Daily Papers

Mathematical geometric problem solving (GPS) often requires effective integration of multimodal information and verifiable logical coherence. Despite the fast development of large language models in general problem solving, it remains unresolved regarding with both methodology and benchmarks, especially given the fact that exiting synthetic GPS benchmarks are often not self-verified and contain noise and self-contradicted information due to the illusion of LLMs. In this paper, we propose a scalable data engine called TrustGeoGen for problem generation, with formal verification to provide a principled benchmark, which we believe lays the foundation for the further development of methods for GPS. The engine synthesizes geometric data through four key innovations: 1) multimodal-aligned generation of diagrams, textual descriptions, and stepwise solutions; 2) formal verification ensuring rule-compliant reasoning paths; 3) a bootstrapping mechanism enabling complexity escalation via recursive state generation and 4) our devised GeoExplore series algorithms simultaneously produce multi-solution variants and self-reflective backtracking traces. By formal logical verification, TrustGeoGen produces GeoTrust-200K dataset with guaranteed modality integrity, along with GeoTrust-test testset. Experiments reveal the state-of-the-art models achieve only 49.17\% accuracy on GeoTrust-test, demonstrating its evaluation stringency. Crucially, models trained on GeoTrust achieve OOD generalization on GeoQA, significantly reducing logical inconsistencies relative to pseudo-label annotated by OpenAI-o1. Our code is available at https://github.com/Alpha-Innovator/TrustGeoGen

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.

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.

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.

Real-valued functions on geometric data -- such as node attributes on a graph -- can be optimized using descriptors from persistent homology, allowing the user to incorporate topological terms in the loss function. When optimizing a single real-valued function (the one-parameter setting), there is a canonical choice of descriptor for persistent homology: the barcode. The operation mapping a real-valued function to its barcode is differentiable almost everywhere, and the convergence of gradient descent for losses using barcodes is relatively well understood. When optimizing a vector-valued function (the multiparameter setting), there is no unique choice of descriptor for multiparameter persistent homology, and many distinct descriptors have been proposed. This calls for the development of a general framework for differentiability and optimization that applies to a wide range of multiparameter homological descriptors. In this article, we develop such a framework and show that it encompasses well-known descriptors of different flavors, such as signed barcodes and the multiparameter persistence landscape. We complement the theory with numerical experiments supporting the idea that optimizing multiparameter homological descriptors can lead to improved performances compared to optimizing one-parameter descriptors, even when using the simplest and most efficiently computable multiparameter descriptors.

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

Persistent homology (PH) provides topological descriptors for geometric data, such as weighted graphs, which are interpretable, stable to perturbations, and invariant under, e.g., relabeling. Most applications of PH focus on the one-parameter case -- where the descriptors summarize the changes in topology of data as it is filtered by a single quantity of interest -- and there is now a wide array of methods enabling the use of one-parameter PH descriptors in data science, which rely on the stable vectorization of these descriptors as elements of a Hilbert space. Although the multiparameter PH (MPH) of data that is filtered by several quantities of interest encodes much richer information than its one-parameter counterpart, the scarceness of stability results for MPH descriptors has so far limited the available options for the stable vectorization of MPH. In this paper, we aim to bring together the best of both worlds by showing how the interpretation of signed barcodes -- a recent family of MPH descriptors -- as signed measures leads to natural extensions of vectorization strategies from one parameter to multiple parameters. The resulting feature vectors are easy to define and to compute, and provably stable. While, as a proof of concept, we focus on simple choices of signed barcodes and vectorizations, we already see notable performance improvements when comparing our feature vectors to state-of-the-art topology-based methods on various types of data.

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.

Topological data analysis (TDA) is an area of data science that focuses on using invariants from algebraic topology to provide multiscale shape descriptors for geometric data sets such as point clouds. One of the most important such descriptors is {\em persistent homology}, which encodes the change in shape as a filtration parameter changes; a typical parameter is the feature scale. For many data sets, it is useful to simultaneously vary multiple filtration parameters, for example feature scale and density. While the theoretical properties of single parameter persistent homology are well understood, less is known about the multiparameter case. In particular, a central question is the problem of representing multiparameter persistent homology by elements of a vector space for integration with standard machine learning algorithms. Existing approaches to this problem either ignore most of the multiparameter information to reduce to the one-parameter case or are heuristic and potentially unstable in the face of noise. In this article, we introduce a new general representation framework that leverages recent results on {\em decompositions} of multiparameter persistent homology. This framework is rich in information, fast to compute, and encompasses previous approaches. Moreover, we establish theoretical stability guarantees under this framework as well as efficient algorithms for practical computation, making this framework an applicable and versatile tool for analyzing geometric and point cloud data. We validate our stability results and algorithms with numerical experiments that demonstrate statistical convergence, prediction accuracy, and fast running times on several real data sets.

Point cloud registration has seen significant advancements with the application of deep learning techniques. However, existing approaches often overlook the potential of integrating radiometric information from RGB images. This limitation reduces their effectiveness in aligning point clouds pairs, especially in regions where geometric data alone is insufficient. When used effectively, radiometric information can enhance the registration process by providing context that is missing from purely geometric data. In this paper, we propose CoFF, a novel Cross-modal Feature Fusion method that utilizes both point cloud geometry and RGB images for pairwise point cloud registration. Assuming that the co-registration between point clouds and RGB images is available, CoFF explicitly addresses the challenges where geometric information alone is unclear, such as in regions with symmetric similarity or planar structures, through a two-stage fusion of 3D point cloud features and 2D image features. It incorporates a cross-modal feature fusion module that assigns pixel-wise image features to 3D input point clouds to enhance learned 3D point features, and integrates patch-wise image features with superpoint features to improve the quality of coarse matching. This is followed by a coarse-to-fine matching module that accurately establishes correspondences using the fused features. We extensively evaluate CoFF on four common datasets: 3DMatch, 3DLoMatch, IndoorLRS, and the recently released ScanNet++ datasets. In addition, we assess CoFF on specific subset datasets containing geometrically ambiguous cases. Our experimental results demonstrate that CoFF achieves state-of-the-art registration performance across all benchmarks, including remarkable registration recalls of 95.9% and 81.6% on the widely-used 3DMatch and 3DLoMatch datasets, respectively...(Truncated to fit arXiv abstract length)

Real-time face orientation recognition is a cutting-edge technology meant to track and analyze facial movements in virtual environments such as online interviews, remote meetings, and virtual classrooms. As the demand for virtual interactions grows, it becomes increasingly important to measure participant engagement, attention, and overall interaction. This research presents a novel solution that leverages the Media Pipe Face Mesh framework to identify facial landmarks and extract geometric data for calculating Euler angles, which determine head orientation in real time. The system tracks 3D facial landmarks and uses this data to compute head movements with a focus on accuracy and responsiveness. By studying Euler angles, the system can identify a user's head orientation with an accuracy of 90\%, even at a distance of up to four feet. This capability offers significant enhancements for monitoring user interaction, allowing for more immersive and interactive virtual ex-periences. The proposed method shows its reliability in evaluating participant attentiveness during online assessments and meetings. Its application goes beyond engagement analysis, potentially providing a means for improving the quality of virtual communication, fostering better understanding between participants, and ensuring a higher level of interaction in digital spaces. This study offers a basis for future developments in enhancing virtual user experiences by integrating real-time facial tracking technologies, paving the way for more adaptive and interactive web-based platform.

Cancer is the second leading cause of death, with chemotherapy as one of the primary forms of treatment. As a result, researchers are turning to drug combination therapy to decrease drug resistance and increase efficacy. Current methods of drug combination screening, such as in vivo and in vitro, are inefficient due to stark time and monetary costs. In silico methods have become increasingly important for screening drugs, but current methods are inaccurate and generalize poorly to unseen anticancer drugs. In this paper, I employ a geometric deep-learning model utilizing a graph attention network that is equivariant to 3D rotations, translations, and reflections with structural motifs. Additionally, the gene expression of cancer cell lines is utilized to classify synergistic drug combinations specific to each cell line. I compared the proposed geometric deep learning framework to current state-of-the-art (SOTA) methods, and the proposed model architecture achieved greater performance on all 12 benchmark tasks performed on the DrugComb dataset. Specifically, the proposed framework outperformed other SOTA methods by an accuracy difference greater than 28%. Based on these results, I believe that the equivariant graph attention network's capability of learning geometric data accounts for the large performance improvements. The model's ability to generalize to foreign drugs is thought to be due to the structural motifs providing a better representation of the molecule. Overall, I believe that the proposed equivariant geometric deep learning framework serves as an effective tool for virtually screening anticancer drug combinations for further validation in a wet lab environment. The code for this work is made available online at: https://github.com/WeToTheMoon/EGAT_DrugSynergy.

Recent works have shown that, when trained at scale, uni-modal 2D vision and text encoders converge to learned features that share remarkable structural properties, despite arising from different representations. However, the role of 3D encoders with respect to other modalities remains unexplored. Furthermore, existing 3D foundation models that leverage large datasets are typically trained with explicit alignment objectives with respect to frozen encoders from other representations. In this work, we investigate the possibility of a posteriori alignment of representations obtained from uni-modal 3D encoders compared to text-based feature spaces. We show that naive post-training feature alignment of uni-modal text and 3D encoders results in limited performance. We then focus on extracting subspaces of the corresponding feature spaces and discover that by projecting learned representations onto well-chosen lower-dimensional subspaces the quality of alignment becomes significantly higher, leading to improved accuracy on matching and retrieval tasks. Our analysis further sheds light on the nature of these shared subspaces, which roughly separate between semantic and geometric data representations. Overall, ours is the first work that helps to establish a baseline for post-training alignment of 3D uni-modal and text feature spaces, and helps to highlight both the shared and unique properties of 3D data compared to other representations.

Unsupervised learning for geometric perception (depth, optical flow, etc.) is of great interest to autonomous systems. Recent works on unsupervised learning have made considerable progress on perceiving geometry; however, they usually ignore the coherence of objects and perform poorly under scenarios with dark and noisy environments. In contrast, supervised learning algorithms, which are robust, require large labeled geometric dataset. This paper introduces SIGNet, a novel framework that provides robust geometry perception without requiring geometrically informative labels. Specifically, SIGNet integrates semantic information to make depth and flow predictions consistent with objects and robust to low lighting conditions. SIGNet is shown to improve upon the state-of-the-art unsupervised learning for depth prediction by 30% (in squared relative error). In particular, SIGNet improves the dynamic object class performance by 39% in depth prediction and 29% in flow prediction. Our code will be made available at https://github.com/mengyuest/SIGNet

Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models, when data are supported on an unknown low-dimensional linear subspace. Our result provides sample complexity bounds for distribution estimation using diffusion models. We show that with a properly chosen neural network architecture, the score function can be both accurately approximated and efficiently estimated. Furthermore, the generated distribution based on the estimated score function captures the data geometric structures and converges to a close vicinity of the data distribution. The convergence rate depends on the subspace dimension, indicating that diffusion models can circumvent the curse of data ambient dimensionality.

In this work, we present a method to generate a configurational level fingerprint for polymers using the Bead-Spring-Model. Unlike some of the previous fingerprinting approaches that employ monomer-level information where atomistic descriptors are computed using quantum chemistry calculations, this approach incorporates configurational information from a coarse-grained model of a long polymer chain. The proposed approach may be advantageous for the study of behavior resulting from large molecular weights. To create this fingerprint, we make use of two kinds of descriptors. First, we calculate certain geometric descriptors like Re2, Rg2 etc. and label them as Calculated Descriptors. Second, we generate a set of data-driven descriptors using an unsupervised autoencoder model and call them Learnt Descriptors. Using a combination of both of them, we are able to learn mappings from the structure to various properties of the polymer chain by training ML models. We test our fingerprint to predict the probability of occurrence of a configuration at equilibrium, which is approximated by a simple linear relationship between the instantaneous internal energy and equilibrium average internal energy.

Deep learning has improved vanishing point detection in images. Yet, deep networks require expensive annotated datasets trained on costly hardware and do not generalize to even slightly different domains, and minor problem variants. Here, we address these issues by injecting deep vanishing point detection networks with prior knowledge. This prior knowledge no longer needs to be learned from data, saving valuable annotation efforts and compute, unlocking realistic few-sample scenarios, and reducing the impact of domain changes. Moreover, the interpretability of the priors allows to adapt deep networks to minor problem variations such as switching between Manhattan and non-Manhattan worlds. We seamlessly incorporate two geometric priors: (i) Hough Transform -- mapping image pixels to straight lines, and (ii) Gaussian sphere -- mapping lines to great circles whose intersections denote vanishing points. Experimentally, we ablate our choices and show comparable accuracy to existing models in the large-data setting. We validate our model's improved data efficiency, robustness to domain changes, adaptability to non-Manhattan settings.

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.

Recent advances in data-driven geometric multi-view 3D reconstruction foundation models (e.g., DUSt3R) have shown remarkable performance across various 3D vision tasks, facilitated by the release of large-scale, high-quality 3D datasets. However, as we observed, constrained by their matching-based principles, the reconstruction quality of existing models suffers significant degradation in challenging regions with limited matching cues, particularly in weakly textured areas and low-light conditions. To mitigate these limitations, we propose to harness the inherent robustness of monocular geometry estimation to compensate for the inherent shortcomings of matching-based methods. Specifically, we introduce a monocular-guided refinement module that integrates monocular geometric priors into multi-view reconstruction frameworks. This integration substantially enhances the robustness of multi-view reconstruction systems, leading to high-quality feed-forward reconstructions. Comprehensive experiments across multiple benchmarks demonstrate that our method achieves substantial improvements in both mutli-view camera pose estimation and point cloud accuracy.

Automatic math problem solving has recently attracted increasing attention as a long-standing AI benchmark. In this paper, we focus on solving geometric problems, which requires a comprehensive understanding of textual descriptions, visual diagrams, and theorem knowledge. However, the existing methods were highly dependent on handcraft rules and were merely evaluated on small-scale datasets. Therefore, we propose a Geometric Question Answering dataset GeoQA, containing 4,998 geometric problems with corresponding annotated programs, which illustrate the solving process of the given problems. Compared with another publicly available dataset GeoS, GeoQA is 25 times larger, in which the program annotations can provide a practical testbed for future research on explicit and explainable numerical reasoning. Moreover, we introduce a Neural Geometric Solver (NGS) to address geometric problems by comprehensively parsing multimodal information and generating interpretable programs. We further add multiple self-supervised auxiliary tasks on NGS to enhance cross-modal semantic representation. Extensive experiments on GeoQA validate the effectiveness of our proposed NGS and auxiliary tasks. However, the results are still significantly lower than human performance, which leaves large room for future research. Our benchmark and code are released at https://github.com/chen-judge/GeoQA .

Are camera poses necessary for multi-view 3D modeling? Existing approaches predominantly assume access to accurate camera poses. While this assumption might hold for dense views, accurately estimating camera poses for sparse views is often elusive. Our analysis reveals that noisy estimated poses lead to degraded performance for existing sparse-view 3D modeling methods. To address this issue, we present LEAP, a novel pose-free approach, therefore challenging the prevailing notion that camera poses are indispensable. LEAP discards pose-based operations and learns geometric knowledge from data. LEAP is equipped with a neural volume, which is shared across scenes and is parameterized to encode geometry and texture priors. For each incoming scene, we update the neural volume by aggregating 2D image features in a feature-similarity-driven manner. The updated neural volume is decoded into the radiance field, enabling novel view synthesis from any viewpoint. On both object-centric and scene-level datasets, we show that LEAP significantly outperforms prior methods when they employ predicted poses from state-of-the-art pose estimators. Notably, LEAP performs on par with prior approaches that use ground-truth poses while running 400times faster than PixelNeRF. We show LEAP generalizes to novel object categories and scenes, and learns knowledge closely resembles epipolar geometry. Project page: https://hwjiang1510.github.io/LEAP/

In computer vision, a larger effective receptive field (ERF) is associated with better performance. While attention natively supports global context, its quadratic complexity limits its applicability to tasks that benefit from high-resolution input. In this work, we extend Hyena, a convolution-based attention replacement, from causal sequences to bidirectional data and two-dimensional image space. We scale Hyena's convolution kernels beyond the feature map size, up to 191times191, to maximize ERF while maintaining sub-quadratic complexity in the number of pixels. We integrate our two-dimensional Hyena, HyenaPixel, and bidirectional Hyena into the MetaFormer framework. For image categorization, HyenaPixel and bidirectional Hyena achieve a competitive ImageNet-1k top-1 accuracy of 84.9% and 85.2%, respectively, with no additional training data, while outperforming other convolutional and large-kernel networks. Combining HyenaPixel with attention further improves accuracy. We attribute the success of bidirectional Hyena to learning the data-dependent geometric arrangement of pixels without a fixed neighborhood definition. Experimental results on downstream tasks suggest that HyenaPixel with large filters and a fixed neighborhood leads to better localization performance.

In this paper, we propose Bootstrapped Language-Image Pretraining-driven Fused State Representation in Proximal Policy Optimization (BLIP-FusePPO), a novel multimodal reinforcement learning (RL) framework for autonomous lane-keeping (LK), in which semantic embeddings generated by a vision-language model (VLM) are directly fused with geometric states, LiDAR observations, and Proportional-Integral-Derivative-based (PID) control feedback within the agent observation space. The proposed method lets the agent learn driving rules that are aware of their surroundings and easy to understand by combining high-level scene understanding from the VLM with low-level control and spatial signals. Our architecture brings together semantic, geometric, and control-aware representations to make policy learning more robust. A hybrid reward function that includes semantic alignment, LK accuracy, obstacle avoidance, and speed regulation helps learning to be more efficient and generalizable. Our method is different from the approaches that only use semantic models to shape rewards. Instead, it directly embeds semantic features into the state representation. This cuts down on expensive runtime inference and makes sure that semantic guidance is always available. The simulation results show that the proposed model is better at LK stability and adaptability than the best vision-based and multimodal RL baselines in a wide range of difficult driving situations. We make our code publicly available.

We present ShapeNet: a richly-annotated, large-scale repository of shapes represented by 3D CAD models of objects. ShapeNet contains 3D models from a multitude of semantic categories and organizes them under the WordNet taxonomy. It is a collection of datasets providing many semantic annotations for each 3D model such as consistent rigid alignments, parts and bilateral symmetry planes, physical sizes, keywords, as well as other planned annotations. Annotations are made available through a public web-based interface to enable data visualization of object attributes, promote data-driven geometric analysis, and provide a large-scale quantitative benchmark for research in computer graphics and vision. At the time of this technical report, ShapeNet has indexed more than 3,000,000 models, 220,000 models out of which are classified into 3,135 categories (WordNet synsets). In this report we describe the ShapeNet effort as a whole, provide details for all currently available datasets, and summarize future plans.

The global positioning system (GPS) has become an indispensable navigation method for field operations with unmanned surface vehicles (USVs) in marine environments. However, GPS may not always be available outdoors because it is vulnerable to natural interference and malicious jamming attacks. Thus, an alternative navigation system is required when the use of GPS is restricted or prohibited. To this end, we present a novel method that utilizes an Unmanned Aerial Vehicle (UAV) to assist in localizing USVs in GNSS-restricted marine environments. In our approach, the UAV flies along the shoreline at a consistent altitude, continuously tracking and detecting the USV using a deep learning-based approach on camera images. Subsequently, triangulation techniques are applied to estimate the USV's position relative to the UAV, utilizing geometric information and datalink range from the UAV. We propose adjusting the UAV's camera angle based on the pixel error between the USV and the image center throughout the localization process to enhance accuracy. Additionally, visual measurements are integrated into an Extended Kalman Filter (EKF) for robust state estimation. To validate our proposed method, we utilize a USV equipped with onboard sensors and a UAV equipped with a camera. A heterogeneous robotic interface is established to facilitate communication between the USV and UAV. We demonstrate the efficacy of our approach through a series of experiments conducted during the ``Muhammad Bin Zayed International Robotic Challenge (MBZIRC-2024)'' in real marine environments, incorporating noisy measurements and ocean disturbances. The successful outcomes indicate the potential of our method to complement GPS for USV navigation.

Diffusion models have attracted significant attention due to the remarkable ability to create content and generate data for tasks like image classification. However, the usage of diffusion models to generate the high-quality object detection data remains an underexplored area, where not only image-level perceptual quality but also geometric conditions such as bounding boxes and camera views are essential. Previous studies have utilized either copy-paste synthesis or layout-to-image (L2I) generation with specifically designed modules to encode the semantic layouts. In this paper, we propose the GeoDiffusion, a simple framework that can flexibly translate various geometric conditions into text prompts and empower pre-trained text-to-image (T2I) diffusion models for high-quality detection data generation. Unlike previous L2I methods, our GeoDiffusion is able to encode not only the bounding boxes but also extra geometric conditions such as camera views in self-driving scenes. Extensive experiments demonstrate GeoDiffusion outperforms previous L2I methods while maintaining 4x training time faster. To the best of our knowledge, this is the first work to adopt diffusion models for layout-to-image generation with geometric conditions and demonstrate that L2I-generated images can be beneficial for improving the performance of object detectors.

Data heterogeneity in federated learning, characterized by a significant misalignment between local and global distributions, leads to divergent local optimization directions and hinders global model training. Existing studies mainly focus on optimizing local updates or global aggregation, but these indirect approaches demonstrate instability when handling highly heterogeneous data distributions, especially in scenarios where label skew and domain skew coexist. To address this, we propose a geometry-guided data generation method that centers on simulating the global embedding distribution locally. We first introduce the concept of the geometric shape of an embedding distribution and then address the challenge of obtaining global geometric shapes under privacy constraints. Subsequently, we propose GGEUR, which leverages global geometric shapes to guide the generation of new samples, enabling a closer approximation to the ideal global distribution. In single-domain scenarios, we augment samples based on global geometric shapes to enhance model generalization; in multi-domain scenarios, we further employ class prototypes to simulate the global distribution across domains. Extensive experimental results demonstrate that our method significantly enhances the performance of existing approaches in handling highly heterogeneous data, including scenarios with label skew, domain skew, and their coexistence. Code published at: https://github.com/WeiDai-David/2025CVPR_GGEUR

Synthetic data is crucial for advancing autonomous driving (AD) systems, yet current state-of-the-art video generation models, despite their visual realism, suffer from subtle geometric distortions that limit their utility for downstream perception tasks. We identify and quantify this critical issue, demonstrating a significant performance gap in 3D object detection when using synthetic versus real data. To address this, we introduce Reinforcement Learning with Geometric Feedback (RLGF), RLGF uniquely refines video diffusion models by incorporating rewards from specialized latent-space AD perception models. Its core components include an efficient Latent-Space Windowing Optimization technique for targeted feedback during diffusion, and a Hierarchical Geometric Reward (HGR) system providing multi-level rewards for point-line-plane alignment, and scene occupancy coherence. To quantify these distortions, we propose GeoScores. Applied to models like DiVE on nuScenes, RLGF substantially reduces geometric errors (e.g., VP error by 21\%, Depth error by 57\%) and dramatically improves 3D object detection mAP by 12.7\%, narrowing the gap to real-data performance. RLGF offers a plug-and-play solution for generating geometrically sound and reliable synthetic videos for AD development.

Significant advancements in Large Multimodal Models (LMMs) have enabled them to tackle complex problems involving visual-mathematical reasoning. However, their ability to identify geometric elements remains underexplored. To address this gap, we introduce Tangram, a novel benchmark designed to evaluate the performance of LMMs on geometric element recognition. Tangram comprises 1,080 diverse geometric diagrams sourced from primary and secondary school exams, competitions, and textbooks, ranging from simple geometric shapes to complex combinations. Each diagram is paired with four questions, resulting in 4,320 visual-question-answer pairs. Unlike existing benchmarks that emphasize higher-level cognition and reasoning, Tangram focuses on understanding geometric elements, requiring models to perform a ``simple yet challenging" counting task. Systematic evaluation of 13 prominent LMMs, such as GPT-4o and Claude 3.5 Sonnet, reveals that these models face significant challenges even in seemingly straightforward tasks. The top-performing model achieves an accuracy of only 53.0%, highlighting a substantial gap compared to human performance. These findings underscore the limitations of current multimodal AI systems in handling basic perception tasks and serve to inspire the development of the next generation of expert-level multimodal foundational models. The data and code will be released soon.

Neural multivariate regression underpins a wide range of domains such as control, robotics, and finance, yet the geometry of its learned representations remains poorly characterized. While neural collapse has been shown to benefit generalization in classification, we find that analogous collapse in regression consistently degrades performance. To explain this contrast, we analyze models through the lens of intrinsic dimension. Across control tasks and synthetic datasets, we estimate the intrinsic dimension of last-layer features (ID_H) and compare it with that of the regression targets (ID_Y). Collapsed models exhibit ID_H < ID_Y, leading to over-compression and poor generalization, whereas non-collapsed models typically maintain ID_H > ID_Y. For the non-collapsed models, performance with respect to ID_H depends on the data quantity and noise levels. From these observations, we identify two regimes (over-compressed and under-compressed) that determine when expanding or reducing feature dimensionality improves performance. Our results provide new geometric insights into neural regression and suggest practical strategies for enhancing generalization.

The enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space. Yet, modern machine learning increasingly encounters richly structured data that is inherently nonEuclidean. This data can exhibit intricate geometric, topological and algebraic structure: from the geometry of the curvature of space-time, to topologically complex interactions between neurons in the brain, to the algebraic transformations describing symmetries of physical systems. Extracting knowledge from such non-Euclidean data necessitates a broader mathematical perspective. Echoing the 19th-century revolutions that gave rise to non-Euclidean geometry, an emerging line of research is redefining modern machine learning with non-Euclidean structures. Its goal: generalizing classical methods to unconventional data types with geometry, topology, and algebra. In this review, we provide an accessible gateway to this fast-growing field and propose a graphical taxonomy that integrates recent advances into an intuitive unified framework. We subsequently extract insights into current challenges and highlight exciting opportunities for future development in this field.

Since a building's floorplans are easily accessible, consistent over time, and inherently robust to changes in visual appearance, self-localization within the floorplan has attracted researchers' interest. However, since floorplans are minimalist representations of a building's structure, modal and geometric differences between visual perceptions and floorplans pose challenges to this task. While existing methods cleverly utilize 2D geometric features and pose filters to achieve promising performance, they fail to address the localization errors caused by frequent visual changes and view occlusions due to variously shaped 3D objects. To tackle these issues, this paper views the 2D Floorplan Localization (FLoc) problem from a higher dimension by injecting 3D geometric priors into the visual FLoc algorithm. For the 3D geometric prior modeling, we first model geometrically aware view invariance using multi-view constraints, i.e., leveraging imaging geometric principles to provide matching constraints between multiple images that see the same points. Then, we further model the view-scene aligned geometric priors, enhancing the cross-modal geometry-color correspondences by associating the scene's surface reconstruction with the RGB frames of the sequence. Both 3D priors are modeled through self-supervised contrastive learning, thus no additional geometric or semantic annotations are required. These 3D priors summarized in extensive realistic scenes bridge the modal gap while improving localization success without increasing the computational burden on the FLoc algorithm. Sufficient comparative studies demonstrate that our method significantly outperforms state-of-the-art methods and substantially boosts the FLoc accuracy. All data and code will be released after the anonymous review.

Diffusion models for single image novel view synthesis (NVS) can generate highly realistic and plausible images, but they are limited in the geometric consistency to the given relative poses. The generated images often show significant errors with respect to the epipolar constraints that should be fulfilled, as given by the target pose. In this paper we address this issue by proposing a methodology to improve the geometric correctness of images generated by a diffusion model for single image NVS. We formulate a loss function based on image matching and epipolar constraints, and optimize the starting noise in a diffusion sampling process such that the generated image should both be a realistic image and fulfill geometric constraints derived from the given target pose. Our method does not require training data or fine-tuning of the diffusion models, and we show that we can apply it to multiple state-of-the-art models for single image NVS. The method is evaluated on the MegaScenes dataset and we show that geometric consistency is improved compared to the baseline models while retaining the quality of the generated images.

