level self-similarity representation. Our contribution is two-fold. (1) We design the first neural point representation on a category level by utilizing the concept of coherent point clouds. The resulting neural point radiance fields store a high level of detail for locally supported object regions. (2) We learn how information is shared between neural points in an unconstrained and unsupervised fashion, which allows to derive unobserved regions of an object during the reconstruction process from given observations. We show that SimNP is able to outperform previous methods in reconstructing symmetric unseen object regions, surpassing methods that build upon category-level or pixel-aligned radiance fields, while providing semantic correspondences between instances

3D vision has rapidly evolved, driven by increasingly diverse data representations, learning paradigms, and modeling strategies. Yet the field remains fragmented across representations and benchmarks, making it difficult to develop unified perspectives on efficiency, fidelity, and scalability. This work provides a data-centric taxonomy of 3D vision that connects geometric representations, datasets, learning frameworks, and applications within a single conceptual map. We begin by analysing the principal structural representations of 3D data--point clouds, meshes, voxels, and 3D Gaussians--along with their acquisition pipelines. We then examine how dataset design, benchmark construction, and supervision regimes shape recent advances, spanning 2D-supervised 3D learning, implicit neural representations, and 4D world modeling. Through this integrative lens, we clarify the relationships among representations, learning paradigms, and downstream tasks in reconstruction, generation, and video modeling, offering a consolidated view of emerging trends toward balancing efficiency and fidelity and toward multimodal geometric grounding.

Generating a complete and explorable 360-degree visual world enables a wide range of downstream applications. While prior works have advanced the field, they remain constrained by either narrow field-of-view limitations, which hinder the synthesis of continuous and holistic scenes, or insufficient camera controllability that restricts free exploration by users or autonomous agents. To address this, we propose PanoWorld-X, a novel framework for high-fidelity and controllable panoramic video generation with diverse camera trajectories. Specifically, we first construct a large-scale dataset of panoramic video-exploration route pairs by simulating camera trajectories in virtual 3D environments via Unreal Engine. As the spherical geometry of panoramic data misaligns with the inductive priors from conventional video diffusion, we then introduce a Sphere-Aware Diffusion Transformer architecture that reprojects equirectangular features onto the spherical surface to model geometric adjacency in latent space, significantly enhancing visual fidelity and spatiotemporal continuity. Extensive experiments demonstrate that our PanoWorld-X achieves superior performance in various aspects, including motion range, control precision, and visual quality, underscoring its potential for real-world applications.

Polygon representation learning is essential for diverse applications, encompassing tasks such as shape coding, building pattern classification, and geographic question answering. While recent years have seen considerable advancements in this field, much of the focus has been on single polygons, overlooking the intricate inner- and inter-polygonal relationships inherent in multipolygons. To address this gap, our study introduces a comprehensive framework specifically designed for learning representations of polygonal geometries, particularly multipolygons. Central to our approach is the incorporation of a heterogeneous visibility graph, which seamlessly integrates both inner- and inter-polygonal relationships. To enhance computational efficiency and minimize graph redundancy, we implement a heterogeneous spanning tree sampling method. Additionally, we devise a rotation-translation invariant geometric representation, ensuring broader applicability across diverse scenarios. Finally, we introduce Multipolygon-GNN, a novel model tailored to leverage the spatial and semantic heterogeneity inherent in the visibility graph. Experiments on five real-world and synthetic datasets demonstrate its ability to capture informative representations for polygonal geometries. Code and data are available at https://github.com/dyu62/PolyGNN{github.com/dyu62/PolyGNN}.

Neural rendering techniques have made substantial progress in generating photo-realistic 3D scenes. The latest 3D Gaussian Splatting technique has achieved high quality novel view synthesis as well as fast rendering speed. However, 3D Gaussians lack proficiency in defining accurate 3D geometric structures despite their explicit primitive representations. This is due to the fact that Gaussian's attributes are primarily tailored and fine-tuned for rendering diverse 2D images by their anisotropic nature. To pave the way for efficient 3D reconstruction, we present Spherical Gaussians, a simple and effective representation for 3D geometric boundaries, from which we can directly reconstruct 3D feature curves from a set of calibrated multi-view images. Spherical Gaussians is optimized from grid initialization with a view-based rendering loss, where a 2D edge map is rendered at a specific view and then compared to the ground-truth edge map extracted from the corresponding image, without the need for any 3D guidance or supervision. Given Spherical Gaussians serve as intermedia for the robust edge representation, we further introduce a novel optimization-based algorithm called SGCR to directly extract accurate parametric curves from aligned Spherical Gaussians. We demonstrate that SGCR outperforms existing state-of-the-art methods in 3D edge reconstruction while enjoying great efficiency.

In this paper, we present a novel, scalable approach for constructing open set, instance-level 3D scene representations, advancing open world understanding of 3D environments. Existing methods require pre-constructed 3D scenes and face scalability issues due to per-point feature vector learning, limiting their efficacy with complex queries. Our method overcomes these limitations by incrementally building instance-level 3D scene representations using 2D foundation models, efficiently aggregating instance-level details such as masks, feature vectors, names, and captions. We introduce fusion schemes for feature vectors to enhance their contextual knowledge and performance on complex queries. Additionally, we explore large language models for robust automatic annotation and spatial reasoning tasks. We evaluate our proposed approach on multiple scenes from ScanNet and Replica datasets demonstrating zero-shot generalization capabilities, exceeding current state-of-the-art methods in open world 3D scene understanding.

Robust 3D representation learning forms the perceptual foundation of spatial intelligence, enabling downstream tasks in scene understanding and embodied AI. However, learning such representations directly from unposed multi-view images remains challenging. Recent self-supervised methods attempt to unify geometry, appearance, and semantics in a feed-forward manner, but they often suffer from weak geometry induction, limited appearance detail, and inconsistencies between geometry and semantics. We introduce UniSplat, a feed-forward framework designed to address these limitations through three complementary components. First, we propose a dual-masking strategy that strengthens geometry induction in the encoder. By masking both encoder and decoder tokens, and targeting decoder masks toward geometry-rich regions, the model is forced to infer structural information from incomplete visual cues, yielding geometry-aware representations even under unposed inputs. Second, we develop a coarse-to-fine Gaussian splatting strategy that reduces appearance-semantics inconsistencies by progressively refining the radiance field. Finally, to enforce geometric-semantic consistency, we introduce a pose-conditioned recalibration mechanism that interrelates the outputs of multiple heads by re-projecting predicted 3D point and semantic maps into the image plane using estimated camera parameters, and aligning them with corresponding RGB and semantic predictions to ensure cross-task consistency, thereby resolving geometry-semantic mismatches. Together, these components yield unified 3D representations that are robust to unposed, sparse-view inputs and generalize across diverse tasks, laying a perceptual foundation for spatial intelligence.

