Daily Papers

High-performance real-time stereo matching methods invariably rely on 3D regularization of the cost volume, which is unfriendly to mobile devices. And 2D regularization based methods struggle in ill-posed regions. In this paper, we present a deployment-friendly 4D cost aggregation network DBStereo, which is based on pure 2D convolutions. Specifically, we first provide a thorough analysis of the decoupling characteristics of 4D cost volume. And design a lightweight bidirectional geometry aggregation block to capture spatial and disparity representation respectively. Through decoupled learning, our approach achieves real-time performance and impressive accuracy simultaneously. Extensive experiments demonstrate that our proposed DBStereo outperforms all existing aggregation-based methods in both inference time and accuracy, even surpassing the iterative-based method IGEV-Stereo. Our study break the empirical design of using 3D convolutions for 4D cost volume and provides a simple yet strong baseline of the proposed decouple aggregation paradigm for further study. Code will be available at (https://github.com/happydummy/DBStereo{https://github.com/happydummy/DBStereo}) soon.

Point cloud sequences are commonly used to accurately detect 3D objects in applications such as autonomous driving. Current top-performing multi-frame detectors mostly follow a Detect-and-Fuse framework, which extracts features from each frame of the sequence and fuses them to detect the objects in the current frame. However, this inevitably leads to redundant computation since adjacent frames are highly correlated. In this paper, we propose an efficient Motion-guided Sequential Fusion (MSF) method, which exploits the continuity of object motion to mine useful sequential contexts for object detection in the current frame. We first generate 3D proposals on the current frame and propagate them to preceding frames based on the estimated velocities. The points-of-interest are then pooled from the sequence and encoded as proposal features. A novel Bidirectional Feature Aggregation (BiFA) module is further proposed to facilitate the interactions of proposal features across frames. Besides, we optimize the point cloud pooling by a voxel-based sampling technique so that millions of points can be processed in several milliseconds. The proposed MSF method achieves not only better efficiency than other multi-frame detectors but also leading accuracy, with 83.12% and 78.30% mAP on the LEVEL1 and LEVEL2 test sets of Waymo Open Dataset, respectively. Codes can be found at https://github.com/skyhehe123/MSF.

Recent works in geometric deep learning have introduced neural networks that allow performing inference tasks on three-dimensional geometric data by defining convolution, and sometimes pooling, operations on triangle meshes. These methods, however, either consider the input mesh as a graph, and do not exploit specific geometric properties of meshes for feature aggregation and downsampling, or are specialized for meshes, but rely on a rigid definition of convolution that does not properly capture the local topology of the mesh. We propose a method that combines the advantages of both types of approaches, while addressing their limitations: we extend a primal-dual framework drawn from the graph-neural-network literature to triangle meshes, and define convolutions on two types of graphs constructed from an input mesh. Our method takes features for both edges and faces of a 3D mesh as input and dynamically aggregates them using an attention mechanism. At the same time, we introduce a pooling operation with a precise geometric interpretation, that allows handling variations in the mesh connectivity by clustering mesh faces in a task-driven fashion. We provide theoretical insights of our approach using tools from the mesh-simplification literature. In addition, we validate experimentally our method in the tasks of shape classification and shape segmentation, where we obtain comparable or superior performance to the state of the art.

Unified 3D foundation models aspire to generate 3D assets and reason about them in language within a single backbone, but their text-3D interaction remains largely implicit. Existing methods concatenate text and 3D tokens into a flat sequence and rely on self-attention, collapsing coarse structural cues and fine geometric details into one undifferentiated representation. We introduce ELSA3D, a unified 3D model that addresses this with elastic semantic anchoring, structuring language and geometric reasoning jointly along matched abstraction scales. ELSA3D represents geometry with a scale-aware octree tokenizer and introduces Anchor Tokens, sparse cross-modal units that select semantic cues, route them to the most relevant 3D scale, retrieve scale-specific geometric evidence, and write the fused signal back into the unified representation, keeping interaction sparse yet precise. A lightweight per-block router makes both computation and reasoning elastic, choosing which text tokens instantiate anchors at which geometric scale so that cross-modal capacity concentrates where alignment is most needed. ELSA3D achieves state-of-the-art performance across image-to-3D generation, text-to-3D generation, and 3D captioning, outperforming the strongest unified baseline while roughly halving FLOPs and inference latency relative to the non-elastic version of the same model.

Recent mesh generation approaches typically tokenize triangle meshes into sequences of tokens and train autoregressive models to generate these tokens sequentially. Despite substantial progress, such token sequences inevitably reuse vertices multiple times to fully represent manifold meshes, as each vertex is shared by multiple faces. This redundancy leads to excessively long token sequences and inefficient generation processes. In this paper, we propose an efficient framework that generates artistic meshes by treating vertices and faces separately, significantly reducing redundancy. We employ an autoregressive model solely for vertex generation, decreasing the token count to approximately 23\% of that required by the most compact existing tokenizer. Next, we leverage a bidirectional transformer to complete the mesh in a single step by capturing inter-vertex relationships and constructing the adjacency matrix that defines the mesh faces. To further improve the generation quality, we introduce a fidelity enhancer to refine vertex positioning into more natural arrangements and propose a post-processing framework to remove undesirable edge connections. Experimental results show that our method achieves more than 8times faster speed on mesh generation compared to state-of-the-art approaches, while producing higher mesh quality.

Based on the theory of homogeneous spaces we derive geometrically optimal edge attributes to be used within the flexible message-passing framework. We formalize the notion of weight sharing in convolutional networks as the sharing of message functions over point-pairs that should be treated equally. We define equivalence classes of point-pairs that are identical up to a transformation in the group and derive attributes that uniquely identify these classes. Weight sharing is then obtained by conditioning message functions on these attributes. As an application of the theory, we develop an efficient equivariant group convolutional network for processing 3D point clouds. The theory of homogeneous spaces tells us how to do group convolutions with feature maps over the homogeneous space of positions R^3, position and orientations R^3 {times} S^2, and the group SE(3) itself. Among these, R^3 {times} S^2 is an optimal choice due to the ability to represent directional information, which R^3 methods cannot, and it significantly enhances computational efficiency compared to indexing features on the full SE(3) group. We support this claim with state-of-the-art results -- in accuracy and speed -- on five different benchmarks in 2D and 3D, including interatomic potential energy prediction, trajectory forecasting in N-body systems, and generating molecules via equivariant diffusion models.

Matching cost aggregation plays a fundamental role in learning-based multi-view stereo networks. However, directly aggregating adjacent costs can lead to suboptimal results due to local geometric inconsistency. Related methods either seek selective aggregation or improve aggregated depth in the 2D space, both are unable to handle geometric inconsistency in the cost volume effectively. In this paper, we propose GoMVS to aggregate geometrically consistent costs, yielding better utilization of adjacent geometries. More specifically, we correspond and propagate adjacent costs to the reference pixel by leveraging the local geometric smoothness in conjunction with surface normals. We achieve this by the geometric consistent propagation (GCP) module. It computes the correspondence from the adjacent depth hypothesis space to the reference depth space using surface normals, then uses the correspondence to propagate adjacent costs to the reference geometry, followed by a convolution for aggregation. Our method achieves new state-of-the-art performance on DTU, Tanks & Temple, and ETH3D datasets. Notably, our method ranks 1st on the Tanks & Temple Advanced benchmark.

The prevalence of relation networks in computer vision is in stark contrast to underexplored point-based methods. In this paper, we explore the possibilities of local relation operators and survey their feasibility. We propose a scalable and efficient module, called group relation aggregator. The module computes a feature of a group based on the aggregation of the features of the inner-group points weighted by geometric relations and semantic relations. We adopt this module to design our RPNet. We further verify the expandability of RPNet, in terms of both depth and width, on the tasks of classification and segmentation. Surprisingly, empirical results show that wider RPNet fits for classification, while deeper RPNet works better on segmentation. RPNet achieves state-of-the-art for classification and segmentation on challenging benchmarks. We also compare our local aggregator with PointNet++, with around 30% parameters and 50% computation saving. Finally, we conduct experiments to reveal the robustness of RPNet with regard to rigid transformation and noises.

The abundance of data has given machine learning considerable momentum in natural sciences and engineering, though modeling of physical processes is often difficult. A particularly tough problem is the efficient representation of geometric boundaries. Triangularized geometric boundaries are well understood and ubiquitous in engineering applications. However, it is notoriously difficult to integrate them into machine learning approaches due to their heterogeneity with respect to size and orientation. In this work, we introduce an effective theory to model particle-boundary interactions, which leads to our new Boundary Graph Neural Networks (BGNNs) that dynamically modify graph structures to obey boundary conditions. The new BGNNs are tested on complex 3D granular flow processes of hoppers, rotating drums and mixers, which are all standard components of modern industrial machinery but still have complicated geometry. BGNNs are evaluated in terms of computational efficiency as well as prediction accuracy of particle flows and mixing entropies. BGNNs are able to accurately reproduce 3D granular flows within simulation uncertainties over hundreds of thousands of simulation timesteps. Most notably, in our experiments, particles stay within the geometric objects without using handcrafted conditions or restrictions.

Subspace clustering seeks to identify subspaces that segment a set of n data points into k (k<<n) groups, which has emerged as a powerful tool for analyzing data from various domains, especially images and videos. Recently, several studies have demonstrated the great potential of subspace clustering models for partitioning vertices in attributed graphs, referred to as SCAG. However, these works either demand significant computational overhead for constructing the nxn self-expressive matrix, or fail to incorporate graph topology and attribute data into the subspace clustering framework effectively, and thus, compromise result quality. Motivated by this, this paper presents two effective and efficient algorithms, S2CAG and M-S2CAG, for SCAG computation. Particularly, S2CAG obtains superb performance through three major contributions. First, we formulate a new objective function for SCAG with a refined representation model for vertices and two non-trivial constraints. On top of that, an efficient linear-time optimization solver is developed based on our theoretically grounded problem transformation and well-thought-out adaptive strategy. We then conduct an in-depth analysis to disclose the theoretical connection of S2CAG to conductance minimization, which further inspires the design of M-S2CAG that maximizes the modularity. Our extensive experiments, comparing S2CAG and M-S2CAG against 17 competitors over 8 benchmark datasets, exhibit that our solutions outperform all baselines in terms of clustering quality measured against the ground truth while delivering high efficiency

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}.

Hierarchical structures are popular in recent vision transformers, however, they require sophisticated designs and massive datasets to work well. In this paper, we explore the idea of nesting basic local transformers on non-overlapping image blocks and aggregating them in a hierarchical way. We find that the block aggregation function plays a critical role in enabling cross-block non-local information communication. This observation leads us to design a simplified architecture that requires minor code changes upon the original vision transformer. The benefits of the proposed judiciously-selected design are threefold: (1) NesT converges faster and requires much less training data to achieve good generalization on both ImageNet and small datasets like CIFAR; (2) when extending our key ideas to image generation, NesT leads to a strong decoder that is 8times faster than previous transformer-based generators; and (3) we show that decoupling the feature learning and abstraction processes via this nested hierarchy in our design enables constructing a novel method (named GradCAT) for visually interpreting the learned model. Source code is available https://github.com/google-research/nested-transformer.

As a fundamental problem in computer vision, 3D object detection is experiencing rapid growth. To extract the point-wise features from the irregularly and sparsely distributed points, previous methods usually take a feature grouping module to aggregate the point features to an object candidate. However, these methods have not yet leveraged the surface geometry of foreground objects to enhance grouping and 3D box generation. In this paper, we propose the RBGNet framework, a voting-based 3D detector for accurate 3D object detection from point clouds. In order to learn better representations of object shape to enhance cluster features for predicting 3D boxes, we propose a ray-based feature grouping module, which aggregates the point-wise features on object surfaces using a group of determined rays uniformly emitted from cluster centers. Considering the fact that foreground points are more meaningful for box estimation, we design a novel foreground biased sampling strategy in downsample process to sample more points on object surfaces and further boost the detection performance. Our model achieves state-of-the-art 3D detection performance on ScanNet V2 and SUN RGB-D with remarkable performance gains. Code will be available at https://github.com/Haiyang-W/RBGNet.

Visual Place Recognition (VPR) aims to match query images against a database using visual cues. State-of-the-art methods aggregate features from deep backbones to form global descriptors. Optimal transport-based aggregation methods reformulate feature-to-cluster assignment as a transport problem, but the standard Sinkhorn algorithm symmetrically treats source and target marginals, limiting effectiveness when image features and cluster centers exhibit substantially different distributions. We propose an asymmetric aggregation VPR method with geometric constraints for locally aggregated descriptors, called A^2GC-VPR. Our method employs row-column normalization averaging with separate marginal calibration, enabling asymmetric matching that adapts to distributional discrepancies in visual place recognition. Geometric constraints are incorporated through learnable coordinate embeddings, computing compatibility scores fused with feature similarities, thereby promoting spatially proximal features to the same cluster and enhancing spatial awareness. Experimental results on MSLS, NordLand, and Pittsburgh datasets demonstrate superior performance, validating the effectiveness of our approach in improving matching accuracy and robustness.

Transformer-based models have been widely demonstrated to be successful in computer vision tasks by modelling long-range dependencies and capturing global representations. However, they are often dominated by features of large patterns leading to the loss of local details (e.g., boundaries and small objects), which are critical in medical image segmentation. To alleviate this problem, we propose a Dual-Aggregation Transformer Network called DuAT, which is characterized by two innovative designs, namely, the Global-to-Local Spatial Aggregation (GLSA) and Selective Boundary Aggregation (SBA) modules. The GLSA has the ability to aggregate and represent both global and local spatial features, which are beneficial for locating large and small objects, respectively. The SBA module is used to aggregate the boundary characteristic from low-level features and semantic information from high-level features for better preserving boundary details and locating the re-calibration objects. Extensive experiments in six benchmark datasets demonstrate that our proposed model outperforms state-of-the-art methods in the segmentation of skin lesion images, and polyps in colonoscopy images. In addition, our approach is more robust than existing methods in various challenging situations such as small object segmentation and ambiguous object boundaries.

Graph foundation models represent a transformative paradigm for learning transferable representations across diverse graph domains. Recent methods leverage large language models to unify graph and text modalities into a shared representation space using contrastive learning. However, systematic evaluations reveal significant performance degradation at structural boundaries where distinct topological patterns converge, with accuracy losses exceeding 20 percentage points. This issue arises from a key limitation: current methods assume all graph structures can be encoded within a single Euclidean space. In reality, tree structures require hyperbolic geometry to preserve hierarchical branching, while cyclic patterns depend on spherical geometry for closure properties. At structural boundaries, nodes experience conflicting geometric constraints that uniform encoding spaces cannot resolve. This raises a crucial challenge: Can alignment frameworks be designed to respect the intrinsic geometric diversity of graph structures? We introduce GraphShaper, a geometry-aware framework that enhances graph encoding through multi-geometric specialization. Our approach employs expert networks tailored to different geometric spaces, dynamically computing fusion weights to adaptively integrate geometric properties based on local structural characteristics. This adaptive fusion preserves structural integrity before alignment with text embeddings. Extensive experiments demonstrate that GraphShaper achieves 9.47\% accuracy improvements on citation networks and 7.63\% on social networks in zero-shot settings.