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

To address the data scarcity associated with 3D assets, 2D-lifting techniques such as Score Distillation Sampling (SDS) have become a widely adopted practice in text-to-3D generation pipelines. However, the diffusion models used in these techniques are prone to viewpoint bias and thus lead to geometric inconsistencies such as the Janus problem. To counter this, we introduce MT3D, a text-to-3D generative model that leverages a high-fidelity 3D object to overcome viewpoint bias and explicitly infuse geometric understanding into the generation pipeline. Firstly, we employ depth maps derived from a high-quality 3D model as control signals to guarantee that the generated 2D images preserve the fundamental shape and structure, thereby reducing the inherent viewpoint bias. Next, we utilize deep geometric moments to ensure geometric consistency in the 3D representation explicitly. By incorporating geometric details from a 3D asset, MT3D enables the creation of diverse and geometrically consistent objects, thereby improving the quality and usability of our 3D representations.

Learning a dense 3D model with fine-scale details from a single facial image is highly challenging and ill-posed. To address this problem, many approaches fit smooth geometries through facial prior while learning details as additional displacement maps or personalized basis. However, these techniques typically require vast datasets of paired multi-view data or 3D scans, whereas such datasets are scarce and expensive. To alleviate heavy data dependency, we present a robust texture-guided geometric detail recovery approach using only a single in-the-wild facial image. More specifically, our method combines high-quality texture completion with the powerful expressiveness of implicit surfaces. Initially, we inpaint occluded facial parts, generate complete textures, and build an accurate multi-view dataset of the same subject. In order to estimate the detailed geometry, we define an implicit signed distance function and employ a physically-based implicit renderer to reconstruct fine geometric details from the generated multi-view images. Our method not only recovers accurate facial details but also decomposes normals, albedos, and shading parts in a self-supervised way. Finally, we register the implicit shape details to a 3D Morphable Model template, which can be used in traditional modeling and rendering pipelines. Extensive experiments demonstrate that the proposed approach can reconstruct impressive facial details from a single image, especially when compared with state-of-the-art methods trained on large datasets.

Large language models (LLMs) have shown remarkable proficiency in human-level reasoning and generation capabilities, which encourages extensive research on their application in mathematical problem solving. However, current work has been largely focused on text-based mathematical problems, with limited investigation in problems involving geometric information. Addressing this gap, we aim to enable LLMs to solve geometric problems by understanding image input. We first analyze the limitations of current Multimodal Large Language Models (MLLMs) in this area: they struggle to accurately comprehending basic geometric elements and their relationships. To overcome these challenges, we take advantage of the unique characteristics of geometric problems (such as unique geometric logical form, and geometric scalability) and the capacity of the textual LLMs to build an enriched multimodal geometry dataset based on existing data. The augmented dataset, Geo170K, contains more than 170K geometric image-caption and question-answer pairs. Utilizing our constructed Geo170K dataset, we develop G-LLaVA, which demonstrates exceptional performance in solving geometric problems, significantly outperforming GPT-4-V on the MathVista benchmark with only 7B parameters.

Compositionality, the notion that the meaning of an expression is constructed from the meaning of its parts and syntactic rules, permits the infinite productivity of human language. For the first time, artificial language models (LMs) are able to match human performance in a number of compositional generalization tasks. However, much remains to be understood about the representational mechanisms underlying these abilities. We take a high-level geometric approach to this problem by relating the degree of compositionality in a dataset to the intrinsic dimensionality of its representations under an LM, a measure of feature complexity. We find not only that the degree of dataset compositionality is reflected in representations' intrinsic dimensionality, but that the relationship between compositionality and geometric complexity arises due to learned linguistic features over training. Finally, our analyses reveal a striking contrast between linear and nonlinear dimensionality, showing that they respectively encode formal and semantic aspects of linguistic composition.

The rapid evolution of Multi-modality Large Language Models (MLLMs) is driving significant advancements in visual understanding and generation. Nevertheless, a comprehensive assessment of their capabilities, concerning the fine-grained physical principles especially in geometric optics, remains underexplored. To address this gap, we introduce GOBench, the first benchmark to systematically evaluate MLLMs' ability across two tasks: 1) Generating Optically Authentic Imagery and 2) Understanding Underlying Optical Phenomena. We curates high-quality prompts of geometric optical scenarios and use MLLMs to construct GOBench-Gen-1k dataset.We then organize subjective experiments to assess the generated imagery based on Optical Authenticity, Aesthetic Quality, and Instruction Fidelity, revealing MLLMs' generation flaws that violate optical principles. For the understanding task, we apply crafted evaluation instructions to test optical understanding ability of eleven prominent MLLMs. The experimental results demonstrate that current models face significant challenges in both optical generation and understanding. The top-performing generative model, GPT-4o-Image, cannot perfectly complete all generation tasks, and the best-performing MLLM model, Gemini-2.5Pro, attains a mere 37.35\% accuracy in optical understanding. Database and codes are publicly available at https://github.com/aiben-ch/GOBench.

Brain-computer interfaces (BCIs) offer transformative potential, but decoding neural signals presents significant challenges. The core premise of this paper is built around demonstrating methods to elucidate the underlying low-dimensional geometric structure present in high-dimensional brainwave data in order to assist in downstream BCI-related neural classification tasks. We demonstrate two pipelines related to electroencephalography (EEG) signal processing: (1) a preliminary pipeline removing noise from individual EEG channels, and (2) a downstream manifold learning pipeline uncovering geometric structure across networks of EEG channels. We conduct preliminary validation using two EEG datasets and situate our demonstration in the context of the BCI-relevant imagined digit decoding problem. Our preliminary pipeline uses an attention-based EEG filtration network to extract clean signal from individual EEG channels. Our primary pipeline uses a fast Fourier transform, a Laplacian eigenmap, a discrete analog of Ricci flow via Ollivier's notion of Ricci curvature, and a graph convolutional network to perform dimensionality reduction on high-dimensional multi-channel EEG data in order to enable regularizable downstream classification. Our system achieves competitive performance with existing signal processing and classification benchmarks; we demonstrate a mean test correlation coefficient of >0.95 at 2 dB on semi-synthetic neural denoising and a downstream EEG-based classification accuracy of 0.97 on distinguishing digit- versus non-digit- thoughts. Results are preliminary and our geometric machine learning pipeline should be validated by more extensive follow-up studies; generalizing these results to larger inter-subject sample sizes, different hardware systems, and broader use cases will be crucial.

Geometric ability is a significant challenge for large language models (LLMs) due to the need for advanced spatial comprehension and abstract thinking. Existing datasets primarily evaluate LLMs on their final answers, but they cannot truly measure their true understanding of geometric structures, as LLMs can arrive at correct answers by coincidence. To fill this gap, we introduce the GeomRel dataset, designed to evaluate LLMs' understanding of geometric structures by isolating the core step of geometric relationship identification in problem-solving. Using this benchmark, we conduct thorough evaluations of diverse LLMs and identify key limitations in understanding geometric structures. We further propose the Geometry Chain-of-Thought (GeoCoT) method, which enhances LLMs' ability to identify geometric relationships, resulting in significant performance improvements.

Automatically extracting the geometric content from the hundreds of thousands of diagrams drawn in historical manuscripts would enable historians to study the diffusion of astronomical knowledge on a global scale. However, state-of-the-art vectorization methods, often designed to tackle modern data, are not adapted to the complexity and diversity of historical astronomical diagrams. Our contribution is thus twofold. First, we introduce a unique dataset of 303 astronomical diagrams from diverse traditions, ranging from the XIIth to the XVIIIth century, annotated with more than 3000 line segments, circles and arcs. Second, we develop a model that builds on DINO-DETR to enable the prediction of multiple geometric primitives. We show that it can be trained solely on synthetic data and accurately predict primitives on our challenging dataset. Our approach widely improves over the LETR baseline, which is restricted to lines, by introducing a meaningful parametrization for multiple primitives, jointly training for detection and parameter refinement, using deformable attention and training on rich synthetic data. Our dataset and code are available on our webpage.

Empirically validating new 3D-printing related algorithms and implementations requires testing data representative of inputs encountered in the wild. An ideal benchmarking dataset should not only draw from the same distribution of shapes people print in terms of class (e.g., toys, mechanisms, jewelry), representation type (e.g., triangle soup meshes) and complexity (e.g., number of facets), but should also capture problems and artifacts endemic to 3D printing models (e.g., self-intersections, non-manifoldness). We observe that the contextual and geometric characteristics of 3D printing models differ significantly from those used for computer graphics applications, not to mention standard models (e.g., Stanford bunny, Armadillo, Fertility). We present a new dataset of 10,000 models collected from an online 3D printing model-sharing database. Via analysis of both geometric (e.g., triangle aspect ratios, manifoldness) and contextual (e.g., licenses, tags, classes) characteristics, we demonstrate that this dataset represents a more concise summary of real-world models used for 3D printing compared to existing datasets. To facilitate future research endeavors, we also present an online query interface to select subsets of the dataset according to project-specific characteristics. The complete dataset and per-model statistical data are freely available to the public.

Geometric information in the normalized digital surface models (nDSM) is highly correlated with the semantic class of the land cover. Exploiting two modalities (RGB and nDSM (height)) jointly has great potential to improve the segmentation performance. However, it is still an under-explored field in remote sensing due to the following challenges. First, the scales of existing datasets are relatively small and the diversity of existing datasets is limited, which restricts the ability of validation. Second, there is a lack of unified benchmarks for performance assessment, which leads to difficulties in comparing the effectiveness of different models. Last, sophisticated multi-modal semantic segmentation methods have not been deeply explored for remote sensing data. To cope with these challenges, in this paper, we introduce a new remote-sensing benchmark dataset for multi-modal semantic segmentation based on RGB-Height (RGB-H) data. Towards a fair and comprehensive analysis of existing methods, the proposed benchmark consists of 1) a large-scale dataset including co-registered RGB and nDSM pairs and pixel-wise semantic labels; 2) a comprehensive evaluation and analysis of existing multi-modal fusion strategies for both convolutional and Transformer-based networks on remote sensing data. Furthermore, we propose a novel and effective Transformer-based intermediary multi-modal fusion (TIMF) module to improve the semantic segmentation performance through adaptive token-level multi-modal fusion.The designed benchmark can foster future research on developing new methods for multi-modal learning on remote sensing data. Extensive analyses of those methods are conducted and valuable insights are provided through the experimental results. Code for the benchmark and baselines can be accessed at https://github.com/EarthNets/RSI-MMSegmentation.

Errors in understanding visual information in images (i.e., visual perception errors) remain a major source of mistakes in Large Vision Language Models (LVLMs). While further analysis is essential, there is a deficiency in datasets for evaluating the visual perception of LVLMs. In this work, we introduce VisOnlyQA, a new dataset designed to directly evaluate the visual perception capabilities of LVLMs on questions about geometric and numerical information in scientific figures. Our dataset enables us to analyze the visual perception of LVLMs for fine-grained visual information, independent of other capabilities such as reasoning. The evaluation set of VisOnlyQA includes 1,200 multiple-choice questions in 12 tasks on four categories of figures. We also provide synthetic training data consisting of 70k instances. Our experiments on VisOnlyQA highlight the following findings: (i) 20 LVLMs we evaluate, including GPT-4o and Gemini 1.5 Pro, work poorly on the visual perception tasks in VisOnlyQA, while human performance is nearly perfect. (ii) Fine-tuning on synthetic training data demonstrates the potential for enhancing the visual perception of LVLMs, but observed improvements are limited to certain tasks and specific models. (iii) Stronger language models improve the visual perception of LVLMs. In summary, our experiments suggest that both training data and model architectures should be improved to enhance the visual perception capabilities of LVLMs. The datasets, code, and model responses are provided at https://github.com/psunlpgroup/VisOnlyQA.

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 .

3D cellular image segmentation methods are commonly divided into non-2D-based and 2D-based approaches, the latter reconstructing 3D shapes from the segmentation results of 2D layers. However, errors in 2D results often propagate, leading to oversegmentations in the final 3D results. To tackle this issue, we introduce an interpretable geometric framework that addresses the oversegmentations by correcting the 2D segmentation results based on geometric information from adjacent layers. Leveraging both geometric (layer-to-layer, 2D) and topological (3D shape) features, we use binary classification to determine whether neighboring cells should be stitched. We develop a pre-trained classifier on public plant cell datasets and validate its performance on animal cell datasets, confirming its effectiveness in correcting oversegmentations under the transfer learning setting. Furthermore, we demonstrate that our framework can be extended to correcting oversegmentation on non-2D-based methods. A clear pipeline is provided for end-users to build the pre-trained model to any labeled dataset.

Multimodal large language models (MLLMs) have made significant progress in integrating visual and linguistic understanding. Existing benchmarks typically focus on high-level semantic capabilities, such as scene understanding and visual reasoning, but often overlook a crucial, foundational ability: geometric perception. Geometric perception involves understanding geometric shapes, structures, and spatial relationships, which are essential for supporting higher-level semantic tasks. Despite its importance, this capability remains underexplored in current MLLM research. To address this gap, we introduce GePBench, a novel benchmark designed to assess the geometric perception abilities of MLLMs. Our extensive evaluations reveal that current state-of-the-art MLLMs exhibit significant deficiencies in geometric perception tasks. Furthermore, we show that models trained with GePBench data demonstrate substantial improvements on a wide range of benchmark tasks, highlighting the critical role of geometric perception in enabling advanced multimodal applications. Our code and datasets will be publicly available.

Neural surface representation has demonstrated remarkable success in the areas of novel view synthesis and 3D reconstruction. However, assessing the geometric quality of 3D reconstructions in the absence of ground truth mesh remains a significant challenge, due to its rendering-based optimization process and entangled learning of appearance and geometry with photometric losses. In this paper, we present a novel framework, i.e, GURecon, which establishes a geometric uncertainty field for the neural surface based on geometric consistency. Different from existing methods that rely on rendering-based measurement, GURecon models a continuous 3D uncertainty field for the reconstructed surface, and is learned by an online distillation approach without introducing real geometric information for supervision. Moreover, in order to mitigate the interference of illumination on geometric consistency, a decoupled field is learned and exploited to finetune the uncertainty field. Experiments on various datasets demonstrate the superiority of GURecon in modeling 3D geometric uncertainty, as well as its plug-and-play extension to various neural surface representations and improvement on downstream tasks such as incremental reconstruction. The code and supplementary material are available on the project website: https://zju3dv.github.io/GURecon/.

G-code (Geometric code) or RS-274 is the most widely used computer numerical control (CNC) and 3D printing programming language. G-code provides machine instructions for the movement of the 3D printer, especially for the nozzle, stage, and extrusion of material for extrusion-based additive manufacturing. Currently there does not exist a large repository of curated CAD models along with their corresponding G-code files for additive manufacturing. To address this issue, we present SLICE-100K, a first-of-its-kind dataset of over 100,000 G-code files, along with their tessellated CAD model, LVIS (Large Vocabulary Instance Segmentation) categories, geometric properties, and renderings. We build our dataset from triangulated meshes derived from Objaverse-XL and Thingi10K datasets. We demonstrate the utility of this dataset by finetuning GPT-2 on a subset of the dataset for G-code translation from a legacy G-code format (Sailfish) to a more modern, widely used format (Marlin). SLICE-100K will be the first step in developing a multimodal foundation model for digital manufacturing.

The process of camera calibration involves estimating the intrinsic and extrinsic parameters, which are essential for accurately performing tasks such as 3D reconstruction, object tracking and augmented reality. In this work, we propose a novel constraints-based loss for measuring the intrinsic (focal length: (f_x, f_y) and principal point: (p_x, p_y)) and extrinsic (baseline: (b), disparity: (d), translation: (t_x, t_y, t_z), and rotation specifically pitch: (theta_p)) camera parameters. Our novel constraints are based on geometric properties inherent in the camera model, including the anatomy of the projection matrix (vanishing points, image of world origin, axis planes) and the orthonormality of the rotation matrix. Thus we proposed a novel Unsupervised Geometric Constraint Loss (UGCL) via a multitask learning framework. Our methodology is a hybrid approach that employs the learning power of a neural network to estimate the desired parameters along with the underlying mathematical properties inherent in the camera projection matrix. This distinctive approach not only enhances the interpretability of the model but also facilitates a more informed learning process. Additionally, we introduce a new CVGL Camera Calibration dataset, featuring over 900 configurations of camera parameters, incorporating 63,600 image pairs that closely mirror real-world conditions. By training and testing on both synthetic and real-world datasets, our proposed approach demonstrates improvements across all parameters when compared to the state-of-the-art (SOTA) benchmarks. The code and the updated dataset can be found here: https://github.com/CVLABLUMS/CVGL-Camera-Calibration

This paper introduces a novel approach to evaluating deep learning models' capacity for in-diagram logic interpretation. Leveraging the intriguing realm of visual illusions, we establish a unique dataset, InDL, designed to rigorously test and benchmark these models. Deep learning has witnessed remarkable progress in domains such as computer vision and natural language processing. However, models often stumble in tasks requiring logical reasoning due to their inherent 'black box' characteristics, which obscure the decision-making process. Our work presents a new lens to understand these models better by focusing on their handling of visual illusions -- a complex interplay of perception and logic. We utilize six classic geometric optical illusions to create a comparative framework between human and machine visual perception. This methodology offers a quantifiable measure to rank models, elucidating potential weaknesses and providing actionable insights for model improvements. Our experimental results affirm the efficacy of our benchmarking strategy, demonstrating its ability to effectively rank models based on their logic interpretation ability. As part of our commitment to reproducible research, the source code and datasets will be made publicly available at https://github.com/rabbit-magic-wh/InDL

The CLEVR dataset has been used extensively in language grounded visual reasoning in Machine Learning (ML) and Natural Language Processing (NLP) domains. We present a graph parser library for CLEVR, that provides functionalities for object-centric attributes and relationships extraction, and construction of structural graph representations for dual modalities. Structural order-invariant representations enable geometric learning and can aid in downstream tasks like language grounding to vision, robotics, compositionality, interpretability, and computational grammar construction. We provide three extensible main components - parser, embedder, and visualizer that can be tailored to suit specific learning setups. We also provide out-of-the-box functionality for seamless integration with popular deep graph neural network (GNN) libraries. Additionally, we discuss downstream usage and applications of the library, and how it accelerates research for the NLP research community.

The integration of geometric reconstruction and generative modeling remains a critical challenge in developing AI systems capable of human-like spatial reasoning. This paper proposes Aether, a unified framework that enables geometry-aware reasoning in world models by jointly optimizing three core capabilities: (1) 4D dynamic reconstruction, (2) action-conditioned video prediction, and (3) goal-conditioned visual planning. Through task-interleaved feature learning, Aether achieves synergistic knowledge sharing across reconstruction, prediction, and planning objectives. Building upon video generation models, our framework demonstrates unprecedented synthetic-to-real generalization despite never observing real-world data during training. Furthermore, our approach achieves zero-shot generalization in both action following and reconstruction tasks, thanks to its intrinsic geometric modeling. Remarkably, even without real-world data, its reconstruction performance far exceeds that of domain-specific models. Additionally, Aether leverages a geometry-informed action space to seamlessly translate predictions into actions, enabling effective autonomous trajectory planning. We hope our work inspires the community to explore new frontiers in physically-reasonable world modeling and its applications.

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

Multimodal large language models have various practical applications that demand strong reasoning abilities. Despite recent advancements, these models still struggle to solve complex geometric problems. A key challenge stems from the lack of high-quality image-text pair datasets for understanding geometric images. Furthermore, most template-based data synthesis pipelines typically fail to generalize to questions beyond their predefined templates. In this paper, we bridge this gap by introducing a complementary process of Reinforcement Learning with Verifiable Rewards (RLVR) into the data generation pipeline. By adopting RLVR to refine captions for geometric images synthesized from 50 basic geometric relations and using reward signals derived from mathematical problem-solving tasks, our pipeline successfully captures the key features of geometry problem-solving. This enables better task generalization and yields non-trivial improvements. Furthermore, even in out-of-distribution scenarios, the generated dataset enhances the general reasoning capabilities of multimodal large language models, yielding accuracy improvements of 2.8%-4.8% in statistics, arithmetic, algebraic, and numerical tasks with non-geometric input images of MathVista and MathVerse, along with 2.4%-3.9% improvements in Art, Design, Tech, and Engineering tasks in MMMU.

For a language model (LM) to faithfully model human language, it must compress vast, potentially infinite information into relatively few dimensions. We propose analyzing compression in (pre-trained) LMs from two points of view: geometric and information-theoretic. We demonstrate that the two views are highly correlated, such that the intrinsic geometric dimension of linguistic data predicts their coding length under the LM. We then show that, in turn, high compression of a linguistic dataset predicts rapid adaptation to that dataset, confirming that being able to compress linguistic information is an important part of successful LM performance. As a practical byproduct of our analysis, we evaluate a battery of intrinsic dimension estimators for the first time on linguistic data, showing that only some encapsulate the relationship between information-theoretic compression, geometric compression, and ease-of-adaptation.

Benefiting from contrastively trained visual encoders on large-scale natural scene images, Large Multimodal Models (LMMs) have achieved remarkable performance across various visual perception tasks. However, the inherent limitations of contrastive learning upon summarized descriptions fundamentally restrict the capabilities of models in meticulous reasoning, particularly in crucial scenarios of geometric problem-solving. To enhance geometric understanding, we propose a novel hard negative contrastive learning framework for the vision encoder, which combines image-based contrastive learning using generation-based hard negatives created by perturbing diagram generation code, and text-based contrastive learning using rule-based negatives derived from modified geometric descriptions and retrieval-based negatives selected based on caption similarity. We train CLIP using our strong negative learning method, namely MMCLIP (Multimodal Math CLIP), and subsequently train an LMM for geometric problem-solving. Experiments show that our trained model, MMGeoLM, significantly outperforms other open-source models on three geometric reasoning benchmarks. Even with a size of 7B, it can rival powerful closed-source models like GPT-4o. We further study the impact of different negative sample construction methods and the number of negative samples on the geometric reasoning performance of LMM, yielding fruitful conclusions. The code and dataset are available at https://github.com/THU-KEG/MMGeoLM.

Estimating the 6D pose of unseen objects from monocular RGB images remains a challenging problem, especially due to the lack of prior object-specific knowledge. To tackle this issue, we propose RefPose, an innovative approach to object pose estimation that leverages a reference image and geometric correspondence as guidance. RefPose first predicts an initial pose by using object templates to render the reference image and establish the geometric correspondence needed for the refinement stage. During the refinement stage, RefPose estimates the geometric correspondence of the query based on the generated references and iteratively refines the pose through a render-and-compare approach. To enhance this estimation, we introduce a correlation volume-guided attention mechanism that effectively captures correlations between the query and reference images. Unlike traditional methods that depend on pre-defined object models, RefPose dynamically adapts to new object shapes by leveraging a reference image and geometric correspondence. This results in robust performance across previously unseen objects. Extensive evaluation on the BOP benchmark datasets shows that RefPose achieves state-of-the-art results while maintaining a competitive runtime.

Rigging and skinning are essential steps to create realistic 3D animations, often requiring significant expertise and manual effort. Traditional attempts at automating these processes rely heavily on geometric heuristics and often struggle with objects of complex geometry. Recent data-driven approaches show potential for better generality, but are often constrained by limited training data. We present the Anymate Dataset, a large-scale dataset of 230K 3D assets paired with expert-crafted rigging and skinning information -- 70 times larger than existing datasets. Using this dataset, we propose a learning-based auto-rigging framework with three sequential modules for joint, connectivity, and skinning weight prediction. We systematically design and experiment with various architectures as baselines for each module and conduct comprehensive evaluations on our dataset to compare their performance. Our models significantly outperform existing methods, providing a foundation for comparing future methods in automated rigging and skinning. Code and dataset can be found at https://anymate3d.github.io/.

Accurate segmentation of topological tubular structures, such as blood vessels and roads, is crucial in various fields, ensuring accuracy and efficiency in downstream tasks. However, many factors complicate the task, including thin local structures and variable global morphologies. In this work, we note the specificity of tubular structures and use this knowledge to guide our DSCNet to simultaneously enhance perception in three stages: feature extraction, feature fusion, and loss constraint. First, we propose a dynamic snake convolution to accurately capture the features of tubular structures by adaptively focusing on slender and tortuous local structures. Subsequently, we propose a multi-view feature fusion strategy to complement the attention to features from multiple perspectives during feature fusion, ensuring the retention of important information from different global morphologies. Finally, a continuity constraint loss function, based on persistent homology, is proposed to constrain the topological continuity of the segmentation better. Experiments on 2D and 3D datasets show that our DSCNet provides better accuracy and continuity on the tubular structure segmentation task compared with several methods. Our codes will be publicly available.

This paper tries to address a fundamental question in point cloud self-supervised learning: what is a good signal we should leverage to learn features from point clouds without annotations? To answer that, we introduce a point cloud representation learning framework, based on geometric feature reconstruction. In contrast to recent papers that directly adopt masked autoencoder (MAE) and only predict original coordinates or occupancy from masked point clouds, our method revisits differences between images and point clouds and identifies three self-supervised learning objectives peculiar to point clouds, namely centroid prediction, normal estimation, and curvature prediction. Combined with occupancy prediction, these four objectives yield an nontrivial self-supervised learning task and mutually facilitate models to better reason fine-grained geometry of point clouds. Our pipeline is conceptually simple and it consists of two major steps: first, it randomly masks out groups of points, followed by a Transformer-based point cloud encoder; second, a lightweight Transformer decoder predicts centroid, normal, and curvature for points in each voxel. We transfer the pre-trained Transformer encoder to a downstream peception model. On the nuScene Datset, our model achieves 3.38 mAP improvment for object detection, 2.1 mIoU gain for segmentation, and 1.7 AMOTA gain for multi-object tracking. We also conduct experiments on the Waymo Open Dataset and achieve significant performance improvements over baselines as well.

While haircut indicates distinct personality, existing avatar generation methods fail to model practical hair due to the general or entangled representation. We propose StrandHead, a novel text to 3D head avatar generation method capable of generating disentangled 3D hair with strand representation. Without using 3D data for supervision, we demonstrate that realistic hair strands can be generated from prompts by distilling 2D generative diffusion models. To this end, we propose a series of reliable priors on shape initialization, geometric primitives, and statistical haircut features, leading to a stable optimization and text-aligned performance. Extensive experiments show that StrandHead achieves the state-of-the-art reality and diversity of generated 3D head and hair. The generated 3D hair can also be easily implemented in the Unreal Engine for physical simulation and other applications. The code will be available at https://xiaokunsun.github.io/StrandHead.github.io.

The advancement of autonomous driving is increasingly reliant on high-quality annotated datasets, especially in the task of 3D occupancy prediction, where the occupancy labels require dense 3D annotation with significant human effort. In this paper, we propose SyntheOcc, which denotes a diffusion model that Synthesize photorealistic and geometric-controlled images by conditioning Occupancy labels in driving scenarios. This yields an unlimited amount of diverse, annotated, and controllable datasets for applications like training perception models and simulation. SyntheOcc addresses the critical challenge of how to efficiently encode 3D geometric information as conditional input to a 2D diffusion model. Our approach innovatively incorporates 3D semantic multi-plane images (MPIs) to provide comprehensive and spatially aligned 3D scene descriptions for conditioning. As a result, SyntheOcc can generate photorealistic multi-view images and videos that faithfully align with the given geometric labels (semantics in 3D voxel space). Extensive qualitative and quantitative evaluations of SyntheOcc on the nuScenes dataset prove its effectiveness in generating controllable occupancy datasets that serve as an effective data augmentation to perception models.

Recent years have witnessed significant progress in developing efficient training and fast sampling approaches for diffusion models. A recent remarkable advancement is the use of stochastic differential equations (SDEs) to describe data perturbation and generative modeling in a unified mathematical framework. In this paper, we reveal several intriguing geometric structures of diffusion models and contribute a simple yet powerful interpretation to their sampling dynamics. Through carefully inspecting a popular variance-exploding SDE and its marginal-preserving ordinary differential equation (ODE) for sampling, we discover that the data distribution and the noise distribution are smoothly connected with an explicit, quasi-linear sampling trajectory, and another implicit denoising trajectory, which even converges faster in terms of visual quality. We also establish a theoretical relationship between the optimal ODE-based sampling and the classic mean-shift (mode-seeking) algorithm, with which we can characterize the asymptotic behavior of diffusion models and identify the score deviation. These new geometric observations enable us to improve previous sampling algorithms, re-examine latent interpolation, as well as re-explain the working principles of distillation-based fast sampling techniques.