Recently, polar-based representation has shown promising properties in perceptual tasks. In addition to Cartesian-based approaches, which separate point clouds unevenly, representing point clouds as polar grids has been recognized as an alternative due to (1) its advantage in robust performance under different resolutions and (2) its superiority in streaming-based approaches. However, state-of-the-art polar-based detection methods inevitably suffer from the feature distortion problem because of the non-uniform division of polar representation, resulting in a non-negligible performance gap compared to Cartesian-based approaches. To tackle this issue, we present PARTNER, a novel 3D object detector in the polar coordinate. PARTNER alleviates the dilemma of feature distortion with global representation re-alignment and facilitates the regression by introducing instance-level geometric information into the detection head. Extensive experiments show overwhelming advantages in streaming-based detection and different resolutions. Furthermore, our method outperforms the previous polar-based works with remarkable margins of 3.68% and 9.15% on Waymo and ONCE validation set, thus achieving competitive results over the state-of-the-art methods.

Panorama has a full FoV (360^circtimes180^circ), offering a more complete visual description than perspective images. Thanks to this characteristic, panoramic depth estimation is gaining increasing traction in 3D vision. However, due to the scarcity of panoramic data, previous methods are often restricted to in-domain settings, leading to poor zero-shot generalization. Furthermore, due to the spherical distortions inherent in panoramas, many approaches rely on perspective splitting (e.g., cubemaps), which leads to suboptimal efficiency. To address these challenges, we propose DA^{2}: Depth Anything in Any Direction, an accurate, zero-shot generalizable, and fully end-to-end panoramic depth estimator. Specifically, for scaling up panoramic data, we introduce a data curation engine for generating high-quality panoramic depth data from perspective, and create sim543K panoramic RGB-depth pairs, bringing the total to sim607K. To further mitigate the spherical distortions, we present SphereViT, which explicitly leverages spherical coordinates to enforce the spherical geometric consistency in panoramic image features, yielding improved performance. A comprehensive benchmark on multiple datasets clearly demonstrates DA^{2}'s SoTA performance, with an average 38% improvement on AbsRel over the strongest zero-shot baseline. Surprisingly, DA^{2} even outperforms prior in-domain methods, highlighting its superior zero-shot generalization. Moreover, as an end-to-end solution, DA^{2} exhibits much higher efficiency over fusion-based approaches. Both the code and the curated panoramic data will be released. Project page: https://depth-any-in-any-dir.github.io/.

Understanding spatial location and relationships is a fundamental capability for modern artificial intelligence systems. Insights from human spatial cognition provide valuable guidance in this domain. Neuroscientific discoveries have highlighted the role of grid cells as a fundamental neural component for spatial representation, including distance computation, path integration, and scale discernment. In this paper, we introduce a novel positional encoding scheme inspired by Fourier analysis and the latest findings in computational neuroscience regarding grid cells. Assuming that grid cells encode spatial position through a summation of Fourier basis functions, we demonstrate the translational invariance of the grid representation during inner product calculations. Additionally, we derive an optimal grid scale ratio for multi-dimensional Euclidean spaces based on principles of biological efficiency. Utilizing these computational principles, we have developed a Grid-cell inspired Positional Encoding technique, termed GridPE, for encoding locations within high-dimensional spaces. We integrated GridPE into the Pyramid Vision Transformer architecture. Our theoretical analysis shows that GridPE provides a unifying framework for positional encoding in arbitrary high-dimensional spaces. Experimental results demonstrate that GridPE significantly enhances the performance of transformers, underscoring the importance of incorporating neuroscientific insights into the design of artificial intelligence systems.

Integration of Large Language Models (LLMs) into visual domain tasks, resulting in visual-LLMs (V-LLMs), has enabled exceptional performance in vision-language tasks, particularly for visual question answering (VQA). However, existing V-LLMs (e.g. BLIP-2, LLaVA) demonstrate weak spatial reasoning and localization awareness. Despite generating highly descriptive and elaborate textual answers, these models fail at simple tasks like distinguishing a left vs right location. In this work, we explore how image-space coordinate based instruction fine-tuning objectives could inject spatial awareness into V-LLMs. We discover optimal coordinate representations, data-efficient instruction fine-tuning objectives, and pseudo-data generation strategies that lead to improved spatial awareness in V-LLMs. Additionally, our resulting model improves VQA across image and video domains, reduces undesired hallucination, and generates better contextual object descriptions. Experiments across 5 vision-language tasks involving 14 different datasets establish the clear performance improvements achieved by our proposed framework.

3D Gaussian Splatting (3DGS) has become the de facto method of 3D representation in many vision tasks. This calls for the 3D understanding directly in this representation space. To facilitate the research in this direction, we first build a large-scale dataset of 3DGS using the commonly used ShapeNet and ModelNet datasets. Our dataset ShapeSplat consists of 65K objects from 87 unique categories, whose labels are in accordance with the respective datasets. The creation of this dataset utilized the compute equivalent of 2 GPU years on a TITAN XP GPU. We utilize our dataset for unsupervised pretraining and supervised finetuning for classification and segmentation tasks. To this end, we introduce \textit{Gaussian-MAE}, which highlights the unique benefits of representation learning from Gaussian parameters. Through exhaustive experiments, we provide several valuable insights. In particular, we show that (1) the distribution of the optimized GS centroids significantly differs from the uniformly sampled point cloud (used for initialization) counterpart; (2) this change in distribution results in degradation in classification but improvement in segmentation tasks when using only the centroids; (3) to leverage additional Gaussian parameters, we propose Gaussian feature grouping in a normalized feature space, along with splats pooling layer, offering a tailored solution to effectively group and embed similar Gaussians, which leads to notable improvement in finetuning tasks.

Latent flow matching for image generation usually transports Gaussian noise to variational autoencoder latents along linear paths. Both endpoints, however, concentrate in thin spherical shells, and a Euclidean chord leaves those shells even when preprocessing aligns their radii. By decomposing each latent token into radial and angular components, we show through component-swap probes that decoded perceptual and semantic content is carried predominantly by direction, with radius contributing much less. We therefore project data latents onto a fixed token radius, use the radial projection of Gaussian noise as the spherical prior, finetune the decoder with the encoder frozen, and replace linear interpolation with spherical linear interpolation. The resulting geodesic paths stay on the sphere at every timestep, and their velocity targets are purely angular by construction. Under matched training, the method consistently improves class-conditional ImageNet-256 FID across different image tokenizers, leaves the diffusion architecture unchanged, and requires no auxiliary encoder or representation-alignment objective.

A well-designed vectorized representation is crucial for the learning systems natively based on 3D Gaussian Splatting. While 3DGS enables efficient and explicit 3D reconstruction, its parameter-based representation remains hard to learn as features, especially for neural-network-based models. Directly feeding raw Gaussian parameters into learning frameworks fails to address the non-unique and heterogeneous nature of the Gaussian parameterization, yielding highly data-dependent models. This challenge motivates us to explore a more principled approach to represent 3D Gaussian Splatting in neural networks that preserves the underlying color and geometric structure while enforcing unique mapping and channel homogeneity. In this paper, we propose an embedding representation of 3DGS based on continuous submanifold fields that encapsulate the intrinsic information of Gaussian primitives, thereby benefiting the learning of 3DGS.