Most 3D generation research focuses on up-projecting 2D foundation models into the 3D space, either by minimizing 2D Score Distillation Sampling (SDS) loss or fine-tuning on multi-view datasets. Without explicit 3D priors, these methods often lead to geometric anomalies and multi-view inconsistency. Recently, researchers have attempted to improve the genuineness of 3D objects by directly training on 3D datasets, albeit at the cost of low-quality texture generation due to the limited texture diversity in 3D datasets. To harness the advantages of both approaches, we propose Bidirectional Diffusion(BiDiff), a unified framework that incorporates both a 3D and a 2D diffusion process, to preserve both 3D fidelity and 2D texture richness, respectively. Moreover, as a simple combination may yield inconsistent generation results, we further bridge them with novel bidirectional guidance. In addition, our method can be used as an initialization of optimization-based models to further improve the quality of 3D model and efficiency of optimization, reducing the generation process from 3.4 hours to 20 minutes. Experimental results have shown that our model achieves high-quality, diverse, and scalable 3D generation. Project website: https://bidiff.github.io/.

We propose a compressive yet effective mesh representation, Blocked and Patchified Tokenization (BPT), facilitating the generation of meshes exceeding 8k faces. BPT compresses mesh sequences by employing block-wise indexing and patch aggregation, reducing their length by approximately 75\% compared to the original sequences. This compression milestone unlocks the potential to utilize mesh data with significantly more faces, thereby enhancing detail richness and improving generation robustness. Empowered with the BPT, we have built a foundation mesh generative model training on scaled mesh data to support flexible control for point clouds and images. Our model demonstrates the capability to generate meshes with intricate details and accurate topology, achieving SoTA performance on mesh generation and reaching the level for direct product usage.

BiSeNet has been proved to be a popular two-stream network for real-time segmentation. However, its principle of adding an extra path to encode spatial information is time-consuming, and the backbones borrowed from pretrained tasks, e.g., image classification, may be inefficient for image segmentation due to the deficiency of task-specific design. To handle these problems, we propose a novel and efficient structure named Short-Term Dense Concatenate network (STDC network) by removing structure redundancy. Specifically, we gradually reduce the dimension of feature maps and use the aggregation of them for image representation, which forms the basic module of STDC network. In the decoder, we propose a Detail Aggregation module by integrating the learning of spatial information into low-level layers in single-stream manner. Finally, the low-level features and deep features are fused to predict the final segmentation results. Extensive experiments on Cityscapes and CamVid dataset demonstrate the effectiveness of our method by achieving promising trade-off between segmentation accuracy and inference speed. On Cityscapes, we achieve 71.9% mIoU on the test set with a speed of 250.4 FPS on NVIDIA GTX 1080Ti, which is 45.2% faster than the latest methods, and achieve 76.8% mIoU with 97.0 FPS while inferring on higher resolution images.

Efficiently quantifying renal structures can provide distinct spatial context and facilitate biomarker discovery for kidney morphology. However, the development and evaluation of the transformer model to segment the renal cortex, medulla, and collecting system remains challenging due to data inefficiency. Inspired by the hierarchical structures in vision transformer, we propose a novel method using a 3D block aggregation transformer for segmenting kidney components on contrast-enhanced CT scans. We construct the first cohort of renal substructures segmentation dataset with 116 subjects under institutional review board (IRB) approval. Our method yields the state-of-the-art performance (Dice of 0.8467) against the baseline approach of 0.8308 with the data-efficient design. The Pearson R achieves 0.9891 between the proposed method and manual standards and indicates the strong correlation and reproducibility for volumetric analysis. We extend the proposed method to the public KiTS dataset, the method leads to improved accuracy compared to transformer-based approaches. We show that the 3D block aggregation transformer can achieve local communication between sequence representations without modifying self-attention, and it can serve as an accurate and efficient quantification tool for characterizing renal structures.

Shape-Text matching is an important task of high-level shape understanding. Current methods mainly represent a 3D shape as multiple 2D rendered views, which obviously can not be understood well due to the structural ambiguity caused by self-occlusion in the limited number of views. To resolve this issue, we directly represent 3D shapes as point clouds, and propose to learn joint embedding of point clouds and texts by bidirectional matching between parts from shapes and words from texts. Specifically, we first segment the point clouds into parts, and then leverage optimal transport method to match parts and words in an optimized feature space, where each part is represented by aggregating features of all points within it and each word is abstracted by its contextual information. We optimize the feature space in order to enlarge the similarities between the paired training samples, while simultaneously maximizing the margin between the unpaired ones. Experiments demonstrate that our method achieves a significant improvement in accuracy over the SOTAs on multi-modal retrieval tasks under the Text2Shape dataset. Codes are available at https://github.com/JLUtangchuan/Parts2Words.

Generating explorable 3D scenes from a single image is a highly challenging problem in 3D vision. Existing methods struggle to support free exploration, often producing severe geometric distortions and noisy artifacts when the viewpoint moves far from the original perspective. We introduce One2Scene, an effective framework that decomposes this ill-posed problem into three tractable sub-tasks to enable immersive explorable scene generation. We first use a panorama generator to produce anchor views from a single input image as initialization. Then, we lift these 2D anchors into an explicit 3D geometric scaffold via a generalizable, feed-forward Gaussian Splatting network. Instead of treating the panorama as a single image for reconstruction, we project it into multiple sparse anchor views and reformulate the reconstruction task as multi-view stereo matching, which allows us to leverage robust geometric priors learned from large-scale multi-view datasets. A bidirectional feature fusion module is used to enforce cross-view consistency, yielding an efficient and geometrically reliable scaffold. Finally, the scaffold serves as a strong prior for a novel view generator to produce photorealistic and geometrically accurate views at arbitrary cameras. By explicitly conditioning on a 3D-consistent scaffold to perform reconstruction, One2Scene works stably under large camera motions, supporting immersive scene exploration. Extensive experiments show that One2Scene substantially outperforms state-of-the-art methods in panorama depth estimation, feed-forward 360° reconstruction, and explorable 3D scene generation. Project page: https://one2scene5406.github.io/

Geometric data augmentation is widely used in segmentation workflows, but polygon annotations are often assumed to remain valid after transformation. This assumption can fail in structured domains such as architectural floorplan analysis, where a region may contain an interior void encoded as part of a single ordered polygon chain. Cropping or clipping can remove bridge vertices in this chain, causing one semantic region to split into disconnected components. We propose a lightweight topology-preserving augmentation strategy that repairs missing adjacency relations in index space while preserving the original vertex order. The method adds minimal overhead and can be integrated into existing preprocessing workflows. Experiments show that the proposed approach achieves near-perfect Cyclic Adjacency Preservation (CAP) across common geometric transformations and improves annotation consistency in polygon-based segmentation.

Voronoi diagrams are essential geometrical structures with numerous applications, particularly astrophysics-driven finite volume methods. While serial algorithms for constructing these entities are well-established, parallel construction remains challenging. This is especially true in distributed memory systems, where each host manages only a subset of the input points. This process requires redistributing points across hosts and accurately computing the corresponding Voronoi cells. In this paper, we introduce a new distributed construction algorithm, which is implemented in our open-source C++ 3-dimensional Voronoi construction framework. Our approach leverages Delaunay triangulation as an intermediate step, which is then transformed into a Voronoi diagram. We introduce the algorithms we implemented for the precise construction and our load-balancing approach and compare the running time with other state-of-the-art frameworks. MadVoro is a versatile tool that can be applied in various scientific domains, such as mesh decomposition, computational physics, chemistry, and machine learning.

Integrating a notion of symmetry into point cloud neural networks is a provably effective way to improve their generalization capability. Of particular interest are E(3) equivariant point cloud networks where Euclidean transformations applied to the inputs are preserved in the outputs. Recent efforts aim to extend networks that are E(3) equivariant, to accommodate inputs made of multiple parts, each of which exhibits local E(3) symmetry. In practical settings, however, the partitioning into individually transforming regions is unknown a priori. Errors in the partition prediction would unavoidably map to errors in respecting the true input symmetry. Past works have proposed different ways to predict the partition, which may exhibit uncontrolled errors in their ability to maintain equivariance to the actual partition. To this end, we introduce APEN: a general framework for constructing approximate piecewise-E(3) equivariant point networks. Our primary insight is that functions that are equivariant with respect to a finer partition will also maintain equivariance in relation to the true partition. Leveraging this observation, we propose a design where the equivariance approximation error at each layers can be bounded solely in terms of (i) uncertainty quantification of the partition prediction, and (ii) bounds on the probability of failing to suggest a proper subpartition of the ground truth one. We demonstrate the effectiveness of APEN using two data types exemplifying part-based symmetry: (i) real-world scans of room scenes containing multiple furniture-type objects; and, (ii) human motions, characterized by articulated parts exhibiting rigid movement. Our empirical results demonstrate the advantage of integrating piecewise E(3) symmetry into network design, showing a distinct improvement in generalization compared to prior works for both classification and segmentation tasks.

Graph Neural Networks (GNNs) have gained significant traction for simulating complex physical systems, with models like MeshGraphNet demonstrating strong performance on unstructured simulation meshes. However, these models face several limitations, including scalability issues, requirement for meshing at inference, and challenges in handling long-range interactions. In this work, we introduce X-MeshGraphNet, a scalable, multi-scale extension of MeshGraphNet designed to address these challenges. X-MeshGraphNet overcomes the scalability bottleneck by partitioning large graphs and incorporating halo regions that enable seamless message passing across partitions. This, combined with gradient aggregation, ensures that training across partitions is equivalent to processing the entire graph at once. To remove the dependency on simulation meshes, X-MeshGraphNet constructs custom graphs directly from tessellated geometry files (e.g., STLs) by generating point clouds on the surface or volume of the object and connecting k-nearest neighbors. Additionally, our model builds multi-scale graphs by iteratively combining coarse and fine-resolution point clouds, where each level refines the previous, allowing for efficient long-range interactions. Our experiments demonstrate that X-MeshGraphNet maintains the predictive accuracy of full-graph GNNs while significantly improving scalability and flexibility. This approach eliminates the need for time-consuming mesh generation at inference, offering a practical solution for real-time simulation across a wide range of applications. The code for reproducing the results presented in this paper is available through NVIDIA Modulus.

Although polygon meshes have been a standard representation in geometry processing, their irregular and combinatorial nature hinders their suitability for learning-based applications. In this work, we introduce a novel learnable mesh representation through a set of local 3D sample Points and their associated Normals and Quadric error metrics (QEM) w.r.t. the underlying shape, which we denote PoNQ. A global mesh is directly derived from PoNQ by efficiently leveraging the knowledge of the local quadric errors. Besides marking the first use of QEM within a neural shape representation, our contribution guarantees both topological and geometrical properties by ensuring that a PoNQ mesh does not self-intersect and is always the boundary of a volume. Notably, our representation does not rely on a regular grid, is supervised directly by the target surface alone, and also handles open surfaces with boundaries and/or sharp features. We demonstrate the efficacy of PoNQ through a learning-based mesh prediction from SDF grids and show that our method surpasses recent state-of-the-art techniques in terms of both surface and edge-based metrics.

The success of the text-guided diffusion model has inspired the development and release of numerous powerful diffusion models within the open-source community. These models are typically fine-tuned on various expert datasets, showcasing diverse denoising capabilities. Leveraging multiple high-quality models to produce stronger generation ability is valuable, but has not been extensively studied. Existing methods primarily adopt parameter merging strategies to produce a new static model. However, they overlook the fact that the divergent denoising capabilities of the models may dynamically change across different states, such as when experiencing different prompts, initial noises, denoising steps, and spatial locations. In this paper, we propose a novel ensembling method, Adaptive Feature Aggregation (AFA), which dynamically adjusts the contributions of multiple models at the feature level according to various states (i.e., prompts, initial noises, denoising steps, and spatial locations), thereby keeping the advantages of multiple diffusion models, while suppressing their disadvantages. Specifically, we design a lightweight Spatial-Aware Block-Wise (SABW) feature aggregator that adaptive aggregates the block-wise intermediate features from multiple U-Net denoisers into a unified one. The core idea lies in dynamically producing an individual attention map for each model's features by comprehensively considering various states. It is worth noting that only SABW is trainable with about 50 million parameters, while other models are frozen. Both the quantitative and qualitative experiments demonstrate the effectiveness of our proposed Adaptive Feature Aggregation method. The code is available at https://github.com/tenvence/afa/.

Foundation models for 3D vision have recently demonstrated remarkable capabilities in 3D perception. However, scaling these models to long-sequence image inputs remains a significant challenge due to inference-time inefficiency. In this work, we present a detailed analysis of VGGT, a state-of-the-art feed-forward visual geometry model and identify its primary bottleneck. Visualization further reveals a token collapse phenomenon in the attention maps. Motivated by these findings, we explore the potential of token merging in the feed-forward visual geometry model. Owing to the unique architectural and task-specific properties of 3D models, directly applying existing merging techniques proves challenging. To this end, we propose FastVGGT, which, for the first time, leverages token merging in the 3D domain through a training-free mechanism for accelerating VGGT. we devise a unique token partitioning strategy tailored to 3D architectures and tasks, effectively eliminating redundant computation while preserving VGGT's powerful reconstruction capacity. Extensive experiments on multiple 3D geometry benchmarks validate the effectiveness of our approach. Notably, with 1000 input images, FastVGGT achieves a 4x speedup over VGGT while mitigating error accumulation in long-sequence scenarios. These findings underscore the potential of token merging as a principled solution for scalable 3D vision systems. Code is available at: https://mystorm16.github.io/fastvggt/.