A triangular mesh is one of the most popular 3D data representations. As such, the deployment of deep neural networks for mesh processing is widely spread and is increasingly attracting more attention. However, neural networks are prone to adversarial attacks, where carefully crafted inputs impair the model's functionality. The need to explore these vulnerabilities is a fundamental factor in the future development of 3D-based applications. Recently, mesh attacks were studied on the semantic level, where classifiers are misled to produce wrong predictions. Nevertheless, mesh surfaces possess complex geometric attributes beyond their semantic meaning, and their analysis often includes the need to encode and reconstruct the geometry of the shape. We propose a novel framework for a geometric adversarial attack on a 3D mesh autoencoder. In this setting, an adversarial input mesh deceives the autoencoder by forcing it to reconstruct a different geometric shape at its output. The malicious input is produced by perturbing a clean shape in the spectral domain. Our method leverages the spectral decomposition of the mesh along with additional mesh-related properties to obtain visually credible results that consider the delicacy of surface distortions. Our code is publicly available at https://github.com/StolikTomer/SAGA.

Cosmological simulations provide a wealth of data in the form of point clouds and directed trees. A crucial goal is to extract insights from this data that shed light on the nature and composition of the Universe. In this paper we introduce CosmoBench, a benchmark dataset curated from state-of-the-art cosmological simulations whose runs required more than 41 million core-hours and generated over two petabytes of data. CosmoBench is the largest dataset of its kind: it contains 34 thousand point clouds from simulations of dark matter halos and galaxies at three different length scales, as well as 25 thousand directed trees that record the formation history of halos on two different time scales. The data in CosmoBench can be used for multiple tasks -- to predict cosmological parameters from point clouds and merger trees, to predict the velocities of individual halos and galaxies from their collective positions, and to reconstruct merger trees on finer time scales from those on coarser time scales. We provide several baselines on these tasks, some based on established approaches from cosmological modeling and others rooted in machine learning. For the latter, we study different approaches -- from simple linear models that are minimally constrained by symmetries to much larger and more computationally-demanding models in deep learning, such as graph neural networks. We find that least-squares fits with a handful of invariant features sometimes outperform deep architectures with many more parameters and far longer training times. Still there remains tremendous potential to improve these baselines by combining machine learning and cosmology to fully exploit the data. CosmoBench sets the stage for bridging cosmology and geometric deep learning at scale. We invite the community to push the frontier of scientific discovery by engaging with this dataset, available at https://cosmobench.streamlit.app

We present layered ray intersections (LaRI), a new method for unseen geometry reasoning from a single image. Unlike conventional depth estimation that is limited to the visible surface, LaRI models multiple surfaces intersected by the camera rays using layered point maps. Benefiting from the compact and layered representation, LaRI enables complete, efficient, and view-aligned geometric reasoning to unify object- and scene-level tasks. We further propose to predict the ray stopping index, which identifies valid intersecting pixels and layers from LaRI's output. We build a complete training data generation pipeline for synthetic and real-world data, including 3D objects and scenes, with necessary data cleaning steps and coordination between rendering engines. As a generic method, LaRI's performance is validated in two scenarios: It yields comparable object-level results to the recent large generative model using 4% of its training data and 17% of its parameters. Meanwhile, it achieves scene-level occluded geometry reasoning in only one feed-forward.

Diffusion models are among the most effective methods for image generation. This is in particular because, unlike GANs, they can be easily conditioned during training to produce elements with desired class or properties. However, guiding a pre-trained diffusion model to generate elements from previously unlabeled data is significantly more challenging. One of the possible solutions was given by the ADM-G guiding approach. Although ADM-G successfully generates elements from the given class, there is a significant quality gap compared to a model originally conditioned on this class. In particular, the FID score obtained by the ADM-G-guided diffusion model is nearly three times lower than the class-conditioned guidance. We demonstrate that this issue is partly due to ADM-G providing minimal guidance during the final stage of the denoising process. To address this problem, we propose GeoGuide, a guidance model based on tracing the distance of the diffusion model's trajectory from the data manifold. The main idea of GeoGuide is to produce normalized adjustments during the backward denoising process. As shown in the experiments, GeoGuide surpasses the probabilistic approach ADM-G with respect to both the FID scores and the quality of the generated images.

Much of the success of deep learning is drawn from building architectures that properly respect underlying symmetry and structure in the data on which they operate - a set of considerations that have been united under the banner of geometric deep learning. Often problems in the physical sciences deal with relatively small sets of points in two- or three-dimensional space wherein translation, rotation, and permutation equivariance are important or even vital for models to be useful in practice. In this work, we present rotation- and permutation-equivariant architectures for deep learning on these small point clouds, composed of a set of products of terms from the geometric algebra and reductions over those products using an attention mechanism. The geometric algebra provides valuable mathematical structure by which to combine vector, scalar, and other types of geometric inputs in a systematic way to account for rotation invariance or covariance, while attention yields a powerful way to impose permutation equivariance. We demonstrate the usefulness of these architectures by training models to solve sample problems relevant to physics, chemistry, and biology.

We introduce ResPlan, a large-scale dataset of 17,000 detailed, structurally rich, and realistic residential floor plans, created to advance spatial AI research. Each plan includes precise annotations of architectural elements (walls, doors, windows, balconies) and functional spaces (such as kitchens, bedrooms, and bathrooms). ResPlan addresses key limitations of existing datasets such as RPLAN (Wu et al., 2019) and MSD (van Engelenburg et al., 2024) by offering enhanced visual fidelity and greater structural diversity, reflecting realistic and non-idealized residential layouts. Designed as a versatile, general-purpose resource, ResPlan supports a wide range of applications including robotics, reinforcement learning, generative AI, virtual and augmented reality, simulations, and game development. Plans are provided in both geometric and graph-based formats, enabling direct integration into simulation engines and fast 3D conversion. A key contribution is an open-source pipeline for geometry cleaning, alignment, and annotation refinement. Additionally, ResPlan includes structured representations of room connectivity, supporting graph-based spatial reasoning tasks. Finally, we present comparative analyses with existing benchmarks and outline several open benchmark tasks enabled by ResPlan. Ultimately, ResPlan offers a significant advance in scale, realism, and usability, providing a robust foundation for developing and benchmarking next-generation spatial intelligence systems.

Logical page segmentation is an important step in document analysis, enabling better semantic representations, information retrieval, and text understanding. Previous approaches define logical segmentation either through text or geometric objects, relying on OCR or precise geometry. To avoid the need for OCR, we define the task purely as segmentation in the image domain. Furthermore, to ensure the evaluation remains unaffected by geometrical variations that do not impact text segmentation, we propose to use only foreground text pixels in the evaluation metric and disregard all background pixels. To support research in logical document segmentation, we introduce TextBite, a dataset of historical Czech documents spanning the 18th to 20th centuries, featuring diverse layouts from newspapers, dictionaries, and handwritten records. The dataset comprises 8,449 page images with 78,863 annotated segments of logically and thematically coherent text. We propose a set of baseline methods combining text region detection and relation prediction. The dataset, baselines and evaluation framework can be accessed at https://github.com/DCGM/textbite-dataset.

Accurate 3D geometric perception is an important prerequisite for a wide range of spatial AI systems. While state-of-the-art methods depend on large-scale training data, acquiring consistent and precise 3D annotations from in-the-wild videos remains a key challenge. In this work, we introduce ViPE, a handy and versatile video processing engine designed to bridge this gap. ViPE efficiently estimates camera intrinsics, camera motion, and dense, near-metric depth maps from unconstrained raw videos. It is robust to diverse scenarios, including dynamic selfie videos, cinematic shots, or dashcams, and supports various camera models such as pinhole, wide-angle, and 360{\deg} panoramas. We have benchmarked ViPE on multiple benchmarks. Notably, it outperforms existing uncalibrated pose estimation baselines by 18%/50% on TUM/KITTI sequences, and runs at 3-5FPS on a single GPU for standard input resolutions. We use ViPE to annotate a large-scale collection of videos. This collection includes around 100K real-world internet videos, 1M high-quality AI-generated videos, and 2K panoramic videos, totaling approximately 96M frames -- all annotated with accurate camera poses and dense depth maps. We open-source ViPE and the annotated dataset with the hope of accelerating the development of spatial AI systems.

LiDAR is an essential sensor for autonomous driving by collecting precise geometric information regarding a scene. %Exploiting this information for perception is interesting as the amount of available data increases. As the performance of various LiDAR perception tasks has improved, generalizations to new environments and sensors has emerged to test these optimized models in real-world conditions. This paper provides a novel dataset, ParisLuco3D, specifically designed for cross-domain evaluation to make it easier to evaluate the performance utilizing various source datasets. Alongside the dataset, online benchmarks for LiDAR semantic segmentation, LiDAR object detection, and LiDAR tracking are provided to ensure a fair comparison across methods. The ParisLuco3D dataset, evaluation scripts, and links to benchmarks can be found at the following website:https://npm3d.fr/parisluco3d

Recent advances in 3D Gaussian Splatting (3DGS) have enabled RGB-only SLAM systems to achieve high-fidelity scene representation. However, the heavy reliance of existing systems on photometric rendering loss for camera tracking undermines their robustness, especially in unbounded outdoor environments with severe viewpoint and illumination changes. To address these challenges, we propose TVG-SLAM, a robust RGB-only 3DGS SLAM system that leverages a novel tri-view geometry paradigm to ensure consistent tracking and high-quality mapping. We introduce a dense tri-view matching module that aggregates reliable pairwise correspondences into consistent tri-view matches, forming robust geometric constraints across frames. For tracking, we propose Hybrid Geometric Constraints, which leverage tri-view matches to construct complementary geometric cues alongside photometric loss, ensuring accurate and stable pose estimation even under drastic viewpoint shifts and lighting variations. For mapping, we propose a new probabilistic initialization strategy that encodes geometric uncertainty from tri-view correspondences into newly initialized Gaussians. Additionally, we design a Dynamic Attenuation of Rendering Trust mechanism to mitigate tracking drift caused by mapping latency. Experiments on multiple public outdoor datasets show that our TVG-SLAM outperforms prior RGB-only 3DGS-based SLAM systems. Notably, in the most challenging dataset, our method improves tracking robustness, reducing the average Absolute Trajectory Error (ATE) by 69.0\% while achieving state-of-the-art rendering quality. The implementation of our method will be released as open-source.

Stellarators are magnetic confinement devices under active development to deliver steady-state carbon-free fusion energy. Their design involves a high-dimensional, constrained optimization problem that requires expensive physics simulations and significant domain expertise. Recent advances in plasma physics and open-source tools have made stellarator optimization more accessible. However, broader community progress is currently bottlenecked by the lack of standardized optimization problems with strong baselines and datasets that enable data-driven approaches, particularly for quasi-isodynamic (QI) stellarator configurations, considered as a promising path to commercial fusion due to their inherent resilience to current-driven disruptions. Here, we release an open dataset of diverse QI-like stellarator plasma boundary shapes, paired with their ideal magnetohydrodynamic (MHD) equilibria and performance metrics. We generated this dataset by sampling a variety of QI fields and optimizing corresponding stellarator plasma boundaries. We introduce three optimization benchmarks of increasing complexity: (1) a single-objective geometric optimization problem, (2) a "simple-to-build" QI stellarator, and (3) a multi-objective ideal-MHD stable QI stellarator that investigates trade-offs between compactness and coil simplicity. For every benchmark, we provide reference code, evaluation scripts, and strong baselines based on classical optimization techniques. Finally, we show how learned models trained on our dataset can efficiently generate novel, feasible configurations without querying expensive physics oracles. By openly releasing the dataset along with benchmark problems and baselines, we aim to lower the entry barrier for optimization and machine learning researchers to engage in stellarator design and to accelerate cross-disciplinary progress toward bringing fusion energy to the grid.

Timber represents an increasingly valuable and versatile resource. However, forestry operations such as harvesting, handling and measuring logs still require substantial human labor in remote environments posing significant safety risks. Progressively automating these tasks has the potential of increasing their efficiency as well as safety, but requires an accurate detection of individual logs as well as live trees and their context. Although initial approaches have been proposed for this challenging application domain, specialized data and algorithms are still too scarce to develop robust solutions. To mitigate this gap, we introduce the TimberVision dataset, consisting of more than 2k annotated RGB images containing a total of 51k trunk components including cut and lateral surfaces, thereby surpassing any existing dataset in this domain in terms of both quantity and detail by a large margin. Based on this data, we conduct a series of ablation experiments for oriented object detection and instance segmentation and evaluate the influence of multiple scene parameters on model performance. We introduce a generic framework to fuse the components detected by our models for both tasks into unified trunk representations. Furthermore, we automatically derive geometric properties and apply multi-object tracking to further enhance robustness. Our detection and tracking approach provides highly descriptive and accurate trunk representations solely from RGB image data, even under challenging environmental conditions. Our solution is suitable for a wide range of application scenarios and can be readily combined with other sensor modalities.

Capturing and maintaining geometric interactions among different body parts is crucial for successful motion retargeting in skinned characters. Existing approaches often overlook body geometries or add a geometry correction stage after skeletal motion retargeting. This results in conflicts between skeleton interaction and geometry correction, leading to issues such as jittery, interpenetration, and contact mismatches. To address these challenges, we introduce a new retargeting framework, MeshRet, which directly models the dense geometric interactions in motion retargeting. Initially, we establish dense mesh correspondences between characters using semantically consistent sensors (SCS), effective across diverse mesh topologies. Subsequently, we develop a novel spatio-temporal representation called the dense mesh interaction (DMI) field. This field, a collection of interacting SCS feature vectors, skillfully captures both contact and non-contact interactions between body geometries. By aligning the DMI field during retargeting, MeshRet not only preserves motion semantics but also prevents self-interpenetration and ensures contact preservation. Extensive experiments on the public Mixamo dataset and our newly-collected ScanRet dataset demonstrate that MeshRet achieves state-of-the-art performance. Code available at https://github.com/abcyzj/MeshRet.

Latent variable collaborative filtering methods have been a standard approach to modelling user-click interactions due to their simplicity and effectiveness. However, there is limited work on analyzing the mathematical properties of these methods in particular on preventing the overfitting towards the identity, and such methods typically utilize loss functions that overlook the geometry between items. In this work, we introduce a notion of generalization gap in collaborative filtering and analyze this with respect to latent collaborative filtering models. We present a geometric upper bound that gives rise to loss functions, and a way to meaningfully utilize the geometry of item-metadata to improve recommendations. We show how these losses can be minimized and gives the recipe to a new latent collaborative filtering algorithm, which we refer to as GeoCF, due to the geometric nature of our results. We then show experimentally that our proposed GeoCF algorithm can outperform other all existing methods on the Movielens20M and Netflix datasets, as well as two large-scale internal datasets. In summary, our work proposes a theoretically sound method which paves a way to better understand generalization of collaborative filtering at large.

Large language models have shown impressive results for multi-hop mathematical reasoning when the input question is only textual. Many mathematical reasoning problems, however, contain both text and image. With the ever-increasing adoption of vision language models (VLMs), understanding their reasoning abilities for such problems is crucial. In this paper, we evaluate the reasoning capabilities of VLMs along various axes through the lens of geometry problems. We procedurally create a synthetic dataset of geometry questions with controllable difficulty levels along multiple axes, thus enabling a systematic evaluation. The empirical results obtained using our benchmark for state-of-the-art VLMs indicate that these models are not as capable in subjects like geometry (and, by generalization, other topics requiring similar reasoning) as suggested by previous benchmarks. This is made especially clear by the construction of our benchmark at various depth levels, since solving higher-depth problems requires long chains of reasoning rather than additional memorized knowledge. We release the dataset for further research in this area.

This is the first paper in a series of work we have accomplished over the past three years. In this paper, we have constructed a consistent formal plane geometry system. This will serve as a crucial bridge between IMO-level plane geometry challenges and readable AI automated reasoning. Within this formal framework, we have been able to seamlessly integrate modern AI models with our formal system. AI is now capable of providing deductive reasoning solutions to IMO-level plane geometry problems, just like handling other natural languages, and these proofs are readable, traceable, and verifiable. We propose the geometry formalization theory (GFT) to guide the development of the geometry formal system. Based on the GFT, we have established the FormalGeo, which consists of 88 geometric predicates and 196 theorems. It can represent, validate, and solve IMO-level geometry problems. we also have crafted the FGPS (formal geometry problem solver) in Python. It serves as both an interactive assistant for verifying problem-solving processes and an automated problem solver. We've annotated the formalgeo7k and formalgeo-imo datasets. The former contains 6,981 (expand to 133,818 through data augmentation) geometry problems, while the latter includes 18 (expand to 2,627 and continuously increasing) IMO-level challenging geometry problems. All annotated problems include detailed formal language descriptions and solutions. Implementation of the formal system and experiments validate the correctness and utility of the GFT. The backward depth-first search method only yields a 2.42% problem-solving failure rate, and we can incorporate deep learning techniques to achieve lower one. The source code of FGPS and datasets are available at https://github.com/BitSecret/FGPS.

The two-stage object pose estimation paradigm first detects semantic keypoints on the image and then estimates the 6D pose by minimizing reprojection errors. Despite performing well on standard benchmarks, existing techniques offer no provable guarantees on the quality and uncertainty of the estimation. In this paper, we inject two fundamental changes, namely conformal keypoint detection and geometric uncertainty propagation, into the two-stage paradigm and propose the first pose estimator that endows an estimation with provable and computable worst-case error bounds. On one hand, conformal keypoint detection applies the statistical machinery of inductive conformal prediction to convert heuristic keypoint detections into circular or elliptical prediction sets that cover the groundtruth keypoints with a user-specified marginal probability (e.g., 90%). Geometric uncertainty propagation, on the other, propagates the geometric constraints on the keypoints to the 6D object pose, leading to a Pose UnceRtainty SEt (PURSE) that guarantees coverage of the groundtruth pose with the same probability. The PURSE, however, is a nonconvex set that does not directly lead to estimated poses and uncertainties. Therefore, we develop RANdom SAmple averaGing (RANSAG) to compute an average pose and apply semidefinite relaxation to upper bound the worst-case errors between the average pose and the groundtruth. On the LineMOD Occlusion dataset we demonstrate: (i) the PURSE covers the groundtruth with valid probabilities; (ii) the worst-case error bounds provide correct uncertainty quantification; and (iii) the average pose achieves better or similar accuracy as representative methods based on sparse keypoints.

Graph neural networks (GNNs) have been used extensively for addressing problems in drug design and discovery. Both ligand and target molecules are represented as graphs with node and edge features encoding information about atomic elements and bonds respectively. Although existing deep learning models perform remarkably well at predicting physicochemical properties and binding affinities, the generation of new molecules with optimized properties remains challenging. Inherently, most GNNs perform poorly in whole-graph representation due to the limitations of the message-passing paradigm. Furthermore, step-by-step graph generation frameworks that use reinforcement learning or other sequential processing can be slow and result in a high proportion of invalid molecules with substantial post-processing needed in order to satisfy the principles of stoichiometry. To address these issues, we propose a representation-first approach to molecular graph generation. We guide the latent representation of an autoencoder by capturing graph structure information with the geometric scattering transform and apply penalties that structure the representation also by molecular properties. We show that this highly structured latent space can be directly used for molecular graph generation by the use of a GAN. We demonstrate that our architecture learns meaningful representations of drug datasets and provides a platform for goal-directed drug synthesis.

We investigate the problem of training generative models on a very sparse collection of 3D models. We use geometrically motivated energies to augment and thus boost a sparse collection of example (training) models. We analyze the Hessian of the as-rigid-as-possible (ARAP) energy to sample from and project to the underlying (local) shape space, and use the augmented dataset to train a variational autoencoder (VAE). We iterate the process of building latent spaces of VAE and augmenting the associated dataset, to progressively reveal a richer and more expressive generative space for creating geometrically and semantically valid samples. Our framework allows us to train generative 3D models even with a small set of good quality 3D models, which are typically hard to curate. We extensively evaluate our method against a set of strong baselines, provide ablation studies and demonstrate application towards establishing shape correspondences. We present multiple examples of interesting and meaningful shape variations even when starting from as few as 3-10 training shapes.

Self-supervised pre-training based on next-token prediction has enabled large language models to capture the underlying structure of text, and has led to unprecedented performance on a large array of tasks when applied at scale. Similarly, autonomous driving generates vast amounts of spatiotemporal data, alluding to the possibility of harnessing scale to learn the underlying geometric and semantic structure of the environment and its evolution over time. In this direction, we propose a geometric and semantic self-supervised pre-training method, GASP, that learns a unified representation by predicting, at any queried future point in spacetime, (1) general occupancy, capturing the evolving structure of the 3D scene; (2) ego occupancy, modeling the ego vehicle path through the environment; and (3) distilled high-level features from a vision foundation model. By modeling geometric and semantic 4D occupancy fields instead of raw sensor measurements, the model learns a structured, generalizable representation of the environment and its evolution through time. We validate GASP on multiple autonomous driving benchmarks, demonstrating significant improvements in semantic occupancy forecasting, online mapping, and ego trajectory prediction. Our results demonstrate that continuous 4D geometric and semantic occupancy prediction provides a scalable and effective pre-training paradigm for autonomous driving. For code and additional visualizations, see \href{https://research.zenseact.com/publications/gasp/.

We present a dataset for investigating the impact of stellar activity on astrometric measurements using NASA's Solar Dynamics Observatory (SDO) images of the Sun. The sensitivity of astrometry for detecting exoplanets is limited by stellar activity (e.g. starspots), which causes the measured "center of flux" of the star to deviate from the true, geometric, center, producing false positive detections. We analyze Helioseismic and Magnetic Imager continuum image data obtained from SDO between July 2015 and December 2022 to examine this "astrometric jitter" phenomenon for the Sun. We employ data processing procedures to clean the images and compute the time series of the sunspot-induced shift between the center of flux and the geometric center. The resulting time series show quasiperiodic variations up to 0.05% of the Sun's radius at its rotation period.

We present PACE, a novel method for modifying motion-captured virtual agents to interact with and move throughout dense, cluttered 3D scenes. Our approach changes a given motion sequence of a virtual agent as needed to adjust to the obstacles and objects in the environment. We first take the individual frames of the motion sequence most important for modeling interactions with the scene and pair them with the relevant scene geometry, obstacles, and semantics such that interactions in the agents motion match the affordances of the scene (e.g., standing on a floor or sitting in a chair). We then optimize the motion of the human by directly altering the high-DOF pose at each frame in the motion to better account for the unique geometric constraints of the scene. Our formulation uses novel loss functions that maintain a realistic flow and natural-looking motion. We compare our method with prior motion generating techniques and highlight the benefits of our method with a perceptual study and physical plausibility metrics. Human raters preferred our method over the prior approaches. Specifically, they preferred our method 57.1% of the time versus the state-of-the-art method using existing motions, and 81.0% of the time versus a state-of-the-art motion synthesis method. Additionally, our method performs significantly higher on established physical plausibility and interaction metrics. Specifically, we outperform competing methods by over 1.2% in terms of the non-collision metric and by over 18% in terms of the contact metric. We have integrated our interactive system with Microsoft HoloLens and demonstrate its benefits in real-world indoor scenes. Our project website is available at https://gamma.umd.edu/pace/.

We introduce GS2E (Gaussian Splatting to Event), a large-scale synthetic event dataset for high-fidelity event vision tasks, captured from real-world sparse multi-view RGB images. Existing event datasets are often synthesized from dense RGB videos, which typically lack viewpoint diversity and geometric consistency, or depend on expensive, difficult-to-scale hardware setups. GS2E overcomes these limitations by first reconstructing photorealistic static scenes using 3D Gaussian Splatting, and subsequently employing a novel, physically-informed event simulation pipeline. This pipeline generally integrates adaptive trajectory interpolation with physically-consistent event contrast threshold modeling. Such an approach yields temporally dense and geometrically consistent event streams under diverse motion and lighting conditions, while ensuring strong alignment with underlying scene structures. Experimental results on event-based 3D reconstruction demonstrate GS2E's superior generalization capabilities and its practical value as a benchmark for advancing event vision research.

In this paper, we introduce MeshGen, an advanced image-to-3D pipeline that generates high-quality 3D meshes with detailed geometry and physically based rendering (PBR) textures. Addressing the challenges faced by existing 3D native diffusion models, such as suboptimal auto-encoder performance, limited controllability, poor generalization, and inconsistent image-based PBR texturing, MeshGen employs several key innovations to overcome these limitations. We pioneer a render-enhanced point-to-shape auto-encoder that compresses meshes into a compact latent space by designing perceptual optimization with ray-based regularization. This ensures that the 3D shapes are accurately represented and reconstructed to preserve geometric details within the latent space. To address data scarcity and image-shape misalignment, we further propose geometric augmentation and generative rendering augmentation techniques, which enhance the model's controllability and generalization ability, allowing it to perform well even with limited public datasets. For the texture generation, MeshGen employs a reference attention-based multi-view ControlNet for consistent appearance synthesis. This is further complemented by our multi-view PBR decomposer that estimates PBR components and a UV inpainter that fills invisible areas, ensuring a seamless and consistent texture across the 3D mesh. Our extensive experiments demonstrate that MeshGen largely outperforms previous methods in both shape and texture generation, setting a new standard for the quality of 3D meshes generated with PBR textures. See our code at https://github.com/heheyas/MeshGen, project page https://heheyas.github.io/MeshGen

We present DrivAerNet++, the largest and most comprehensive multimodal dataset for aerodynamic car design. DrivAerNet++ comprises 8,000 diverse car designs modeled with high-fidelity computational fluid dynamics (CFD) simulations. The dataset includes diverse car configurations such as fastback, notchback, and estateback, with different underbody and wheel designs to represent both internal combustion engines and electric vehicles. Each entry in the dataset features detailed 3D meshes, parametric models, aerodynamic coefficients, and extensive flow and surface field data, along with segmented parts for car classification and point cloud data. This dataset supports a wide array of machine learning applications including data-driven design optimization, generative modeling, surrogate model training, CFD simulation acceleration, and geometric classification. With more than 39 TB of publicly available engineering data, DrivAerNet++ fills a significant gap in available resources, providing high-quality, diverse data to enhance model training, promote generalization, and accelerate automotive design processes. Along with rigorous dataset validation, we also provide ML benchmarking results on the task of aerodynamic drag prediction, showcasing the breadth of applications supported by our dataset. This dataset is set to significantly impact automotive design and broader engineering disciplines by fostering innovation and improving the fidelity of aerodynamic evaluations.

Existing visual parsers for molecule diagrams translate pixel-based raster images such as PNGs to chemical structure representations (e.g., SMILES). However, PDFs created by word processors including LaTeX and Word provide explicit locations and shapes for characters, lines, and polygons. We extract symbols from born-digital PDF molecule images and then apply simple graph transformations to capture both visual and chemical structure in editable ChemDraw files (CDXML). Our fast ( PDF rightarrow visual graph rightarrow chemical graph ) pipeline does not require GPUs, Optical Character Recognition (OCR) or vectorization. We evaluate on standard benchmarks using SMILES strings, along with a novel evaluation that provides graph-based metrics and error compilation using LgEval. The geometric information in born-digital PDFs produces a highly accurate parser, motivating generating training data for visual parsers that recognize from raster images, with extracted graphics, visual structure, and chemical structure as annotations. To do this we render SMILES strings in Indigo, parse molecule structure, and then validate recognized structure to select correct files.

The field of 4D world modeling - aiming to jointly capture spatial geometry and temporal dynamics - has witnessed remarkable progress in recent years, driven by advances in large-scale generative models and multimodal learning. However, the development of truly general 4D world models remains fundamentally constrained by the availability of high-quality data. Existing datasets and benchmarks often lack the dynamic complexity, multi-domain diversity, and spatial-temporal annotations required to support key tasks such as 4D geometric reconstruction, future prediction, and camera-control video generation. To address this gap, we introduce OmniWorld, a large-scale, multi-domain, multi-modal dataset specifically designed for 4D world modeling. OmniWorld consists of a newly collected OmniWorld-Game dataset and several curated public datasets spanning diverse domains. Compared with existing synthetic datasets, OmniWorld-Game provides richer modality coverage, larger scale, and more realistic dynamic interactions. Based on this dataset, we establish a challenging benchmark that exposes the limitations of current state-of-the-art (SOTA) approaches in modeling complex 4D environments. Moreover, fine-tuning existing SOTA methods on OmniWorld leads to significant performance gains across 4D reconstruction and video generation tasks, strongly validating OmniWorld as a powerful resource for training and evaluation. We envision OmniWorld as a catalyst for accelerating the development of general-purpose 4D world models, ultimately advancing machines' holistic understanding of the physical world.