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

Learning depth from spherical panoramas is becoming a popular research topic because a panorama has a full field-of-view of the environment and provides a relatively complete description of a scene. However, applying well-studied CNNs for perspective images to the standard representation of spherical panoramas, i.e., the equirectangular projection, is suboptimal, as it becomes distorted towards the poles. Another representation is the cubemap projection, which is distortion-free but discontinued on edges and limited in the field-of-view. This paper introduces a new framework to fuse features from the two projections, unidirectionally feeding the cubemap features to the equirectangular features only at the decoding stage. Unlike the recent bidirectional fusion approach operating at both the encoding and decoding stages, our fusion scheme is much more efficient. Besides, we also designed a more effective fusion module for our fusion scheme. Experiments verify the effectiveness of our proposed fusion strategy and module, and our model achieves state-of-the-art performance on four popular datasets. Additional experiments show that our model also has the advantages of model complexity and generalization capability.The code is available at https://github.com/alibaba/UniFuse-Unidirectional-Fusion.

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.

Remarkable advances have been achieved recently in learning neural representations that characterize object geometry, while generating textured objects suitable for downstream applications and 3D rendering remains at an early stage. In particular, reconstructing textured geometry from images of real objects is a significant challenge -- reconstructed geometry is often inexact, making realistic texturing a significant challenge. We present Mesh2Tex, which learns a realistic object texture manifold from uncorrelated collections of 3D object geometry and photorealistic RGB images, by leveraging a hybrid mesh-neural-field texture representation. Our texture representation enables compact encoding of high-resolution textures as a neural field in the barycentric coordinate system of the mesh faces. The learned texture manifold enables effective navigation to generate an object texture for a given 3D object geometry that matches to an input RGB image, which maintains robustness even under challenging real-world scenarios where the mesh geometry approximates an inexact match to the underlying geometry in the RGB image. Mesh2Tex can effectively generate realistic object textures for an object mesh to match real images observations towards digitization of real environments, significantly improving over previous state of the art.

Despite high semantic alignment, modern text-to-image (T2I) generative models still struggle to synthesize diverse images from a given prompt. This lack of diversity not only restricts user choice, but also risks amplifying societal biases. In this work, we enhance the T2I diversity through a geometric lens. Unlike most existing methods that rely primarily on entropy-based guidance to increase sample dissimilarity, we introduce Geometry-Aware Spherical Sampling (GASS) to enhance diversity by explicitly controlling both prompt-dependent and prompt-independent sources of variation. Specifically, we decompose the diversity measure in CLIP embeddings using two orthogonal directions: the text embedding, which captures semantic variation related to the prompt, and an identified orthogonal direction that captures prompt-independent variation (e.g., backgrounds). Based on this decomposition, GASS increases the geometric projection spread of generated image embeddings along both axes and guides the T2I sampling process via expanded predictions along the generation trajectory. Our experiments on different frozen T2I backbones (U-Net and DiT, diffusion and flow) and benchmarks demonstrate the effectiveness of disentangled diversity enhancement with minimal impact on image fidelity and semantic alignment.

The Strong Platonic Representation Hypothesis suggests that representational convergence in artificial neural networks can be harnessed constructively: embeddings can be translated across models through a universal latent space without paired data. We ask whether an analogous geometry can be recovered across human brains. Using fMRI data from the Natural Scenes Dataset, we propose a self-supervised encoder that learns subject-specific embeddings from brain data alone by exploiting repeated stimulus presentations. We show that these independently learned spaces can be translated across subjects using unsupervised orthogonal rotations, without paired cross-subject samples or intermediate model representations. Synchronizing pairwise rotations into a single shared latent space further improves cross-subject retrieval, indicating that subject-specific spaces are mutually compatible with a common coordinate system. These results provide evidence for a shared neural geometry in the human visual cortex: subject-specific fMRI representations are approximately isometric across individuals and can be translated through purely geometric transformations.

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.

Recent advances in deep generative models have led to immense progress in 3D shape synthesis. While existing models are able to synthesize shapes represented as voxels, point-clouds, or implicit functions, these methods only indirectly enforce the plausibility of the final 3D shape surface. Here we present a 3D shape synthesis framework (SurfGen) that directly applies adversarial training to the object surface. Our approach uses a differentiable spherical projection layer to capture and represent the explicit zero isosurface of an implicit 3D generator as functions defined on the unit sphere. By processing the spherical representation of 3D object surfaces with a spherical CNN in an adversarial setting, our generator can better learn the statistics of natural shape surfaces. We evaluate our model on large-scale shape datasets, and demonstrate that the end-to-end trained model is capable of generating high fidelity 3D shapes with diverse topology.

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

We introduce the Sphere Encoder, an efficient generative framework capable of producing images in a single forward pass and competing with many-step diffusion models using fewer than five steps. Our approach works by learning an encoder that maps natural images uniformly onto a spherical latent space, and a decoder that maps random latent vectors back to the image space. Trained solely through image reconstruction losses, the model generates an image by simply decoding a random point on the sphere. Our architecture naturally supports conditional generation, and looping the encoder/decoder a few times can further enhance image quality. Across several datasets, the sphere encoder approach yields performance competitive with state of the art diffusions, but with a small fraction of the inference cost. Project page is available at https://sphere-encoder.github.io .

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

Model dimension (d_{model}) is a fundamental hyperparameter in transformer language models, yet its role in setting the geometric limits of feature representation remains under-explored. Grounded in the Linear Representation and Superposition Hypotheses - which propose that models encode features as near-orthogonal directions in latent space - we develop a framework for estimating how many such directions a model can support. We first establish the embedding matrix as a measurable proxy for near-orthogonality constraints across the latent space: the boundary between meaningful token relationships and incidental similarity in the pairwise cosine similarity distribution gives a concrete estimate of the model's accepted deviation varepsilon from perfect orthogonality. Applying this metric across dozens of open-source models reveals two classes: models with high varepsilon whose embeddings lack near-orthogonal structure, and models with low varepsilon that maintain it. We then show that the standard Johnson-Lindenstrauss lemma greatly underestimates the packing efficiency of trained representations, and derive an adjusted capacity formula in which the number of near-orthogonal directions depends on the ratio of vectors to dimensions (k/d) rather than the raw count - a single modification that cuts prediction error by two orders of magnitude with no extra parameters. Combining these results, we define representational capacity as an upper bound on the number of distinguishable directions available for features and embeddings in a model's latent space. Capacity is exponentially sensitive to varepsilon, and larger models favor tighter orthogonality constraints over maximizing raw capacity - a pattern compatible with several explanations (a stability-capacity trade-off, a ceiling on usable concepts, or confounds with model scale) that we leave to future work.

Geographic location is essential for modeling tasks in fields ranging from ecology to epidemiology to the Earth system sciences. However, extracting relevant and meaningful characteristics of a location can be challenging, often entailing expensive data fusion or data distillation from global imagery datasets. To address this challenge, we introduce Satellite Contrastive Location-Image Pretraining (SatCLIP), a global, general-purpose geographic location encoder that learns an implicit representation of locations from openly available satellite imagery. Trained location encoders provide vector embeddings summarizing the characteristics of any given location for convenient usage in diverse downstream tasks. We show that SatCLIP embeddings, pretrained on globally sampled multi-spectral Sentinel-2 satellite data, can be used in various predictive tasks that depend on location information but not necessarily satellite imagery, including temperature prediction, animal recognition in imagery, and population density estimation. Across tasks, SatCLIP embeddings consistently outperform embeddings from existing pretrained location encoders, ranging from models trained on natural images to models trained on semantic context. SatCLIP embeddings also help to improve geographic generalization. This demonstrates the potential of general-purpose location encoders and opens the door to learning meaningful representations of our planet from the vast, varied, and largely untapped modalities of geospatial data.