The grand vision of enabling persistent, large-scale 3D visual geometry understanding is shackled by the irreconcilable demands of scalability and long-term stability. While offline models like VGGT achieve inspiring geometry capability, their batch-based nature renders them irrelevant for live systems. Streaming architectures, though the intended solution for live operation, have proven inadequate. Existing methods either fail to support truly infinite-horizon inputs or suffer from catastrophic drift over long sequences. We shatter this long-standing dilemma with InfiniteVGGT, a causal visual geometry transformer that operationalizes the concept of a rolling memory through a bounded yet adaptive and perpetually expressive KV cache. Capitalizing on this, we devise a training-free, attention-agnostic pruning strategy that intelligently discards obsolete information, effectively ``rolling'' the memory forward with each new frame. Fully compatible with FlashAttention, InfiniteVGGT finally alleviates the compromise, enabling infinite-horizon streaming while outperforming existing streaming methods in long-term stability. The ultimate test for such a system is its performance over a truly infinite horizon, a capability that has been impossible to rigorously validate due to the lack of extremely long-term, continuous benchmarks. To address this critical gap, we introduce the Long3D benchmark, which, for the first time, enables a rigorous evaluation of continuous 3D geometry estimation on sequences about 10,000 frames. This provides the definitive evaluation platform for future research in long-term 3D geometry understanding. Code is available at: https://github.com/AutoLab-SAI-SJTU/InfiniteVGGT

Problems involving geometric data arise in a variety of fields, including computer vision, robotics, chemistry, and physics. Such data can take numerous forms, such as points, direction vectors, planes, or transformations, but to date there is no single architecture that can be applied to such a wide variety of geometric types while respecting their symmetries. In this paper we introduce the Geometric Algebra Transformer (GATr), a general-purpose architecture for geometric data. GATr represents inputs, outputs, and hidden states in the projective geometric algebra, which offers an efficient 16-dimensional vector space representation of common geometric objects as well as operators acting on them. GATr is equivariant with respect to E(3), the symmetry group of 3D Euclidean space. As a transformer, GATr is scalable, expressive, and versatile. In experiments with n-body modeling and robotic planning, GATr shows strong improvements over non-geometric baselines.

Many machine learning tasks involve learning functions that are known to be invariant or equivariant to certain symmetries of the input data. However, it is often challenging to design neural network architectures that respect these symmetries while being expressive and computationally efficient. For example, Euclidean motion invariant/equivariant graph or point cloud neural networks. We introduce Frame Averaging (FA), a general purpose and systematic framework for adapting known (backbone) architectures to become invariant or equivariant to new symmetry types. Our framework builds on the well known group averaging operator that guarantees invariance or equivariance but is intractable. In contrast, we observe that for many important classes of symmetries, this operator can be replaced with an averaging operator over a small subset of the group elements, called a frame. We show that averaging over a frame guarantees exact invariance or equivariance while often being much simpler to compute than averaging over the entire group. Furthermore, we prove that FA-based models have maximal expressive power in a broad setting and in general preserve the expressive power of their backbone architectures. Using frame averaging, we propose a new class of universal Graph Neural Networks (GNNs), universal Euclidean motion invariant point cloud networks, and Euclidean motion invariant Message Passing (MP) GNNs. We demonstrate the practical effectiveness of FA on several applications including point cloud normal estimation, beyond 2-WL graph separation, and n-body dynamics prediction, achieving state-of-the-art results in all of these benchmarks.

The recent advancements in 3D Gaussian Splatting (3DGS) have demonstrated remarkable potential in novel view synthesis tasks. The divide-and-conquer paradigm has enabled large-scale scene reconstruction, but significant challenges remain in scene partitioning, optimization, and merging processes. This paper introduces BlockGaussian, a novel framework incorporating a content-aware scene partition strategy and visibility-aware block optimization to achieve efficient and high-quality large-scale scene reconstruction. Specifically, our approach considers the content-complexity variation across different regions and balances computational load during scene partitioning, enabling efficient scene reconstruction. To tackle the supervision mismatch issue during independent block optimization, we introduce auxiliary points during individual block optimization to align the ground-truth supervision, which enhances the reconstruction quality. Furthermore, we propose a pseudo-view geometry constraint that effectively mitigates rendering degradation caused by airspace floaters during block merging. Extensive experiments on large-scale scenes demonstrate that our approach achieves state-of-the-art performance in both reconstruction efficiency and rendering quality, with a 5x speedup in optimization and an average PSNR improvement of 1.21 dB on multiple benchmarks. Notably, BlockGaussian significantly reduces computational requirements, enabling large-scale scene reconstruction on a single 24GB VRAM device. The project page is available at https://github.com/SunshineWYC/BlockGaussian

Automated theorem proving in Euclidean geometry, particularly for International Mathematical Olympiad (IMO) level problems, remains a major challenge and an important research focus in Artificial Intelligence. In this paper, we present a highly efficient method for geometry theorem proving that runs entirely on CPUs without relying on neural network-based inference. Our initial study shows that a simple random strategy for adding auxiliary points can achieve silver-medal level human performance on IMO. Building on this, we propose HAGeo, a Heuristic-based method for adding Auxiliary constructions in Geometric deduction that solves 28 of 30 problems on the IMO-30 benchmark, achieving gold-medal level performance and surpassing AlphaGeometry, a competitive neural network-based approach, by a notable margin. To evaluate our method and existing approaches more comprehensively, we further construct HAGeo-409, a benchmark consisting of 409 geometry problems with human-assessed difficulty levels. Compared with the widely used IMO-30, our benchmark poses greater challenges and provides a more precise evaluation, setting a higher bar for geometry theorem proving.

Transformer has recently gained considerable popularity in low-level vision tasks, including image super-resolution (SR). These networks utilize self-attention along different dimensions, spatial or channel, and achieve impressive performance. This inspires us to combine the two dimensions in Transformer for a more powerful representation capability. Based on the above idea, we propose a novel Transformer model, Dual Aggregation Transformer (DAT), for image SR. Our DAT aggregates features across spatial and channel dimensions, in the inter-block and intra-block dual manner. Specifically, we alternately apply spatial and channel self-attention in consecutive Transformer blocks. The alternate strategy enables DAT to capture the global context and realize inter-block feature aggregation. Furthermore, we propose the adaptive interaction module (AIM) and the spatial-gate feed-forward network (SGFN) to achieve intra-block feature aggregation. AIM complements two self-attention mechanisms from corresponding dimensions. Meanwhile, SGFN introduces additional non-linear spatial information in the feed-forward network. Extensive experiments show that our DAT surpasses current methods. Code and models are obtainable at https://github.com/zhengchen1999/DAT.

In this paper we show that visual diffusion models can serve as effective geometric solvers: they can directly reason about geometric problems by working in pixel space. We first demonstrate this on the Inscribed Square Problem, a long-standing problem in geometry that asks whether every Jordan curve contains four points forming a square. We then extend the approach to two other well-known hard geometric problems: the Steiner Tree Problem and the Simple Polygon Problem. Our method treats each problem instance as an image and trains a standard visual diffusion model that transforms Gaussian noise into an image representing a valid approximate solution that closely matches the exact one. The model learns to transform noisy geometric structures into correct configurations, effectively recasting geometric reasoning as image generation. Unlike prior work that necessitates specialized architectures and domain-specific adaptations when applying diffusion to parametric geometric representations, we employ a standard visual diffusion model that operates on the visual representation of the problem. This simplicity highlights a surprising bridge between generative modeling and geometric problem solving. Beyond the specific problems studied here, our results point toward a broader paradigm: operating in image space provides a general and practical framework for approximating notoriously hard problems, and opens the door to tackling a far wider class of challenging geometric tasks.

We introduce the problem of material-aware part grouping in untextured meshes. Many real-world shapes, such as scales of pinecones or windows of buildings, contain repeated structures that share the same material but exhibit geometric variations. When assigning materials to such meshes, these repeated parts often require piece-by-piece manual identification and selection, which is tedious and time-consuming. To address this, we propose Material Magic Wand, a tool that allows artists to select part groups based on their estimated material properties -- when one part is selected, our algorithm automatically retrieves all other parts likely to share the same material. The key component of our approach is a part encoder that generates a material-aware embedding for each 3D part, accounting for both local geometry and global context. We train our model with a supervised contrastive loss that brings embeddings of material-consistent parts closer while separating those of different materials; therefore, part grouping can be achieved by retrieving embeddings that are close to the embedding of the selected part. To benchmark this task, we introduce a curated dataset of 100 shapes with 241 part-level queries. We verify the effectiveness of our method through extensive experiments and demonstrate its practical value in an interactive material assignment application.

Open-vocabulary 3D scene understanding is indispensable for embodied agents. Recent works leverage pretrained vision-language models (VLMs) for object segmentation and project them to point clouds to build 3D maps. Despite progress, a point cloud is a set of unordered coordinates that requires substantial storage space and does not directly convey occupancy information or spatial relation, making existing methods inefficient for downstream tasks, e.g., path planning and text-based object retrieval. To address these issues, we propose Octree-Graph, a novel scene representation for open-vocabulary 3D scene understanding. Specifically, a Chronological Group-wise Segment Merging (CGSM) strategy and an Instance Feature Aggregation (IFA) algorithm are first designed to get 3D instances and corresponding semantic features. Subsequently, an adaptive-octree structure is developed that stores semantics and depicts the occupancy of an object adjustably according to its shape. Finally, the Octree-Graph is constructed where each adaptive-octree acts as a graph node, and edges describe the spatial relations among nodes. Extensive experiments on various tasks are conducted on several widely-used datasets, demonstrating the versatility and effectiveness of our method. Code is available https://github.com/yifeisu/OV-Octree-Graph{here}.

The big empirical success of group equivariant networks has led in recent years to the sprouting of a great variety of equivariant network architectures. A particular focus has thereby been on rotation and reflection equivariant CNNs for planar images. Here we give a general description of E(2)-equivariant convolutions in the framework of Steerable CNNs. The theory of Steerable CNNs thereby yields constraints on the convolution kernels which depend on group representations describing the transformation laws of feature spaces. We show that these constraints for arbitrary group representations can be reduced to constraints under irreducible representations. A general solution of the kernel space constraint is given for arbitrary representations of the Euclidean group E(2) and its subgroups. We implement a wide range of previously proposed and entirely new equivariant network architectures and extensively compare their performances. E(2)-steerable convolutions are further shown to yield remarkable gains on CIFAR-10, CIFAR-100 and STL-10 when used as a drop-in replacement for non-equivariant convolutions.

Generating high-quality 3D objects from textual descriptions remains a challenging problem due to computational cost, the scarcity of 3D data, and complex 3D representations. We introduce Geometry Image Diffusion (GIMDiffusion), a novel Text-to-3D model that utilizes geometry images to efficiently represent 3D shapes using 2D images, thereby avoiding the need for complex 3D-aware architectures. By integrating a Collaborative Control mechanism, we exploit the rich 2D priors of existing Text-to-Image models such as Stable Diffusion. This enables strong generalization even with limited 3D training data (allowing us to use only high-quality training data) as well as retaining compatibility with guidance techniques such as IPAdapter. In short, GIMDiffusion enables the generation of 3D assets at speeds comparable to current Text-to-Image models. The generated objects consist of semantically meaningful, separate parts and include internal structures, enhancing both usability and versatility.

Existing Transformer-based models for point cloud analysis suffer from quadratic complexity, leading to compromised point cloud resolution and information loss. In contrast, the newly proposed Mamba model, based on state space models (SSM), outperforms Transformer in multiple areas with only linear complexity. However, the straightforward adoption of Mamba does not achieve satisfactory performance on point cloud tasks. In this work, we present Mamba3D, a state space model tailored for point cloud learning to enhance local feature extraction, achieving superior performance, high efficiency, and scalability potential. Specifically, we propose a simple yet effective Local Norm Pooling (LNP) block to extract local geometric features. Additionally, to obtain better global features, we introduce a bidirectional SSM (bi-SSM) with both a token forward SSM and a novel backward SSM that operates on the feature channel. Extensive experimental results show that Mamba3D surpasses Transformer-based counterparts and concurrent works in multiple tasks, with or without pre-training. Notably, Mamba3D achieves multiple SoTA, including an overall accuracy of 92.6% (train from scratch) on the ScanObjectNN and 95.1% (with single-modal pre-training) on the ModelNet40 classification task, with only linear complexity.

The generation of production-ready quad-dominant meshes is a cornerstone of modern 3D content creation. Generating anisotropic quad-dominant meshes from point clouds is challenging, as existing methods are typically limited to producing either pure triangular meshes or pure quadrilateral meshes with isotropic densities. In this paper, we present QuadLink, a unified framework consisting of three stages for quad-dominant mesh generation by linking points into structured faces. QuadLink formulates polygonal mesh generation as a hybrid centroid-conditioned vertex linking model: it first predicts a unified set of anchors (vertices and face centroids), then learns centroid-conditioned links that associate vertices with face centroids, and finally assembles polygonal faces with a quad-first strategy guided by robust geometric verification strategies. This link-based formulation enables efficient generation of sparse and anisotropic quad-dominant meshes with coherent edge flow and meanwhile supporting hybrid polygonal topology. To construct training data for this model, we further introduce a Tri-to-Quad Operator that converts artistic triangle meshes into quad-dominant training data via global merge selection. Extensive experiments show that QuadLink produces production-ready quad-dominant meshes from point clouds and achieves improved geometric fidelity and topological quality compared to prior baselines. Our method natively supports hybrid polygonal topology, generalizing to arbitrary n-gon meshes without architectural changes.

Graph Neural Networks (GNNs) have been shown to be effective models for different predictive tasks on graph-structured data. Recent work on their expressive power has focused on isomorphism tasks and countable feature spaces. We extend this theoretical framework to include continuous features - which occur regularly in real-world input domains and within the hidden layers of GNNs - and we demonstrate the requirement for multiple aggregation functions in this context. Accordingly, we propose Principal Neighbourhood Aggregation (PNA), a novel architecture combining multiple aggregators with degree-scalers (which generalize the sum aggregator). Finally, we compare the capacity of different models to capture and exploit the graph structure via a novel benchmark containing multiple tasks taken from classical graph theory, alongside existing benchmarks from real-world domains, all of which demonstrate the strength of our model. With this work, we hope to steer some of the GNN research towards new aggregation methods which we believe are essential in the search for powerful and robust models.

Existing Large Multimodal Models (LMMs) struggle with mathematical geometric reasoning due to a lack of high-quality image-text paired data. Current geometric data generation approaches, which apply preset templates to generate geometric data or use Large Language Models (LLMs) to rephrase questions and answers (Q&A), unavoidably limit data accuracy and diversity. To synthesize higher-quality data, we propose a two-stage Reverse Chain-of-Thought (R-CoT) geometry problem generation pipeline. First, we introduce GeoChain to produce high-fidelity geometric images and corresponding descriptions highlighting relations among geometric elements. We then design a Reverse A&Q method that reasons step-by-step based on the descriptions and generates questions in reverse from the reasoning results. Experiments demonstrate that the proposed method brings significant and consistent improvements on multiple LMM baselines, achieving new performance records in the 2B, 7B, and 8B settings. Notably, R-CoT-8B significantly outperforms previous state-of-the-art open-source mathematical models by 16.6% on MathVista and 9.2% on GeoQA, while also surpassing the closed-source model GPT-4o by an average of 13% across both datasets. The code is available at https://github.com/dle666/R-CoT.