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

The reconstruction of indoor scenes remains challenging due to the inherent complexity of spatial structures and the prevalence of textureless regions. Recent advancements in 3D Gaussian Splatting have improved novel view synthesis with accelerated processing but have yet to deliver comparable performance in surface reconstruction. In this paper, we introduce 2DGS-Room, a novel method leveraging 2D Gaussian Splatting for high-fidelity indoor scene reconstruction. Specifically, we employ a seed-guided mechanism to control the distribution of 2D Gaussians, with the density of seed points dynamically optimized through adaptive growth and pruning mechanisms. To further improve geometric accuracy, we incorporate monocular depth and normal priors to provide constraints for details and textureless regions respectively. Additionally, multi-view consistency constraints are employed to mitigate artifacts and further enhance reconstruction quality. Extensive experiments on ScanNet and ScanNet++ datasets demonstrate that our method achieves state-of-the-art performance in indoor scene reconstruction.

Articulated objects, as prevalent entities in human life, their 3D representations play crucial roles across various applications. However, achieving both high-fidelity textured surface reconstruction and dynamic generation for articulated objects remains challenging for existing methods. In this paper, we present REArtGS, a novel framework that introduces additional geometric and motion constraints to 3D Gaussian primitives, enabling high-quality textured surface reconstruction and generation for articulated objects. Specifically, given multi-view RGB images of arbitrary two states of articulated objects, we first introduce an unbiased Signed Distance Field (SDF) guidance to regularize Gaussian opacity fields, enhancing geometry constraints and improving surface reconstruction quality. Then we establish deformable fields for 3D Gaussians constrained by the kinematic structures of articulated objects, achieving unsupervised generation of surface meshes in unseen states. Extensive experiments on both synthetic and real datasets demonstrate our approach achieves high-quality textured surface reconstruction for given states, and enables high-fidelity surface generation for unseen states. Codes will be released after acceptance and the project website is at https://sites.google.com/view/reartgs/home.

Estimating the 6D pose of objects unseen during training is highly desirable yet challenging. Zero-shot object 6D pose estimation methods address this challenge by leveraging additional task-specific supervision provided by large-scale, photo-realistic synthetic datasets. However, their performance heavily depends on the quality and diversity of rendered data and they require extensive training. In this work, we show how to tackle the same task but without training on specific data. We propose FreeZe, a novel solution that harnesses the capabilities of pre-trained geometric and vision foundation models. FreeZe leverages 3D geometric descriptors learned from unrelated 3D point clouds and 2D visual features learned from web-scale 2D images to generate discriminative 3D point-level descriptors. We then estimate the 6D pose of unseen objects by 3D registration based on RANSAC. We also introduce a novel algorithm to solve ambiguous cases due to geometrically symmetric objects that is based on visual features. We comprehensively evaluate FreeZe across the seven core datasets of the BOP Benchmark, which include over a hundred 3D objects and 20,000 images captured in various scenarios. FreeZe consistently outperforms all state-of-the-art approaches, including competitors extensively trained on synthetic 6D pose estimation data. Code will be publicly available at https://andreacaraffa.github.io/freeze.

Face anti-spoofing (FAS) is indispensable for a face recognition system. Many texture-driven countermeasures were developed against presentation attacks (PAs), but the performance against unseen domains or unseen spoofing types is still unsatisfactory. Instead of exhaustively collecting all the spoofing variations and making binary decisions of live/spoof, we offer a new perspective on the FAS task to distinguish between normal and abnormal movements of live and spoof presentations. We propose Geometry-Aware Interaction Network (GAIN), which exploits dense facial landmarks with spatio-temporal graph convolutional network (ST-GCN) to establish a more interpretable and modularized FAS model. Additionally, with our cross-attention feature interaction mechanism, GAIN can be easily integrated with other existing methods to significantly boost performance. Our approach achieves state-of-the-art performance in the standard intra- and cross-dataset evaluations. Moreover, our model outperforms state-of-the-art methods by a large margin in the cross-dataset cross-type protocol on CASIA-SURF 3DMask (+10.26% higher AUC score), exhibiting strong robustness against domain shifts and unseen spoofing types.

We present the P^3 dataset, a large-scale multimodal benchmark for building vectorization, constructed from aerial LiDAR point clouds, high-resolution aerial imagery, and vectorized 2D building outlines, collected across three continents. The dataset contains over 10 billion LiDAR points with decimeter-level accuracy and RGB images at a ground sampling distance of 25 centimeter. While many existing datasets primarily focus on the image modality, P^3 offers a complementary perspective by also incorporating dense 3D information. We demonstrate that LiDAR point clouds serve as a robust modality for predicting building polygons, both in hybrid and end-to-end learning frameworks. Moreover, fusing aerial LiDAR and imagery further improves accuracy and geometric quality of predicted polygons. The P^3 dataset is publicly available, along with code and pretrained weights of three state-of-the-art models for building polygon prediction at https://github.com/raphaelsulzer/PixelsPointsPolygons .

With Neural Radiance Fields (NeRFs) arising as a powerful 3D representation, research has investigated its various downstream tasks, including inpainting NeRFs with 2D images. Despite successful efforts addressing the view consistency and geometry quality, prior methods yet suffer from occlusion in NeRF inpainting tasks, where 2D prior is severely limited in forming a faithful reconstruction of the scene to inpaint. To address this, we propose a novel approach that enables cross-view information sharing during knowledge distillation from a diffusion model, effectively propagating occluded information across limited views. Additionally, to align the distillation direction across multiple sampled views, we apply a grid-based denoising strategy and incorporate additional rendered views to enhance cross-view consistency. To assess our approach's capability of handling occlusion cases, we construct a dataset consisting of challenging scenes with severe occlusion, in addition to existing datasets. Compared with baseline methods, our method demonstrates better performance in cross-view consistency and faithfulness in reconstruction, while preserving high rendering quality and fidelity.

Image-based 3D generation has vast applications in robotics and gaming, where high-quality, diverse outputs and consistent 3D representations are crucial. However, existing methods have limitations: 3D diffusion models are limited by dataset scarcity and the absence of strong pre-trained priors, while 2D diffusion-based approaches struggle with geometric consistency. We propose a method that leverages 2D diffusion models' implicit 3D reasoning ability while ensuring 3D consistency via Gaussian-splatting-based geometric distillation. Specifically, the proposed Gaussian Splatting Decoder enforces 3D consistency by transforming SV3D latent outputs into an explicit 3D representation. Unlike SV3D, which only relies on implicit 2D representations for video generation, Gaussian Splatting explicitly encodes spatial and appearance attributes, enabling multi-view consistency through geometric constraints. These constraints correct view inconsistencies, ensuring robust geometric consistency. As a result, our approach simultaneously generates high-quality, multi-view-consistent images and accurate 3D models, providing a scalable solution for single-image-based 3D generation and bridging the gap between 2D Diffusion diversity and 3D structural coherence. Experimental results demonstrate state-of-the-art multi-view consistency and strong generalization across diverse datasets. The code will be made publicly available upon acceptance.

Temporal knowledge graphs represent temporal facts (s,p,o,tau) relating a subject s and an object o via a relation label p at time tau, where tau could be a time point or time interval. Temporal knowledge graphs may exhibit static temporal patterns at distinct points in time and dynamic temporal patterns between different timestamps. In order to learn a rich set of static and dynamic temporal patterns and apply them for inference, several embedding approaches have been suggested in the literature. However, as most of them resort to single underlying embedding spaces, their capability to model all kinds of temporal patterns was severely limited by having to adhere to the geometric property of their one embedding space. We lift this limitation by an embedding approach that maps temporal facts into a product space of several heterogeneous geometric subspaces with distinct geometric properties, i.e.\ Complex, Dual, and Split-complex spaces. In addition, we propose a temporal-geometric attention mechanism to integrate information from different geometric subspaces conveniently according to the captured relational and temporal information. Experimental results on standard temporal benchmark datasets favorably evaluate our approach against state-of-the-art models.

The recent integration of deep learning and pairwise similarity annotation-based constrained clustering -- i.e., deep constrained clustering (DCC) -- has proven effective for incorporating weak supervision into massive data clustering: Less than 1% of pair similarity annotations can often substantially enhance the clustering accuracy. However, beyond empirical successes, there is a lack of understanding of DCC. In addition, many DCC paradigms are sensitive to annotation noise, but performance-guaranteed noisy DCC methods have been largely elusive. This work first takes a deep look into a recently emerged logistic loss function of DCC, and characterizes its theoretical properties. Our result shows that the logistic DCC loss ensures the identifiability of data membership under reasonable conditions, which may shed light on its effectiveness in practice. Building upon this understanding, a new loss function based on geometric factor analysis is proposed to fend against noisy annotations. It is shown that even under unknown annotation confusions, the data membership can still be provably identified under our proposed learning criterion. The proposed approach is tested over multiple datasets to validate our claims.

In document image rectification, there exist rich geometric constraints between the distorted image and the ground truth one. However, such geometric constraints are largely ignored in existing advanced solutions, which limits the rectification performance. To this end, we present DocGeoNet for document image rectification by introducing explicit geometric representation. Technically, two typical attributes of the document image are involved in the proposed geometric representation learning, i.e., 3D shape and textlines. Our motivation arises from the insight that 3D shape provides global unwarping cues for rectifying a distorted document image while overlooking the local structure. On the other hand, textlines complementarily provide explicit geometric constraints for local patterns. The learned geometric representation effectively bridges the distorted image and the ground truth one. Extensive experiments show the effectiveness of our framework and demonstrate the superiority of our DocGeoNet over state-of-the-art methods on both the DocUNet Benchmark dataset and our proposed DIR300 test set. The code is available at https://github.com/fh2019ustc/DocGeoNet.

Geometric alignment appears in a variety of applications, ranging from domain adaptation, optimal transport, and normalizing flows in machine learning; optical flow and learned augmentation in computer vision and deformable registration within biomedical imaging. A recurring challenge is the alignment of domains whose topology is not the same; a problem that is routinely ignored, potentially introducing bias in downstream analysis. As a first step towards solving such alignment problems, we propose an unsupervised algorithm for the detection of changes in image topology. The model is based on a conditional variational auto-encoder and detects topological changes between two images during the registration step. We account for both topological changes in the image under spatial variation and unexpected transformations. Our approach is validated on two tasks and datasets: detection of topological changes in microscopy images of cells, and unsupervised anomaly detection brain imaging.

Datasets have gained an enormous amount of popularity in the computer vision community, from training and evaluation of Deep Learning-based methods to benchmarking Simultaneous Localization and Mapping (SLAM). Without a doubt, synthetic imagery bears a vast potential due to scalability in terms of amounts of data obtainable without tedious manual ground truth annotations or measurements. Here, we present a dataset with the aim of providing a higher degree of photo-realism, larger scale, more variability as well as serving a wider range of purposes compared to existing datasets. Our dataset leverages the availability of millions of professional interior designs and millions of production-level furniture and object assets -- all coming with fine geometric details and high-resolution texture. We render high-resolution and high frame-rate video sequences following realistic trajectories while supporting various camera types as well as providing inertial measurements. Together with the release of the dataset, we will make executable program of our interactive simulator software as well as our renderer available at https://interiornetdataset.github.io. To showcase the usability and uniqueness of our dataset, we show benchmarking results of both sparse and dense SLAM algorithms.

We introduce Geo4D, a method to repurpose video diffusion models for monocular 3D reconstruction of dynamic scenes. By leveraging the strong dynamic prior captured by such video models, Geo4D can be trained using only synthetic data while generalizing well to real data in a zero-shot manner. Geo4D predicts several complementary geometric modalities, namely point, depth, and ray maps. It uses a new multi-modal alignment algorithm to align and fuse these modalities, as well as multiple sliding windows, at inference time, thus obtaining robust and accurate 4D reconstruction of long videos. Extensive experiments across multiple benchmarks show that Geo4D significantly surpasses state-of-the-art video depth estimation methods, including recent methods such as MonST3R, which are also designed to handle dynamic scenes.

Recent advances in multimodal large language models (MLLMs) have shown impressive reasoning capabilities. However, further enhancing existing MLLMs necessitates high-quality vision-language datasets with carefully curated task complexities, which are both costly and challenging to scale. Although recent self-improving models that iteratively refine themselves offer a feasible solution, they still suffer from two core challenges: (i) most existing methods augment visual or textual data separately, resulting in discrepancies in data complexity (e.g., over-simplified diagrams paired with redundant textual descriptions); and (ii) the evolution of data and models is also separated, leading to scenarios where models are exposed to tasks with mismatched difficulty levels. To address these issues, we propose C2-Evo, an automatic, closed-loop self-improving framework that jointly evolves both training data and model capabilities. Specifically, given a base dataset and a base model, C2-Evo enhances them by a cross-modal data evolution loop and a data-model evolution loop. The former loop expands the base dataset by generating complex multimodal problems that combine structured textual sub-problems with iteratively specified geometric diagrams, while the latter loop adaptively selects the generated problems based on the performance of the base model, to conduct supervised fine-tuning and reinforcement learning alternately. Consequently, our method continuously refines its model and training data, and consistently obtains considerable performance gains across multiple mathematical reasoning benchmarks. Our code, models, and datasets will be released.

The scarcity of annotations poses a significant challenge in medical image analysis. Large-scale pre-training has emerged as a promising label-efficient solution, owing to the utilization of large-scale data, large models, and advanced pre-training techniques. However, its development in medical images remains underexplored. The primary challenge lies in harnessing large-scale unlabeled data and learning high-level semantics without annotations. We observe that 3D medical images exhibit consistent geometric context, i.e., consistent geometric relations between different organs, which leads to a promising way for learning consistent representations. Motivated by this, we introduce a simple-yet-effective Volume Contrast (VoCo) framework to leverage geometric context priors for self-supervision. Given an input volume, we extract base crops from different regions to construct positive and negative pairs for contrastive learning. Then we predict the contextual position of a random crop by contrasting its similarity to the base crops. In this way, VoCo encodes the inherent geometric context into model representations, facilitating high-level semantic learning without annotations. Specifically, we (1) introduce the largest medical pre-training dataset PreCT-160K; (2) investigate scaling laws and propose guidelines for tailoring different model sizes to various medical tasks; (3) build a benchmark encompassing 48 medical tasks. Extensive experiments highlight the superiority of VoCo. Codes at https://github.com/Luffy03/Large-Scale-Medical.

Deep learning approaches have provided state-of-the-art performance in many applications by relying on large and overparameterized neural networks. However, such networks have been shown to be very brittle and are difficult to deploy on resource-limited platforms. Model pruning, i.e., reducing the size of the network, is a widely adopted strategy that can lead to a more robust and compact model. Many heuristics exist for model pruning, but empirical studies show that some heuristics improve performance whereas others can make models more brittle or have other side effects. This work aims to shed light on how different pruning methods alter the network's internal feature representation and the corresponding impact on model performance. To facilitate a comprehensive comparison and characterization of the high-dimensional model feature space, we introduce a visual geometric analysis of feature representations. We decomposed and evaluated a set of critical geometric concepts from the common adopted classification loss, and used them to design a visualization system to compare and highlight the impact of pruning on model performance and feature representation. The proposed tool provides an environment for in-depth comparison of pruning methods and a comprehensive understanding of how model response to common data corruption. By leveraging the proposed visualization, machine learning researchers can reveal the similarities between pruning methods and redundant in robustness evaluation benchmarks, obtain geometric insights about the differences between pruned models that achieve superior robustness performance, and identify samples that are robust or fragile to model pruning and common data corruption to model pruning and data corruption but also obtain insights and explanations on how some pruned models achieve superior robustness performance.

Deep neural networks remain vulnerable to adversarial examples despite advances in architectures and training paradigms. We investigate how training data characteristics affect adversarial robustness across 36 state-of-the-art vision models spanning supervised, self-supervised, and contrastive learning approaches, trained on datasets from 1.2M to 22B images. Models were evaluated under six black-box attack categories: random perturbations, two types of geometric masks, COCO object manipulations, ImageNet-C corruptions, and ImageNet-R style shifts. Robustness follows a logarithmic scaling law with both data volume and model size: a tenfold increase in data reduces attack success rate (ASR) on average by ~3.2%, whereas a tenfold increase in model size reduces ASR on average by ~13.4%. Notably, some self-supervised models trained on curated datasets, such as DINOv2, outperform others trained on much larger but less curated datasets, challenging the assumption that scale alone drives robustness. Adversarial fine-tuning of ResNet50s improves generalization across structural variations but not across color distributions. Human evaluation reveals persistent gaps between human and machine vision. These results show that while scaling improves robustness, data quality, architecture, and training objectives play a more decisive role than raw scale in achieving broad-spectrum adversarial resilience.

FourCastNet 3 advances global weather modeling by implementing a scalable, geometric machine learning (ML) approach to probabilistic ensemble forecasting. The approach is designed to respect spherical geometry and to accurately model the spatially correlated probabilistic nature of the problem, resulting in stable spectra and realistic dynamics across multiple scales. FourCastNet 3 delivers forecasting accuracy that surpasses leading conventional ensemble models and rivals the best diffusion-based methods, while producing forecasts 8 to 60 times faster than these approaches. In contrast to other ML approaches, FourCastNet 3 demonstrates excellent probabilistic calibration and retains realistic spectra, even at extended lead times of up to 60 days. All of these advances are realized using a purely convolutional neural network architecture tailored for spherical geometry. Scalable and efficient large-scale training on 1024 GPUs and more is enabled by a novel training paradigm for combined model- and data-parallelism, inspired by domain decomposition methods in classical numerical models. Additionally, FourCastNet 3 enables rapid inference on a single GPU, producing a 60-day global forecast at 0.25{\deg}, 6-hourly resolution in under 4 minutes. Its computational efficiency, medium-range probabilistic skill, spectral fidelity, and rollout stability at subseasonal timescales make it a strong candidate for improving meteorological forecasting and early warning systems through large ensemble predictions.

Real-world data collection for robotics is costly and resource-intensive, requiring skilled operators and expensive hardware. Simulations offer a scalable alternative but often fail to achieve sim-to-real generalization due to geometric and visual gaps. To address these challenges, we propose a 3D-photorealistic real-to-sim system, namely, RE^3SIM, addressing geometric and visual sim-to-real gaps. RE^3SIM employs advanced 3D reconstruction and neural rendering techniques to faithfully recreate real-world scenarios, enabling real-time rendering of simulated cross-view cameras within a physics-based simulator. By utilizing privileged information to collect expert demonstrations efficiently in simulation, and train robot policies with imitation learning, we validate the effectiveness of the real-to-sim-to-real pipeline across various manipulation task scenarios. Notably, with only simulated data, we can achieve zero-shot sim-to-real transfer with an average success rate exceeding 58%. To push the limit of real-to-sim, we further generate a large-scale simulation dataset, demonstrating how a robust policy can be built from simulation data that generalizes across various objects. Codes and demos are available at: http://xshenhan.github.io/Re3Sim/.

While impressive progress has recently been made in image-oriented facial attribute translation, shape-oriented 3D facial attribute translation remains an unsolved issue. This is primarily limited by the lack of 3D generative models and ineffective usage of 3D facial data. We propose a learning framework for 3D facial attribute translation to relieve these limitations. Firstly, we customize a novel geometric map for 3D shape representation and embed it in an end-to-end generative adversarial network. The geometric map represents 3D shapes symmetrically on a square image grid, while preserving the neighboring relationship of 3D vertices in a local least-square sense. This enables effective learning for the latent representation of data with different attributes. Secondly, we employ a unified and unpaired learning framework for multi-domain attribute translation. It not only makes effective usage of data correlation from multiple domains, but also mitigates the constraint for hardly accessible paired data. Finally, we propose a hierarchical architecture for the discriminator to guarantee robust results against both global and local artifacts. We conduct extensive experiments to demonstrate the advantage of the proposed framework over the state-of-the-art in generating high-fidelity facial shapes. Given an input 3D facial shape, the proposed framework is able to synthesize novel shapes of different attributes, which covers some downstream applications, such as expression transfer, gender translation, and aging. Code at https://github.com/NaughtyZZ/3D_facial_shape_attribute_translation_ssgmap.

This paper introduces a new interpretation of the Variational Autoencoder framework by taking a fully geometric point of view. We argue that vanilla VAE models unveil naturally a Riemannian structure in their latent space and that taking into consideration those geometrical aspects can lead to better interpolations and an improved generation procedure. This new proposed sampling method consists in sampling from the uniform distribution deriving intrinsically from the learned Riemannian latent space and we show that using this scheme can make a vanilla VAE competitive and even better than more advanced versions on several benchmark datasets. Since generative models are known to be sensitive to the number of training samples we also stress the method's robustness in the low data regime.

Every hour, huge amounts of visual contents are posted on social media and user-generated content platforms. To find relevant videos by means of a natural language query, text-video retrieval methods have received increased attention over the past few years. Data augmentation techniques were introduced to increase the performance on unseen test examples by creating new training samples with the application of semantics-preserving techniques, such as color space or geometric transformations on images. Yet, these techniques are usually applied on raw data, leading to more resource-demanding solutions and also requiring the shareability of the raw data, which may not always be true, e.g. copyright issues with clips from movies or TV series. To address this shortcoming, we propose a multimodal data augmentation technique which works in the feature space and creates new videos and captions by mixing semantically similar samples. We experiment our solution on a large scale public dataset, EPIC-Kitchens-100, and achieve considerable improvements over a baseline method, improved state-of-the-art performance, while at the same time performing multiple ablation studies. We release code and pretrained models on Github at https://github.com/aranciokov/FSMMDA_VideoRetrieval.

When facing data with imbalanced classes or groups, practitioners follow an intriguing strategy to achieve best results. They throw away examples until the classes or groups are balanced in size, and then perform empirical risk minimization on the reduced training set. This opposes common wisdom in learning theory, where the expected error is supposed to decrease as the dataset grows in size. In this work, we leverage extreme value theory to address this apparent contradiction. Our results show that the tails of the data distribution play an important role in determining the worst-group-accuracy of linear classifiers. When learning on data with heavy tails, throwing away data restores the geometric symmetry of the resulting classifier, and therefore improves its worst-group generalization.

We study a version of adversarial classification where an adversary is empowered to corrupt data inputs up to some distance varepsilon, using tools from variational analysis. In particular, we describe necessary conditions associated with the optimal classifier subject to such an adversary. Using the necessary conditions, we derive a geometric evolution equation which can be used to track the change in classification boundaries as varepsilon varies. This evolution equation may be described as an uncoupled system of differential equations in one dimension, or as a mean curvature type equation in higher dimension. In one dimension, and under mild assumptions on the data distribution, we rigorously prove that one can use the initial value problem starting from varepsilon=0, which is simply the Bayes classifier, in order to solve for the global minimizer of the adversarial problem for small values of varepsilon. In higher dimensions we provide a similar result, albeit conditional to the existence of regular solutions of the initial value problem. In the process of proving our main results we obtain a result of independent interest connecting the original adversarial problem with an optimal transport problem under no assumptions on whether classes are balanced or not. Numerical examples illustrating these ideas are also presented.

Though recent advances in vision-language models (VLMs) have achieved remarkable progress across a wide range of multimodal tasks, understanding 3D spatial relationships from limited views remains a significant challenge. Previous reasoning methods typically rely on pure text (e.g., topological cognitive maps) or on 2D visual cues. However, their limited representational capacity hinders performance in specific tasks that require 3D spatial imagination. To address this limitation, we propose 3DThinker, a framework that can effectively exploits the rich geometric information embedded within images while reasoning, like humans do. Our framework is the first to enable 3D mentaling during reasoning without any 3D prior input, and it does not rely on explicitly labeled 3D data for training. Specifically, our training consists of two stages. First, we perform supervised training to align the 3D latent generated by VLM while reasoning with that of a 3D foundation model (e.g., VGGT). Then, we optimize the entire reasoning trajectory solely based on outcome signals, thereby refining the underlying 3D mentaling. Extensive experiments across multiple benchmarks show that 3DThinker consistently outperforms strong baselines and offers a new perspective toward unifying 3D representations into multimodal reasoning. Our code will be available at https://github.com/zhangquanchen/3DThinker.

Facial emotion recognition (FER) models trained only on pixels often fail to generalize across datasets because facial appearance is an indirect and biased proxy for underlying affect. We present NeuroGaze-Distill, a cross-modal distillation framework that transfers brain-informed priors into an image-only FER student via static Valence/Arousal (V/A) prototypes and a depression-inspired geometric prior (D-Geo). A teacher trained on EEG topographic maps from DREAMER (with MAHNOB-HCI as unlabeled support) produces a consolidated 5x5 V/A prototype grid that is frozen and reused; no EEG-face pairing and no non-visual signals at deployment are required. The student (ResNet-18/50) is trained on FERPlus with conventional CE/KD and two lightweight regularizers: (i) Proto-KD (cosine) aligns student features to the static prototypes; (ii) D-Geo softly shapes the embedding geometry in line with affective findings often reported in depression research (e.g., anhedonia-like contraction in high-valence regions). We evaluate both within-domain (FERPlus validation) and cross-dataset protocols (AffectNet-mini; optional CK+), reporting standard 8-way scores alongside present-only Macro-F1 and balanced accuracy to fairly handle label-set mismatch. Ablations attribute consistent gains to prototypes and D-Geo, and favor 5x5 over denser grids for stability. The method is simple, deployable, and improves robustness without architectural complexity.

AR/VR applications and robots need to know when the scene has changed. An example is when objects are moved, added, or removed from the scene. We propose a 3D object discovery method that is based only on scene changes. Our method does not need to encode any assumptions about what is an object, but rather discovers objects by exploiting their coherent move. Changes are initially detected as differences in the depth maps and segmented as objects if they undergo rigid motions. A graph cut optimization propagates the changing labels to geometrically consistent regions. Experiments show that our method achieves state-of-the-art performance on the 3RScan dataset against competitive baselines. The source code of our method can be found at https://github.com/katadam/ObjectsCanMove.

Recent advances in camera-controllable video generation have been constrained by the reliance on static-scene datasets with relative-scale camera annotations, such as RealEstate10K. While these datasets enable basic viewpoint control, they fail to capture dynamic scene interactions and lack metric-scale geometric consistency-critical for synthesizing realistic object motions and precise camera trajectories in complex environments. To bridge this gap, we introduce the first fully open-source, high-resolution dynamic-scene dataset with metric-scale camera annotations in https://github.com/ZGCTroy/RealCam-Vid.

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.

Point cloud registration approaches often fail when the overlap between point clouds is low due to noisy point correspondences. This work introduces a novel cross-attention mechanism tailored for Transformer-based architectures that tackles this problem, by fusing information from coordinates and features at the super-point level between point clouds. This formulation has remained unexplored primarily because it must guarantee rotation and translation invariance since point clouds reside in different and independent reference frames. We integrate the Gromov-Wasserstein distance into the cross-attention formulation to jointly compute distances between points across different point clouds and account for their geometric structure. By doing so, points from two distinct point clouds can attend to each other under arbitrary rigid transformations. At the point level, we also devise a self-attention mechanism that aggregates the local geometric structure information into point features for fine matching. Our formulation boosts the number of inlier correspondences, thereby yielding more precise registration results compared to state-of-the-art approaches. We have conducted an extensive evaluation on 3DMatch, 3DLoMatch, KITTI, and 3DCSR datasets.

Scale-aware monocular depth estimation poses a significant challenge in computer-aided endoscopic navigation. However, existing depth estimation methods that do not consider the geometric priors struggle to learn the absolute scale from training with monocular endoscopic sequences. Additionally, conventional methods face difficulties in accurately estimating details on tissue and instruments boundaries. In this paper, we tackle these problems by proposing a novel enhanced scale-aware framework that only uses monocular images with geometric modeling for depth estimation. Specifically, we first propose a multi-resolution depth fusion strategy to enhance the quality of monocular depth estimation. To recover the precise scale between relative depth and real-world values, we further calculate the 3D poses of instruments in the endoscopic scenes by algebraic geometry based on the image-only geometric primitives (i.e., boundaries and tip of instruments). Afterwards, the 3D poses of surgical instruments enable the scale recovery of relative depth maps. By coupling scale factors and relative depth estimation, the scale-aware depth of the monocular endoscopic scenes can be estimated. We evaluate the pipeline on in-house endoscopic surgery videos and simulated data. The results demonstrate that our method can learn the absolute scale with geometric modeling and accurately estimate scale-aware depth for monocular scenes.