This work explores the use of spatial context as a source of free and plentiful supervisory signal for training a rich visual representation. Given only a large, unlabeled image collection, we extract random pairs of patches from each image and train a convolutional neural net to predict the position of the second patch relative to the first. We argue that doing well on this task requires the model to learn to recognize objects and their parts. We demonstrate that the feature representation learned using this within-image context indeed captures visual similarity across images. For example, this representation allows us to perform unsupervised visual discovery of objects like cats, people, and even birds from the Pascal VOC 2011 detection dataset. Furthermore, we show that the learned ConvNet can be used in the R-CNN framework and provides a significant boost over a randomly-initialized ConvNet, resulting in state-of-the-art performance among algorithms which use only Pascal-provided training set annotations.

Novel view synthesis from an in-the-wild video is difficult due to challenges like scene dynamics and lack of parallax. While existing methods have shown promising results with implicit neural radiance fields, they are slow to train and render. This paper revisits explicit video representations to synthesize high-quality novel views from a monocular video efficiently. We treat static and dynamic video content separately. Specifically, we build a global static scene model using an extended plane-based scene representation to synthesize temporally coherent novel video. Our plane-based scene representation is augmented with spherical harmonics and displacement maps to capture view-dependent effects and model non-planar complex surface geometry. We opt to represent the dynamic content as per-frame point clouds for efficiency. While such representations are inconsistency-prone, minor temporal inconsistencies are perceptually masked due to motion. We develop a method to quickly estimate such a hybrid video representation and render novel views in real time. Our experiments show that our method can render high-quality novel views from an in-the-wild video with comparable quality to state-of-the-art methods while being 100x faster in training and enabling real-time rendering.

Precise spatial understanding from multi-view images remains a fundamental challenge for Multimodal Large Language Models (MLLMs), as their visual representations are predominantly semantic and lack explicit geometric grounding. While existing approaches augment visual tokens with geometric cues from visual geometry models, their MLLM is still required to implicitly infer the underlying 3D structure of the scene from these augmented tokens, limiting its spatial reasoning capability. To address this issue, we introduce Cog3DMap, a framework that recurrently constructs an explicit 3D memory from multi-view images, where each token is grounded in 3D space and possesses both semantic and geometric information. By feeding these tokens into the MLLM, our framework enables direct reasoning over a spatially structured 3D map, achieving state-of-the-art performance on various spatial reasoning benchmarks. Code will be made publicly available.

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

Existing Multimodal Large Language Models (MLLMs) struggle with 3D spatial reasoning, as they fail to construct structured abstractions of the 3D environment depicted in video inputs. To bridge this gap, drawing inspiration from cognitive theories of allocentric spatial reasoning, we investigate how to enable MLLMs to model and reason over text-based spatial representations of video. Specifically, we introduce Textual Representation of Allocentric Context from Egocentric Video (TRACE), a prompting method that induces MLLMs to generate text-based representations of 3D environments as intermediate reasoning traces for more accurate spatial question answering. TRACE encodes meta-context, camera trajectories, and detailed object entities to support structured spatial reasoning over egocentric videos. Extensive experiments on VSI-Bench and OST-Bench demonstrate that TRACE yields notable and consistent improvements over prior prompting strategies across a diverse range of MLLM backbones, spanning different parameter scales and training schemas. We further present ablation studies to validate our design choices, along with detailed analyses that probe the bottlenecks of 3D spatial reasoning in MLLMs.

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

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.

3D shape generation aims to produce innovative 3D content adhering to specific conditions and constraints. Existing methods often decompose 3D shapes into a sequence of localized components, treating each element in isolation without considering spatial consistency. As a result, these approaches exhibit limited versatility in 3D data representation and shape generation, hindering their ability to generate highly diverse 3D shapes that comply with the specified constraints. In this paper, we introduce a novel spatial-aware 3D shape generation framework that leverages 2D plane representations for enhanced 3D shape modeling. To ensure spatial coherence and reduce memory usage, we incorporate a hybrid shape representation technique that directly learns a continuous signed distance field representation of the 3D shape using orthogonal 2D planes. Additionally, we meticulously enforce spatial correspondences across distinct planes using a transformer-based autoencoder structure, promoting the preservation of spatial relationships in the generated 3D shapes. This yields an algorithm that consistently outperforms state-of-the-art 3D shape generation methods on various tasks, including unconditional shape generation, multi-modal shape completion, single-view reconstruction, and text-to-shape synthesis.

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.

In representation learning, uniformity refers to the uniform feature distribution in the latent space (i.e., unit hypersphere). Previous work has shown that improving uniformity contributes to the learning of under-represented classes. However, most of the previous work focused on classification; the representation space of imbalanced regression remains unexplored. Classification-based methods are not suitable for regression tasks because they cluster features into distinct groups without considering the continuous and ordered nature essential for regression. In a geometric aspect, we uniquely focus on ensuring uniformity in the latent space for imbalanced regression through two key losses: enveloping and homogeneity. The enveloping loss encourages the induced trace to uniformly occupy the surface of a hypersphere, while the homogeneity loss ensures smoothness, with representations evenly spaced at consistent intervals. Our method integrates these geometric principles into the data representations via a Surrogate-driven Representation Learning (SRL) framework. Experiments with real-world regression and operator learning tasks highlight the importance of uniformity in imbalanced regression and validate the efficacy of our geometry-based loss functions.

We present 3D Spatial MultiModal Memory (M3), a multimodal memory system designed to retain information about medium-sized static scenes through video sources for visual perception. By integrating 3D Gaussian Splatting techniques with foundation models, M3 builds a multimodal memory capable of rendering feature representations across granularities, encompassing a wide range of knowledge. In our exploration, we identify two key challenges in previous works on feature splatting: (1) computational constraints in storing high-dimensional features for each Gaussian primitive, and (2) misalignment or information loss between distilled features and foundation model features. To address these challenges, we propose M3 with key components of principal scene components and Gaussian memory attention, enabling efficient training and inference. To validate M3, we conduct comprehensive quantitative evaluations of feature similarity and downstream tasks, as well as qualitative visualizations to highlight the pixel trace of Gaussian memory attention. Our approach encompasses a diverse range of foundation models, including vision-language models (VLMs), perception models, and large multimodal and language models (LMMs/LLMs). Furthermore, to demonstrate real-world applicability, we deploy M3's feature field in indoor scenes on a quadruped robot. Notably, we claim that M3 is the first work to address the core compression challenges in 3D feature distillation.