Visual recognition requires rich representations that span levels from low to high, scales from small to large, and resolutions from fine to coarse. Even with the depth of features in a convolutional network, a layer in isolation is not enough: compounding and aggregating these representations improves inference of what and where. Architectural efforts are exploring many dimensions for network backbones, designing deeper or wider architectures, but how to best aggregate layers and blocks across a network deserves further attention. Although skip connections have been incorporated to combine layers, these connections have been "shallow" themselves, and only fuse by simple, one-step operations. We augment standard architectures with deeper aggregation to better fuse information across layers. Our deep layer aggregation structures iteratively and hierarchically merge the feature hierarchy to make networks with better accuracy and fewer parameters. Experiments across architectures and tasks show that deep layer aggregation improves recognition and resolution compared to existing branching and merging schemes. The code is at https://github.com/ucbdrive/dla.

Recent advancements in autoregressive transformers have demonstrated remarkable potential for generating artist-quality meshes. However, the token ordering strategies employed by existing methods typically fail to meet professional artist standards, where coordinate-based sorting yields inefficiently long sequences, and patch-based heuristics disrupt the continuous edge flow and structural regularity essential for high-quality modeling. To address these limitations, we propose Strips as Tokens (SATO), a novel framework with a token ordering strategy inspired by triangle strips. By constructing the sequence as a connected chain of faces that explicitly encodes UV boundaries, our method naturally preserves the organized edge flow and semantic layout characteristic of artist-created meshes. A key advantage of this formulation is its unified representation, enabling the same token sequence to be decoded into either a triangle or quadrilateral mesh. This flexibility facilitates joint training on both data types: large-scale triangle data provides fundamental structural priors, while high-quality quad data enhances the geometric regularity of the outputs. Extensive experiments demonstrate that SATO consistently outperforms prior methods in terms of geometric quality, structural coherence, and UV segmentation.

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.

Accurate 3D medical image segmentation requires both long-range volumetric context and fine boundary preservation. CNN-based methods have limited global dependency modeling, while Transformer-based models are often computationally expensive for dense 3D inputs. Recent Mamba-based methods provide an efficient alternative, but existing volumetric designs still depend on repeated high-resolution scanning, forward-only sequential modeling, and fixed directional summation, causing high cost, scan-order bias, and suboptimal directional aggregation. We propose BiSegMamba, an efficient bidirectional tri-oriented Mamba network for 3D medical image segmentation. BiSegMamba follows a compact-to-detail design, where a progressive compacting stem (PCS) enables efficient latent-space reasoning while retaining shallow high-resolution features for reconstruction. A multi-scale spatial mixer (MSSM) captures local anatomical patterns in early stages, and the proposed bidirectional tri-oriented Ortho Mamba (Bi-ToOM) block models long-range dependencies from multiple orthogonal views using jointly processed forward and backward scan sequences. Adaptive directional fusion (ADF) learns input-dependent channel-wise weights across scan orientations, replacing fixed summation with orientation-aware fusion. Experiments on a collected carotid CTA dataset and three public benchmarks, BraTS2023, ACDC, and AMOS-CT, show that BiSegMamba generalizes well across vascular, cardiac, brain tumor, and abdominal multi-organ segmentation tasks. Compared with SegMamba-V2, BiSegMamba achieves slightly better performance on BraTS2023 and clear improvements on ACDC and the carotid dataset, while reducing computational cost by up to 77.9% FLOPs, demonstrating a strong accuracy-efficiency balance for general 3D medical image segmentation.

Despite recent advances in multimodal reasoning, representing auxiliary geometric constructions remains a fundamental challenge for multimodal large language models (MLLMs). Such constructions are absent from the original diagram and must be introduced before theorems apply. Existing approaches predominantly rely on explicit construction paradigms, including text-based geometric specification, visual-token interleaving during reasoning, and tool-augmented geometric execution. However, these methods either fail to faithfully represent complex spatial relationships, incur representation mismatch between discrete symbols and continuous geometric structures, or rely on external capabilities that hinder end-to-end optimization. To address these limitations, we propose LatentGeo, a framework that learns continuous latent visual representations to internalize auxiliary geometric constructions without pixel-level rendering or external executors. We design a three-stage curriculum that progressively aligns and internalizes these latent representations through auxiliary visual supervision, followed by LaGDPO, a latent-aware reinforcement learning procedure that stabilizes latent representations during policy optimization while improving end-task correctness. To systematically evaluate construction-centric representation quality, we introduce GeoAux, a new benchmark targeting visually dependent geometry problems, and conduct experiments on GeoAux and MathVerse. Results show that LatentGeo achieves substantial gains on geometric reasoning tasks, particularly those requiring auxiliary constructions. Extensive analyses and ablation studies further validate the effectiveness of each component in our framework.

Geometry problems are a crucial testbed for AI reasoning capabilities. Most existing geometry solving systems cannot express problems within a unified framework, thus are difficult to integrate with other mathematical fields. Besides, since most geometric proofs rely on intuitive diagrams, verifying geometry problems is particularly challenging. To address these gaps, we introduce LeanGeo, a unified formal system for formalizing and solving competition-level geometry problems within the Lean 4 theorem prover. LeanGeo features a comprehensive library of high-level geometric theorems with Lean's foundational logic, enabling rigorous proof verification and seamless integration with Mathlib. We also present LeanGeo-Bench, a formal geometry benchmark in LeanGeo, comprising problems from the International Mathematical Olympiad (IMO) and other advanced sources. Our evaluation demonstrates the capabilities and limitations of state-of-the-art Large Language Models on this benchmark, highlighting the need for further advancements in automated geometric reasoning. We open source the theorem library and the benchmark of LeanGeo at https://github.com/project-numina/LeanGeo/tree/master.

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.

Empowered by large-scale training, vision-language models (VLMs) achieve strong image and video understanding, yet their ability to perform spatial reasoning in both static scenes and dynamic videos remains limited. Recent advances try to handle this limitation by injecting geometry tokens from pretrained 3D foundation models into VLMs. Nevertheless, we observe that naive token fusion followed by standard fine-tuning in this line of work often leaves such geometric cues underutilized for spatial reasoning, as VLMs tend to rely heavily on 2D visual cues. In this paper, we propose GeoSR, a framework designed to make geometry matter by encouraging VLMs to actively reason with geometry tokens. GeoSR introduces two key components: (1) Geometry-Unleashing Masking, which strategically masks portions of 2D vision tokens during training to weaken non-geometric shortcuts and force the model to consult geometry tokens for spatial reasoning; and (2) Geometry-Guided Fusion, a gated routing mechanism that adaptively amplifies geometry token contributions in regions where geometric evidence is critical. Together, these designs unleash the potential of geometry tokens for spatial reasoning tasks. Extensive experiments on both static and dynamic spatial reasoning benchmarks demonstrate that GeoSR consistently outperforms prior methods and establishes new state-of-the-art performance by effectively leveraging geometric information. The project page is available at https://suhzhang.github.io/GeoSR/.

Let T be a rooted and weighted tree, where the weight of any node is equal to the sum of the weights of its children. The popular Treemap algorithm visualizes such a tree as a hierarchical partition of a square into rectangles, where the area of the rectangle corresponding to any node in T is equal to the weight of that node. The aspect ratio of the rectangles in such a rectangular partition necessarily depends on the weights and can become arbitrarily high. We introduce a new hierarchical partition scheme, called a polygonal partition, which uses convex polygons rather than just rectangles. We present two methods for constructing polygonal partitions, both having guarantees on the worst-case aspect ratio of the constructed polygons; in particular, both methods guarantee a bound on the aspect ratio that is independent of the weights of the nodes. We also consider rectangular partitions with slack, where the areas of the rectangles may differ slightly from the weights of the corresponding nodes. We show that this makes it possible to obtain partitions with constant aspect ratio. This result generalizes to hyper-rectangular partitions in R^d. We use these partitions with slack for embedding ultrametrics into d-dimensional Euclidean space: we give a rm polylog(Delta)-approximation algorithm for embedding n-point ultrametrics into R^d with minimum distortion, where Delta denotes the spread of the metric, i.e., the ratio between the largest and the smallest distance between two points. The previously best-known approximation ratio for this problem was polynomial in n. This is the first algorithm for embedding a non-trivial family of weighted-graph metrics into a space of constant dimension that achieves polylogarithmic approximation ratio.

The generation of quadrilateral-dominant meshes is a cornerstone of professional 3D content creation. However, existing generative models generate quad meshes by first generating triangle meshes and then merging triangles into quadrilaterals with some specific rules, which typically produces quad meshes with poor topology. In this paper, we introduce QuadGPT, the first autoregressive framework for generating quadrilateral meshes in an end-to-end manner. QuadGPT formulates this as a sequence prediction paradigm, distinguished by two key innovations: a unified tokenization method to handle mixed topologies of triangles and quadrilaterals, and a specialized Reinforcement Learning fine-tuning method tDPO for better generation quality. Extensive experiments demonstrate that QuadGPT significantly surpasses previous triangle-to-quad conversion pipelines in both geometric accuracy and topological quality. Our work establishes a new benchmark for native quad-mesh generation and showcases the power of combining large-scale autoregressive models with topology-aware RL refinement for creating structured 3D assets.

Generating a street-level 3D scene from a single satellite image is a crucial yet challenging task. Current methods present a stark trade-off: geometry-colorization models achieve high geometric fidelity but are typically building-focused and lack semantic diversity. In contrast, proxy-based models use feed-forward image-to-3D frameworks to generate holistic scenes by jointly learning geometry and texture, a process that yields rich content but coarse and unstable geometry. We attribute these geometric failures to the extreme viewpoint gap and sparse, inconsistent supervision inherent in satellite-to-street data. We introduce Sat3DGen to address these fundamental challenges, which embodies a geometry-first methodology. This methodology enhances the feed-forward paradigm by integrating novel geometric constraints with a perspective-view training strategy, explicitly countering the primary sources of geometric error. This geometry-centric strategy yields a dramatic leap in both 3D accuracy and photorealism. For validation, we first constructed a new benchmark by pairing the VIGOR-OOD test set with high-resolution DSM data. On this benchmark, our method improves geometric RMSE from 6.76m to 5.20m. Crucially, this geometric leap also boosts photorealism, reducing the Fréchet Inception Distance (FID) from sim40 to 19 against the leading method, Sat2Density++, despite using no extra tailored image-quality modules. We demonstrate the versatility of our high-quality 3D assets through diverse downstream applications, including semantic-map-to-3D synthesis, multi-camera video generation, large-scale meshing, and unsupervised single-image Digital Surface Model (DSM) estimation. The code has been released on https://github.com/qianmingduowan/Sat3DGen.

Reconstructing 3D representations from 2D inputs is a fundamental task in computer vision and graphics, serving as a cornerstone for understanding and interacting with the physical world. While traditional methods achieve high fidelity, they are limited by slow per-scene optimization or category-specific training, which hinders their practical deployment and scalability. Hence, generalizable feed-forward 3D reconstruction has witnessed rapid development in recent years. By learning a model that maps images directly to 3D representations in a single forward pass, these methods enable efficient reconstruction and robust cross-scene generalization. Our survey is motivated by a critical observation: despite the diverse geometric output representations, ranging from implicit fields to explicit primitives, existing feed-forward approaches share similar high-level architectural patterns, such as image feature extraction backbones, multi-view information fusion mechanisms, and geometry-aware design principles. Consequently, we abstract away from these representation differences and instead focus on model design, proposing a novel taxonomy centered on model design strategies that are agnostic to the output format. Our proposed taxonomy organizes the research directions into five key problems that drive recent research development: feature enhancement, geometry awareness, model efficiency, augmentation strategies and temporal-aware models. To support this taxonomy with empirical grounding and standardized evaluation, we further comprehensively review related benchmarks and datasets, and extensively discuss and categorize real-world applications based on feed-forward 3D models. Finally, we outline future directions to address open challenges such as scalability, evaluation standards, and world modeling.

Geometric spatial reasoning forms the foundation of many applications in artificial intelligence, yet the ability of large language models (LLMs) to operate over geometric spatial information expressed in procedural code remains underexplored. In this paper, we address this gap by formalizing the Program-to-Geometry task, which challenges models to translate programmatic drawing code into accurate and abstract geometric reasoning. To evaluate this capability, we present GeoGramBench, a benchmark of 500 carefully refined problems organized by a tailored three-level taxonomy that considers geometric complexity rather than traditional mathematical reasoning complexity. Our comprehensive evaluation of 17 frontier LLMs reveals consistent and pronounced deficiencies: even the most advanced models achieve less than 50% accuracy at the highest abstraction level. These results highlight the unique challenges posed by program-driven spatial reasoning and establish GeoGramBench as a valuable resource for advancing research in symbolic-to-spatial geometric reasoning. Project page: https://github.com/LiAuto-DSR/GeoGramBench.

Point cloud is an important type of geometric data structure. Due to its irregular format, most researchers transform such data to regular 3D voxel grids or collections of images. This, however, renders data unnecessarily voluminous and causes issues. In this paper, we design a novel type of neural network that directly consumes point clouds and well respects the permutation invariance of points in the input. Our network, named PointNet, provides a unified architecture for applications ranging from object classification, part segmentation, to scene semantic parsing. Though simple, PointNet is highly efficient and effective. Empirically, it shows strong performance on par or even better than state of the art. Theoretically, we provide analysis towards understanding of what the network has learnt and why the network is robust with respect to input perturbation and corruption.

Point cloud registration is a task to estimate the rigid transformation between two unaligned scans, which plays an important role in many computer vision applications. Previous learning-based works commonly focus on supervised registration, which have limitations in practice. Recently, with the advance of inexpensive RGB-D sensors, several learning-based works utilize RGB-D data to achieve unsupervised registration. However, most of existing unsupervised methods follow a cascaded design or fuse RGB-D data in a unidirectional manner, which do not fully exploit the complementary information in the RGB-D data. To leverage the complementary information more effectively, we propose a network implementing multi-scale bidirectional fusion between RGB images and point clouds generated from depth images. By bidirectionally fusing visual and geometric features in multi-scales, more distinctive deep features for correspondence estimation can be obtained, making our registration more accurate. Extensive experiments on ScanNet and 3DMatch demonstrate that our method achieves new state-of-the-art performance. Code will be released at https://github.com/phdymz/PointMBF

Information retrieval is a rapidly evolving field. However it still faces significant limitations in the scientific and industrial vast amounts of information, such as semantic divergence and vocabulary gaps in sparse retrieval, low precision and lack of interpretability in semantic search, or hallucination and outdated information in generative models. In this paper, we introduce a two-block approach to tackle these hurdles for long documents. The first block enhances language understanding in sparse retrieval by query expansion to retrieve relevant documents. The second block deepens the result by providing comprehensive and informative answers to the complex question using only the information spread in the long document, enabling bidirectional engagement. At various stages of the pipeline, intermediate results are presented to users to facilitate understanding of the system's reasoning. We believe this bidirectional approach brings significant advancements in terms of transparency, logical thinking, and comprehensive understanding in the field of scientific information retrieval.