This paper presents a new open-source high-fidelity dataset for Machine Learning (ML) containing 355 geometric variants of the Windsor body, to help the development and testing of ML surrogate models for external automotive aerodynamics. Each Computational Fluid Dynamics (CFD) simulation was run with a GPU-native high-fidelity Wall-Modeled Large-Eddy Simulations (WMLES) using a Cartesian immersed-boundary method using more than 280M cells to ensure the greatest possible accuracy. The dataset contains geometry variants that exhibits a wide range of flow characteristics that are representative of those observed on road-cars. The dataset itself contains the 3D time-averaged volume & boundary data as well as the geometry and force & moment coefficients. This paper discusses the validation of the underlying CFD methods as well as contents and structure of the dataset. To the authors knowledge, this represents the first, large-scale high-fidelity CFD dataset for the Windsor body with a permissive open-source license (CC-BY-SA).

In recent years, transformer-based models have exhibited considerable potential in point cloud instance segmentation. Despite the promising performance achieved by existing methods, they encounter challenges such as instance query initialization problems and excessive reliance on stacked layers, rendering them incompatible with large-scale 3D scenes. This paper introduces a novel method, named SGIFormer, for 3D instance segmentation, which is composed of the Semantic-guided Mix Query (SMQ) initialization and the Geometric-enhanced Interleaving Transformer (GIT) decoder. Specifically, the principle of our SMQ initialization scheme is to leverage the predicted voxel-wise semantic information to implicitly generate the scene-aware query, yielding adequate scene prior and compensating for the learnable query set. Subsequently, we feed the formed overall query into our GIT decoder to alternately refine instance query and global scene features for further capturing fine-grained information and reducing complex design intricacies simultaneously. To emphasize geometric property, we consider bias estimation as an auxiliary task and progressively integrate shifted point coordinates embedding to reinforce instance localization. SGIFormer attains state-of-the-art performance on ScanNet V2, ScanNet200 datasets, and the challenging high-fidelity ScanNet++ benchmark, striking a balance between accuracy and efficiency. The code, weights, and demo videos are publicly available at https://rayyoh.github.io/sgiformer.

Decision-based black-box attacks often necessitate a large number of queries to craft an adversarial example. Moreover, decision-based attacks based on querying boundary points in the estimated normal vector direction often suffer from inefficiency and convergence issues. In this paper, we propose a novel query-efficient curvature-aware geometric decision-based black-box attack (CGBA) that conducts boundary search along a semicircular path on a restricted 2D plane to ensure finding a boundary point successfully irrespective of the boundary curvature. While the proposed CGBA attack can work effectively for an arbitrary decision boundary, it is particularly efficient in exploiting the low curvature to craft high-quality adversarial examples, which is widely seen and experimentally verified in commonly used classifiers under non-targeted attacks. In contrast, the decision boundaries often exhibit higher curvature under targeted attacks. Thus, we develop a new query-efficient variant, CGBA-H, that is adapted for the targeted attack. In addition, we further design an algorithm to obtain a better initial boundary point at the expense of some extra queries, which considerably enhances the performance of the targeted attack. Extensive experiments are conducted to evaluate the performance of our proposed methods against some well-known classifiers on the ImageNet and CIFAR10 datasets, demonstrating the superiority of CGBA and CGBA-H over state-of-the-art non-targeted and targeted attacks, respectively. The source code is available at https://github.com/Farhamdur/CGBA.

The cascade of 2D geometric transformations were exploited to model relations between entities in a knowledge graph (KG), leading to an effective KG embedding (KGE) model, CompoundE. Furthermore, the rotation in the 3D space was proposed as a new KGE model, Rotate3D, by leveraging its non-commutative property. Inspired by CompoundE and Rotate3D, we leverage 3D compound geometric transformations, including translation, rotation, scaling, reflection, and shear and propose a family of KGE models, named CompoundE3D, in this work. CompoundE3D allows multiple design variants to match rich underlying characteristics of a KG. Since each variant has its own advantages on a subset of relations, an ensemble of multiple variants can yield superior performance. The effectiveness and flexibility of CompoundE3D are experimentally verified on four popular link prediction datasets.

Learning effective protein representations is critical in a variety of tasks in biology such as predicting protein function or structure. Existing approaches usually pretrain protein language models on a large number of unlabeled amino acid sequences and then finetune the models with some labeled data in downstream tasks. Despite the effectiveness of sequence-based approaches, the power of pretraining on known protein structures, which are available in smaller numbers only, has not been explored for protein property prediction, though protein structures are known to be determinants of protein function. In this paper, we propose to pretrain protein representations according to their 3D structures. We first present a simple yet effective encoder to learn the geometric features of a protein. We pretrain the protein graph encoder by leveraging multiview contrastive learning and different self-prediction tasks. Experimental results on both function prediction and fold classification tasks show that our proposed pretraining methods outperform or are on par with the state-of-the-art sequence-based methods, while using much less pretraining data. Our implementation is available at https://github.com/DeepGraphLearning/GearNet.

We present LRM-Zero, a Large Reconstruction Model (LRM) trained entirely on synthesized 3D data, achieving high-quality sparse-view 3D reconstruction. The core of LRM-Zero is our procedural 3D dataset, Zeroverse, which is automatically synthesized from simple primitive shapes with random texturing and augmentations (e.g., height fields, boolean differences, and wireframes). Unlike previous 3D datasets (e.g., Objaverse) which are often captured or crafted by humans to approximate real 3D data, Zeroverse completely ignores realistic global semantics but is rich in complex geometric and texture details that are locally similar to or even more intricate than real objects. We demonstrate that our LRM-Zero, trained with our fully synthesized Zeroverse, can achieve high visual quality in the reconstruction of real-world objects, competitive with models trained on Objaverse. We also analyze several critical design choices of Zeroverse that contribute to LRM-Zero's capability and training stability. Our work demonstrates that 3D reconstruction, one of the core tasks in 3D vision, can potentially be addressed without the semantics of real-world objects. The Zeroverse's procedural synthesis code and interactive visualization are available at: https://desaixie.github.io/lrm-zero/.

Surface reconstruction from multi-view images is a challenging task, with solutions often requiring a large number of sampled images with high overlap. We seek to develop a method for few-view reconstruction, for the case of the human foot. To solve this task, we must extract rich geometric cues from RGB images, before carefully fusing them into a final 3D object. Our FOUND approach tackles this, with 4 main contributions: (i) SynFoot, a synthetic dataset of 50,000 photorealistic foot images, paired with ground truth surface normals and keypoints; (ii) an uncertainty-aware surface normal predictor trained on our synthetic dataset; (iii) an optimization scheme for fitting a generative foot model to a series of images; and (iv) a benchmark dataset of calibrated images and high resolution ground truth geometry. We show that our normal predictor outperforms all off-the-shelf equivalents significantly on real images, and our optimization scheme outperforms state-of-the-art photogrammetry pipelines, especially for a few-view setting. We release our synthetic dataset and baseline 3D scans to the research community.

Cluster analysis relies on effective benchmarks for evaluating and comparing different algorithms. Simulation studies on synthetic data are popular because important features of the data sets, such as the overlap between clusters, or the variation in cluster shapes, can be effectively varied. Unfortunately, creating evaluation scenarios is often laborious, as practitioners must translate higher-level scenario descriptions like "clusters with very different shapes" into lower-level geometric parameters such as cluster centers, covariance matrices, etc. To make benchmarks more convenient and informative, we propose synthetic data generation based on direct specification of high-level scenarios, either through verbal descriptions or high-level geometric parameters. Our open-source Python package repliclust implements this workflow, making it easy to set up interpretable and reproducible benchmarks for cluster analysis. A demo of data generation from verbal inputs is available at https://demo.repliclust.org.

Recent advances in Multimodal Large Language Models (MLLMs) have achieved remarkable progress in general domains and demonstrated promise in multimodal mathematical reasoning. However, applying MLLMs to geometry problem solving (GPS) remains challenging due to lack of accurate step-by-step solution data and severe hallucinations during reasoning. In this paper, we propose GeoGen, a pipeline that can automatically generates step-wise reasoning paths for geometry diagrams. By leveraging the precise symbolic reasoning, GeoGen produces large-scale, high-quality question-answer pairs. To further enhance the logical reasoning ability of MLLMs, we train GeoLogic, a Large Language Model (LLM) using synthetic data generated by GeoGen. Serving as a bridge between natural language and symbolic systems, GeoLogic enables symbolic tools to help verifying MLLM outputs, making the reasoning process more rigorous and alleviating hallucinations. Experimental results show that our approach consistently improves the performance of MLLMs, achieving remarkable results on benchmarks for geometric reasoning tasks. This improvement stems from our integration of the strengths of LLMs and symbolic systems, which enables a more reliable and interpretable approach for the GPS task. Codes are available at https://github.com/ycpNotFound/GeoGen.

We present GeoManip, a framework to enable generalist robots to leverage essential conditions derived from object and part relationships, as geometric constraints, for robot manipulation. For example, cutting the carrot requires adhering to a geometric constraint: the blade of the knife should be perpendicular to the carrot's direction. By interpreting these constraints through symbolic language representations and translating them into low-level actions, GeoManip bridges the gap between natural language and robotic execution, enabling greater generalizability across diverse even unseen tasks, objects, and scenarios. Unlike vision-language-action models that require extensive training, operates training-free by utilizing large foundational models: a constraint generation module that predicts stage-specific geometric constraints and a geometry parser that identifies object parts involved in these constraints. A solver then optimizes trajectories to satisfy inferred constraints from task descriptions and the scene. Furthermore, GeoManip learns in-context and provides five appealing human-robot interaction features: on-the-fly policy adaptation, learning from human demonstrations, learning from failure cases, long-horizon action planning, and efficient data collection for imitation learning. Extensive evaluations on both simulations and real-world scenarios demonstrate GeoManip's state-of-the-art performance, with superior out-of-distribution generalization while avoiding costly model training.

We present DIRECT-3D, a diffusion-based 3D generative model for creating high-quality 3D assets (represented by Neural Radiance Fields) from text prompts. Unlike recent 3D generative models that rely on clean and well-aligned 3D data, limiting them to single or few-class generation, our model is directly trained on extensive noisy and unaligned `in-the-wild' 3D assets, mitigating the key challenge (i.e., data scarcity) in large-scale 3D generation. In particular, DIRECT-3D is a tri-plane diffusion model that integrates two innovations: 1) A novel learning framework where noisy data are filtered and aligned automatically during the training process. Specifically, after an initial warm-up phase using a small set of clean data, an iterative optimization is introduced in the diffusion process to explicitly estimate the 3D pose of objects and select beneficial data based on conditional density. 2) An efficient 3D representation that is achieved by disentangling object geometry and color features with two separate conditional diffusion models that are optimized hierarchically. Given a prompt input, our model generates high-quality, high-resolution, realistic, and complex 3D objects with accurate geometric details in seconds. We achieve state-of-the-art performance in both single-class generation and text-to-3D generation. We also demonstrate that DIRECT-3D can serve as a useful 3D geometric prior of objects, for example to alleviate the well-known Janus problem in 2D-lifting methods such as DreamFusion. The code and models are available for research purposes at: https://github.com/qihao067/direct3d.

We introduce Metric3D v2, a geometric foundation model for zero-shot metric depth and surface normal estimation from a single image, which is crucial for metric 3D recovery. While depth and normal are geometrically related and highly complimentary, they present distinct challenges. SoTA monocular depth methods achieve zero-shot generalization by learning affine-invariant depths, which cannot recover real-world metrics. Meanwhile, SoTA normal estimation methods have limited zero-shot performance due to the lack of large-scale labeled data. To tackle these issues, we propose solutions for both metric depth estimation and surface normal estimation. For metric depth estimation, we show that the key to a zero-shot single-view model lies in resolving the metric ambiguity from various camera models and large-scale data training. We propose a canonical camera space transformation module, which explicitly addresses the ambiguity problem and can be effortlessly plugged into existing monocular models. For surface normal estimation, we propose a joint depth-normal optimization module to distill diverse data knowledge from metric depth, enabling normal estimators to learn beyond normal labels. Equipped with these modules, our depth-normal models can be stably trained with over 16 million of images from thousands of camera models with different-type annotations, resulting in zero-shot generalization to in-the-wild images with unseen camera settings. Our method enables the accurate recovery of metric 3D structures on randomly collected internet images, paving the way for plausible single-image metrology. Our project page is at https://JUGGHM.github.io/Metric3Dv2.

World models for autonomous driving have the potential to dramatically improve the reasoning capabilities of today's systems. However, most works focus on camera data, with only a few that leverage lidar data or combine both to better represent autonomous vehicle sensor setups. In addition, raw sensor predictions are less actionable than 3D occupancy predictions, but there are no works examining the effects of combining both multimodal sensor data and 3D occupancy prediction. In this work, we perform a set of experiments with a MUltimodal World Model with Geometric VOxel representations (MUVO) to evaluate different sensor fusion strategies to better understand the effects on sensor data prediction. We also analyze potential weaknesses of current sensor fusion approaches and examine the benefits of additionally predicting 3D occupancy.

We present a box-free bottom-up approach for the tasks of pose estimation and instance segmentation of people in multi-person images using an efficient single-shot model. The proposed PersonLab model tackles both semantic-level reasoning and object-part associations using part-based modeling. Our model employs a convolutional network which learns to detect individual keypoints and predict their relative displacements, allowing us to group keypoints into person pose instances. Further, we propose a part-induced geometric embedding descriptor which allows us to associate semantic person pixels with their corresponding person instance, delivering instance-level person segmentations. Our system is based on a fully-convolutional architecture and allows for efficient inference, with runtime essentially independent of the number of people present in the scene. Trained on COCO data alone, our system achieves COCO test-dev keypoint average precision of 0.665 using single-scale inference and 0.687 using multi-scale inference, significantly outperforming all previous bottom-up pose estimation systems. We are also the first bottom-up method to report competitive results for the person class in the COCO instance segmentation task, achieving a person category average precision of 0.417.

We present a dataset of large-scale indoor spaces that provides a variety of mutually registered modalities from 2D, 2.5D and 3D domains, with instance-level semantic and geometric annotations. The dataset covers over 6,000m2 and contains over 70,000 RGB images, along with the corresponding depths, surface normals, semantic annotations, global XYZ images (all in forms of both regular and 360{\deg} equirectangular images) as well as camera information. It also includes registered raw and semantically annotated 3D meshes and point clouds. The dataset enables development of joint and cross-modal learning models and potentially unsupervised approaches utilizing the regularities present in large-scale indoor spaces. The dataset is available here: http://3Dsemantics.stanford.edu/

It is inherently ambiguous to lift 2D results from pre-trained diffusion models to a 3D world for text-to-3D generation. 2D diffusion models solely learn view-agnostic priors and thus lack 3D knowledge during the lifting, leading to the multi-view inconsistency problem. We find that this problem primarily stems from geometric inconsistency, and avoiding misplaced geometric structures substantially mitigates the problem in the final outputs. Therefore, we improve the consistency by aligning the 2D geometric priors in diffusion models with well-defined 3D shapes during the lifting, addressing the vast majority of the problem. This is achieved by fine-tuning the 2D diffusion model to be viewpoint-aware and to produce view-specific coordinate maps of canonically oriented 3D objects. In our process, only coarse 3D information is used for aligning. This "coarse" alignment not only resolves the multi-view inconsistency in geometries but also retains the ability in 2D diffusion models to generate detailed and diversified high-quality objects unseen in the 3D datasets. Furthermore, our aligned geometric priors (AGP) are generic and can be seamlessly integrated into various state-of-the-art pipelines, obtaining high generalizability in terms of unseen shapes and visual appearance while greatly alleviating the multi-view inconsistency problem. Our method represents a new state-of-the-art performance with an 85+% consistency rate by human evaluation, while many previous methods are around 30%. Our project page is https://sweetdreamer3d.github.io/

Affine correspondences have received significant attention due to their benefits in tasks like image matching and pose estimation. Existing methods for extracting affine correspondences still have many limitations in terms of performance; thus, exploring a new paradigm is crucial. In this paper, we present a new pipeline designed for extracting accurate affine correspondences by integrating dense matching and geometric constraints. Specifically, a novel extraction framework is introduced, with the aid of dense matching and a novel keypoint scale and orientation estimator. For this purpose, we propose loss functions based on geometric constraints, which can effectively improve accuracy by supervising neural networks to learn feature geometry. The experimental show that the accuracy and robustness of our method outperform the existing ones in image matching tasks. To further demonstrate the effectiveness of the proposed method, we applied it to relative pose estimation. Affine correspondences extracted by our method lead to more accurate poses than the baselines on a range of real-world datasets. The code is available at https://github.com/stilcrad/DenseAffine.

Vision-Language Models (VLMs) have shown remarkable capabilities in spatial reasoning, yet they remain fundamentally limited to qualitative precision and lack the computational precision required for real-world robotics. Current approaches fail to leverage metric cues from depth sensors and camera calibration, instead reducing geometric problems to pattern recognition tasks that cannot deliver the centimeter-level accuracy essential for robotic manipulation. We present TIGeR (Tool-Integrated Geometric Reasoning), a novel framework that transforms VLMs from perceptual estimators to geometric computers by enabling them to generate and execute precise geometric computations through external tools. Rather than attempting to internalize complex geometric operations within neural networks, TIGeR empowers models to recognize geometric reasoning requirements, synthesize appropriate computational code, and invoke specialized libraries for exact calculations. To support this paradigm, we introduce TIGeR-300K, a comprehensive tool-invocation-oriented dataset covering point transformations, pose estimation, and spatial compatibility verification, complete with tool invocation sequences and intermediate computations. Through a two-stage training pipeline combining supervised fine-tuning (SFT) and reinforcement fine-tuning (RFT) with our proposed hierarchical reward design, TIGeR achieves SOTA performance on geometric reasoning benchmarks while demonstrating centimeter-level precision in real-world robotic manipulation tasks.

In text-driven 3D scene generation, object layout serves as a crucial intermediate representation that bridges high-level language instructions with detailed geometric output. It not only provides a structural blueprint for ensuring physical plausibility but also supports semantic controllability and interactive editing. However, the learning capabilities of current 3D indoor layout generation models are constrained by the limited scale, diversity, and annotation quality of existing datasets. To address this, we introduce M3DLayout, a large-scale, multi-source dataset for 3D indoor layout generation. M3DLayout comprises 15,080 layouts and over 258k object instances, integrating three distinct sources: real-world scans, professional CAD designs, and procedurally generated scenes. Each layout is paired with detailed structured text describing global scene summaries, relational placements of large furniture, and fine-grained arrangements of smaller items. This diverse and richly annotated resource enables models to learn complex spatial and semantic patterns across a wide variety of indoor environments. To assess the potential of M3DLayout, we establish a benchmark using a text-conditioned diffusion model. Experimental results demonstrate that our dataset provides a solid foundation for training layout generation models. Its multi-source composition enhances diversity, notably through the Inf3DLayout subset which provides rich small-object information, enabling the generation of more complex and detailed scenes. We hope that M3DLayout can serve as a valuable resource for advancing research in text-driven 3D scene synthesis.

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

Characteristic classes, which are abstract topological invariants associated with vector bundles, have become an important notion in modern physics with surprising real-world consequences. As a representative example, the incredible properties of topological insulators, which are insulators in their bulk but conductors on their surface, can be completely characterized by a specific characteristic class associated with their electronic band structure, the first Chern class. Given their importance to next generation computing and the computational challenge of calculating them using first-principles approaches, there is a need to develop machine learning approaches to predict the characteristic classes associated with a material system. To aid in this program we introduce the {Haldane bundle dataset}, which consists of synthetically generated complex line bundles on the 2-torus. We envision this dataset, which is not as challenging as noisy and sparsely measured real-world datasets but (as we show) still difficult for off-the-shelf architectures, to be a testing ground for architectures that incorporate the rich topological and geometric priors underlying characteristic classes.

Depth images captured by Time-of-Flight (ToF) sensors are prone to noise, requiring denoising for reliable downstream applications. Previous works either focus on single-frame processing, or perform multi-frame processing without considering depth variations at corresponding pixels across frames, leading to undesirable temporal inconsistency and spatial ambiguity. In this paper, we propose a novel ToF depth denoising network leveraging motion-invariant graph fusion to simultaneously enhance temporal stability and spatial sharpness. Specifically, despite depth shifts across frames, graph structures exhibit temporal self-similarity, enabling cross-frame geometric attention for graph fusion. Then, by incorporating an image smoothness prior on the fused graph and data fidelity term derived from ToF noise distribution, we formulate a maximum a posterior problem for ToF denoising. Finally, the solution is unrolled into iterative filters whose weights are adaptively learned from the graph-informed geometric attention, producing a high-performance yet interpretable network. Experimental results demonstrate that the proposed scheme achieves state-of-the-art performance in terms of accuracy and consistency on synthetic DVToF dataset and exhibits robust generalization on the real Kinectv2 dataset. Source code will be released at https://github.com/davidweidawang/GIGA-ToF{https://github.com/davidweidawang/GIGA-ToF}.

In this work, we introduce CAD-Coder, a novel framework that reformulates text-to-CAD as the generation of CadQuery scripts - a Python-based, parametric CAD language. This representation enables direct geometric validation, a richer modeling vocabulary, and seamless integration with existing LLMs. To further enhance code validity and geometric fidelity, we propose a two-stage learning pipeline: (1) supervised fine-tuning on paired text-CadQuery data, and (2) reinforcement learning with Group Reward Policy Optimization (GRPO), guided by a CAD-specific reward comprising both a geometric reward (Chamfer Distance) and a format reward. We also introduce a chain-of-thought (CoT) planning process to improve model reasoning, and construct a large-scale, high-quality dataset of 110K text-CadQuery-3D model triplets and 1.5K CoT samples via an automated pipeline. Extensive experiments demonstrate that CAD-Coder enables LLMs to generate diverse, valid, and complex CAD models directly from natural language, advancing the state of the art of text-to-CAD generation and geometric reasoning.

Metamaterials, engineered materials with architected structures across multiple length scales, offer unprecedented and tunable mechanical properties that surpass those of conventional materials. However, leveraging advanced machine learning (ML) for metamaterial discovery is hindered by three fundamental challenges: (C1) Data Heterogeneity Challenge arises from heterogeneous data sources, heterogeneous composition scales, and heterogeneous structure categories; (C2) Model Complexity Challenge stems from the intricate geometric constraints of ML models, which complicate their adaptation to metamaterial structures; and (C3) Human-AI Collaboration Challenge comes from the "dual black-box'' nature of sophisticated ML models and the need for intuitive user interfaces. To tackle these challenges, we introduce a unified framework, named MetamatBench, that operates on three levels. (1) At the data level, we integrate and standardize 5 heterogeneous, multi-modal metamaterial datasets. (2) The ML level provides a comprehensive toolkit that adapts 17 state-of-the-art ML methods for metamaterial discovery. It also includes a comprehensive evaluation suite with 12 novel performance metrics with finite element-based assessments to ensure accurate and reliable model validation. (3) The user level features a visual-interactive interface that bridges the gap between complex ML techniques and non-ML researchers, advancing property prediction and inverse design of metamaterials for research and applications. MetamatBench offers a unified platform deployed at http://zhoulab-1.cs.vt.edu:5550 that enables machine learning researchers and practitioners to develop and evaluate new methodologies in metamaterial discovery. For accessibility and reproducibility, we open-source our benchmark and the codebase at https://github.com/cjpcool/Metamaterial-Benchmark.

Robust 6DoF pose estimation with mobile devices is the foundation for applications in robotics, augmented reality, and digital twin localization. In this paper, we extensively investigate the robustness of existing RGBD-based 6DoF pose estimation methods against varying levels of depth sensor noise. We highlight that existing 6DoF pose estimation methods suffer significant performance discrepancies due to depth measurement inaccuracies. In response to the robustness issue, we present a simple and effective transformer-based 6DoF pose estimation approach called DTTDNet, featuring a novel geometric feature filtering module and a Chamfer distance loss for training. Moreover, we advance the field of robust 6DoF pose estimation and introduce a new dataset -- Digital Twin Tracking Dataset Mobile (DTTD-Mobile), tailored for digital twin object tracking with noisy depth data from the mobile RGBD sensor suite of the Apple iPhone 14 Pro. Extensive experiments demonstrate that DTTDNet significantly outperforms state-of-the-art methods at least 4.32, up to 60.74 points in ADD metrics on the DTTD-Mobile. More importantly, our approach exhibits superior robustness to varying levels of measurement noise, setting a new benchmark for robustness to measurement noise. The project page is publicly available at https://openark-berkeley.github.io/DTTDNet/.

Emerging 3D geometric foundation models, such as DUSt3R, offer a promising approach for in-the-wild 3D vision tasks. However, due to the high-dimensional nature of the problem space and scarcity of high-quality 3D data, these pre-trained models still struggle to generalize to many challenging circumstances, such as limited view overlap or low lighting. To address this, we propose LoRA3D, an efficient self-calibration pipeline to specialize the pre-trained models to target scenes using their own multi-view predictions. Taking sparse RGB images as input, we leverage robust optimization techniques to refine multi-view predictions and align them into a global coordinate frame. In particular, we incorporate prediction confidence into the geometric optimization process, automatically re-weighting the confidence to better reflect point estimation accuracy. We use the calibrated confidence to generate high-quality pseudo labels for the calibrating views and use low-rank adaptation (LoRA) to fine-tune the models on the pseudo-labeled data. Our method does not require any external priors or manual labels. It completes the self-calibration process on a single standard GPU within just 5 minutes. Each low-rank adapter requires only 18MB of storage. We evaluated our method on more than 160 scenes from the Replica, TUM and Waymo Open datasets, achieving up to 88% performance improvement on 3D reconstruction, multi-view pose estimation and novel-view rendering.

In this work, we focused on deep learning image processing in the context of oral rare diseases, which pose challenges due to limited data availability. A crucial step involves teeth detection, segmentation and numbering in panoramic radiographs. To this end, we used a dataset consisting of 156 panoramic radiographs from individuals with rare oral diseases and labeled by experts. We trained the Detection Transformer (DETR) neural network for teeth detection, segmentation, and numbering the 52 teeth classes. In addition, we used data augmentation techniques, including geometric transformations. Finally, we generated new panoramic images using inpainting techniques with stable diffusion, by removing teeth from a panoramic radiograph and integrating teeth into it. The results showed a mAP exceeding 0,69 for DETR without data augmentation. The mAP was improved to 0,82 when data augmentation techniques are used. Furthermore, we observed promising performances when using new panoramic radiographs generated with inpainting technique, with mAP of 0,76.

Modern deep neural networks have achieved impressive performance on tasks from image classification to natural language processing. Surprisingly, these complex systems with massive amounts of parameters exhibit the same structural properties in their last-layer features and classifiers across canonical datasets when training until convergence. In particular, it has been observed that the last-layer features collapse to their class-means, and those class-means are the vertices of a simplex Equiangular Tight Frame (ETF). This phenomenon is known as Neural Collapse (NC). Recent papers have theoretically shown that NC emerges in the global minimizers of training problems with the simplified "unconstrained feature model". In this context, we take a step further and prove the NC occurrences in deep linear networks for the popular mean squared error (MSE) and cross entropy (CE) losses, showing that global solutions exhibit NC properties across the linear layers. Furthermore, we extend our study to imbalanced data for MSE loss and present the first geometric analysis of NC under bias-free setting. Our results demonstrate the convergence of the last-layer features and classifiers to a geometry consisting of orthogonal vectors, whose lengths depend on the amount of data in their corresponding classes. Finally, we empirically validate our theoretical analyses on synthetic and practical network architectures with both balanced and imbalanced scenarios.

The exploitation of syntactic graphs (SyGs) as a word's context has been shown to be beneficial for distributional semantic models (DSMs), both at the level of individual word representations and in deriving phrasal representations via composition. However, notwithstanding the potential performance benefit, the syntactically-aware DSMs proposed to date have huge numbers of parameters (compared to conventional DSMs) and suffer from data sparsity. Furthermore, the encoding of the SyG links (i.e., the syntactic relations) has been largely limited to linear maps. The knowledge graphs' literature, on the other hand, has proposed light-weight models employing different geometric transformations (GTs) to encode edges in a knowledge graph (KG). Our work explores the possibility of adopting this family of models to encode SyGs. Furthermore, we investigate which GT better encodes syntactic relations, so that these representations can be used to enhance phrase-level composition via syntactic contextualisation.