Vision-Language Models (VLMs) have recently emerged as powerful tools, excelling in tasks that integrate visual and textual comprehension, such as image captioning, visual question answering, and image-text retrieval. However, existing benchmarks for VLMs include spatial components, which often fail to isolate spatial reasoning from related tasks such as object detection or semantic comprehension. In this paper, we address these deficiencies with a multi-faceted approach towards understanding spatial reasoning. Informed by the diverse and multi-dimensional nature of human spatial reasoning abilities, we present a detailed analysis that first delineates the core elements of spatial reasoning: spatial relations, orientation and navigation, mental rotation, and spatial visualization, and then assesses the performance of these models in both synthetic and real-world images, bridging controlled and naturalistic contexts. We analyze 13 state-of-the-art Vision-Language Models, uncovering pivotal insights into their spatial reasoning performance. Our results reveal profound shortcomings in current VLMs, with average accuracy across the 13 models approximating random chance, highlighting spatial reasoning as a persistent obstacle. This work not only exposes the pressing need to advance spatial reasoning within VLMs but also establishes a solid platform for future exploration. Code available on GitHub (https://github.com/stogiannidis/srbench) and dataset available on HuggingFace (https://huggingface.co/datasets/stogiannidis/srbench).

Diagrams serve as a fundamental form of visual language, representing complex concepts and their inter-relationships through structured symbols, shapes, and spatial arrangements. Unlike natural images, their inherently symbolic and abstract nature poses significant challenges for Multimodal Large Language Models (MLLMs). However, current benchmarks conflate perceptual and reasoning tasks, making it difficult to assess whether MLLMs genuinely understand mathematical diagrams beyond superficial pattern recognition. To address this gap, we introduce MATHGLANCE, a benchmark specifically designed to isolate and evaluate mathematical perception in MLLMs. MATHGLANCE comprises 1.2K images and 1.6K carefully curated questions spanning four perception tasks: shape classification, object counting, relationship identification, and object grounding, covering diverse domains including plane geometry, solid geometry, and graphical representations. Our evaluation of MLLMs reveals that their ability to understand diagrams is notably limited, particularly in fine-grained grounding tasks. In response, we construct GeoPeP, a perception-oriented dataset of 200K structured geometry image-text pairs explicitly annotated with geometric primitives and precise spatial relationships. Training MLLM on GeoPeP leads to significant gains in perceptual accuracy, which in turn substantially improves mathematical reasoning. Our benchmark and dataset establish critical standards for evaluating and advancing multimodal mathematical understanding, providing valuable resources and insights to foster future MLLM research.

Though Gaussian splatting has achieved impressive results in novel view synthesis, it requires millions of primitives to model highly textured scenes, even when the geometry of the scene is simple. We propose a representation that goes beyond point-based rendering and decouples geometry and appearance in order to achieve a compact representation. We use surfels for geometry and a combination of a global neural field and per-primitive colours for appearance. The neural field textures a fixed number of primitives for each pixel, ensuring that the added compute is low. Our representation matches the perceptual quality of 3D Gaussian splatting while using 9.7times fewer primitives and 5.5times less memory on outdoor scenes and using 31times fewer primitives and 3.7times less memory on indoor scenes. Our representation also renders twice as fast as existing textured primitives while improving upon their visual quality.

Graph neural networks have recently achieved great successes in predicting quantum mechanical properties of molecules. These models represent a molecule as a graph using only the distance between atoms (nodes). They do not, however, consider the spatial direction from one atom to another, despite directional information playing a central role in empirical potentials for molecules, e.g. in angular potentials. To alleviate this limitation we propose directional message passing, in which we embed the messages passed between atoms instead of the atoms themselves. Each message is associated with a direction in coordinate space. These directional message embeddings are rotationally equivariant since the associated directions rotate with the molecule. We propose a message passing scheme analogous to belief propagation, which uses the directional information by transforming messages based on the angle between them. Additionally, we use spherical Bessel functions and spherical harmonics to construct theoretically well-founded, orthogonal representations that achieve better performance than the currently prevalent Gaussian radial basis representations while using fewer than 1/4 of the parameters. We leverage these innovations to construct the directional message passing neural network (DimeNet). DimeNet outperforms previous GNNs on average by 76% on MD17 and by 31% on QM9. Our implementation is available online.

Out-of-distribution (OOD) generalization is critical for machine learning models deployed in the real world. However, achieving this can be fundamentally challenging, as it requires the ability to learn invariant features across different domains or environments. In this paper, we propose a novel framework HYPO (HYPerspherical OOD generalization) that provably learns domain-invariant representations in a hyperspherical space. In particular, our hyperspherical learning algorithm is guided by intra-class variation and inter-class separation principles -- ensuring that features from the same class (across different training domains) are closely aligned with their class prototypes, while different class prototypes are maximally separated. We further provide theoretical justifications on how our prototypical learning objective improves the OOD generalization bound. Through extensive experiments on challenging OOD benchmarks, we demonstrate that our approach outperforms competitive baselines and achieves superior performance. Code is available at https://github.com/deeplearning-wisc/hypo.

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

Recent advancements in autonomous driving, augmented reality, robotics, and embodied intelligence have necessitated 3D perception algorithms. However, current 3D perception methods, particularly small models, struggle with processing logical reasoning, question-answering, and handling open scenario categories. On the other hand, generative multimodal large language models (MLLMs) excel in general capacity but underperform in 3D tasks, due to weak spatial and local object perception, poor text-based geometric numerical output, and inability to handle camera focal variations. To address these challenges, we propose the following solutions: Spatial-Enhanced Local Feature Mining for better spatial feature extraction, 3D Query Token-Derived Info Decoding for precise geometric regression, and Geometry Projection-Based 3D Reasoning for handling camera focal length variations. We employ parameter-efficient fine-tuning for a pre-trained MLLM and develop LLMI3D, a powerful 3D perception MLLM. Additionally, we have constructed the IG3D dataset, which provides fine-grained descriptions and question-answer annotations. Extensive experiments demonstrate that our LLMI3D achieves state-of-the-art performance, significantly outperforming existing methods.

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

Although Multimodal Large Language Models have achieved remarkable progress, they still struggle with complex 3D spatial reasoning due to the reliance on 2D visual priors. Existing approaches typically mitigate this limitation either through computationally expensive post-training procedures on limited 3D datasets or through rigid tool-calling mechanisms that lack explicit geometric understanding and viewpoint flexibility. To address these challenges, we propose a training-free framework that introduces a Visual Chain-of-Thought mechanism grounded in explicit 3D reconstruction. The proposed pipeline first reconstructs a high-fidelity 3D mesh from a single image using MLLM-guided keyword extraction and mask generation at multiple granularities. Subsequently, the framework leverages an external knowledge base to iteratively compute optimal camera extrinsic parameters and synthesize novel views, thereby emulating human perspective-taking. Extensive experiments demonstrate that the proposed approach significantly enhances spatial comprehension. Specifically, the framework outperforms specialized spatial models and general-purpose MLLMs, including GPT-5.2 and Gemini-2.5-Flash, on major benchmarks such as 3DSRBench and Rel3D.

Multimodal Large Language Models (MLLMs) excel at 2D semantic understanding but lack intrinsic 3D awareness, resulting in representations that fail to maintain geometric and spatial consistency across video frames. Given the scarcity of large-scale 3D data, we present GeoVR, a novel framework that learns geometric representations using purely 2D video sequences. This approach effectively restructures the semantic latent space within MLLMs to unlock spatial intelligence. Rather than employing superficial feature mixing, GeoVR reshapes the internal representations of the MLLM by distilling geometry knowledge from pre-trained 3D foundation models. This is accomplished through a multi-objective learning strategy driven by four complementary geometric targets: (1) estimating inter-frame camera poses to embed varying viewpoint dynamics, (2) regressing dense depth maps to anchor physical distances, (3) predicting a metric scale factor for real-world calibration, and (4) distilling multi-scale 3D features to align the intermediate feature space. Guided by these explicit physical and geometric constraints, the model's internal representations naturally develop strong 3D awareness. Extensive experiments on spatial reasoning benchmarks demonstrate that GeoVR achieves state-of-the-art performance, establishing a new paradigm for endowing foundation models with spatial intelligence.