Model merging aims to combine multiple models into one without additional training. Naïve parameter-space averaging can be fragile under architectural symmetries, as their geometry does not take them into account. In this work we show that not only the geometry, but also the averaging procedure itself, must be symmetry-invariant to achieve symmetry-aware merges. Consequently, we propose a general solution: merging as Fréchet averaging, i.e., selecting parameters that minimize a sum of geodesic distances on an appropriate manifold. In this view, the key design choice is the overall geometry, i.e., the choice of metric, manifold, and distance approximation, that determines what it means for two models to be "close". We show that Fréchet averaging, combined with simplifying assumptions, contains Fisher merging. Building on this, we examine the particular case of low-rank adapters (LoRA), whose symmetries induce a distinct geometry: that of a quotient manifold. We outline the limitations of current LoRA merging methods, propose a practical algorithm for this setting, and show how they compare with other commonly used approaches.

Graph neural networks (GNNs) have been shown to be highly sensitive to the choice of aggregation function. While summing over a node's neighbours can approximate any permutation-invariant function over discrete inputs, Cohen-Karlik et al. [2020] proved there are set-aggregation problems for which summing cannot generalise to unbounded inputs, proposing recurrent neural networks regularised towards permutation-invariance as a more expressive aggregator. We show that these results carry over to the graph domain: GNNs equipped with recurrent aggregators are competitive with state-of-the-art permutation-invariant aggregators, on both synthetic benchmarks and real-world problems. However, despite the benefits of recurrent aggregators, their O(V) depth makes them both difficult to parallelise and harder to train on large graphs. Inspired by the observation that a well-behaved aggregator for a GNN is a commutative monoid over its latent space, we propose a framework for constructing learnable, commutative, associative binary operators. And with this, we construct an aggregator of O(log V) depth, yielding exponential improvements for both parallelism and dependency length while achieving performance competitive with recurrent aggregators. Based on our empirical observations, our proposed learnable commutative monoid (LCM) aggregator represents a favourable tradeoff between efficient and expressive aggregators.

We present MegaBlocks, a system for efficient Mixture-of-Experts (MoE) training on GPUs. Our system is motivated by the limitations of current frameworks, which restrict the dynamic routing in MoE layers to satisfy the constraints of existing software and hardware. These formulations force a tradeoff between model quality and hardware efficiency, as users must choose between dropping tokens from the computation or wasting computation and memory on padding. To address these limitations, we reformulate MoE computation in terms of block-sparse operations and develop new block-sparse GPU kernels that efficiently handle the dynamism present in MoEs. Our approach never drops tokens and maps efficiently to modern hardware, enabling end-to-end training speedups of up to 40% over MoEs trained with the state-of-the-art Tutel library and 2.4x over DNNs trained with the highly-optimized Megatron-LM framework.

We propose HyperSteiner -- an efficient heuristic algorithm for computing Steiner minimal trees in the hyperbolic space. HyperSteiner extends the Euclidean Smith-Lee-Liebman algorithm, which is grounded in a divide-and-conquer approach involving the Delaunay triangulation. The central idea is rephrasing Steiner tree problems with three terminals as a system of equations in the Klein-Beltrami model. Motivated by the fact that hyperbolic geometry is well-suited for representing hierarchies, we explore applications to hierarchy discovery in data. Results show that HyperSteiner infers more realistic hierarchies than the Minimum Spanning Tree and is more scalable to large datasets than Neighbor Joining.

In stark contrast to the case of images, finding a concise, learnable discrete representation of 3D surfaces remains a challenge. In particular, while polygon meshes are arguably the most common surface representation used in geometry processing, their irregular and combinatorial structure often make them unsuitable for learning-based applications. In this work, we present VoroMesh, a novel and differentiable Voronoi-based representation of watertight 3D shape surfaces. From a set of 3D points (called generators) and their associated occupancy, we define our boundary representation through the Voronoi diagram of the generators as the subset of Voronoi faces whose two associated (equidistant) generators are of opposite occupancy: the resulting polygon mesh forms a watertight approximation of the target shape's boundary. To learn the position of the generators, we propose a novel loss function, dubbed VoroLoss, that minimizes the distance from ground truth surface samples to the closest faces of the Voronoi diagram which does not require an explicit construction of the entire Voronoi diagram. A direct optimization of the Voroloss to obtain generators on the Thingi32 dataset demonstrates the geometric efficiency of our representation compared to axiomatic meshing algorithms and recent learning-based mesh representations. We further use VoroMesh in a learning-based mesh prediction task from input SDF grids on the ABC dataset, and show comparable performance to state-of-the-art methods while guaranteeing closed output surfaces free of self-intersections.

Modern monocular 3D reconstruction methods and vision-language models (VLMs) demonstrate impressive results on standard benchmarks, yet recent works cast doubt on their true understanding of geometric properties. We introduce GOQ, a comprehensive benchmark specifically designed to evaluate the geometric reasoning capabilities of vision and vision-language foundation models. GIQ comprises synthetic and real-world images and corresponding 3D meshes of diverse polyhedra covering varying levels of complexity and symmetry, from Platonic, Archimedean, Johnson, and Catalan solids to stellations and compound shapes. Through systematic experiments involving monocular 3D reconstruction, 3D symmetry detection, mental rotation tests, and zero-shot shape classification tasks, we reveal significant shortcomings in current models. State-of-the-art reconstruction algorithms trained on extensive 3D datasets struggle to reconstruct even basic geometric Platonic solids accurately. Next, although foundation models may be shown via linear and non-linear probing to capture specific 3D symmetry elements, they falter significantly in tasks requiring detailed geometric differentiation, such as mental rotation. Moreover, advanced vision-language assistants such as ChatGPT, Gemini and Claud exhibit remarkably low accuracy in interpreting basic shape properties such as face geometry, convexity, and compound structures of complex polyhedra. GIQ is publicly available at toomanymatts.github.io/giq-benchmark/, providing a structured platform to benchmark critical gaps in geometric intelligence and facilitate future progress in robust, geometry-aware representation learning.

Covariance matrices have proven highly effective across many scientific fields. Since these matrices lie within the Symmetric Positive Definite (SPD) manifold - a Riemannian space with intrinsic non-Euclidean geometry, the primary challenge in representation learning is to respect this underlying geometric structure. Drawing inspiration from the success of Euclidean deep learning, researchers have developed neural networks on the SPD manifolds for more faithful covariance embedding learning. A notable advancement in this area is the implementation of Riemannian batch normalization (RBN), which has been shown to improve the performance of SPD network models. Nonetheless, the Riemannian metric beneath the existing RBN might fail to effectively deal with the ill-conditioned SPD matrices (ICSM), undermining the effectiveness of RBN. In contrast, the Bures-Wasserstein metric (BWM) demonstrates superior performance for ill-conditioning. In addition, the recently introduced Generalized BWM (GBWM) parameterizes the vanilla BWM via an SPD matrix, allowing for a more nuanced representation of vibrant geometries of the SPD manifold. Therefore, we propose a novel RBN algorithm based on the GBW geometry, incorporating a learnable metric parameter. Moreover, the deformation of GBWM by matrix power is also introduced to further enhance the representational capacity of GBWM-based RBN. Experimental results on different datasets validate the effectiveness of our proposed method.

Node clustering is a powerful tool in the analysis of networks. We introduce a graph neural network framework, named DIGRAC, to obtain node embeddings for directed networks in a self-supervised manner, including a novel probabilistic imbalance loss, which can be used for network clustering. Here, we propose directed flow imbalance measures, which are tightly related to directionality, to reveal clusters in the network even when there is no density difference between clusters. In contrast to standard approaches in the literature, in this paper, directionality is not treated as a nuisance, but rather contains the main signal. DIGRAC optimizes directed flow imbalance for clustering without requiring label supervision, unlike existing graph neural network methods, and can naturally incorporate node features, unlike existing spectral methods. Extensive experimental results on synthetic data, in the form of directed stochastic block models, and real-world data at different scales, demonstrate that our method, based on flow imbalance, attains state-of-the-art results on directed graph clustering when compared against 10 state-of-the-art methods from the literature, for a wide range of noise and sparsity levels, graph structures, and topologies, and even outperforms supervised methods.

3D vision foundation models like Visual Geometry Grounded Transformer (VGGT) have advanced greatly in geometric perception. However, it is time-consuming and memory-intensive for long sequences, limiting application to large-scale scenes beyond hundreds of images. To address this, we propose LiteVGGT, achieving up to 10x speedup and substantial memory reduction, enabling efficient processing of 1000-image scenes. We derive two key insights for 3D reconstruction: (1) tokens from local image regions have inherent geometric correlations, leading to high similarity and computational redundancy; (2) token similarity across adjacent network layers remains stable, allowing for reusable merge decisions. Guided by these, we design a simple yet efficient strategy, dubbed geometry-aware cached token merging. We analyze each token's geometric importance, optimizing anchor token selection to better preserve key information for reconstruction. We also cache and reuse merge indices across layers, substantially reducing latency with minimal accuracy impact. This strategy retains VGGT's core performance, enabling efficient fine-tuning and FP8 quantization for further gains. Extensive experiments validate LiteVGGT's effectiveness, scalability, and robustness. Project page: https://garlicba.github.io/LiteVGGT/

Large Language Models frequently hallucinate in precision-critical domains such as technical diagramming and mechanical design, where outputs must satisfy strict geometric constraints. We study open-ended geometric synthesis from natural language: translating free-form descriptions into precise constructions whose entities must simultaneously satisfy dozens of interacting constraints. To make this tractable, we release PyGeoX, a programmable geometric DSL that compiles declarative constraints into a differentiable loss, and PyGeoX-Bench, a stratified suite of 300 problems with per-constraint verifiable rewards. Using PyGeoX as a verifier, we identify a failure mode we call Outlier Gradient Masking: under global-norm rewards (any scheme that aggregates residuals through a single norm, for example, exp(-MSE)), a single outlier constraint can nullify the learning signal across all others. To address this, we propose Saturating Additive Rewards (SAR), which decompose the reward into bounded per-constraint terms, preserving partial progress and ensuring consistent gradients even under severe violations. Against MSE-based rewards, the natural baseline for geometry solvers, SAR improves the hard-tier solving rate by 2.3times, and the resulting 8B model is competitive with much larger frontier systems on this benchmark. We release the engine, benchmark, and data at https://github.com/Huawei-AI4Math/PyGeoX.

We introduce PyTorch Geometric, a library for deep learning on irregularly structured input data such as graphs, point clouds and manifolds, built upon PyTorch. In addition to general graph data structures and processing methods, it contains a variety of recently published methods from the domains of relational learning and 3D data processing. PyTorch Geometric achieves high data throughput by leveraging sparse GPU acceleration, by providing dedicated CUDA kernels and by introducing efficient mini-batch handling for input examples of different size. In this work, we present the library in detail and perform a comprehensive comparative study of the implemented methods in homogeneous evaluation scenarios.

Multi-domain graph pre-training integrates knowledge from diverse domains to enhance performance in the target domains, which is crucial for building graph foundation models. Despite initial success, existing solutions often fall short of answering a fundamental question: how is knowledge integrated or transferred across domains? This theoretical limitation motivates us to rethink the consistency and transferability between model pre-training and domain adaptation. In this paper, we propose a fresh Riemannian geometry perspective, whose core idea is to merge any graph dataset into a unified, smooth Riemannian manifold, enabling a systematic understanding of knowledge integration and transfer. To achieve this, our key contribution is the theoretical establishment of neural manifold gluing, which first characterizes local geometry using an adaptive orthogonal frame and then "glues" the local pieces together into a coherent whole. Building on this theory, we present the GraphGlue framework, which supports batched pre-training with EMA prototyping and provides a transferability measure based on geometric consistence. Extensive experiments demonstrate its superior performance across diverse graph domains. Moreover, we empirically validated GraphGlue's geometric scaling law, showing that larger quantities of datasets improve model transferability by producing a smoother manifold. Codes are available at https://github.com/RiemannGraph/GraphGlue.

Multi-relational graphs (MRGs) are an expressive data structure for modeling diverse interactions/relations among real objects (i.e., nodes), which pervade extensive applications and scenarios. Given an MRG G with N nodes, partitioning the node set therein into K disjoint clusters (MRGC) is a fundamental task in analyzing MRGs, which has garnered considerable attention. However, the majority of existing solutions towards MRGC either yield severely compromised result quality by ineffective fusion of heterogeneous graph structures and attributes, or struggle to cope with sizable MRGs with millions of nodes and billions of edges due to the adoption of sophisticated and costly deep learning models. In this paper, we present DEMM and DEMM+, two effective MRGC approaches to address the limitations above. Specifically, our algorithms are built on novel two-stage optimization objectives, where the former seeks to derive high-caliber node feature vectors by optimizing the multi-relational Dirichlet energy specialized for MRGs, while the latter minimizes the Dirichlet energy of clustering results over the node affinity graph. In particular, DEMM+ achieves significantly higher scalability and efficiency over our based method DEMM through a suite of well-thought-out optimizations. Key technical contributions include (i) a highly efficient approximation solver for constructing node feature vectors, and (ii) a theoretically-grounded problem transformation with carefully-crafted techniques that enable linear-time clustering without explicitly materializing the NxN dense affinity matrix. Further, we extend DEMM+ to handle attribute-less MRGs through non-trivial adaptations. Extensive experiments, comparing DEMM+ against 20 baselines over 11 real MRGs, exhibit that DEMM+ is consistently superior in terms of clustering quality measured against ground-truth labels, while often being remarkably faster.

Geometric diagrams are critical in conveying mathematical and scientific concepts, yet traditional diagram generation methods are often manual and resource-intensive. While text-to-image generation has made strides in photorealistic imagery, creating accurate geometric diagrams remains a challenge due to the need for precise spatial relationships and the scarcity of geometry-specific datasets. This paper presents MagicGeo, a training-free framework for generating geometric diagrams from textual descriptions. MagicGeo formulates the diagram generation process as a coordinate optimization problem, ensuring geometric correctness through a formal language solver, and then employs coordinate-aware generation. The framework leverages the strong language translation capability of large language models, while formal mathematical solving ensures geometric correctness. We further introduce MagicGeoBench, a benchmark dataset of 220 geometric diagram descriptions, and demonstrate that MagicGeo outperforms current methods in both qualitative and quantitative evaluations. This work provides a scalable, accurate solution for automated diagram generation, with significant implications for educational and academic applications.

Polygonal meshes are ubiquitous, but have only played a relatively minor role in the deep learning revolution. State-of-the-art neural generative models for 3D shapes learn implicit functions and generate meshes via expensive iso-surfacing. We overcome these challenges by employing a classical spatial data structure from computer graphics, Binary Space Partitioning (BSP), to facilitate 3D learning. The core operation of BSP involves recursive subdivision of 3D space to obtain convex sets. By exploiting this property, we devise BSP-Net, a network that learns to represent a 3D shape via convex decomposition without supervision. The network is trained to reconstruct a shape using a set of convexes obtained from a BSP-tree built over a set of planes, where the planes and convexes are both defined by learned network weights. BSP-Net directly outputs polygonal meshes from the inferred convexes. The generated meshes are watertight, compact (i.e., low-poly), and well suited to represent sharp geometry. We show that the reconstruction quality by BSP-Net is competitive with those from state-of-the-art methods while using much fewer primitives. We also explore variations to BSP-Net including using a more generic decoder for reconstruction, more general primitives than planes, as well as training a generative model with variational auto-encoders. Code is available at https://github.com/czq142857/BSP-NET-original.