Current methods for 3D scene reconstruction from sparse posed images employ intermediate 3D representations such as neural fields, voxel grids, or 3D Gaussians, to achieve multi-view consistent scene appearance and geometry. In this paper we introduce MVGD, a diffusion-based architecture capable of direct pixel-level generation of images and depth maps from novel viewpoints, given an arbitrary number of input views. Our method uses raymap conditioning to both augment visual features with spatial information from different viewpoints, as well as to guide the generation of images and depth maps from novel views. A key aspect of our approach is the multi-task generation of images and depth maps, using learnable task embeddings to guide the diffusion process towards specific modalities. We train this model on a collection of more than 60 million multi-view samples from publicly available datasets, and propose techniques to enable efficient and consistent learning in such diverse conditions. We also propose a novel strategy that enables the efficient training of larger models by incrementally fine-tuning smaller ones, with promising scaling behavior. Through extensive experiments, we report state-of-the-art results in multiple novel view synthesis benchmarks, as well as multi-view stereo and video depth estimation.

Object counting is pivotal for understanding the composition of scenes. Previously, this task was dominated by class-specific methods, which have gradually evolved into more adaptable class-agnostic strategies. However, these strategies come with their own set of limitations, such as the need for manual exemplar input and multiple passes for multiple categories, resulting in significant inefficiencies. This paper introduces a new, more practical approach enabling simultaneous counting of multiple object categories using an open vocabulary framework. Our solution, OmniCount, stands out by using semantic and geometric insights from pre-trained models to count multiple categories of objects as specified by users, all without additional training. OmniCount distinguishes itself by generating precise object masks and leveraging point prompts via the Segment Anything Model for efficient counting. To evaluate OmniCount, we created the OmniCount-191 benchmark, a first-of-its-kind dataset with multi-label object counts, including points, bounding boxes, and VQA annotations. Our comprehensive evaluation in OmniCount-191, alongside other leading benchmarks, demonstrates OmniCount's exceptional performance, significantly outpacing existing solutions and heralding a new era in object counting technology.

Geometry problem-solving (GPS), a challenging task requiring both visual comprehension and symbolic reasoning, effectively measures the reasoning capabilities of multimodal large language models (MLLMs). Humans exhibit strong reasoning ability in this task through accurate identification and adaptive application of geometric principles within visual contexts. However, existing benchmarks fail to jointly assess both dimensions of the human-like geometric reasoning mechanism in MLLMs, remaining a critical gap in assessing their ability to tackle GPS. To this end, we introduce GeoSense, the first comprehensive bilingual benchmark designed to systematically evaluate the geometric reasoning abilities of MLLMs through the lens of geometric principles. GeoSense features a five-level hierarchical framework of geometric principles spanning plane and solid geometry, an intricately annotated dataset of 1,789 problems, and an innovative evaluation strategy. Through extensive experiments on GeoSense with various open-source and closed-source MLLMs, we observe that Gemini-2.0-pro-flash performs best, achieving an overall score of 65.3. Our in-depth analysis reveals that the identification and application of geometric principles remain a bottleneck for leading MLLMs, jointly hindering their reasoning abilities. These findings underscore GeoSense's potential to guide future advancements in MLLMs' geometric reasoning capabilities, paving the way for more robust and human-like reasoning in artificial intelligence.

The development of Machine Learning (ML) methods for Computational Fluid Dynamics (CFD) is currently limited by the lack of openly available training data. This paper presents a new open-source dataset comprising of high fidelity, scale-resolving CFD simulations of 500 geometric variations of the Ahmed Car Body - a simplified car-like shape that exhibits many of the flow topologies that are present on bluff bodies such as road vehicles. The dataset contains simulation results that exhibit a broad set of fundamental flow physics such as geometry and pressure-induced flow separation as well as 3D vortical structures. Each variation of the Ahmed car body were run using a high-fidelity, time-accurate, hybrid Reynolds-Averaged Navier-Stokes (RANS) - Large-Eddy Simulation (LES) turbulence modelling approach using the open-source CFD code OpenFOAM. The dataset contains boundary, volume, geometry, and time-averaged forces/moments in widely used open-source formats. In addition, the OpenFOAM case setup is provided so that others can reproduce or extend the dataset. This represents to the authors knowledge, the first open-source large-scale dataset using high-fidelity CFD methods for the widely used Ahmed car body that is available to freely download with a permissive license (CC-BY-SA).

State-of-the-art visual localization approaches generally rely on a first image retrieval step whose role is crucial. Yet, retrieval often struggles when facing varying conditions, due to e.g. weather or time of day, with dramatic consequences on the visual localization accuracy. In this paper, we improve this retrieval step and tailor it to the final localization task. Among the several changes we advocate for, we propose to synthesize variants of the training set images, obtained from generative text-to-image models, in order to automatically expand the training set towards a number of nameable variations that particularly hurt visual localization. After expanding the training set, we propose a training approach that leverages the specificities and the underlying geometry of this mix of real and synthetic images. We experimentally show that those changes translate into large improvements for the most challenging visual localization datasets. Project page: https://europe.naverlabs.com/ret4loc

Since their inception, embeddings have become a primary ingredient in many flavours of Natural Language Processing (NLP) tasks supplanting earlier types of representation. Even though multilingual embeddings have been used for the increasing number of multilingual tasks, due to the scarcity of parallel training data, low-resource languages such as Sinhala, tend to focus more on monolingual embeddings. Then when it comes to the aforementioned multi-lingual tasks, it is challenging to utilize these monolingual embeddings given that even if the embedding spaces have a similar geometric arrangement due to an identical training process, the embeddings of the languages considered are not aligned. This is solved by the embedding alignment task. Even in this, high-resource language pairs are in the limelight while low-resource languages such as Sinhala which is in dire need of help seem to have fallen by the wayside. In this paper, we try to align Sinhala and English word embedding spaces based on available alignment techniques and introduce a benchmark for Sinhala language embedding alignment. In addition to that, to facilitate the supervised alignment, as an intermediate task, we also introduce Sinhala-English alignment datasets. These datasets serve as our anchor datasets for supervised word embedding alignment. Even though we do not obtain results comparable to the high-resource languages such as French, German, or Chinese, we believe our work lays the groundwork for more specialized alignment between English and Sinhala embeddings.

Flow-based 3D generation models typically require dozens of sampling steps during inference. Though few-step distillation methods, particularly Consistency Models (CMs), have achieved substantial advancements in accelerating 2D diffusion models, they remain under-explored for more complex 3D generation tasks. In this study, we propose a novel framework, MDT-dist, for few-step 3D flow distillation. Our approach is built upon a primary objective: distilling the pretrained model to learn the Marginal-Data Transport. Directly learning this objective needs to integrate the velocity fields, while this integral is intractable to be implemented. Therefore, we propose two optimizable objectives, Velocity Matching (VM) and Velocity Distillation (VD), to equivalently convert the optimization target from the transport level to the velocity and the distribution level respectively. Velocity Matching (VM) learns to stably match the velocity fields between the student and the teacher, but inevitably provides biased gradient estimates. Velocity Distillation (VD) further enhances the optimization process by leveraging the learned velocity fields to perform probability density distillation. When evaluated on the pioneer 3D generation framework TRELLIS, our method reduces sampling steps of each flow transformer from 25 to 1 or 2, achieving 0.68s (1 step x 2) and 0.94s (2 steps x 2) latency with 9.0x and 6.5x speedup on A800, while preserving high visual and geometric fidelity. Extensive experiments demonstrate that our method significantly outperforms existing CM distillation methods, and enables TRELLIS to achieve superior performance in few-step 3D generation.

Vision Language Models (VLMs) achieve strong performance on many vision-language tasks but often struggle with spatial reasoningx2014a prerequisite for many applications. Empirically, we find that a dataset produced by a current training data generation pipeline has a 57.6% human validation rate. These rates stem from current limitations: single-image 3D reconstruction introduces cascading modeling errors and requires wide answer tolerances, while caption-based methods require hyper-detailed annotations and suffer from generative hallucinations. We present GRAID, built on the key insight that qualitative spatial relationships can be reliably determined from 2D geometric primitives alone. By operating exclusively on 2D bounding boxes from standard object detectors, GRAID avoids both 3D reconstruction errors and generative hallucinations, resulting in datasets that are of higher quality than existing tools that produce similar datasets as validated by human evaluations. We apply our framework to the BDD100k, NuImages, and Waymo datasets, generating over 8.5 million high-quality VQA pairs creating questions spanning spatial relations, counting, ranking, and size comparisons. We evaluate one of the datasets and find it achieves 91.16% human-validated accuracyx2014compared to 57.6% on a dataset generated by recent work. Critically, we demonstrate that when trained on GRAID data, models learn spatial reasoning concepts that generalize: models fine-tuned on 6 question types improve on over 10 held-out types, with accuracy gains of 47.5% on BDD and 37.9% on NuImages for Llama 3.2B 11B, and when trained on all questions types, achieve improvements on several existing benchmarks such as BLINK. The GRAID framework, datasets, and additional information can be found this https URL{here}.

The field of adversarial robustness has long established that adversarial examples can successfully transfer between image classifiers and that text jailbreaks can successfully transfer between language models (LMs). However, a pair of recent studies reported being unable to successfully transfer image jailbreaks between vision-language models (VLMs). To explain this striking difference, we propose a fundamental distinction regarding the transferability of attacks against machine learning models: attacks in the input data-space can transfer, whereas attacks in model representation space do not, at least not without geometric alignment of representations. We then provide theoretical and empirical evidence of this hypothesis in four different settings. First, we mathematically prove this distinction in a simple setting where two networks compute the same input-output map but via different representations. Second, we construct representation-space attacks against image classifiers that are as successful as well-known data-space attacks, but fail to transfer. Third, we construct representation-space attacks against LMs that successfully jailbreak the attacked models but again fail to transfer. Fourth, we construct data-space attacks against VLMs that successfully transfer to new VLMs, and we show that representation space attacks can transfer when VLMs' latent geometries are sufficiently aligned in post-projector space. Our work reveals that adversarial transfer is not an inherent property of all attacks but contingent on their operational domain - the shared data-space versus models' unique representation spaces - a critical insight for building more robust models.

Recently, significant advances have been made in 3D object generation. Building upon the generated geometry, current pipelines typically employ image diffusion models to generate multi-view RGB images, followed by UV texture reconstruction through texture baking. While 3D geometry generation has improved significantly, supported by multiple open-source frameworks, 3D texture generation remains underexplored. In this work, we systematically investigate 3D texture generation through the lens of three core dimensions: reference-texture alignment, geometry-texture consistency, and local texture quality. To tackle these issues, we propose MVPainter, which employs data filtering and augmentation strategies to enhance texture fidelity and detail, and introduces ControlNet-based geometric conditioning to improve texture-geometry alignment. Furthermore, we extract physically-based rendering (PBR) attributes from the generated views to produce PBR meshes suitable for real-world rendering applications. MVPainter achieves state-of-the-art results across all three dimensions, as demonstrated by human-aligned evaluations. To facilitate further research and reproducibility, we also release our full pipeline as an open-source system, including data construction, model architecture, and evaluation tools.

Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an alternative approach, utilizing neural networks combined with ODE solvers to learn continuous latent representations through parameterized vector fields. Neural Stochastic Differential Equations (Neural SDEs) extend Neural ODEs by incorporating a diffusion term, although this addition is not trivial, particularly when addressing irregular intervals and missing values. Consequently, careful design of drift and diffusion functions is crucial for maintaining stability and enhancing performance, while incautious choices can result in adverse properties such as the absence of strong solutions, stochastic destabilization, or unstable Euler discretizations, significantly affecting Neural SDEs' performance. In this study, we propose three stable classes of Neural SDEs: Langevin-type SDE, Linear Noise SDE, and Geometric SDE. Then, we rigorously demonstrate their robustness in maintaining excellent performance under distribution shift, while effectively preventing overfitting. To assess the effectiveness of our approach, we conduct extensive experiments on four benchmark datasets for interpolation, forecasting, and classification tasks, and analyze the robustness of our methods with 30 public datasets under different missing rates. Our results demonstrate the efficacy of the proposed method in handling real-world irregular time series data.

3D-aware face generators are typically trained on 2D real-life face image datasets that primarily consist of near-frontal face data, and as such, they are unable to construct one-quarter headshot 3D portraits with complete head, neck, and shoulder geometry. Two reasons account for this issue: First, existing facial recognition methods struggle with extracting facial data captured from large camera angles or back views. Second, it is challenging to learn a distribution of 3D portraits covering the one-quarter headshot region from single-view data due to significant geometric deformation caused by diverse body poses. To this end, we first create the dataset 360{\deg}-Portrait-HQ (360{\deg}PHQ for short) which consists of high-quality single-view real portraits annotated with a variety of camera parameters (the yaw angles span the entire 360{\deg} range) and body poses. We then propose 3DPortraitGAN, the first 3D-aware one-quarter headshot portrait generator that learns a canonical 3D avatar distribution from the 360{\deg}PHQ dataset with body pose self-learning. Our model can generate view-consistent portrait images from all camera angles with a canonical one-quarter headshot 3D representation. Our experiments show that the proposed framework can accurately predict portrait body poses and generate view-consistent, realistic portrait images with complete geometry from all camera angles.

LiDAR place recognition approaches based on deep learning suffer a significant degradation in performance when there is a shift between the distribution of the training and testing datasets, with re-training often required to achieve top performance. However, obtaining accurate ground truth on new environments can be prohibitively expensive, especially in complex or GPS-deprived environments. To address this issue we propose GeoAdapt, which introduces a novel auxiliary classification head to generate pseudo-labels for re-training on unseen environments in a self-supervised manner. GeoAdapt uses geometric consistency as a prior to improve the robustness of our generated pseudo-labels against domain shift, improving the performance and reliability of our Test-Time Adaptation approach. Comprehensive experiments show that GeoAdapt significantly boosts place recognition performance across moderate to severe domain shifts, and is competitive with fully supervised test-time adaptation approaches. Our code will be available at https://github.com/csiro-robotics/GeoAdapt.

We introduce the task of 3D visual grounding in large-scale dynamic scenes based on natural linguistic descriptions and online captured multi-modal visual data, including 2D images and 3D LiDAR point clouds. We present a novel method, dubbed WildRefer, for this task by fully utilizing the rich appearance information in images, the position and geometric clues in point cloud as well as the semantic knowledge of language descriptions. Besides, we propose two novel datasets, i.e., STRefer and LifeRefer, which focus on large-scale human-centric daily-life scenarios accompanied with abundant 3D object and natural language annotations. Our datasets are significant for the research of 3D visual grounding in the wild and has huge potential to boost the development of autonomous driving and service robots. Extensive experiments and ablation studies demonstrate that our method achieves state-of-the-art performance on the proposed benchmarks. The code is provided in https://github.com/4DVLab/WildRefer.

We present FaceVerse, a fine-grained 3D Neural Face Model, which is built from hybrid East Asian face datasets containing 60K fused RGB-D images and 2K high-fidelity 3D head scan models. A novel coarse-to-fine structure is proposed to take better advantage of our hybrid dataset. In the coarse module, we generate a base parametric model from large-scale RGB-D images, which is able to predict accurate rough 3D face models in different genders, ages, etc. Then in the fine module, a conditional StyleGAN architecture trained with high-fidelity scan models is introduced to enrich elaborate facial geometric and texture details. Note that different from previous methods, our base and detailed modules are both changeable, which enables an innovative application of adjusting both the basic attributes and the facial details of 3D face models. Furthermore, we propose a single-image fitting framework based on differentiable rendering. Rich experiments show that our method outperforms the state-of-the-art methods.

3D building models are critical for applications in architecture, energy simulation, and navigation. Yet, generating accurate and semantically rich 3D buildings automatically remains a major challenge due to the lack of large-scale annotated datasets in the public domain. Inspired by the success of synthetic data in computer vision, we introduce SYNBUILD-3D, a large, diverse, and multi-modal dataset of over 6.2 million synthetic 3D residential buildings at Level of Detail (LoD) 4. In the dataset, each building is represented through three distinct modalities: a semantically enriched 3D wireframe graph at LoD 4 (Modality I), the corresponding floor plan images (Modality II), and a LiDAR-like roof point cloud (Modality III). The semantic annotations for each building wireframe are derived from the corresponding floor plan images and include information on rooms, doors, and windows. Through its tri-modal nature, future work can use SYNBUILD-3D to develop novel generative AI algorithms that automate the creation of 3D building models at LoD 4, subject to predefined floor plan layouts and roof geometries, while enforcing semantic-geometric consistency. Dataset and code samples are publicly available at https://github.com/kdmayer/SYNBUILD-3D.

3D scene reconstruction from 2D images has been a long-standing task. Instead of estimating per-frame depth maps and fusing them in 3D, recent research leverages the neural implicit surface as a unified representation for 3D reconstruction. Equipped with data-driven pre-trained geometric cues, these methods have demonstrated promising performance. However, inaccurate prior estimation, which is usually inevitable, can lead to suboptimal reconstruction quality, particularly in some geometrically complex regions. In this paper, we propose a two-stage training process, decouple view-dependent and view-independent colors, and leverage two novel consistency constraints to enhance detail reconstruction performance without requiring extra priors. Additionally, we introduce an essential mask scheme to adaptively influence the selection of supervision constraints, thereby improving performance in a self-supervised paradigm. Experiments on synthetic and real-world datasets show the capability of reducing the interference from prior estimation errors and achieving high-quality scene reconstruction with rich geometric details.

This paper presents GPSM4K, a comprehensive geometry multimodal dataset tailored to augment the problem-solving capabilities of Large Vision Language Models (LVLMs). GPSM4K encompasses 2157 multimodal question-answer pairs manually extracted from mathematics textbooks spanning grades 7-12 and is further augmented to 5340 problems, consisting of both numerical and theorem-proving questions. In contrast to PGPS9k, Geometry3K, and Geo170K which feature only objective-type questions, GPSM4K offers detailed step-by-step solutions in a consistent format, facilitating a comprehensive evaluation of problem-solving approaches. This dataset serves as an excellent benchmark for assessing the geometric reasoning capabilities of LVLMs. Evaluation of our test set shows that there is scope for improvement needed in open-source language models in geometry problem-solving. Finetuning on our training set increases the geometry problem-solving capabilities of models. Further, We also evaluate the effectiveness of techniques such as image captioning and Retrieval Augmentation generation (RAG) on model performance. We leveraged LLM to automate the task of final answer evaluation by providing ground truth and predicted solutions. This research will help to assess and improve the geometric reasoning capabilities of LVLMs.

Neural networks embed the geometric structure of a data manifold lying in a high-dimensional space into latent representations. Ideally, the distribution of the data points in the latent space should depend only on the task, the data, the loss, and other architecture-specific constraints. However, factors such as the random weights initialization, training hyperparameters, or other sources of randomness in the training phase may induce incoherent latent spaces that hinder any form of reuse. Nevertheless, we empirically observe that, under the same data and modeling choices, the angles between the encodings within distinct latent spaces do not change. In this work, we propose the latent similarity between each sample and a fixed set of anchors as an alternative data representation, demonstrating that it can enforce the desired invariances without any additional training. We show how neural architectures can leverage these relative representations to guarantee, in practice, invariance to latent isometries and rescalings, effectively enabling latent space communication: from zero-shot model stitching to latent space comparison between diverse settings. We extensively validate the generalization capability of our approach on different datasets, spanning various modalities (images, text, graphs), tasks (e.g., classification, reconstruction) and architectures (e.g., CNNs, GCNs, transformers).

Causal representation learning seeks to extract high-level latent factors from low-level sensory data. Most existing methods rely on observational data and structural assumptions (e.g., conditional independence) to identify the latent factors. However, interventional data is prevalent across applications. Can interventional data facilitate causal representation learning? We explore this question in this paper. The key observation is that interventional data often carries geometric signatures of the latent factors' support (i.e. what values each latent can possibly take). For example, when the latent factors are causally connected, interventions can break the dependency between the intervened latents' support and their ancestors'. Leveraging this fact, we prove that the latent causal factors can be identified up to permutation and scaling given data from perfect do interventions. Moreover, we can achieve block affine identification, namely the estimated latent factors are only entangled with a few other latents if we have access to data from imperfect interventions. These results highlight the unique power of interventional data in causal representation learning; they can enable provable identification of latent factors without any assumptions about their distributions or dependency structure.

The role of the attention mechanism in encoding linguistic knowledge has received special interest in NLP. However, the ability of the attention heads to judge the grammatical acceptability of a sentence has been underexplored. This paper approaches the paradigm of acceptability judgments with topological data analysis (TDA), showing that the geometric properties of the attention graph can be efficiently exploited for two standard practices in linguistics: binary judgments and linguistic minimal pairs. Topological features enhance the BERT-based acceptability classifier scores by 8%-24% on CoLA in three languages (English, Italian, and Swedish). By revealing the topological discrepancy between attention maps of minimal pairs, we achieve the human-level performance on the BLiMP benchmark, outperforming nine statistical and Transformer LM baselines. At the same time, TDA provides the foundation for analyzing the linguistic functions of attention heads and interpreting the correspondence between the graph features and grammatical phenomena.

We present STream3R, a novel approach to 3D reconstruction that reformulates pointmap prediction as a decoder-only Transformer problem. Existing state-of-the-art methods for multi-view reconstruction either depend on expensive global optimization or rely on simplistic memory mechanisms that scale poorly with sequence length. In contrast, STream3R introduces an streaming framework that processes image sequences efficiently using causal attention, inspired by advances in modern language modeling. By learning geometric priors from large-scale 3D datasets, STream3R generalizes well to diverse and challenging scenarios, including dynamic scenes where traditional methods often fail. Extensive experiments show that our method consistently outperforms prior work across both static and dynamic scene benchmarks. Moreover, STream3R is inherently compatible with LLM-style training infrastructure, enabling efficient large-scale pretraining and fine-tuning for various downstream 3D tasks. Our results underscore the potential of causal Transformer models for online 3D perception, paving the way for real-time 3D understanding in streaming environments. More details can be found in our project page: https://nirvanalan.github.io/projects/stream3r.

6D object pose estimation suffers from reduced accuracy when applied to metallic objects. We set out to improve the state-of-the-art by addressing challenges such as reflections and specular highlights in industrial applications. Our novel BOP-compatible dataset, featuring a diverse set of metallic objects (cans, household, and industrial items) under various lighting and background conditions, provides additional geometric and visual cues. We demonstrate that these cues can be effectively leveraged to enhance overall performance. To illustrate the usefulness of the additional features, we improve upon the GDRNPP algorithm by introducing an additional keypoint prediction and material estimator head in order to improve spatial scene understanding. Evaluations on the new dataset show improved accuracy for metallic objects, supporting the hypothesis that additional geometric and visual cues can improve learning.

Foundation models trained on vast amounts of data have demonstrated remarkable reasoning and generation capabilities in the domains of text, images, audio and video. Our goal at Roblox is to build such a foundation model for 3D intelligence, a model that can support developers in producing all aspects of a Roblox experience, from generating 3D objects and scenes to rigging characters for animation to producing programmatic scripts describing object behaviors. We discuss three key design requirements for such a 3D foundation model and then present our first step towards building such a model. We expect that 3D geometric shapes will be a core data type and describe our solution for 3D shape tokenizer. We show how our tokenization scheme can be used in applications for text-to-shape generation, shape-to-text generation and text-to-scene generation. We demonstrate how these applications can collaborate with existing large language models (LLMs) to perform scene analysis and reasoning. We conclude with a discussion outlining our path to building a fully unified foundation model for 3D intelligence.

Self-supervised learning converts raw perceptual data such as images to a compact space where simple Euclidean distances measure meaningful variations in data. In this paper, we extend this formulation by adding additional geometric structure to the embedding space by enforcing transformations of input space to correspond to simple (i.e., linear) transformations of embedding space. Specifically, in the contrastive learning setting, we introduce an equivariance objective and theoretically prove that its minima forces augmentations on input space to correspond to rotations on the spherical embedding space. We show that merely combining our equivariant loss with a non-collapse term results in non-trivial representations, without requiring invariance to data augmentations. Optimal performance is achieved by also encouraging approximate invariance, where input augmentations correspond to small rotations. Our method, CARE: Contrastive Augmentation-induced Rotational Equivariance, leads to improved performance on downstream tasks, and ensures sensitivity in embedding space to important variations in data (e.g., color) that standard contrastive methods do not achieve. Code is available at https://github.com/Sharut/CARE.

Visual and linguistic concepts naturally organize themselves in a hierarchy, where a textual concept ``dog'' entails all images that contain dogs. Despite being intuitive, current large-scale vision and language models such as CLIP do not explicitly capture such hierarchy. We propose MERU, a contrastive model that yields hyperbolic representations of images and text. Hyperbolic spaces have suitable geometric properties to embed tree-like data, so MERU can better capture the underlying hierarchy in image-text data. Our results show that MERU learns a highly interpretable representation space while being competitive with CLIP's performance on multi-modal tasks like image classification and image-text retrieval.

We introduce Temporal Residual Jacobians as a novel representation to enable data-driven motion transfer. Our approach does not assume access to any rigging or intermediate shape keyframes, produces geometrically and temporally consistent motions, and can be used to transfer long motion sequences. Central to our approach are two coupled neural networks that individually predict local geometric and temporal changes that are subsequently integrated, spatially and temporally, to produce the final animated meshes. The two networks are jointly trained, complement each other in producing spatial and temporal signals, and are supervised directly with 3D positional information. During inference, in the absence of keyframes, our method essentially solves a motion extrapolation problem. We test our setup on diverse meshes (synthetic and scanned shapes) to demonstrate its superiority in generating realistic and natural-looking animations on unseen body shapes against SoTA alternatives. Supplemental video and code are available at https://temporaljacobians.github.io/ .

We propose a novel neural deformable model (NDM) targeting at the reconstruction and modeling of 3D bi-ventricular shape of the heart from 2D sparse cardiac magnetic resonance (CMR) imaging data. We model the bi-ventricular shape using blended deformable superquadrics, which are parameterized by a set of geometric parameter functions and are capable of deforming globally and locally. While global geometric parameter functions and deformations capture gross shape features from visual data, local deformations, parameterized as neural diffeomorphic point flows, can be learned to recover the detailed heart shape.Different from iterative optimization methods used in conventional deformable model formulations, NDMs can be trained to learn such geometric parameter functions, global and local deformations from a shape distribution manifold. Our NDM can learn to densify a sparse cardiac point cloud with arbitrary scales and generate high-quality triangular meshes automatically. It also enables the implicit learning of dense correspondences among different heart shape instances for accurate cardiac shape registration. Furthermore, the parameters of NDM are intuitive, and can be used by a physician without sophisticated post-processing. Experimental results on a large CMR dataset demonstrate the improved performance of NDM over conventional methods.

A droplet impacting a deep fluid bath is as common as rain over the ocean. If the impact is sufficiently gentle, the mediating air layer remains intact, and the droplet may rebound completely from the interface. In this work, we experimentally investigate the role of translational bath motion on the bouncing to coalescence transition. Over a range of parameters, we find that the relative bath motion systematically decreases the normal Weber number required to transition from bouncing to merging. Direct numerical simulations demonstrate that the depression created during impact combined with the translational motion of the bath enhances the air layer drainage on the upstream side of the droplet, ultimately favoring coalescence. A simple geometric argument is presented that rationalizes the collapse of the experimental threshold data, extending what is known for the case of axisymmetric normal impacts to the more general 3D scenario of interest herein.

The choice of data representation is a key factor in the success of deep learning in geometric tasks. For instance, DUSt3R recently introduced the concept of viewpoint-invariant point maps, generalizing depth prediction and showing that all key problems in the 3D reconstruction of static scenes can be reduced to predicting such point maps. In this paper, we develop an analogous concept for a very different problem: the reconstruction of the 3D shape and pose of deformable objects. To this end, we introduce Dual Point Maps (DualPM), where a pair of point maps is extracted from the same image-one associating pixels to their 3D locations on the object and the other to a canonical version of the object in its rest pose. We also extend point maps to amodal reconstruction to recover the complete shape of the object, even through self-occlusions. We show that 3D reconstruction and 3D pose estimation can be reduced to the prediction of DualPMs. Empirically, we demonstrate that this representation is a suitable target for deep networks to predict. Specifically, we focus on modeling quadrupeds, showing that DualPMs can be trained purely on synthetic 3D data, consisting of one or two models per category, while generalizing effectively to real images. With this approach, we achieve significant improvements over previous methods for the 3D analysis and reconstruction of such objects.