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

We propose a new representation for encoding 3D shapes as neural fields. The representation is designed to be compatible with the transformer architecture and to benefit both shape reconstruction and shape generation. Existing works on neural fields are grid-based representations with latents defined on a regular grid. In contrast, we define latents on irregular grids, enabling our representation to be sparse and adaptive. In the context of shape reconstruction from point clouds, our shape representation built on irregular grids improves upon grid-based methods in terms of reconstruction accuracy. For shape generation, our representation promotes high-quality shape generation using auto-regressive probabilistic models. We show different applications that improve over the current state of the art. First, we show results for probabilistic shape reconstruction from a single higher resolution image. Second, we train a probabilistic model conditioned on very low resolution images. Third, we apply our model to category-conditioned generation. All probabilistic experiments confirm that we are able to generate detailed and high quality shapes to yield the new state of the art in generative 3D shape modeling.

In visual computing, 3D geometry is represented in many different forms including meshes, point clouds, voxel grids, level sets, and depth images. Each representation is suited for different tasks thus making the transformation of one representation into another (forward map) an important and common problem. We propose Omnidirectional Distance Fields (ODFs), a new 3D shape representation that encodes geometry by storing the depth to the object's surface from any 3D position in any viewing direction. Since rays are the fundamental unit of an ODF, it can be used to easily transform to and from common 3D representations like meshes or point clouds. Different from level set methods that are limited to representing closed surfaces, ODFs are unsigned and can thus model open surfaces (e.g., garments). We demonstrate that ODFs can be effectively learned with a neural network (NeuralODF) despite the inherent discontinuities at occlusion boundaries. We also introduce efficient forward mapping algorithms for transforming ODFs to and from common 3D representations. Specifically, we introduce an efficient Jumping Cubes algorithm for generating meshes from ODFs. Experiments demonstrate that NeuralODF can learn to capture high-quality shape by overfitting to a single object, and also learn to generalize on common shape categories.

3D Gaussian Splatting (3DGS) has emerged as a dominant novel-view synthesis technique, but its high memory consumption severely limits its applicability on edge devices. A growing number of 3DGS compression methods have been proposed to make 3DGS more efficient, yet most only focus on storage compression and fail to address the critical bottleneck of rendering memory. To address this problem, we introduce MEGS^{2}, a novel memory-efficient framework that tackles this challenge by jointly optimizing two key factors: the total primitive number and the parameters per primitive, achieving unprecedented memory compression. Specifically, we replace the memory-intensive spherical harmonics with lightweight, arbitrarily oriented spherical Gaussian lobes as our color representations. More importantly, we propose a unified soft pruning framework that models primitive-number and lobe-number pruning as a single constrained optimization problem. Experiments show that MEGS^{2} achieves a 50% static VRAM reduction and a 40% rendering VRAM reduction compared to existing methods, while maintaining comparable rendering quality. Project page: https://megs-2.github.io/

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 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.

Real-world applications, such as autonomous driving and humanoid robot manipulation, require precise spatial perception. However, it remains underexplored how Vision-Language Models (VLMs) recognize spatial relationships and perceive spatial movement. In this work, we introduce a spatial evaluation pipeline and construct a corresponding benchmark. Specifically, we categorize spatial understanding into two main types: absolute spatial understanding, which involves querying the absolute spatial position (e.g., left, right) of an object within an image, and 3D spatial understanding, which includes movement and rotation. Notably, our dataset is entirely synthetic, enabling the generation of test samples at a low cost while also preventing dataset contamination. We conduct experiments on multiple state-of-the-art VLMs and observe that there is significant room for improvement in their spatial understanding abilities. Explicitly, in our experiments, humans achieve near-perfect performance on all tasks, whereas current VLMs attain human-level performance only on the two simplest tasks. For the remaining tasks, the performance of VLMs is distinctly lower than that of humans. In fact, the best-performing Vision-Language Models even achieve near-zero scores on multiple tasks. The dataset and code are available on https://github.com/kong13661/LRR-Bench.

Recovering the 3D scene geometry from a single view is a fundamental yet ill-posed problem in computer vision. While classical depth estimation methods infer only a 2.5D scene representation limited to the image plane, recent approaches based on radiance fields reconstruct a full 3D representation. However, these methods still struggle with occluded regions since inferring geometry without visual observation requires (i) semantic knowledge of the surroundings, and (ii) reasoning about spatial context. We propose KYN, a novel method for single-view scene reconstruction that reasons about semantic and spatial context to predict each point's density. We introduce a vision-language modulation module to enrich point features with fine-grained semantic information. We aggregate point representations across the scene through a language-guided spatial attention mechanism to yield per-point density predictions aware of the 3D semantic context. We show that KYN improves 3D shape recovery compared to predicting density for each 3D point in isolation. We achieve state-of-the-art results in scene and object reconstruction on KITTI-360, and show improved zero-shot generalization compared to prior work. Project page: https://ruili3.github.io/kyn.

Traditional deep learning models rely on methods such as softmax cross-entropy and ArcFace loss for tasks like classification and face recognition. These methods mainly explore angular features in a hyperspherical space, often resulting in entangled inter-class features due to dense angular data across many classes. In this paper, a new field of feature exploration is proposed known as HyperSpaceX which enhances class discrimination by exploring both angular and radial dimensions in multi-hyperspherical spaces, facilitated by a novel DistArc loss. The proposed DistArc loss encompasses three feature arrangement components: two angular and one radial, enforcing intra-class binding and inter-class separation in multi-radial arrangement, improving feature discriminability. Evaluation of HyperSpaceX framework for the novel representation utilizes a proposed predictive measure that accounts for both angular and radial elements, providing a more comprehensive assessment of model accuracy beyond standard metrics. Experiments across seven object classification and six face recognition datasets demonstrate state-of-the-art (SoTA) results obtained from HyperSpaceX, achieving up to a 20% performance improvement on large-scale object datasets in lower dimensions and up to 6% gain in higher dimensions.

Monocular 3D estimation is crucial for visual perception. However, current methods fall short by relying on oversimplified assumptions, such as pinhole camera models or rectified images. These limitations severely restrict their general applicability, causing poor performance in real-world scenarios with fisheye or panoramic images and resulting in substantial context loss. To address this, we present UniK3D, the first generalizable method for monocular 3D estimation able to model any camera. Our method introduces a spherical 3D representation which allows for better disentanglement of camera and scene geometry and enables accurate metric 3D reconstruction for unconstrained camera models. Our camera component features a novel, model-independent representation of the pencil of rays, achieved through a learned superposition of spherical harmonics. We also introduce an angular loss, which, together with the camera module design, prevents the contraction of the 3D outputs for wide-view cameras. A comprehensive zero-shot evaluation on 13 diverse datasets demonstrates the state-of-the-art performance of UniK3D across 3D, depth, and camera metrics, with substantial gains in challenging large-field-of-view and panoramic settings, while maintaining top accuracy in conventional pinhole small-field-of-view domains. Code and models are available at github.com/lpiccinelli-eth/unik3d .