NVIDIA's CUTLASS library provides a robust and expressive set of methods for describing and manipulating multi-dimensional tensor data on the GPU. These methods are conceptually grounded in the abstract notion of a CuTe layout and a rich algebra of such layouts, including operations such as composition, logical product, and logical division. In this paper, we present a categorical framework for understanding this layout algebra by focusing on a naturally occurring class of tractable layouts. To this end, we define two categories Tuple and Nest whose morphisms give rise to layouts. We define a suite of operations on morphisms in these categories and prove their compatibility with the corresponding layout operations. Moreover, we give a complete characterization of the layouts which arise from our construction. Finally, we provide a Python implementation of our categorical constructions, along with tests that demonstrate alignment with CUTLASS behavior. This implementation can be found at our git repository https://github.com/ColfaxResearch/layout-categories.

We present a learning-based method, namely GeoUDF,to tackle the long-standing and challenging problem of reconstructing a discrete surface from a sparse point cloud.To be specific, we propose a geometry-guided learning method for UDF and its gradient estimation that explicitly formulates the unsigned distance of a query point as the learnable affine averaging of its distances to the tangent planes of neighboring points on the surface. Besides,we model the local geometric structure of the input point clouds by explicitly learning a quadratic polynomial for each point. This not only facilitates upsampling the input sparse point cloud but also naturally induces unoriented normal, which further augments UDF estimation. Finally, to extract triangle meshes from the predicted UDF we propose a customized edge-based marching cube module. We conduct extensive experiments and ablation studies to demonstrate the significant advantages of our method over state-of-the-art methods in terms of reconstruction accuracy, efficiency, and generality. The source code is publicly available at https://github.com/rsy6318/GeoUDF.

Recent interest in point cloud analysis has led rapid progress in designing deep learning methods for 3D models. However, state-of-the-art models are not robust to rotations, which remains an unknown prior to real applications and harms the model performance. In this work, we introduce a novel Patch-wise Rotation-invariant network (PaRot), which achieves rotation invariance via feature disentanglement and produces consistent predictions for samples with arbitrary rotations. Specifically, we design a siamese training module which disentangles rotation invariance and equivariance from patches defined over different scales, e.g., the local geometry and global shape, via a pair of rotations. However, our disentangled invariant feature loses the intrinsic pose information of each patch. To solve this problem, we propose a rotation-invariant geometric relation to restore the relative pose with equivariant information for patches defined over different scales. Utilising the pose information, we propose a hierarchical module which implements intra-scale and inter-scale feature aggregation for 3D shape learning. Moreover, we introduce a pose-aware feature propagation process with the rotation-invariant relative pose information embedded. Experiments show that our disentanglement module extracts high-quality rotation-robust features and the proposed lightweight model achieves competitive results in rotated 3D object classification and part segmentation tasks. Our project page is released at: https://patchrot.github.io/.

3D Gaussian Splatting (3DGS) has emerged as a prominent paradigm for 3D reconstruction and novel view synthesis. However, it remains vulnerable to severe artifacts when trained under sparse-view constraints. While recent methods attempt to rectify artifacts in rendered views using image diffusion models, they typically rely on multi-view self-attention to retrieve information from reference images. We observe that this mechanism often fails when the rendered novel views output by 3DGS are heavily corrupted: damaged query features lead to erroneous cross-view retrieval, resulting in inconsistent rendering refinement. To address this, we propose GeoQuery, a geometry-guided diffusion framework that integrates generative priors with explicit geometric cues via a novel Geometry-guided Cross-view Attention (GCA) mechanism. First, by leveraging predicted depth maps and camera poses, we construct a geometry-induced correspondence field to sample reference features, forming a geometry-aligned proxy query that replaces the corrupted rendering features. Furthermore, we design a new cross-view feature aggregation pipeline, in which we restrict the cross-view attention to a local window around each proxy query to effectively retrieve useful features while suppressing spurious matches. GeoQuery can be seamlessly integrated into existing diffusion-based pipelines, enabling robust reconstruction even under extreme view sparsity. Extensive experiments on sparse-view novel view synthesis and rendering artifact removal demonstrate the effectiveness of our approach.

Transformers achieve strong performance across diverse domains but implicitly assume Euclidean geometry in their attention mechanisms, limiting their effectiveness on data with non-Euclidean structure. While recent extensions to hyperbolic and spherical spaces show promise for hierarchical and cyclical patterns, respectively, they require committing to a single geometry a priori, reducing flexibility when data exhibits mixed geometric properties. We introduce the Curvature-Adaptive Transformer (CAT), a novel architecture that dynamically learns per-token routing across three geometric attention branches through a lightweight, differentiable gating mechanism. Unlike fixed-geometry approaches, CAT enables adaptive geometric specialization, routing tokens to the appropriate curvature based on their local relational structure. The routing network provides interpretable curvature preferences while each branch employs geometry-specific operations optimized for its respective manifold. On knowledge graph completion benchmarks (FB15k-237, WN18RR), CAT achieves approximately 10% improvements in MRR and Hits@10 over fixed-geometry baselines with minimal overhead (5% parameter increase, comparable inference time). These results demonstrate that learned geometric adaptation outperforms any single fixed geometry for complex relational reasoning, establishing CAT as a scalable and interpretable foundation for mixture-of-geometry architectures across language, vision, and multimodal domains.

Image outpainting is a very intriguing problem as the outside of a given image can be continuously filled by considering as the context of the image. This task has two main challenges. The first is to maintain the spatial consistency in contents of generated regions and the original input. The second is to generate a high-quality large image with a small amount of adjacent information. Conventional image outpainting methods generate inconsistent, blurry, and repeated pixels. To alleviate the difficulty of an outpainting problem, we propose a novel image outpainting method using bidirectional boundary region rearrangement. We rearrange the image to benefit from the image inpainting task by reflecting more directional information. The bidirectional boundary region rearrangement enables the generation of the missing region using bidirectional information similar to that of the image inpainting task, thereby generating the higher quality than the conventional methods using unidirectional information. Moreover, we use the edge map generator that considers images as original input with structural information and hallucinates the edges of unknown regions to generate the image. Our proposed method is compared with other state-of-the-art outpainting and inpainting methods both qualitatively and quantitatively. We further compared and evaluated them using BRISQUE, one of the No-Reference image quality assessment (IQA) metrics, to evaluate the naturalness of the output. The experimental results demonstrate that our method outperforms other methods and generates new images with 360{\deg}panoramic characteristics.

Recent advancements in neural visual geometry, including transformer-based models such as VGGT and Pi3, have achieved impressive accuracy on 3D reconstruction tasks. However, their reliance on full attention makes them fundamentally limited by GPU memory capacity, preventing them from scaling to large, unordered image collections. We introduce MERG3R, a training-free divide-and-conquer framework that enables geometric foundation models to operate far beyond their native memory limits. MERG3R first reorders and partitions unordered images into overlapping, geometrically diverse subsets that can be reconstructed independently. It then merges the resulting local reconstructions through an efficient global alignment and confidence-weighted bundle adjustment procedure, producing a globally consistent 3D model. Our framework is model-agnostic and can be paired with existing neural geometry models. Across large-scale datasets, including 7-Scenes, NRGBD, Tanks & Temples, and Cambridge Landmarks, MERG3R consistently improves reconstruction accuracy, memory efficiency, and scalability, enabling high-quality reconstruction when the dataset exceeds memory capacity limits.

We propose Equiangular Basis Vectors (EBVs) for classification tasks. In deep neural networks, models usually end with a k-way fully connected layer with softmax to handle different classification tasks. The learning objective of these methods can be summarized as mapping the learned feature representations to the samples' label space. While in metric learning approaches, the main objective is to learn a transformation function that maps training data points from the original space to a new space where similar points are closer while dissimilar points become farther apart. Different from previous methods, our EBVs generate normalized vector embeddings as "predefined classifiers" which are required to not only be with the equal status between each other, but also be as orthogonal as possible. By minimizing the spherical distance of the embedding of an input between its categorical EBV in training, the predictions can be obtained by identifying the categorical EBV with the smallest distance during inference. Various experiments on the ImageNet-1K dataset and other downstream tasks demonstrate that our method outperforms the general fully connected classifier while it does not introduce huge additional computation compared with classical metric learning methods. Our EBVs won the first place in the 2022 DIGIX Global AI Challenge, and our code is open-source and available at https://github.com/NJUST-VIPGroup/Equiangular-Basis-Vectors.

Large-scale vision foundation models such as Segment Anything (SAM) demonstrate impressive performance in zero-shot image segmentation at multiple levels of granularity. However, these zero-shot predictions are rarely 3D-consistent. As the camera viewpoint changes in a scene, so do the segmentation predictions, as well as the characterizations of "coarse" or "fine" granularity. In this work, we address the challenging task of lifting multi-granular and view-inconsistent image segmentations into a hierarchical and 3D-consistent representation. We learn a novel feature field within a Neural Radiance Field (NeRF) representing a 3D scene, whose segmentation structure can be revealed at different scales by simply using different thresholds on feature distance. Our key idea is to learn an ultrametric feature space, which unlike a Euclidean space, exhibits transitivity in distance-based grouping, naturally leading to a hierarchical clustering. Put together, our method takes view-inconsistent multi-granularity 2D segmentations as input and produces a hierarchy of 3D-consistent segmentations as output. We evaluate our method and several baselines on synthetic datasets with multi-view images and multi-granular segmentation, showcasing improved accuracy and viewpoint-consistency. We additionally provide qualitative examples of our model's 3D hierarchical segmentations in real world scenes. The code and dataset are available at https://github.com/hardyho/ultrametric_feature_fields

The capability to learn latent representations plays a key role in the effectiveness of recent machine learning methods. An active frontier in representation learning is understanding representations for combinatorial structures which may not admit well-behaved local neighborhoods or distance functions. For example, for polygons, slightly perturbing vertex locations might lead to significant changes in their combinatorial structure and may even lead to invalid polygons. In this paper, we investigate representations to capture the underlying combinatorial structures of polygons. Specifically, we study the open problem of Visibility Reconstruction: Given a visibility graph G, construct a polygon P whose visibility graph is G. We introduce VisDiff, a novel diffusion-based approach to reconstruct a polygon from its given visibility graph G. Our method first estimates the signed distance function (SDF) of P from G. Afterwards, it extracts ordered vertex locations that have the pairwise visibility relationship given by the edges of G. Our main insight is that going through the SDF significantly improves learning for reconstruction. In order to train VisDiff, we make two main contributions: (1) We design novel loss components for computing the visibility in a differentiable manner and (2) create a carefully curated dataset. We use this dataset to benchmark our method and achieve 21% improvement in F1-Score over standard methods. We also demonstrate effective generalization to out-of-distribution polygon types and show that learning a generative model allows us to sample the set of polygons with a given visibility graph. Finally, we extend our method to the related combinatorial problem of reconstruction from a triangulation. We achieve 95% classification accuracy of triangulation edges and a 4% improvement in Chamfer distance compared to current architectures.

Geometric deep learning, i.e., designing neural networks to handle the ubiquitous geometric data such as point clouds and graphs, have achieved great successes in the last decade. One critical inductive bias is that the model can maintain invariance towards various transformations such as translation, rotation, and scaling. The existing graph neural network (GNN) approaches can only maintain permutation-invariance, failing to guarantee invariance with respect to other transformations. Besides GNNs, other works design sophisticated transformation-invariant layers, which are computationally expensive and difficult to be extended. To solve this problem, we revisit why the existing neural networks cannot maintain transformation invariance when handling geometric data. Our findings show that transformation-invariant and distance-preserving initial representations are sufficient to achieve transformation invariance rather than needing sophisticated neural layer designs. Motivated by these findings, we propose Transformation Invariant Neural Networks (TinvNN), a straightforward and general framework for geometric data. Specifically, we realize transformation-invariant and distance-preserving initial point representations by modifying multi-dimensional scaling before feeding the representations into neural networks. We prove that TinvNN can strictly guarantee transformation invariance, being general and flexible enough to be combined with the existing neural networks. Extensive experimental results on point cloud analysis and combinatorial optimization demonstrate the effectiveness and general applicability of our proposed method. Based on the experimental results, we advocate that TinvNN should be considered a new starting point and an essential baseline for further studies of transformation-invariant geometric deep learning.

Boundary information plays a significant role in 2D image segmentation, while usually being ignored in 3D point cloud segmentation where ambiguous features might be generated in feature extraction, leading to misclassification in the transition area between two objects. In this paper, firstly, we propose a Boundary Prediction Module (BPM) to predict boundary points. Based on the predicted boundary, a boundary-aware Geometric Encoding Module (GEM) is designed to encode geometric information and aggregate features with discrimination in a neighborhood, so that the local features belonging to different categories will not be polluted by each other. To provide extra geometric information for boundary-aware GEM, we also propose a light-weight Geometric Convolution Operation (GCO), making the extracted features more distinguishing. Built upon the boundary-aware GEM, we build our network and test it on benchmarks like ScanNet v2, S3DIS. Results show our methods can significantly improve the baseline and achieve state-of-the-art performance. Code is available at https://github.com/JchenXu/BoundaryAwareGEM.

Scalable Vector Graphics (SVGs) are central to modern design workflows, offering scaling without distortion and precise editability. However, for single object SVGs, generating multi-view consistent SVGs from a single-view input remains underexplored. We present a three stage framework that produces multi-view SVGs with geometric and color consistency from a single SVG input. First, the rasterized input is lifted to a 3D representation and rendered under target camera poses, producing multi-view images of the object. Next, we extend the temporal memory mechanism of Segment Anything 2 (SAM2) to the spatial domain, constructing a spatial memory bank that establishes part level correspondences across neighboring views, yielding cleaner and more consistent vector paths and color assignments without retraining. Finally, during the raster to vector conversion, we perform path consolidation and structural optimization to reduce redundancy while preserving boundaries and semantics. The resulting SVGs exhibit strong geometric and color consistency across views, significantly reduce redundant paths, and retain fine structural details. This work bridges generative modeling and structured vector representation, providing a scalable route to single input, object level multi-view SVG generation and supporting applications such as asset creation and semantic vector editing.