Accurate, real-time 3D reconstruction of human heads from monocular images and videos underlies numerous visual applications. As 3D ground truth data is hard to come by at scale, previous methods have sought to learn from abundant 2D videos in a self-supervised manner. Typically, this involves the use of differentiable mesh rendering, which is effective but faces limitations. To improve on this, we propose SHeaP (Self-supervised Head Geometry Predictor Learned via 2D Gaussians). Given a source image, we predict a 3DMM mesh and a set of Gaussians that are rigged to this mesh. We then reanimate this rigged head avatar to match a target frame, and backpropagate photometric losses to both the 3DMM and Gaussian prediction networks. We find that using Gaussians for rendering substantially improves the effectiveness of this self-supervised approach. Training solely on 2D data, our method surpasses existing self-supervised approaches in geometric evaluations on the NoW benchmark for neutral faces and a new benchmark for non-neutral expressions. Our method also produces highly expressive meshes, outperforming state-of-the-art in emotion classification.

We use new cosmic microwave background (CMB) primary temperature and polarization anisotropy measurements from the Atacama Cosmology Telescope (ACT) Data Release 6 (DR6) to test foundational assumptions of the standard cosmological model and set constraints on extensions to it. We derive constraints from the ACT DR6 power spectra alone, as well as in combination with legacy data from Planck. To break geometric degeneracies, we include ACT and Planck CMB lensing data and baryon acoustic oscillation data from DESI Year-1, and further add supernovae measurements from Pantheon+ for models that affect the late-time expansion history. We verify the near-scale-invariance (running of the spectral index d n_s/dln k = 0.0062 pm 0.0052) and adiabaticity of the primordial perturbations. Neutrino properties are consistent with Standard Model predictions: we find no evidence for new light, relativistic species that are free-streaming (N_{rm eff} = 2.86 pm 0.13, which combined with external BBN data becomes N_{rm eff} = 2.89 pm 0.11), for non-zero neutrino masses (sum m_nu < 0.082 eV at 95% CL), or for neutrino self-interactions. We also find no evidence for self-interacting dark radiation (N_{rm idr} < 0.134), early-universe variation of fundamental constants, early dark energy, primordial magnetic fields, or modified recombination. Our data are consistent with standard BBN, the FIRAS-inferred CMB temperature, a dark matter component that is collisionless and with only a small fraction allowed as axion-like particles, a cosmological constant, and the late-time growth rate predicted by general relativity. We find no statistically significant preference for a departure from the baseline LambdaCDM model. In general, models introduced to increase the Hubble constant or to decrease the amplitude of density fluctuations inferred from the primary CMB are not favored by our data.

Semi-Supervised Visual Grounding (SSVG) is a new challenge for its sparse labeled data with the need for multimodel understanding. A previous study, RefTeacher, makes the first attempt to tackle this task by adopting the teacher-student framework to provide pseudo confidence supervision and attention-based supervision. However, this approach is incompatible with current state-of-the-art visual grounding models, which follow the Transformer-based pipeline. These pipelines directly regress results without region proposals or foreground binary classification, rendering them unsuitable for fitting in RefTeacher due to the absence of confidence scores. Furthermore, the geometric difference in teacher and student inputs, stemming from different data augmentations, induces natural misalignment in attention-based constraints. To establish a compatible SSVG framework, our paper proposes the ACTive REtraining approach for Semi-Supervised Visual Grounding, abbreviated as ACTRESS. Initially, the model is enhanced by incorporating an additional quantized detection head to expose its detection confidence. Building upon this, ACTRESS consists of an active sampling strategy and a selective retraining strategy. The active sampling strategy iteratively selects high-quality pseudo labels by evaluating three crucial aspects: Faithfulness, Robustness, and Confidence, optimizing the utilization of unlabeled data. The selective retraining strategy retrains the model with periodic re-initialization of specific parameters, facilitating the model's escape from local minima. Extensive experiments demonstrates our superior performance on widely-used benchmark datasets.

Learning the distribution of data on Riemannian manifolds is crucial for modeling data from non-Euclidean space, which is required by many applications in diverse scientific fields. Yet, existing generative models on manifolds suffer from expensive divergence computation or rely on approximations of heat kernel. These limitations restrict their applicability to simple geometries and hinder scalability to high dimensions. In this work, we introduce the Riemannian Diffusion Mixture, a principled framework for building a generative diffusion process on manifolds. Instead of following the denoising approach of previous diffusion models, we construct a diffusion process using a mixture of bridge processes derived on general manifolds without requiring heat kernel estimations. We develop a geometric understanding of the mixture process, deriving the drift as a weighted mean of tangent directions to the data points that guides the process toward the data distribution. We further propose a scalable training objective for learning the mixture process that readily applies to general manifolds. Our method achieves superior performance on diverse manifolds with dramatically reduced number of in-training simulation steps for general manifolds.

We explore the task of geometric reconstruction of images captured from a mixture of ground and aerial views. Current state-of-the-art learning-based approaches fail to handle the extreme viewpoint variation between aerial-ground image pairs. Our hypothesis is that the lack of high-quality, co-registered aerial-ground datasets for training is a key reason for this failure. Such data is difficult to assemble precisely because it is difficult to reconstruct in a scalable way. To overcome this challenge, we propose a scalable framework combining pseudo-synthetic renderings from 3D city-wide meshes (e.g., Google Earth) with real, ground-level crowd-sourced images (e.g., MegaDepth). The pseudo-synthetic data simulates a wide range of aerial viewpoints, while the real, crowd-sourced images help improve visual fidelity for ground-level images where mesh-based renderings lack sufficient detail, effectively bridging the domain gap between real images and pseudo-synthetic renderings. Using this hybrid dataset, we fine-tune several state-of-the-art algorithms and achieve significant improvements on real-world, zero-shot aerial-ground tasks. For example, we observe that baseline DUSt3R localizes fewer than 5% of aerial-ground pairs within 5 degrees of camera rotation error, while fine-tuning with our data raises accuracy to nearly 56%, addressing a major failure point in handling large viewpoint changes. Beyond camera estimation and scene reconstruction, our dataset also improves performance on downstream tasks like novel-view synthesis in challenging aerial-ground scenarios, demonstrating the practical value of our approach in real-world applications.

Scaling artist-designed meshes to high triangle numbers remains challenging for autoregressive generative models. Existing transformer-based methods suffer from long-sequence bottlenecks and limited quantization resolution, primarily due to the large number of tokens required and constrained quantization granularity. These issues prevent faithful reproduction of fine geometric details and structured density patterns. We introduce MeshMosaic, a novel local-to-global framework for artist mesh generation that scales to over 100K triangles--substantially surpassing prior methods, which typically handle only around 8K faces. MeshMosaic first segments shapes into patches, generating each patch autoregressively and leveraging shared boundary conditions to promote coherence, symmetry, and seamless connectivity between neighboring regions. This strategy enhances scalability to high-resolution meshes by quantizing patches individually, resulting in more symmetrical and organized mesh density and structure. Extensive experiments across multiple public datasets demonstrate that MeshMosaic significantly outperforms state-of-the-art methods in both geometric fidelity and user preference, supporting superior detail representation and practical mesh generation for real-world applications.

High-fidelity 3D asset generation is crucial for various industries. While recent 3D pretrained models show strong capability in producing realistic content, most are built upon diffusion models and follow a two-stage pipeline that first generates geometry and then synthesizes appearance. Such a decoupled design tends to produce geometry-texture misalignment and non-negligible cost. In this paper, we propose UniLat3D, a unified framework that encodes geometry and appearance in a single latent space, enabling direct single-stage generation. Our key contribution is a geometry-appearance Unified VAE, which compresses high-resolution sparse features into a compact latent representation -- UniLat. UniLat integrates structural and visual information into a dense low-resolution latent, which can be efficiently decoded into diverse 3D formats, e.g., 3D Gaussians and meshes. Based on this unified representation, we train a single flow-matching model to map Gaussian noise directly into UniLat, eliminating redundant stages. Trained solely on public datasets, UniLat3D produces high-quality 3D assets in seconds from a single image, achieving superior appearance fidelity and geometric quality. More demos \& code are available at https://unilat3d.github.io/

Effectively representing materials as text has the potential to leverage the vast advancements of large language models (LLMs) for discovering new materials. While LLMs have shown remarkable success in various domains, their application to materials science remains underexplored. A fundamental challenge is the lack of understanding of how to best utilize text-based representations for materials modeling. This challenge is further compounded by the absence of a comprehensive benchmark to rigorously evaluate the capabilities and limitations of these text representations in capturing the complexity of material systems. To address this gap, we propose MatText, a suite of benchmarking tools and datasets designed to systematically evaluate the performance of language models in modeling materials. MatText encompasses nine distinct text-based representations for material systems, including several novel representations. Each representation incorporates unique inductive biases that capture relevant information and integrate prior physical knowledge about materials. Additionally, MatText provides essential tools for training and benchmarking the performance of language models in the context of materials science. These tools include standardized dataset splits for each representation, probes for evaluating sensitivity to geometric factors, and tools for seamlessly converting crystal structures into text. Using MatText, we conduct an extensive analysis of the capabilities of language models in modeling materials. Our findings reveal that current language models consistently struggle to capture the geometric information crucial for materials modeling across all representations. Instead, these models tend to leverage local information, which is emphasized in some of our novel representations. Our analysis underscores MatText's ability to reveal shortcomings of text-based methods for materials design.

While recent advances in neural radiance field enable realistic digitization for large-scale scenes, the image-capturing process is still time-consuming and labor-intensive. Previous works attempt to automate this process using the Next-Best-View (NBV) policy for active 3D reconstruction. However, the existing NBV policies heavily rely on hand-crafted criteria, limited action space, or per-scene optimized representations. These constraints limit their cross-dataset generalizability. To overcome them, we propose GenNBV, an end-to-end generalizable NBV policy. Our policy adopts a reinforcement learning (RL)-based framework and extends typical limited action space to 5D free space. It empowers our agent drone to scan from any viewpoint, and even interact with unseen geometries during training. To boost the cross-dataset generalizability, we also propose a novel multi-source state embedding, including geometric, semantic, and action representations. We establish a benchmark using the Isaac Gym simulator with the Houses3K and OmniObject3D datasets to evaluate this NBV policy. Experiments demonstrate that our policy achieves a 98.26% and 97.12% coverage ratio on unseen building-scale objects from these datasets, respectively, outperforming prior solutions.

We present GenesisGeo, an automated theorem prover in Euclidean geometry. We have open-sourced a large-scale geometry dataset of 21.8 million geometric problems, over 3 million of which contain auxiliary constructions. Specially, we significantly accelerate the symbolic deduction engine DDARN by 120x through theorem matching, combined with a C++ implementation of its core components. Furthermore, we build our neuro-symbolic prover, GenesisGeo, upon Qwen3-0.6B-Base, which solves 24 of 30 problems (IMO silver medal level) in the IMO-AG-30 benchmark using a single model, and achieves 26 problems (IMO gold medal level) with a dual-model ensemble.

This paper investigates the direct application of standardized designs on the robot for conducting robot hand-eye calibration by employing 3D scanners with collaborative robots. The well-established geometric features of the robot flange are exploited by directly capturing its point cloud data. In particular, an iterative method is proposed to facilitate point cloud processing toward a refined calibration outcome. Several extensive experiments are conducted over a range of collaborative robots, including Universal Robots UR5 & UR10 e-series, Franka Emika, and AUBO i5 using an industrial-grade 3D scanner Photoneo Phoxi S & M and a commercial-grade 3D scanner Microsoft Azure Kinect DK. Experimental results show that translational and rotational errors converge efficiently to less than 0.28 mm and 0.25 degrees, respectively, achieving a hand-eye calibration accuracy as high as the camera's resolution, probing the hardware limit. A welding seam tracking system is presented, combining the flange-based calibration method with soft tactile sensing. The experiment results show that the system enables the robot to adjust its motion in real-time, ensuring consistent weld quality and paving the way for more efficient and adaptable manufacturing processes.

Learning spatial-temporal correspondences in cardiac motion from images is important for understanding the underlying dynamics of cardiac anatomical structures. Many methods explicitly impose smoothness constraints such as the L_2 norm on the displacement vector field (DVF), while usually ignoring biomechanical feasibility in the transformation. Other geometric constraints either regularize specific regions of interest such as imposing incompressibility on the myocardium or introduce additional steps such as training a separate network-based regularizer on physically simulated datasets. In this work, we propose an explicit biomechanics-informed prior as regularization on the predicted DVF in modeling a more generic biomechanically plausible transformation within all cardiac structures without introducing additional training complexity. We validate our methods on two publicly available datasets in the context of 2D MRI data and perform extensive experiments to illustrate the effectiveness and robustness of our proposed methods compared to other competing regularization schemes. Our proposed methods better preserve biomechanical properties by visual assessment and show advantages in segmentation performance using quantitative evaluation metrics. The code is publicly available at https://github.com/Voldemort108X/bioinformed_reg.

Feed-forward 3D generative models like the Large Reconstruction Model (LRM) have demonstrated exceptional generation speed. However, the transformer-based methods do not leverage the geometric priors of the triplane component in their architecture, often leading to sub-optimal quality given the limited size of 3D data and slow training. In this work, we present the Convolutional Reconstruction Model (CRM), a high-fidelity feed-forward single image-to-3D generative model. Recognizing the limitations posed by sparse 3D data, we highlight the necessity of integrating geometric priors into network design. CRM builds on the key observation that the visualization of triplane exhibits spatial correspondence of six orthographic images. First, it generates six orthographic view images from a single input image, then feeds these images into a convolutional U-Net, leveraging its strong pixel-level alignment capabilities and significant bandwidth to create a high-resolution triplane. CRM further employs Flexicubes as geometric representation, facilitating direct end-to-end optimization on textured meshes. Overall, our model delivers a high-fidelity textured mesh from an image in just 10 seconds, without any test-time optimization.

Generating faithful visualizations of human faces requires capturing both coarse and fine-level details of the face geometry and appearance. Existing methods are either data-driven, requiring an extensive corpus of data not publicly accessible to the research community, or fail to capture fine details because they rely on geometric face models that cannot represent fine-grained details in texture with a mesh discretization and linear deformation designed to model only a coarse face geometry. We introduce a method that bridges this gap by drawing inspiration from traditional computer graphics techniques. Unseen expressions are modeled by blending appearance from a sparse set of extreme poses. This blending is performed by measuring local volumetric changes in those expressions and locally reproducing their appearance whenever a similar expression is performed at test time. We show that our method generalizes to unseen expressions, adding fine-grained effects on top of smooth volumetric deformations of a face, and demonstrate how it generalizes beyond faces.

The standard approach for visual place recognition is to use global image descriptors to retrieve the most similar database images for a given query image. The results can then be further improved with re-ranking methods that re-order the top scoring images. However, existing methods focus on re-ranking based on the same image descriptors that were used for the initial retrieval, which we argue provides limited additional signal. In this work we propose Generalized Contextual Similarity Aggregation (GCSA), which is a graph neural network-based re-ranking method that, in addition to the visual descriptors, can leverage other types of available side information. This can for example be other sensor data (such as signal strength of nearby WiFi or BlueTooth endpoints) or geometric properties such as camera poses for database images. In many applications this information is already present or can be acquired with low effort. Our architecture leverages the concept of affinity vectors to allow for a shared encoding of the heterogeneous multi-modal input. Two large-scale datasets, covering both outdoor and indoor localization scenarios, are utilized for training and evaluation. In experiments we show significant improvement not only on image retrieval metrics, but also for the downstream visual localization task.

Predicting realistic ground views from satellite imagery in urban scenes is a challenging task due to the significant view gaps between satellite and ground-view images. We propose a novel pipeline to tackle this challenge, by generating geospecifc views that maximally respect the weak geometry and texture from multi-view satellite images. Different from existing approaches that hallucinate images from cues such as partial semantics or geometry from overhead satellite images, our method directly predicts ground-view images at geolocation by using a comprehensive set of information from the satellite image, resulting in ground-level images with a resolution boost at a factor of ten or more. We leverage a novel building refinement method to reduce geometric distortions in satellite data at ground level, which ensures the creation of accurate conditions for view synthesis using diffusion networks. Moreover, we proposed a novel geospecific prior, which prompts distribution learning of diffusion models to respect image samples that are closer to the geolocation of the predicted images. We demonstrate our pipeline is the first to generate close-to-real and geospecific ground views merely based on satellite images.

While static word embedding models are known to represent linguistic analogies as parallel lines in high-dimensional space, the underlying mechanism as to why they result in such geometric structures remains obscure. We find that an elementary contrastive-style method employed over distributional information performs competitively with popular word embedding models on analogy recovery tasks, while achieving dramatic speedups in training time. Further, we demonstrate that a contrastive loss is sufficient to create these parallel structures in word embeddings, and establish a precise relationship between the co-occurrence statistics and the geometric structure of the resulting word embeddings.

3D Gaussian Splatting (3DGS) excels in photorealistic scene reconstruction but struggles with stylized scenarios (e.g., cartoons, games) due to fragmented textures, semantic misalignment, and limited adaptability to abstract aesthetics. We propose StyleMe3D, a holistic framework for 3D GS style transfer that integrates multi-modal style conditioning, multi-level semantic alignment, and perceptual quality enhancement. Our key insights include: (1) optimizing only RGB attributes preserves geometric integrity during stylization; (2) disentangling low-, medium-, and high-level semantics is critical for coherent style transfer; (3) scalability across isolated objects and complex scenes is essential for practical deployment. StyleMe3D introduces four novel components: Dynamic Style Score Distillation (DSSD), leveraging Stable Diffusion's latent space for semantic alignment; Contrastive Style Descriptor (CSD) for localized, content-aware texture transfer; Simultaneously Optimized Scale (SOS) to decouple style details and structural coherence; and 3D Gaussian Quality Assessment (3DG-QA), a differentiable aesthetic prior trained on human-rated data to suppress artifacts and enhance visual harmony. Evaluated on NeRF synthetic dataset (objects) and tandt db (scenes) datasets, StyleMe3D outperforms state-of-the-art methods in preserving geometric details (e.g., carvings on sculptures) and ensuring stylistic consistency across scenes (e.g., coherent lighting in landscapes), while maintaining real-time rendering. This work bridges photorealistic 3D GS and artistic stylization, unlocking applications in gaming, virtual worlds, and digital art.

We use tools from geometric statistics to analyze the usual estimation procedure of a template shape. This applies to shapes from landmarks, curves, surfaces, images etc. We demonstrate the asymptotic bias of the template shape estimation using the stratified geometry of the shape space. We give a Taylor expansion of the bias with respect to a parameter sigma describing the measurement error on the data. We propose two bootstrap procedures that quantify the bias and correct it, if needed. They are applicable for any type of shape data. We give a rule of thumb to provide intuition on whether the bias has to be corrected. This exhibits the parameters that control the bias' magnitude. We illustrate our results on simulated and real shape data.

Pancreatic cancer carries a poor prognosis and relies on endoscopic ultrasound (EUS) for targeted biopsy and radiotherapy. However, the speckle noise, low contrast, and unintuitive appearance of EUS make segmentation of pancreatic tumors with fully supervised deep learning (DL) models both error-prone and dependent on large, expert-curated annotation datasets. To address these challenges, we present TextSAM-EUS, a novel, lightweight, text-driven adaptation of the Segment Anything Model (SAM) that requires no manual geometric prompts at inference. Our approach leverages text prompt learning (context optimization) through the BiomedCLIP text encoder in conjunction with a LoRA-based adaptation of SAM's architecture to enable automatic pancreatic tumor segmentation in EUS, tuning only 0.86% of the total parameters. On the public Endoscopic Ultrasound Database of the Pancreas, TextSAM-EUS with automatic prompts attains 82.69% Dice and 85.28% normalized surface distance (NSD), and with manual geometric prompts reaches 83.10% Dice and 85.70% NSD, outperforming both existing state-of-the-art (SOTA) supervised DL models and foundation models (e.g., SAM and its variants). As the first attempt to incorporate prompt learning in SAM-based medical image segmentation, TextSAM-EUS offers a practical option for efficient and robust automatic EUS segmentation. Code is available at https://github.com/HealthX-Lab/TextSAM-EUS .

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

We present Buffer Anytime, a framework for estimation of depth and normal maps (which we call geometric buffers) from video that eliminates the need for paired video--depth and video--normal training data. Instead of relying on large-scale annotated video datasets, we demonstrate high-quality video buffer estimation by leveraging single-image priors with temporal consistency constraints. Our zero-shot training strategy combines state-of-the-art image estimation models based on optical flow smoothness through a hybrid loss function, implemented via a lightweight temporal attention architecture. Applied to leading image models like Depth Anything V2 and Marigold-E2E-FT, our approach significantly improves temporal consistency while maintaining accuracy. Experiments show that our method not only outperforms image-based approaches but also achieves results comparable to state-of-the-art video models trained on large-scale paired video datasets, despite using no such paired video data.

Aerial imagery analysis is critical for many research fields. However, obtaining frequent high-quality aerial images is not always accessible due to its high effort and cost requirements. One solution is to use the Ground-to-Aerial (G2A) technique to synthesize aerial images from easily collectible ground images. However, G2A is rarely studied, because of its challenges, including but not limited to, the drastic view changes, occlusion, and range of visibility. In this paper, we present a novel Geometric Preserving Ground-to-Aerial (G2A) image synthesis (GPG2A) model that can generate realistic aerial images from ground images. GPG2A consists of two stages. The first stage predicts the Bird's Eye View (BEV) segmentation (referred to as the BEV layout map) from the ground image. The second stage synthesizes the aerial image from the predicted BEV layout map and text descriptions of the ground image. To train our model, we present a new multi-modal cross-view dataset, namely VIGORv2 which is built upon VIGOR with newly collected aerial images, maps, and text descriptions. Our extensive experiments illustrate that GPG2A synthesizes better geometry-preserved aerial images than existing models. We also present two applications, data augmentation for cross-view geo-localization and sketch-based region search, to further verify the effectiveness of our GPG2A. The code and data will be publicly available.

Extracting planes from a 3D scene is useful for downstream tasks in robotics and augmented reality. In this paper we tackle the problem of estimating the planar surfaces in a scene from posed images. Our first finding is that a surprisingly competitive baseline results from combining popular clustering algorithms with recent improvements in 3D geometry estimation. However, such purely geometric methods are understandably oblivious to plane semantics, which are crucial to discerning distinct planes. To overcome this limitation, we propose a method that predicts multi-view consistent plane embeddings that complement geometry when clustering points into planes. We show through extensive evaluation on the ScanNetV2 dataset that our new method outperforms existing approaches and our strong geometric baseline for the task of plane estimation.

Modern operating room is becoming increasingly complex, requiring innovative intra-operative support systems. While the focus of surgical data science has largely been on video analysis, integrating surgical computer vision with language capabilities is emerging as a necessity. Our work aims to advance Visual Question Answering (VQA) in the surgical context with scene graph knowledge, addressing two main challenges in the current surgical VQA systems: removing question-condition bias in the surgical VQA dataset and incorporating scene-aware reasoning in the surgical VQA model design. First, we propose a Surgical Scene Graph-based dataset, SSG-QA, generated by employing segmentation and detection models on publicly available datasets. We build surgical scene graphs using spatial and action information of instruments and anatomies. These graphs are fed into a question engine, generating diverse QA pairs. Our SSG-QA dataset provides a more complex, diverse, geometrically grounded, unbiased, and surgical action-oriented dataset compared to existing surgical VQA datasets. We then propose SSG-QA-Net, a novel surgical VQA model incorporating a lightweight Scene-embedded Interaction Module (SIM), which integrates geometric scene knowledge in the VQA model design by employing cross-attention between the textual and the scene features. Our comprehensive analysis of the SSG-QA dataset shows that SSG-QA-Net outperforms existing methods across different question types and complexities. We highlight that the primary limitation in the current surgical VQA systems is the lack of scene knowledge to answer complex queries. We present a novel surgical VQA dataset and model and show that results can be significantly improved by incorporating geometric scene features in the VQA model design. The source code and the dataset will be made publicly available at: https://github.com/CAMMA-public/SSG-QA

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.

Point cloud analysis is challenging due to irregularity and unordered data structure. To capture the 3D geometries, prior works mainly rely on exploring sophisticated local geometric extractors using convolution, graph, or attention mechanisms. These methods, however, incur unfavorable latency during inference, and the performance saturates over the past few years. In this paper, we present a novel perspective on this task. We notice that detailed local geometrical information probably is not the key to point cloud analysis -- we introduce a pure residual MLP network, called PointMLP, which integrates no sophisticated local geometrical extractors but still performs very competitively. Equipped with a proposed lightweight geometric affine module, PointMLP delivers the new state-of-the-art on multiple datasets. On the real-world ScanObjectNN dataset, our method even surpasses the prior best method by 3.3% accuracy. We emphasize that PointMLP achieves this strong performance without any sophisticated operations, hence leading to a superior inference speed. Compared to most recent CurveNet, PointMLP trains 2x faster, tests 7x faster, and is more accurate on ModelNet40 benchmark. We hope our PointMLP may help the community towards a better understanding of point cloud analysis. The code is available at https://github.com/ma-xu/pointMLP-pytorch.

Fuzzy similarity join is an important database operator widely used in practice. So far the research community has focused exclusively on optimizing fuzzy join scalability. However, practitioners today also struggle to optimize fuzzy-join quality, because they face a daunting space of parameters (e.g., distance-functions, distance-thresholds, tokenization-options, etc.), and often have to resort to a manual trial-and-error approach to program these parameters in order to optimize fuzzy-join quality. This key challenge of automatically generating high-quality fuzzy-join programs has received surprisingly little attention thus far. In this work, we study the problem of "auto-program" fuzzy-joins. Leveraging a geometric interpretation of distance-functions, we develop an unsupervised Auto-FuzzyJoin framework that can infer suitable fuzzy-join programs on given input tables, without requiring explicit human input such as labeled training data. Using Auto-FuzzyJoin, users only need to provide two input tables L and R, and a desired precision target tau (say 0.9). Auto-FuzzyJoin leverages the fact that one of the input is a reference table to automatically program fuzzy-joins that meet the precision target tau in expectation, while maximizing fuzzy-join recall (defined as the number of correctly joined records). Experiments on both existing benchmarks and a new benchmark with 50 fuzzy-join tasks created from Wikipedia data suggest that the proposed Auto-FuzzyJoin significantly outperforms existing unsupervised approaches, and is surprisingly competitive even against supervised approaches (e.g., Magellan and DeepMatcher) when 50\% of ground-truth labels are used as training data.

In this work, we propose DiT360, a DiT-based framework that performs hybrid training on perspective and panoramic data for panoramic image generation. For the issues of maintaining geometric fidelity and photorealism in generation quality, we attribute the main reason to the lack of large-scale, high-quality, real-world panoramic data, where such a data-centric view differs from prior methods that focus on model design. Basically, DiT360 has several key modules for inter-domain transformation and intra-domain augmentation, applied at both the pre-VAE image level and the post-VAE token level. At the image level, we incorporate cross-domain knowledge through perspective image guidance and panoramic refinement, which enhance perceptual quality while regularizing diversity and photorealism. At the token level, hybrid supervision is applied across multiple modules, which include circular padding for boundary continuity, yaw loss for rotational robustness, and cube loss for distortion awareness. Extensive experiments on text-to-panorama, inpainting, and outpainting tasks demonstrate that our method achieves better boundary consistency and image fidelity across eleven quantitative metrics. Our code is available at https://github.com/Insta360-Research-Team/DiT360.

Foundation models pre-trained on massive unlabeled datasets have revolutionized natural language and computer vision, exhibiting remarkable generalization capabilities, thus highlighting the importance of pre-training. Yet, efforts in robotics have struggled to achieve similar success, limited by either the need for costly robotic annotations or the lack of representations that effectively model the physical world. In this paper, we introduce ARM4R, an Auto-regressive Robotic Model that leverages low-level 4D Representations learned from human video data to yield a better pre-trained robotic model. Specifically, we focus on utilizing 3D point tracking representations from videos derived by lifting 2D representations into 3D space via monocular depth estimation across time. These 4D representations maintain a shared geometric structure between the points and robot state representations up to a linear transformation, enabling efficient transfer learning from human video data to low-level robotic control. Our experiments show that ARM4R can transfer efficiently from human video data to robotics and consistently improves performance on tasks across various robot environments and configurations.