We describe a novel method for the application of Convolutional Neural Networks (CNNs) to fields defined on the sphere, using the HEALPix tessellation scheme. Specifically, We have developed a pixel-based approach to implement convolutional layers on the spherical surface, similarly to what is commonly done for CNNs in Euclidian space. The algorithm is fully integrable with existing libraries for NNs (e.g., PyTorch or TensorFlow). We present two applications: (i) recognition of handwritten digits projected on the sphere; (ii) estimation of cosmological parameter from Cosmic Microwave Background (CMB) simulated maps. We have built a simple NN architecture, consisting in four convolutional+pooling layers, and have used it for all the applications explored herein. For what concerns the handwritten digits, our CNN reaches an accuracy of about 95%, comparable with other existing spherical CNNs. For CMB applications, we have tested the CNN on the estimation of a "mock" parameter, defining the angular scale at which the power spectrum of a Gaussian field projected on the sphere peaks. We have estimated this parameter directly from maps, in several cases: temperature and polarization, presence of noise and partial sky coverage. In all the cases, the NN performances are comparable with those from standard spectrum-based bayesian methods. We demonstrate, for the first time, the capability of CNNs to extract information from polarization fields and to distinguish between E and B-modes. Lastly, we have applied our CNN to the estimation of the Thomson scattering optical depth at reionization (tau) from simulated CMB maps. Even without any specific optimization of the NN architecture, we reach an accuracy comparable with standard bayesian methods. This work represents a first step towards the exploitation of NNs in CMB parameter estimation and demonstrates the feasibility of our approach.

Representational analysis explores how input data of a neural system are encoded in high dimensional spaces of its distributed neural activations, and how we can compare different systems, for instance, artificial neural networks and brains, on those grounds. While existing methods offer important insights, they typically do not account for local intrinsic geometrical properties within the high-dimensional representation spaces. To go beyond these limitations, we explore Ollivier-Ricci curvature and Ricci flow as tools to study the alignment of representations between humans and artificial neural systems on a geometric level. As a proof-of-principle study, we compared the representations of face stimuli between VGG-Face, a human-aligned version of VGG-Face, and corresponding human similarity judgments from a large online study. Using this discrete geometric framework, we were able to identify local structural similarities and differences by examining the distributions of node and edge curvature and higher-level properties by detecting and comparing community structure in the representational graphs.

As large language models (LLMs) evolve, their integration with 3D spatial data (3D-LLMs) has seen rapid progress, offering unprecedented capabilities for understanding and interacting with physical spaces. This survey provides a comprehensive overview of the methodologies enabling LLMs to process, understand, and generate 3D data. Highlighting the unique advantages of LLMs, such as in-context learning, step-by-step reasoning, open-vocabulary capabilities, and extensive world knowledge, we underscore their potential to significantly advance spatial comprehension and interaction within embodied Artificial Intelligence (AI) systems. Our investigation spans various 3D data representations, from point clouds to Neural Radiance Fields (NeRFs). It examines their integration with LLMs for tasks such as 3D scene understanding, captioning, question-answering, and dialogue, as well as LLM-based agents for spatial reasoning, planning, and navigation. The paper also includes a brief review of other methods that integrate 3D and language. The meta-analysis presented in this paper reveals significant progress yet underscores the necessity for novel approaches to harness the full potential of 3D-LLMs. Hence, with this paper, we aim to chart a course for future research that explores and expands the capabilities of 3D-LLMs in understanding and interacting with the complex 3D world. To support this survey, we have established a project page where papers related to our topic are organized and listed: https://github.com/ActiveVisionLab/Awesome-LLM-3D.

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.

Recently, implicit neural representations have gained popularity for learning-based 3D reconstruction. While demonstrating promising results, most implicit approaches are limited to comparably simple geometry of single objects and do not scale to more complicated or large-scale scenes. The key limiting factor of implicit methods is their simple fully-connected network architecture which does not allow for integrating local information in the observations or incorporating inductive biases such as translational equivariance. In this paper, we propose Convolutional Occupancy Networks, a more flexible implicit representation for detailed reconstruction of objects and 3D scenes. By combining convolutional encoders with implicit occupancy decoders, our model incorporates inductive biases, enabling structured reasoning in 3D space. We investigate the effectiveness of the proposed representation by reconstructing complex geometry from noisy point clouds and low-resolution voxel representations. We empirically find that our method enables the fine-grained implicit 3D reconstruction of single objects, scales to large indoor scenes, and generalizes well from synthetic to real data.

Fourier Neural Operators (FNOs) have proven to be an efficient and effective method for resolution-independent operator learning in a broad variety of application areas across scientific machine learning. A key reason for their success is their ability to accurately model long-range dependencies in spatio-temporal data by learning global convolutions in a computationally efficient manner. To this end, FNOs rely on the discrete Fourier transform (DFT), however, DFTs cause visual and spectral artifacts as well as pronounced dissipation when learning operators in spherical coordinates since they incorrectly assume a flat geometry. To overcome this limitation, we generalize FNOs on the sphere, introducing Spherical FNOs (SFNOs) for learning operators on spherical geometries. We apply SFNOs to forecasting atmospheric dynamics, and demonstrate stable auto\-regressive rollouts for a year of simulated time (1,460 steps), while retaining physically plausible dynamics. The SFNO has important implications for machine learning-based simulation of climate dynamics that could eventually help accelerate our response to climate change.

Representing complex objects with basic geometric primitives has long been a topic in computer vision. Primitive-based representations have the merits of compactness and computational efficiency in higher-level tasks such as physics simulation, collision checking, and robotic manipulation. Unlike previous works which extract polygonal meshes from a signed distance function (SDF), in this paper, we present a novel method, named Marching-Primitives, to obtain a primitive-based abstraction directly from an SDF. Our method grows geometric primitives (such as superquadrics) iteratively by analyzing the connectivity of voxels while marching at different levels of signed distance. For each valid connected volume of interest, we march on the scope of voxels from which a primitive is able to be extracted in a probabilistic sense and simultaneously solve for the parameters of the primitive to capture the underlying local geometry. We evaluate the performance of our method on both synthetic and real-world datasets. The results show that the proposed method outperforms the state-of-the-art in terms of accuracy, and is directly generalizable among different categories and scales. The code is open-sourced at https://github.com/ChirikjianLab/Marching-Primitives.git.

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

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

Simulations are the best approximation to experimental laboratories in astrophysics and cosmology. However, the complexity, richness, and large size of their outputs severely limit the interpretability of their predictions. We describe a new, unbiased, and machine learning based approach to obtaining useful scientific insights from a broad range of simulations. The method can be used on today's largest simulations and will be essential to solve the extreme data exploration and analysis challenges posed by the Exascale era. Furthermore, this concept is so flexible, that it will also enable explorative access to observed data. Our concept is based on applying nonlinear dimensionality reduction to learn compact representations of the data in a low-dimensional space. The simulation data is projected onto this space for interactive inspection, visual interpretation, sample selection, and local analysis. We present a prototype using a rotational invariant hyperspherical variational convolutional autoencoder, utilizing a power distribution in the latent space, and trained on galaxies from IllustrisTNG simulation. Thereby, we obtain a natural Hubble tuning fork like similarity space that can be visualized interactively on the surface of a sphere by exploiting the power of HiPS tilings in Aladin Lite.