3D object detectors for point clouds often rely on a pooling-based PointNet to encode sparse points into grid-like voxels or pillars. In this paper, we identify that the common PointNet design introduces an information bottleneck that limits 3D object detection accuracy and scalability. To address this limitation, we propose PVTransformer: a transformer-based point-to-voxel architecture for 3D detection. Our key idea is to replace the PointNet pooling operation with an attention module, leading to a better point-to-voxel aggregation function. Our design respects the permutation invariance of sparse 3D points while being more expressive than the pooling-based PointNet. Experimental results show our PVTransformer achieves much better performance compared to the latest 3D object detectors. On the widely used Waymo Open Dataset, our PVTransformer achieves state-of-the-art 76.5 mAPH L2, outperforming the prior art of SWFormer by +1.7 mAPH L2.

3D Gaussian Splatting (3DGS) has recently emerged as a powerful paradigm for photorealistic view synthesis, representing scenes with spatially distributed Gaussian primitives. While highly effective for rendering, achieving accurate and complete surface reconstruction remains challenging due to the unstructured nature of the representation and the absence of explicit geometric supervision. In this work, we propose DiGS, a unified framework that embeds Signed Distance Field (SDF) learning directly into the 3DGS pipeline, thereby enforcing strong and interpretable surface priors. By associating each Gaussian with a learnable SDF value, DiGS explicitly aligns primitives with underlying geometry and improves cross-view consistency. To further ensure dense and coherent coverage, we design a geometry-guided grid growth strategy that adaptively distributes Gaussians along geometry-consistent regions under a multi-scale hierarchy. Extensive experiments on standard benchmarks, including DTU, Mip-NeRF 360, and Tanks& Temples, demonstrate that DiGS consistently improves reconstruction accuracy and completeness while retaining high rendering fidelity.

We present Stable Part Diffusion 4D (SP4D), a framework for generating paired RGB and kinematic part videos from monocular inputs. Unlike conventional part segmentation methods that rely on appearance-based semantic cues, SP4D learns to produce kinematic parts - structural components aligned with object articulation and consistent across views and time. SP4D adopts a dual-branch diffusion model that jointly synthesizes RGB frames and corresponding part segmentation maps. To simplify the architecture and flexibly enable different part counts, we introduce a spatial color encoding scheme that maps part masks to continuous RGB-like images. This encoding allows the segmentation branch to share the latent VAE from the RGB branch, while enabling part segmentation to be recovered via straightforward post-processing. A Bidirectional Diffusion Fusion (BiDiFuse) module enhances cross-branch consistency, supported by a contrastive part consistency loss to promote spatial and temporal alignment of part predictions. We demonstrate that the generated 2D part maps can be lifted to 3D to derive skeletal structures and harmonic skinning weights with few manual adjustments. To train and evaluate SP4D, we construct KinematicParts20K, a curated dataset of over 20K rigged objects selected and processed from Objaverse XL (Deitke et al., 2023), each paired with multi-view RGB and part video sequences. Experiments show that SP4D generalizes strongly to diverse scenarios, including real-world videos, novel generated objects, and rare articulated poses, producing kinematic-aware outputs suitable for downstream animation and motion-related tasks.

Meshes are among the most common 3D scene representations, but directly generating meshes is challenging because the representation contains important symmetries, including permutation invariance of faces and vertices. MeshFlow learns to generate triangle meshes directly as triangle soups, avoiding the need to serialize meshes into long autoregressive sequences. We adopt equivariant optimal-transport flow matching models that respect the key symmetries of triangle soups: arbitrary permutations of faces and permutations of the vertices within each face. Toward this goal, we propose a simple yet effective modification to the Diffusion Transformer architecture, resulting in a scalable network capable of modeling a velocity field while maintaining the desired equivariance. We further introduce an optimal-transport-based training objective that improves convergence by eliminating supervision signals that violate these symmetries. MeshFlow achieves mesh quality comparable to state-of-the-art autoregressive mesh generators while providing about an 18times speedup during inference. Project page is at https://qiisun.github.io/MeshFlow/.

This paper introduces a Transformer-based integrative feature and cost aggregation network designed for dense matching tasks. In the context of dense matching, many works benefit from one of two forms of aggregation: feature aggregation, which pertains to the alignment of similar features, or cost aggregation, a procedure aimed at instilling coherence in the flow estimates across neighboring pixels. In this work, we first show that feature aggregation and cost aggregation exhibit distinct characteristics and reveal the potential for substantial benefits stemming from the judicious use of both aggregation processes. We then introduce a simple yet effective architecture that harnesses self- and cross-attention mechanisms to show that our approach unifies feature aggregation and cost aggregation and effectively harnesses the strengths of both techniques. Within the proposed attention layers, the features and cost volume both complement each other, and the attention layers are interleaved through a coarse-to-fine design to further promote accurate correspondence estimation. Finally at inference, our network produces multi-scale predictions, computes their confidence scores, and selects the most confident flow for final prediction. Our framework is evaluated on standard benchmarks for semantic matching, and also applied to geometric matching, where we show that our approach achieves significant improvements compared to existing methods.

In this paper, we present a deep learning-based framework for solving geometric construction problems through visual reasoning, which is useful for automated geometry theorem proving. Constructible problems in geometry often ask for the sequence of straightedge-and-compass constructions to construct a given goal given some initial setup. Our EuclidNet framework leverages the neural network architecture Mask R-CNN to extract the visual features from the initial setup and goal configuration with extra points of intersection, and then generate possible construction steps as intermediary data models that are used as feedback in the training process for further refinement of the construction step sequence. This process is repeated recursively until either a solution is found, in which case we backtrack the path for a step-by-step construction guide, or the problem is identified as unsolvable. Our EuclidNet framework is validated on complex Japanese Sangaku geometry problems, demonstrating its capacity to leverage backtracking for deep visual reasoning of challenging problems.

This paper presents a simple yet effective approach to modeling space-time correspondences in the context of video object segmentation. Unlike most existing approaches, we establish correspondences directly between frames without re-encoding the mask features for every object, leading to a highly efficient and robust framework. With the correspondences, every node in the current query frame is inferred by aggregating features from the past in an associative fashion. We cast the aggregation process as a voting problem and find that the existing inner-product affinity leads to poor use of memory with a small (fixed) subset of memory nodes dominating the votes, regardless of the query. In light of this phenomenon, we propose using the negative squared Euclidean distance instead to compute the affinities. We validated that every memory node now has a chance to contribute, and experimentally showed that such diversified voting is beneficial to both memory efficiency and inference accuracy. The synergy of correspondence networks and diversified voting works exceedingly well, achieves new state-of-the-art results on both DAVIS and YouTubeVOS datasets while running significantly faster at 20+ FPS for multiple objects without bells and whistles.

Understanding how two hands interact with each other is a key component of accurate 3D interacting hand mesh recovery. However, recent Transformer-based methods struggle to learn the interaction between two hands as they directly utilize two hand features as input tokens, which results in distant token problem. The distant token problem represents that input tokens are in heterogeneous spaces, leading Transformer to fail in capturing correlation between input tokens. Previous Transformer-based methods suffer from the problem especially when poses of two hands are very different as they project features from a backbone to separate left and right hand-dedicated features. We present EANet, extract-and-adaptation network, with EABlock, the main component of our network. Rather than directly utilizing two hand features as input tokens, our EABlock utilizes two complementary types of novel tokens, SimToken and JoinToken, as input tokens. Our two novel tokens are from a combination of separated two hand features; hence, it is much more robust to the distant token problem. Using the two type of tokens, our EABlock effectively extracts interaction feature and adapts it to each hand. The proposed EANet achieves the state-of-the-art performance on 3D interacting hands benchmarks. The codes are available at https://github.com/jkpark0825/EANet.

Recent advancements in image animation have utilized diffusion models to breathe life into static images. However, existing controllable frameworks typically rely on Lagrangian motion guidance, where optical flow is estimated relative to the initial frame. This paper revisits the same optical-flow primitive through a more local supervision design: we use adjacent-frame Eulerian motion fields to guide generation, where the motion signal always describes a short temporal hop. This shift enables parallelized training and provides bounded-error supervision throughout the generation process. To mitigate the drift artifacts common in adjacent frame generation, we introduce a Bidirectional Geometric Consistency mechanism, which computes a forward-backward cycle check to mathematically identify and mask occluded regions, preventing the model from learning incorrect warping objectives. Extensive experiments demonstrate that our approach accelerates training, preserves temporal coherence, and reduces dynamic artifacts compared to reference-based baselines.

Multimodal large language models (MLLMs) have exhibited remarkable performance in various visual tasks, yet still struggle with spatial reasoning. Recent efforts mitigate this by injecting geometric features from 3D foundation models, but rely on static single-layer extractions. We identify that such an approach induces a task misalignment bias: the geometric features naturally evolve towards 3D pretraining objectives, which may contradict the heterogeneous spatial demands of MLLMs, rendering any single layer fundamentally insufficient. To resolve this, we propose GeoAlign, a novel framework that dynamically aggregates multi-layer geometric features to realign with the actual demands. GeoAlign constructs a hierarchical geometric feature bank and leverages the MLLM's original visual tokens as content-aware queries to perform layer-wise sparse routing, adaptively fetching the suitable geometric features for each patch. Extensive experiments on VSI-Bench, ScanQA, and SQA3D demonstrate that our compact 4B model effectively achieves state-of-the-art performance, even outperforming larger existing MLLMs.

The discovery of extremal structures in mathematics requires navigating vast and nonconvex landscapes where analytical methods offer little guidance and brute-force search becomes intractable. We introduce FlowBoost, a closed-loop generative framework that learns to discover rare and extremal geometric structures by combining three components: (i) a geometry-aware conditional flow-matching model that learns to sample high-quality configurations, (ii) reward-guided policy optimization with action exploration that directly optimizes the generation process toward the objective while maintaining diversity, and (iii) stochastic local search for both training-data generation and final refinement. Unlike prior open-loop approaches, such as PatternBoost that retrains on filtered discrete samples, or AlphaEvolve which relies on frozen Large Language Models (LLMs) as evolutionary mutation operators, FlowBoost enforces geometric feasibility during sampling, and propagates reward signal directly into the generative model, closing the optimization loop and requiring much smaller training sets and shorter training times, and reducing the required outer-loop iterations by orders of magnitude, while eliminating dependence on LLMs. We demonstrate the framework on four geometric optimization problems: sphere packing in hypercubes, circle packing maximizing sum of radii, the Heilbronn triangle problem, and star discrepancy minimization. In several cases, FlowBoost discovers configurations that match or exceed the best known results. For circle packings, we improve the best known lower bounds, surpassing the LLM-based system AlphaEvolve while using substantially fewer computational resources.

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.

We present a computational framework that transforms single images into 3D physical objects. The visual geometry of a physical object in an image is determined by three orthogonal attributes: mechanical properties, external forces, and rest-shape geometry. Existing single-view 3D reconstruction methods often overlook this underlying composition, presuming rigidity or neglecting external forces. Consequently, the reconstructed objects fail to withstand real-world physical forces, resulting in instability or undesirable deformation -- diverging from their intended designs as depicted in the image. Our optimization framework addresses this by embedding physical compatibility into the reconstruction process. We explicitly decompose the three physical attributes and link them through static equilibrium, which serves as a hard constraint, ensuring that the optimized physical shapes exhibit desired physical behaviors. Evaluations on a dataset collected from Objaverse demonstrate that our framework consistently enhances the physical realism of 3D models over existing methods. The utility of our framework extends to practical applications in dynamic simulations and 3D printing, where adherence to physical compatibility is paramount.

Open-vocabulary 3D object detection aims to localize and recognize objects beyond a fixed training taxonomy. In multi-view RGB settings, recent approaches often decouple geometry-based instance construction from semantic labeling, generating class-agnostic fragments and assigning open-vocabulary categories post hoc. While flexible, such decoupling leaves instance construction governed primarily by geometric consistency, without semantic constraints during merging. When geometric evidence is view-dependent and incomplete, this geometry-only merging can lead to irreversible association errors, including over-merging of distinct objects or fragmentation of a single instance. We propose Group3D, a multi-view open-vocabulary 3D detection framework that integrates semantic constraints directly into the instance construction process. Group3D maintains a scene-adaptive vocabulary derived from a multimodal large language model (MLLM) and organizes it into semantic compatibility groups that encode plausible cross-view category equivalence. These groups act as merge-time constraints: 3D fragments are associated only when they satisfy both semantic compatibility and geometric consistency. This semantically gated merging mitigates geometry-driven over-merging while absorbing multi-view category variability. Group3D supports both pose-known and pose-free settings, relying only on RGB observations. Experiments on ScanNet and ARKitScenes demonstrate that Group3D achieves state-of-the-art performance in multi-view open-vocabulary 3D detection, while exhibiting strong generalization in zero-shot scenarios. The project page is available at https://ubin108.github.io/Group3D/.

We address the problem of performing backpropagation for computation graphs involving 3D transformation groups SO(3), SE(3), and Sim(3). 3D transformation groups are widely used in 3D vision and robotics, but they do not form vector spaces and instead lie on smooth manifolds. The standard backpropagation approach, which embeds 3D transformations in Euclidean spaces, suffers from numerical difficulties. We introduce a new library, which exploits the group structure of 3D transformations and performs backpropagation in the tangent spaces of manifolds. We show that our approach is numerically more stable, easier to implement, and beneficial to a diverse set of tasks. Our plug-and-play PyTorch library is available at https://github.com/princeton-vl/lietorch.

Modern ML applications increasingly rely on complex deep learning models and large datasets. There has been an exponential growth in the amount of computation needed to train the largest models. Therefore, to scale computation and data, these models are inevitably trained in a distributed manner in clusters of nodes, and their updates are aggregated before being applied to the model. However, a distributed setup is prone to Byzantine failures of individual nodes, components, and software. With data augmentation added to these settings, there is a critical need for robust and efficient aggregation systems. We define the quality of workers as reconstruction ratios in (0,1], and formulate aggregation as a Maximum Likelihood Estimation procedure using Beta densities. We show that the Regularized form of log-likelihood wrt subspace can be approximately solved using iterative least squares solver, and provide convergence guarantees using recent Convex Optimization landscape results. Our empirical findings demonstrate that our approach significantly enhances the robustness of state-of-the-art Byzantine resilient aggregators. We evaluate our method in a distributed setup with a parameter server, and show simultaneous improvements in communication efficiency and accuracy across various tasks. The code is publicly available at https://github.com/hamidralmasi/FlagAggregator

Aggregating information from features across different layers is an essential operation for dense prediction models. Despite its limited expressiveness, feature concatenation dominates the choice of aggregation operations. In this paper, we introduce Attentive Feature Aggregation (AFA) to fuse different network layers with more expressive non-linear operations. AFA exploits both spatial and channel attention to compute weighted average of the layer activations. Inspired by neural volume rendering, we extend AFA with Scale-Space Rendering (SSR) to perform late fusion of multi-scale predictions. AFA is applicable to a wide range of existing network designs. Our experiments show consistent and significant improvements on challenging semantic segmentation benchmarks, including Cityscapes, BDD100K, and Mapillary Vistas, at negligible computational and parameter overhead. In particular, AFA improves the performance of the Deep Layer Aggregation (DLA) model by nearly 6% mIoU on Cityscapes. Our experimental analyses show that AFA learns to progressively refine segmentation maps and to improve boundary details, leading to new state-of-the-art results on boundary detection benchmarks on BSDS500 and NYUDv2. Code and video resources are available at http://vis.xyz/pub/dla-afa.