While Multimodal Large Language Models demonstrate impressive semantic capabilities, they often suffer from spatial blindness, struggling with fine-grained geometric reasoning and physical dynamics. Existing solutions typically rely on explicit 3D modalities or complex geometric scaffolding, which are limited by data scarcity and generalization challenges. In this work, we propose a paradigm shift by leveraging the implicit spatial prior within large-scale video generation models. We posit that to synthesize temporally coherent videos, these models inherently learn robust 3D structural priors and physical laws. We introduce VEGA-3D (Video Extracted Generative Awareness), a plug-and-play framework that repurposes a pre-trained video diffusion model as a Latent World Simulator. By extracting spatiotemporal features from intermediate noise levels and integrating them with semantic representations via a token-level adaptive gated fusion mechanism, we enrich MLLMs with dense geometric cues without explicit 3D supervision. Extensive experiments across 3D scene understanding, spatial reasoning, and embodied manipulation benchmarks demonstrate that our method outperforms state-of-the-art baselines, validating that generative priors provide a scalable foundation for physical-world understanding. Code is publicly available at https://github.com/H-EmbodVis/VEGA-3D.

In this paper, we question whether we have a reliable self-supervised point cloud model that can be used for diverse 3D tasks via simple linear probing, even with limited data and minimal computation. We find that existing 3D self-supervised learning approaches fall short when evaluated on representation quality through linear probing. We hypothesize that this is due to what we term the "geometric shortcut", which causes representations to collapse to low-level spatial features. This challenge is unique to 3D and arises from the sparse nature of point cloud data. We address it through two key strategies: obscuring spatial information and enhancing the reliance on input features, ultimately composing a Sonata of 140k point clouds through self-distillation. Sonata is simple and intuitive, yet its learned representations are strong and reliable: zero-shot visualizations demonstrate semantic grouping, alongside strong spatial reasoning through nearest-neighbor relationships. Sonata demonstrates exceptional parameter and data efficiency, tripling linear probing accuracy (from 21.8% to 72.5%) on ScanNet and nearly doubling performance with only 1% of the data compared to previous approaches. Full fine-tuning further advances SOTA across both 3D indoor and outdoor perception tasks.

Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically learn embeddings in Euclidean vector spaces, which do not account for this property. For this purpose, we introduce a new approach for learning hierarchical representations of symbolic data by embedding them into hyperbolic space -- or more precisely into an n-dimensional Poincar\'e ball. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity. We introduce an efficient algorithm to learn the embeddings based on Riemannian optimization and show experimentally that Poincar\'e embeddings outperform Euclidean embeddings significantly on data with latent hierarchies, both in terms of representation capacity and in terms of generalization ability.

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

We present Im2SurfTex, a method that generates textures for input 3D shapes by learning to aggregate multi-view image outputs produced by 2D image diffusion models onto the shapes' texture space. Unlike existing texture generation techniques that use ad hoc backprojection and averaging schemes to blend multiview images into textures, often resulting in texture seams and artifacts, our approach employs a trained neural module to boost texture coherency. The key ingredient of our module is to leverage neural attention and appropriate positional encodings of image pixels based on their corresponding 3D point positions, normals, and surface-aware coordinates as encoded in geodesic distances within surface patches. These encodings capture texture correlations between neighboring surface points, ensuring better texture continuity. Experimental results show that our module improves texture quality, achieving superior performance in high-resolution texture generation.

Data-driven approaches like deep learning are rapidly advancing planetary science, particularly in Mars exploration. Despite recent progress, most existing benchmarks remain confined to closed-set supervised visual tasks and do not support text-guided retrieval for geospatial discovery. We introduce MarsRetrieval, a retrieval benchmark for evaluating vision-language models for Martian geospatial discovery. MarsRetrieval includes three tasks: (1) paired image-text retrieval, (2) landform retrieval, and (3) global geo-localization, covering multiple spatial scales and diverse geomorphic origins. We propose a unified retrieval-centric protocol to benchmark multimodal embedding architectures, including contrastive dual-tower encoders and generative vision-language models. Our evaluation shows MarsRetrieval is challenging: even strong foundation models often fail to capture domain-specific geomorphic distinctions. We further show that domain-specific fine-tuning is critical for generalizable geospatial discovery in planetary settings. Our code is available at https://github.com/ml-stat-Sustech/MarsRetrieval

Vision-Language Models (VLMs) still lack robustness in spatial intelligence, demonstrating poor performance on spatial understanding and reasoning tasks. We attribute this gap to the absence of a visual geometry learning process capable of reconstructing 3D space from 2D images. We present G^2VLM, a geometry grounded vision-language model that bridges two fundamental aspects of spatial intelligence: spatial 3D reconstruction and spatial understanding. G^2VLM natively leverages learned 3D visual geometry features to directly predict 3D attributes and enhance spatial reasoning tasks via in-context learning and interleaved reasoning. Our unified design is highly scalable for spatial understanding: it trains on abundant multi-view image and video data, while simultaneously leveraging the benefits of 3D visual priors that are typically only derived from hard-to-collect annotations. Experimental results demonstrate G^2VLM is proficient in both tasks, achieving comparable results to state-of-the-art feed-forward 3D reconstruction models and achieving better or competitive results across spatial understanding and reasoning tasks. By unifying a semantically strong VLM with low-level 3D vision tasks, we hope G^2VLM can serve as a strong baseline for the community and unlock more future applications, such as 3D scene editing.

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

Neural Radiance Fields (NeRF) and Gaussian Splatting (GS) have recently transformed 3D scene representation and rendering. NeRF achieves high-fidelity novel view synthesis by learning volumetric representations through neural networks, but its implicit encoding makes editing and physical interaction challenging. In contrast, GS represents scenes as explicit collections of Gaussian primitives, enabling real-time rendering, faster training, and more intuitive manipulation. This explicit structure has made GS particularly well-suited for interactive editing and integration with physics-based simulation. In this paper, we introduce GENIE (Gaussian Encoding for Neural Radiance Fields Interactive Editing), a hybrid model that combines the photorealistic rendering quality of NeRF with the editable and structured representation of GS. Instead of using spherical harmonics for appearance modeling, we assign each Gaussian a trainable feature embedding. These embeddings are used to condition a NeRF network based on the k nearest Gaussians to each query point. To make this conditioning efficient, we introduce Ray-Traced Gaussian Proximity Search (RT-GPS), a fast nearest Gaussian search based on a modified ray-tracing pipeline. We also integrate a multi-resolution hash grid to initialize and update Gaussian features. Together, these components enable real-time, locality-aware editing: as Gaussian primitives are repositioned or modified, their interpolated influence is immediately reflected in the rendered output. By combining the strengths of implicit and explicit representations, GENIE supports intuitive scene manipulation, dynamic interaction, and compatibility with physical simulation, bridging the gap between geometry-based editing and neural rendering. The code can be found under (https://github.com/MikolajZielinski/genie)