3D part amodal segmentation--decomposing a 3D shape into complete, semantically meaningful parts, even when occluded--is a challenging but crucial task for 3D content creation and understanding. Existing 3D part segmentation methods only identify visible surface patches, limiting their utility. Inspired by 2D amodal segmentation, we introduce this novel task to the 3D domain and propose a practical, two-stage approach, addressing the key challenges of inferring occluded 3D geometry, maintaining global shape consistency, and handling diverse shapes with limited training data. First, we leverage existing 3D part segmentation to obtain initial, incomplete part segments. Second, we introduce HoloPart, a novel diffusion-based model, to complete these segments into full 3D parts. HoloPart utilizes a specialized architecture with local attention to capture fine-grained part geometry and global shape context attention to ensure overall shape consistency. We introduce new benchmarks based on the ABO and PartObjaverse-Tiny datasets and demonstrate that HoloPart significantly outperforms state-of-the-art shape completion methods. By incorporating HoloPart with existing segmentation techniques, we achieve promising results on 3D part amodal segmentation, opening new avenues for applications in geometry editing, animation, and material assignment.

The topic of stitching images with globally natural structures holds paramount significance. Current methodologies exhibit the ability to preserve local geometric structures, yet fall short in maintaining relationships between these geometric structures. In this paper, we endeavor to safeguard the overall, OBJect-level structures within images based on Global Similarity Prior, while concurrently mitigating distortion and ghosting artifacts with OBJ-GSP. Our approach leverages the Segment Anything Model to extract geometric structures with semantic information, enhancing the algorithm's ability to preserve objects in a manner that aligns more intuitively with human perception. We seek to identify spatial constraints that govern the relationships between various geometric boundaries. Recognizing that multiple geometric boundaries collectively define complete objects, we employ triangular meshes to safeguard not only individual geometric structures but also the overall shapes of objects within the images. Empirical evaluations across multiple image stitching datasets demonstrate that our method establishes a new state-of-the-art benchmark in image stitching. Our implementation and dataset is publicly available at https://github.com/RussRobin/OBJ-GSP .

Recent feed-forward models have significantly advanced geometry perception for inferring dense 3D structure from sensor observations. However, its essential capabilities remain fragmented across multiple incompatible paradigms, including online perception, offline reconstruction, multi-modal integration, long-horizon scalability, and metric-scale estimation. We present UniT, a unified model built upon a novel Group Autoregressive Transformer, which reformulates these seemingly disparate capabilities within a single framework. The key idea is to treat groups of sensor observations as the basic autoregressive units and predict the corresponding point maps in an anchor-free and scale-adaptive manner. More specifically, diverse view configurations in both online and offline settings are naturally unified within a single group autoregression process. By varying the group size, online mode operates over multiple autoregressive steps with single-frame groups, whereas offline mode aggregates a multi-frame group in a single forward pass. Meanwhile, a queue-style KV caching mechanism ensures bounded autoregressive memory over long horizons. This is enabled by reducing long-range dependencies on early frames through anchor-free relational modeling, thereby allowing outdated memory to be discarded on the fly. To improve metric-scale generalization across scenes, a scale-adaptive geometry loss is further introduced within this framework. It couples relative geometric constraints with a partial absolute scale term, implicitly regularizing global scale and inducing a progressive transition from scale-invariant geometry to metric-scale solutions. Together with a dedicated modal attention module for integrating auxiliary modalities, UniT achieves state-of-the-art performance in unified geometry perception, as validated on ten benchmarks spanning seven representative tasks.

In this work, we propose SAM3D, a novel framework that is able to predict masks in 3D point clouds by leveraging the Segment-Anything Model (SAM) in RGB images without further training or finetuning. For a point cloud of a 3D scene with posed RGB images, we first predict segmentation masks of RGB images with SAM, and then project the 2D masks into the 3D points. Later, we merge the 3D masks iteratively with a bottom-up merging approach. At each step, we merge the point cloud masks of two adjacent frames with the bidirectional merging approach. In this way, the 3D masks predicted from different frames are gradually merged into the 3D masks of the whole 3D scene. Finally, we can optionally ensemble the result from our SAM3D with the over-segmentation results based on the geometric information of the 3D scenes. Our approach is experimented with ScanNet dataset and qualitative results demonstrate that our SAM3D achieves reasonable and fine-grained 3D segmentation results without any training or finetuning of SAM.

Backward Filtering Forward Guiding (BFFG) is a bidirectional algorithm proposed in Mider et al. [2021] and studied more in depth in a general setting in Van der Meulen and Schauer [2022]. In category theory, optics have been proposed for modelling systems with bidirectional data flow. We connect BFFG with optics and prove that different ways of composing the building blocks of BFFG correspond to equivalent optics.

This work presents SGCDet, a novel multi-view indoor 3D object detection framework based on adaptive 3D volume construction. Unlike previous approaches that restrict the receptive field of voxels to fixed locations on images, we introduce a geometry and context aware aggregation module to integrate geometric and contextual information within adaptive regions in each image and dynamically adjust the contributions from different views, enhancing the representation capability of voxel features. Furthermore, we propose a sparse volume construction strategy that adaptively identifies and selects voxels with high occupancy probabilities for feature refinement, minimizing redundant computation in free space. Benefiting from the above designs, our framework achieves effective and efficient volume construction in an adaptive way. Better still, our network can be supervised using only 3D bounding boxes, eliminating the dependence on ground-truth scene geometry. Experimental results demonstrate that SGCDet achieves state-of-the-art performance on the ScanNet, ScanNet200 and ARKitScenes datasets. The source code is available at https://github.com/RM-Zhang/SGCDet.

Visual Place Recognition (VPR) has been traditionally formulated as a single-image retrieval task. Using multiple views offers clear advantages, yet this setting remains relatively underexplored and existing methods often struggle to generalize across diverse environments. In this work we introduce UniPR-3D, the first VPR architecture that effectively integrates information from multiple views. UniPR-3D builds on a VGGT backbone capable of encoding multi-view 3D representations, which we adapt by designing feature aggregators and fine-tune for the place recognition task. To construct our descriptor, we jointly leverage the 3D tokens and intermediate 2D tokens produced by VGGT. Based on their distinct characteristics, we design dedicated aggregation modules for 2D and 3D features, allowing our descriptor to capture fine-grained texture cues while also reasoning across viewpoints. To further enhance generalization, we incorporate both single- and multi-frame aggregation schemes, along with a variable-length sequence retrieval strategy. Our experiments show that UniPR-3D sets a new state of the art, outperforming both single- and multi-view baselines and highlighting the effectiveness of geometry-grounded tokens for VPR. Our code and models will be made publicly available on Github https://github.com/dtc111111/UniPR-3D.

This paper tackles the task of learning to generate signals over triangle meshes in a triangulation-agnostic manner, meaning the trained model can be applied to different meshes and triangulations effectively. Practically, the paper adapts the flow matching (FM) paradigm to a mesh-based, triangulation-agnostic setting. Theoretically, it proposes a specific noise distribution which is triangulation agnostic, to be used inside the FM model's denoising process. While noise distributions are usually trivial to devise for, e.g., images, devising a triangulation-agnostic distribution proves to be a much more difficult task. We formulate a mathematical definition of triangulation agnosticism of distributions, via their spectrum. We then show that a discretization of a specific Gaussian random field called a Matérn process holds these desired properties, and provides a simple and efficient sampling algorithm. We use it as our noise model, and adapt FM to the triangulation-agnostic setting by using a state-of-the-art approach for learning signals on meshes in the gradient domain -- PoissonNet -- as the denoiser. We conduct experiments on elaborate tasks such as sampling elastic rest states, and generating poses of humanoids. Our method is shown to be capable of producing highly realistic results for meshes of over one million triangles, significantly exceeding the state-of-the-art in quality and diversity.

The field of autonomous driving has attracted considerable interest in approaches that directly infer 3D objects in the Bird's Eye View (BEV) from multiple cameras. Some attempts have also explored utilizing 2D detectors from single images to enhance the performance of 3D detection. However, these approaches rely on a two-stage process with separate detectors, where the 2D detection results are utilized only once for token selection or query initialization. In this paper, we present a single model termed SimPB, which simultaneously detects 2D objects in the perspective view and 3D objects in the BEV space from multiple cameras. To achieve this, we introduce a hybrid decoder consisting of several multi-view 2D decoder layers and several 3D decoder layers, specifically designed for their respective detection tasks. A Dynamic Query Allocation module and an Adaptive Query Aggregation module are proposed to continuously update and refine the interaction between 2D and 3D results, in a cyclic 3D-2D-3D manner. Additionally, Query-group Attention is utilized to strengthen the interaction among 2D queries within each camera group. In the experiments, we evaluate our method on the nuScenes dataset and demonstrate promising results for both 2D and 3D detection tasks. Our code is available at: https://github.com/nullmax-vision/SimPB.

Multi-Grid Back-Projection (MGBP) is a fully-convolutional network architecture that can learn to restore images and videos with upscaling artifacts. Using the same strategy of multi-grid partial differential equation (PDE) solvers this multiscale architecture scales computational complexity efficiently with increasing output resolutions. The basic processing block is inspired in the iterative back-projection (IBP) algorithm and constitutes a type of cross-scale residual block with feedback from low resolution references. The architecture performs in par with state-of-the-arts alternatives for regression targets that aim to recover an exact copy of a high resolution image or video from which only a downscale image is known. A perceptual quality target aims to create more realistic outputs by introducing artificial changes that can be different from a high resolution original content as long as they are consistent with the low resolution input. For this target we propose a strategy using noise inputs in different resolution scales to control the amount of artificial details generated in the output. The noise input controls the amount of innovation that the network uses to create artificial realistic details. The effectiveness of this strategy is shown in benchmarks and it is explained as a particular strategy to traverse the perception-distortion plane.

Recent advances in large language models (LLMs) have demonstrated remarkable capabilities across diverse domains, particularly in mathematical reasoning, amid which geometry problem solving remains a challenging area where auxiliary construction plays a enssential role. Existing approaches either achieve suboptimal performance or rely on massive LLMs (e.g., GPT-4o), incurring massive computational costs. We posit that reinforcement learning with verifiable reward (e.g., GRPO) offers a promising direction for training smaller models that effectively combine auxiliary construction with robust geometric reasoning. However, directly applying GRPO to geometric reasoning presents fundamental limitations due to its dependence on unconditional rewards, which leads to indiscriminate and counterproductive auxiliary constructions. To address these challenges, we propose Group Contrastive Policy Optimization (GCPO), a novel reinforcement learning framework featuring two key innovations: (1) Group Contrastive Masking, which adaptively provides positive or negative reward signals for auxiliary construction based on contextual utility, and a (2) length reward that promotes longer reasoning chains. Building on GCPO, we develop GeometryZero, a family of affordable-size geometric reasoning models that judiciously determine when to employ auxiliary construction. Our extensive empirical evaluation across popular geometric benchmarks (Geometry3K, MathVista) demonstrates that GeometryZero models consistently outperform baselines (e.g. GRPO), achieving an average improvement of 4.29% across all benchmarks.

Polygonal meshes provide an efficient representation for 3D shapes. They explicitly capture both shape surface and topology, and leverage non-uniformity to represent large flat regions as well as sharp, intricate features. This non-uniformity and irregularity, however, inhibits mesh analysis efforts using neural networks that combine convolution and pooling operations. In this paper, we utilize the unique properties of the mesh for a direct analysis of 3D shapes using MeshCNN, a convolutional neural network designed specifically for triangular meshes. Analogous to classic CNNs, MeshCNN combines specialized convolution and pooling layers that operate on the mesh edges, by leveraging their intrinsic geodesic connections. Convolutions are applied on edges and the four edges of their incident triangles, and pooling is applied via an edge collapse operation that retains surface topology, thereby, generating new mesh connectivity for the subsequent convolutions. MeshCNN learns which edges to collapse, thus forming a task-driven process where the network exposes and expands the important features while discarding the redundant ones. We demonstrate the effectiveness of our task-driven pooling on various learning tasks applied to 3D meshes.

Modern neural architectures for 3D point cloud processing contain both convolutional layers and attention blocks, but the best way to assemble them remains unclear. We analyse the role of different computational blocks in 3D point cloud networks and find an intuitive behaviour: convolution is adequate to extract low-level geometry at high-resolution in early layers, where attention is expensive without bringing any benefits; attention captures high-level semantics and context in low-resolution, deep layers more efficiently. Guided by this design principle, we propose a new, improved 3D point cloud backbone that employs convolutions in early stages and switches to attention for deeper layers. To avoid the loss of spatial layout information when discarding redundant convolution layers, we introduce a novel, training-free 3D positional encoding, PointROPE. The resulting LitePT model has 3.6times fewer parameters, runs 2times faster, and uses 2times less memory than the state-of-the-art Point Transformer V3, but nonetheless matches or even outperforms it on a range of tasks and datasets. Code and models are available at: https://github.com/prs-eth/LitePT.

This paper proposes a simple but effective graph-based agglomerative algorithm, for clustering high-dimensional data. We explore the different roles of two fundamental concepts in graph theory, indegree and outdegree, in the context of clustering. The average indegree reflects the density near a sample, and the average outdegree characterizes the local geometry around a sample. Based on such insights, we define the affinity measure of clusters via the product of average indegree and average outdegree. The product-based affinity makes our algorithm robust to noise. The algorithm has three main advantages: good performance, easy implementation, and high computational efficiency. We test the algorithm on two fundamental computer vision problems: image clustering and object matching. Extensive experiments demonstrate that it outperforms the state-of-the-arts in both applications.

The analysis of tabular data has traditionally been dominated by gradient-boosted decision trees (GBDTs), known for their proficiency with mixed categorical and numerical features. However, recent deep learning innovations are challenging this dominance. We introduce Mambular, an adaptation of the Mamba architecture optimized for tabular data. We extensively benchmark Mambular against state-of-the-art models, including neural networks and tree-based methods, and demonstrate its competitive performance across diverse datasets. Additionally, we explore various adaptations of Mambular to understand its effectiveness for tabular data. We investigate different pooling strategies, feature interaction mechanisms, and bi-directional processing. Our analysis shows that interpreting features as a sequence and passing them through Mamba layers results in surprisingly performant models. The results highlight Mambulars potential as a versatile and powerful architecture for tabular data analysis, expanding the scope of deep learning applications in this domain. The source code is available at https://github.com/basf/mamba-tabular.