Data-driven methods such as reinforcement and imitation learning have achieved remarkable success in robot autonomy. However, their data-centric nature still hinders them from generalizing well to ever-changing environments. Moreover, collecting large datasets for robotic tasks is often impractical and expensive. To overcome these challenges, we introduce a new self-supervised neural-symbolic (NeSy) computational framework, imperative learning (IL), for robot autonomy, leveraging the generalization abilities of symbolic reasoning. The framework of IL consists of three primary components: a neural module, a reasoning engine, and a memory system. We formulate IL as a special bilevel optimization (BLO), which enables reciprocal learning over the three modules. This overcomes the label-intensive obstacles associated with data-driven approaches and takes advantage of symbolic reasoning concerning logical reasoning, physical principles, geometric analysis, etc. We discuss several optimization techniques for IL and verify their effectiveness in five distinct robot autonomy tasks including path planning, rule induction, optimal control, visual odometry, and multi-robot routing. Through various experiments, we show that IL can significantly enhance robot autonomy capabilities and we anticipate that it will catalyze further research across diverse domains.

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

AI-driven geometric problem solving is a complex vision-language task that requires accurate diagram interpretation, mathematical reasoning, and robust cross-modal grounding. A foundational yet underexplored capability for this task is the ability to identify and interpret geometric elements based on natural language queries. To address this, we introduce the task of Referring Expression Comprehension (REC) for geometric problems, which evaluates whether models can localize points, shapes, and spatial relations in diagrams in response to textual prompts. We present GeoRef, a benchmark dataset constructed from existing geometric problem corpora, featuring diverse, high-quality annotations and queries. Due to the lack of annotated data for this task, we generate a large-scale synthetic training dataset using a structured geometric formal language, enabling broad coverage of geometric concepts and facilitating model adaptation. We explore two fine-tuning approaches: Supervised Fine-Tuning (SFT) and Group Relative Policy Optimization (GRPO). Our results show that GRPO significantly outperforms SFT by better aligning model behavior with task-specific rewards. Furthermore, we propose a verify-and-regenerate mechanism that detects incorrect predictions and re-infers answers using contextual reasoning history, further boosting accuracy. Notably, even state-of-the-art Multimodal Large Language Models (MLLMs) struggle with this task, underscoring the necessity of explicitly evaluating and strengthening geometric grounding as a prerequisite for robust geometric problem solving. Moreover, models trained on GeoRef demonstrate measurable improvements on downstream geometric reasoning tasks, highlighting the broader value of REC as a foundation for multimodal mathematical understanding.

We address the challenge of creating 3D assets for household articulated objects from a single image. Prior work on articulated object creation either requires multi-view multi-state input, or only allows coarse control over the generation process. These limitations hinder the scalability and practicality for articulated object modeling. In this work, we propose a method to generate articulated objects from a single image. Observing the object in resting state from an arbitrary view, our method generates an articulated object that is visually consistent with the input image. To capture the ambiguity in part shape and motion posed by a single view of the object, we design a diffusion model that learns the plausible variations of objects in terms of geometry and kinematics. To tackle the complexity of generating structured data with attributes in multiple domains, we design a pipeline that produces articulated objects from high-level structure to geometric details in a coarse-to-fine manner, where we use a part connectivity graph and part abstraction as proxies. Our experiments show that our method outperforms the state-of-the-art in articulated object creation by a large margin in terms of the generated object realism, resemblance to the input image, and reconstruction quality.

Cosmological data probe massive neutrinos via their effects on the geometry of the Universe and the growth of structure, both of which are degenerate with the late-time expansion history. We clarify the nature of these degeneracies and the individual roles of both probes in neutrino mass inference. Geometry is strongly sensitive to neutrino masses: within LambdaCDM, the primary cosmic microwave background anisotropies alone impose that the matter fraction Omega_m must increase fivefold with increasing neutrino mass. Moreover, large-scale structure observables, like weak lensing of the CMB, are dimensionless and thus depend not on the matter density (as often quoted) but in fact the matter fraction. We explore the consequential impact of this distinction on the interplay between probes of structure, low-redshift distances, and CMB anisotropies. We derive constraints on the neutrino's masses independently from their suppression of structure and impact on geometry, showing that the latter is at least as important as the former. While the Dark Energy Spectroscopic Instrument's recent baryon acoustic oscillation data place stringent bounds largely deriving from their geometric incompatibility with massive neutrinos, all recent type Ia supernova datasets drive marginal preferences for nonzero neutrino masses because they prefer substantially larger matter fractions. Recent CMB lensing data, however, neither exclude neutrinos' suppression of structure nor constrain it strongly enough to discriminate between mass hierarchies. Current data thus evince not a need for modified dynamics of neutrino perturbations or structure growth but rather an inconsistent compatibility with massive neutrinos' impact on the expansion history. We identify two of DESI's measurements that strongly influence its constraints, and we also discuss neutrino mass measurements in models that alter the sound horizon.

Machine learning techniques are essential tools to compute efficient, yet accurate, force fields for atomistic simulations. This approach has recently been extended to incorporate quantum computational methods, making use of variational quantum learning models to predict potential energy surfaces and atomic forces from ab initio training data. However, the trainability and scalability of such models are still limited, due to both theoretical and practical barriers. Inspired by recent developments in geometric classical and quantum machine learning, here we design quantum neural networks that explicitly incorporate, as a data-inspired prior, an extensive set of physically relevant symmetries. We find that our invariant quantum learning models outperform their more generic counterparts on individual molecules of growing complexity. Furthermore, we study a water dimer as a minimal example of a system with multiple components, showcasing the versatility of our proposed approach and opening the way towards larger simulations. Our results suggest that molecular force fields generation can significantly profit from leveraging the framework of geometric quantum machine learning, and that chemical systems represent, in fact, an interesting and rich playground for the development and application of advanced quantum machine learning tools.

Identifying key patterns of tactics implemented by rival teams, and developing effective responses, lies at the heart of modern football. However, doing so algorithmically remains an open research challenge. To address this unmet need, we propose TacticAI, an AI football tactics assistant developed and evaluated in close collaboration with domain experts from Liverpool FC. We focus on analysing corner kicks, as they offer coaches the most direct opportunities for interventions and improvements. TacticAI incorporates both a predictive and a generative component, allowing the coaches to effectively sample and explore alternative player setups for each corner kick routine and to select those with the highest predicted likelihood of success. We validate TacticAI on a number of relevant benchmark tasks: predicting receivers and shot attempts and recommending player position adjustments. The utility of TacticAI is validated by a qualitative study conducted with football domain experts at Liverpool FC. We show that TacticAI's model suggestions are not only indistinguishable from real tactics, but also favoured over existing tactics 90% of the time, and that TacticAI offers an effective corner kick retrieval system. TacticAI achieves these results despite the limited availability of gold-standard data, achieving data efficiency through geometric deep learning.

Audio-visual zero-shot learning aims to classify samples consisting of a pair of corresponding audio and video sequences from classes that are not present during training. An analysis of the audio-visual data reveals a large degree of hyperbolicity, indicating the potential benefit of using a hyperbolic transformation to achieve curvature-aware geometric learning, with the aim of exploring more complex hierarchical data structures for this task. The proposed approach employs a novel loss function that incorporates cross-modality alignment between video and audio features in the hyperbolic space. Additionally, we explore the use of multiple adaptive curvatures for hyperbolic projections. The experimental results on this very challenging task demonstrate that our proposed hyperbolic approach for zero-shot learning outperforms the SOTA method on three datasets: VGGSound-GZSL, UCF-GZSL, and ActivityNet-GZSL achieving a harmonic mean (HM) improvement of around 3.0%, 7.0%, and 5.3%, respectively.

Object-centric learning (OCL) aspires general and compositional understanding of scenes by representing a scene as a collection of object-centric representations. OCL has also been extended to multi-view image and video datasets to apply various data-driven inductive biases by utilizing geometric or temporal information in the multi-image data. Single-view images carry less information about how to disentangle a given scene than videos or multi-view images do. Hence, owing to the difficulty of applying inductive biases, OCL for single-view images remains challenging, resulting in inconsistent learning of object-centric representation. To this end, we introduce a novel OCL framework for single-view images, SLot Attention via SHepherding (SLASH), which consists of two simple-yet-effective modules on top of Slot Attention. The new modules, Attention Refining Kernel (ARK) and Intermediate Point Predictor and Encoder (IPPE), respectively, prevent slots from being distracted by the background noise and indicate locations for slots to focus on to facilitate learning of object-centric representation. We also propose a weak semi-supervision approach for OCL, whilst our proposed framework can be used without any assistant annotation during the inference. Experiments show that our proposed method enables consistent learning of object-centric representation and achieves strong performance across four datasets. Code is available at https://github.com/object-understanding/SLASH.

A key step in any scanning-based asset creation workflow is to convert unordered point clouds to a surface. Classical methods (e.g., Poisson reconstruction) start to degrade in the presence of noisy and partial scans. Hence, deep learning based methods have recently been proposed to produce complete surfaces, even from partial scans. However, such data-driven methods struggle to generalize to new shapes with large geometric and topological variations. We present Points2Surf, a novel patch-based learning framework that produces accurate surfaces directly from raw scans without normals. Learning a prior over a combination of detailed local patches and coarse global information improves generalization performance and reconstruction accuracy. Our extensive comparison on both synthetic and real data demonstrates a clear advantage of our method over state-of-the-art alternatives on previously unseen classes (on average, Points2Surf brings down reconstruction error by 30\% over SPR and by 270\%+ over deep learning based SotA methods) at the cost of longer computation times and a slight increase in small-scale topological noise in some cases. Our source code, pre-trained model, and dataset are available on: https://github.com/ErlerPhilipp/points2surf

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

Point clouds provide a flexible geometric representation suitable for countless applications in computer graphics; they also comprise the raw output of most 3D data acquisition devices. While hand-designed features on point clouds have long been proposed in graphics and vision, however, the recent overwhelming success of convolutional neural networks (CNNs) for image analysis suggests the value of adapting insight from CNN to the point cloud world. Point clouds inherently lack topological information so designing a model to recover topology can enrich the representation power of point clouds. To this end, we propose a new neural network module dubbed EdgeConv suitable for CNN-based high-level tasks on point clouds including classification and segmentation. EdgeConv acts on graphs dynamically computed in each layer of the network. It is differentiable and can be plugged into existing architectures. Compared to existing modules operating in extrinsic space or treating each point independently, EdgeConv has several appealing properties: It incorporates local neighborhood information; it can be stacked applied to learn global shape properties; and in multi-layer systems affinity in feature space captures semantic characteristics over potentially long distances in the original embedding. We show the performance of our model on standard benchmarks including ModelNet40, ShapeNetPart, and S3DIS.

A language model (LM) is a mapping from a linguistic context to an output token. However, much remains to be known about this mapping, including how its geometric properties relate to its function. We take a high-level geometric approach to its analysis, observing, across five pre-trained transformer-based LMs and three input datasets, a distinct phase characterized by high intrinsic dimensionality. During this phase, representations (1) correspond to the first full linguistic abstraction of the input; (2) are the first to viably transfer to downstream tasks; (3) predict each other across different LMs. Moreover, we find that an earlier onset of the phase strongly predicts better language modelling performance. In short, our results suggest that a central high-dimensionality phase underlies core linguistic processing in many common LM architectures.

We present MatDecompSDF, a novel framework for recovering high-fidelity 3D shapes and decomposing their physically-based material properties from multi-view images. The core challenge of inverse rendering lies in the ill-posed disentanglement of geometry, materials, and illumination from 2D observations. Our method addresses this by jointly optimizing three neural components: a neural Signed Distance Function (SDF) to represent complex geometry, a spatially-varying neural field for predicting PBR material parameters (albedo, roughness, metallic), and an MLP-based model for capturing unknown environmental lighting. The key to our approach is a physically-based differentiable rendering layer that connects these 3D properties to the input images, allowing for end-to-end optimization. We introduce a set of carefully designed physical priors and geometric regularizations, including a material smoothness loss and an Eikonal loss, to effectively constrain the problem and achieve robust decomposition. Extensive experiments on both synthetic and real-world datasets (e.g., DTU) demonstrate that MatDecompSDF surpasses state-of-the-art methods in geometric accuracy, material fidelity, and novel view synthesis. Crucially, our method produces editable and relightable assets that can be seamlessly integrated into standard graphics pipelines, validating its practical utility for digital content creation.

This work addresses the problem of active 3D mapping, where an agent must find an efficient trajectory to exhaustively reconstruct a new scene. Previous approaches mainly predict the next best view near the agent's location, which is prone to getting stuck in local areas. Additionally, existing indoor datasets are insufficient due to limited geometric complexity and inaccurate ground truth meshes. To overcome these limitations, we introduce a novel dataset AiMDoom with a map generator for the Doom video game, enabling to better benchmark active 3D mapping in diverse indoor environments. Moreover, we propose a new method we call next-best-path (NBP), which predicts long-term goals rather than focusing solely on short-sighted views. The model jointly predicts accumulated surface coverage gains for long-term goals and obstacle maps, allowing it to efficiently plan optimal paths with a unified model. By leveraging online data collection, data augmentation and curriculum learning, NBP significantly outperforms state-of-the-art methods on both the existing MP3D dataset and our AiMDoom dataset, achieving more efficient mapping in indoor environments of varying complexity.

Sparse RGBD scene completion is a challenging task especially when considering consistent textures and geometries throughout the entire scene. Different from existing solutions that rely on human-designed text prompts or predefined camera trajectories, we propose GenRC, an automated training-free pipeline to complete a room-scale 3D mesh with high-fidelity textures. To achieve this, we first project the sparse RGBD images to a highly incomplete 3D mesh. Instead of iteratively generating novel views to fill in the void, we utilized our proposed E-Diffusion to generate a view-consistent panoramic RGBD image which ensures global geometry and appearance consistency. Furthermore, we maintain the input-output scene stylistic consistency through textual inversion to replace human-designed text prompts. To bridge the domain gap among datasets, E-Diffusion leverages models trained on large-scale datasets to generate diverse appearances. GenRC outperforms state-of-the-art methods under most appearance and geometric metrics on ScanNet and ARKitScenes datasets, even though GenRC is not trained on these datasets nor using predefined camera trajectories. Project page: https://minfenli.github.io/GenRC

In this work, we introduce CC3D, a conditional generative model that synthesizes complex 3D scenes conditioned on 2D semantic scene layouts, trained using single-view images. Different from most existing 3D GANs that limit their applicability to aligned single objects, we focus on generating complex scenes with multiple objects, by modeling the compositional nature of 3D scenes. By devising a 2D layout-based approach for 3D synthesis and implementing a new 3D field representation with a stronger geometric inductive bias, we have created a 3D GAN that is both efficient and of high quality, while allowing for a more controllable generation process. Our evaluations on synthetic 3D-FRONT and real-world KITTI-360 datasets demonstrate that our model generates scenes of improved visual and geometric quality in comparison to previous works.

Estimating accurate and temporally consistent 3D human geometry from videos is a challenging problem in computer vision. Existing methods, primarily optimized for single images, often suffer from temporal inconsistencies and fail to capture fine-grained dynamic details. To address these limitations, we present GeoMan, a novel architecture designed to produce accurate and temporally consistent depth and normal estimations from monocular human videos. GeoMan addresses two key challenges: the scarcity of high-quality 4D training data and the need for metric depth estimation to accurately model human size. To overcome the first challenge, GeoMan employs an image-based model to estimate depth and normals for the first frame of a video, which then conditions a video diffusion model, reframing video geometry estimation task as an image-to-video generation problem. This design offloads the heavy lifting of geometric estimation to the image model and simplifies the video model's role to focus on intricate details while using priors learned from large-scale video datasets. Consequently, GeoMan improves temporal consistency and generalizability while requiring minimal 4D training data. To address the challenge of accurate human size estimation, we introduce a root-relative depth representation that retains critical human-scale details and is easier to be estimated from monocular inputs, overcoming the limitations of traditional affine-invariant and metric depth representations. GeoMan achieves state-of-the-art performance in both qualitative and quantitative evaluations, demonstrating its effectiveness in overcoming longstanding challenges in 3D human geometry estimation from videos.

Recovering high-quality depth maps from compressed sources has gained significant attention due to the limitations of consumer-grade depth cameras and the bandwidth restrictions during data transmission. However, current methods still suffer from two challenges. First, bit-depth compression produces a uniform depth representation in regions with subtle variations, hindering the recovery of detailed information. Second, densely distributed random noise reduces the accuracy of estimating the global geometric structure of the scene. To address these challenges, we propose a novel framework, termed geometry-decoupled network (GDNet), for compressed depth map super-resolution that decouples the high-quality depth map reconstruction process by handling global and detailed geometric features separately. To be specific, we propose the fine geometry detail encoder (FGDE), which is designed to aggregate fine geometry details in high-resolution low-level image features while simultaneously enriching them with complementary information from low-resolution context-level image features. In addition, we develop the global geometry encoder (GGE) that aims at suppressing noise and extracting global geometric information effectively via constructing compact feature representation in a low-rank space. We conduct experiments on multiple benchmark datasets, demonstrating that our GDNet significantly outperforms current methods in terms of geometric consistency and detail recovery. In the ECCV 2024 AIM Compressed Depth Upsampling Challenge, our solution won the 1st place award. Our codes are available at: https://github.com/Ian0926/GDNet.

Large language models (LLMs) have demonstrated significant capabilities in mathematical reasoning, particularly with text-based mathematical problems. However, current multi-modal large language models (MLLMs), especially those specialized in mathematics, tend to focus predominantly on solving geometric problems but ignore the diversity of visual information available in other areas of mathematics. Moreover, the geometric information for these specialized mathematical MLLMs is derived from several public datasets, which are typically limited in diversity and complexity. To address these limitations, we aim to construct a fine-tuning dataset named MathVL, and develop a series of specialized mathematical MLLMs termed MathGLM-Vision by conducting Supervised Fine-Tuning (SFT) on MathVL with various parameter-scale backbones. To extensively evaluate the effectiveness of MathGLM-Vision, we conduct experiments on several public benchmarks and our curated MathVL-test consisting of 2,000 problems. Experimental results demonstrate that MathGLM-Vision achieves significant improvements compared with some existing models, including backbone models and open-source mathematical MLLMs. These findings indicate the importance of diversity dataset in enhancing the mathematical reasoning abilities of MLLMs.

As transformers are equivariant to the permutation of input tokens, encoding the positional information of tokens is necessary for many tasks. However, since existing positional encoding schemes have been initially designed for NLP tasks, their suitability for vision tasks, which typically exhibit different structural properties in their data, is questionable. We argue that existing positional encoding schemes are suboptimal for 3D vision tasks, as they do not respect their underlying 3D geometric structure. Based on this hypothesis, we propose a geometry-aware attention mechanism that encodes the geometric structure of tokens as relative transformation determined by the geometric relationship between queries and key-value pairs. By evaluating on multiple novel view synthesis (NVS) datasets in the sparse wide-baseline multi-view setting, we show that our attention, called Geometric Transform Attention (GTA), improves learning efficiency and performance of state-of-the-art transformer-based NVS models without any additional learned parameters and only minor computational overhead.

As video games evolve into expansive, detailed worlds, visual quality becomes essential, yet increasingly challenging. Traditional testing methods, limited by resources, face difficulties in addressing the plethora of potential bugs. Machine learning offers scalable solutions; however, heavy reliance on large labeled datasets remains a constraint. Addressing this challenge, we propose a novel method, utilizing unlabeled gameplay and domain-specific augmentations to generate datasets & self-supervised objectives used during pre-training or multi-task settings for downstream visual bug detection. Our methodology uses weak-supervision to scale datasets for the crafted objectives and facilitates both autonomous and interactive weak-supervision, incorporating unsupervised clustering and/or an interactive approach based on text and geometric prompts. We demonstrate on first-person player clipping/collision bugs (FPPC) within the expansive Giantmap game world, that our approach is very effective, improving over a strong supervised baseline in a practical, very low-prevalence, low data regime (0.336 rightarrow 0.550 F1 score). With just 5 labeled "good" exemplars (i.e., 0 bugs), our self-supervised objective alone captures enough signal to outperform the low-labeled supervised settings. Building on large-pretrained vision models, our approach is adaptable across various visual bugs. Our results suggest applicability in curating datasets for broader image and video tasks within video games beyond visual bugs.

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.

One-shot coreset selection aims to select a representative subset of the training data, given a pruning rate, that can later be used to train future models while retaining high accuracy. State-of-the-art coreset selection methods pick the highest importance examples based on an importance metric and are found to perform well at low pruning rates. However, at high pruning rates, they suffer from a catastrophic accuracy drop, performing worse than even random sampling. This paper explores the reasons behind this accuracy drop both theoretically and empirically. We first propose a novel metric to measure the coverage of a dataset on a specific distribution by extending the classical geometric set cover problem to a distribution cover problem. This metric helps explain why coresets selected by SOTA methods at high pruning rates perform poorly compared to random sampling because of worse data coverage. We then propose a novel one-shot coreset selection method, Coverage-centric Coreset Selection (CCS), that jointly considers overall data coverage upon a distribution as well as the importance of each example. We evaluate CCS on five datasets and show that, at high pruning rates (e.g., 90%), it achieves significantly better accuracy than previous SOTA methods (e.g., at least 19.56% higher on CIFAR10) as well as random selection (e.g., 7.04% higher on CIFAR10) and comparable accuracy at low pruning rates. We make our code publicly available at https://github.com/haizhongzheng/Coverage-centric-coreset-selection.

Despite significant advances in image anomaly detection and segmentation, few methods use 3D information. We utilize a recently introduced 3D anomaly detection dataset to evaluate whether or not using 3D information is a lost opportunity. First, we present a surprising finding: standard color-only methods outperform all current methods that are explicitly designed to exploit 3D information. This is counter-intuitive as even a simple inspection of the dataset shows that color-only methods are insufficient for images containing geometric anomalies. This motivates the question: how can anomaly detection methods effectively use 3D information? We investigate a range of shape representations including hand-crafted and deep-learning-based; we demonstrate that rotation invariance plays the leading role in the performance. We uncover a simple 3D-only method that beats all recent approaches while not using deep learning, external pre-training datasets, or color information. As the 3D-only method cannot detect color and texture anomalies, we combine it with color-based features, significantly outperforming previous state-of-the-art. Our method, dubbed BTF (Back to the Feature) achieves pixel-wise ROCAUC: 99.3% and PRO: 96.4% on MVTec 3D-AD.

Multimodal large language models (MLLMs) have made rapid progress in recent years, yet continue to struggle with low-level visual perception (LLVP) -- particularly the ability to accurately describe the geometric details of an image. This capability is crucial for applications in areas such as robotics, medical image analysis, and manufacturing. In this paper, we first introduce Geoperception, a benchmark designed to evaluate an MLLM's ability to accurately transcribe 2D geometric information from an image. Using this benchmark, we demonstrate the limitations of leading MLLMs, and then conduct a comprehensive empirical study to explore strategies for improving their performance on geometric tasks. Our findings highlight the benefits of certain model architectures, training techniques, and data strategies, including the use of high-fidelity synthetic data and multi-stage training with a data curriculum. Notably, we find that a data curriculum enables models to learn challenging geometry understanding tasks which they fail to learn from scratch. Leveraging these insights, we develop Euclid, a family of models specifically optimized for strong low-level geometric perception. Although purely trained on synthetic multimodal data, Euclid shows strong generalization ability to novel geometry shapes. For instance, Euclid outperforms the best closed-source model, Gemini-1.5-Pro, by up to 58.56% on certain Geoperception benchmark tasks and 10.65% on average across all tasks.

We tackle the challenge of generating the infinitely extendable 3D world -- large, continuous environments with coherent geometry and realistic appearance. Existing methods face key challenges: 2D-lifting approaches suffer from geometric and appearance inconsistencies across views, 3D implicit representations are hard to scale up, and current 3D foundation models are mostly object-centric, limiting their applicability to scene-level generation. Our key insight is leveraging strong generation priors from pre-trained 3D models for structured scene block generation. To this end, we propose WorldGrow, a hierarchical framework for unbounded 3D scene synthesis. Our method features three core components: (1) a data curation pipeline that extracts high-quality scene blocks for training, making the 3D structured latent representations suitable for scene generation; (2) a 3D block inpainting mechanism that enables context-aware scene extension; and (3) a coarse-to-fine generation strategy that ensures both global layout plausibility and local geometric/textural fidelity. Evaluated on the large-scale 3D-FRONT dataset, WorldGrow achieves SOTA performance in geometry reconstruction, while uniquely supporting infinite scene generation with photorealistic and structurally consistent outputs. These results highlight its capability for constructing large-scale virtual environments and potential for building future world models.

Videos inherently represent 2D projections of a dynamic 3D world. However, our analysis suggests that video diffusion models trained solely on raw video data often fail to capture meaningful geometric-aware structure in their learned representations. To bridge this gap between video diffusion models and the underlying 3D nature of the physical world, we propose Geometry Forcing, a simple yet effective method that encourages video diffusion models to internalize latent 3D representations. Our key insight is to guide the model's intermediate representations toward geometry-aware structure by aligning them with features from a pretrained geometric foundation model. To this end, we introduce two complementary alignment objectives: Angular Alignment, which enforces directional consistency via cosine similarity, and Scale Alignment, which preserves scale-related information by regressing unnormalized geometric features from normalized diffusion representation. We evaluate Geometry Forcing on both camera view-conditioned and action-conditioned video generation tasks. Experimental results demonstrate that our method substantially improves visual quality and 3D consistency over the baseline methods. Project page: https://GeometryForcing.github.io.

We propose SelfSplat, a novel 3D Gaussian Splatting model designed to perform pose-free and 3D prior-free generalizable 3D reconstruction from unposed multi-view images. These settings are inherently ill-posed due to the lack of ground-truth data, learned geometric information, and the need to achieve accurate 3D reconstruction without finetuning, making it difficult for conventional methods to achieve high-quality results. Our model addresses these challenges by effectively integrating explicit 3D representations with self-supervised depth and pose estimation techniques, resulting in reciprocal improvements in both pose accuracy and 3D reconstruction quality. Furthermore, we incorporate a matching-aware pose estimation network and a depth refinement module to enhance geometry consistency across views, ensuring more accurate and stable 3D reconstructions. To present the performance of our method, we evaluated it on large-scale real-world datasets, including RealEstate10K, ACID, and DL3DV. SelfSplat achieves superior results over previous state-of-the-art methods in both appearance and geometry quality, also demonstrates strong cross-dataset generalization capabilities. Extensive ablation studies and analysis also validate the effectiveness of our proposed methods. Code and pretrained models are available at https://gynjn.github.io/selfsplat/

Finding correspondences between images is a fundamental problem in computer vision. In this paper, we show that correspondence emerges in image diffusion models without any explicit supervision. We propose a simple strategy to extract this implicit knowledge out of diffusion networks as image features, namely DIffusion FeaTures (DIFT), and use them to establish correspondences between real images. Without any additional fine-tuning or supervision on the task-specific data or annotations, DIFT is able to outperform both weakly-supervised methods and competitive off-the-shelf features in identifying semantic, geometric, and temporal correspondences. Particularly for semantic correspondence, DIFT from Stable Diffusion is able to outperform DINO and OpenCLIP by 19 and 14 accuracy points respectively on the challenging SPair-71k benchmark. It even outperforms the state-of-the-art supervised methods on 9 out of 18 categories while remaining on par for the overall performance. Project page: https://diffusionfeatures.github.io

With the rise of generative AI, synthesizing figures from text captions becomes a compelling application. However, achieving high geometric precision and editability requires representing figures as graphics programs in languages like TikZ, and aligned training data (i.e., graphics programs with captions) remains scarce. Meanwhile, large amounts of unaligned graphics programs and captioned raster images are more readily available. We reconcile these disparate data sources by presenting TikZero, which decouples graphics program generation from text understanding by using image representations as an intermediary bridge. It enables independent training on graphics programs and captioned images and allows for zero-shot text-guided graphics program synthesis during inference. We show that our method substantially outperforms baselines that can only operate with caption-aligned graphics programs. Furthermore, when leveraging caption-aligned graphics programs as a complementary training signal, TikZero matches or exceeds the performance of much larger models, including commercial systems like GPT-4o. Our code, datasets, and select models are publicly available.

Unsupervised Domain Adaptation has been an efficient approach to transferring the semantic segmentation model across data distributions. Meanwhile, the recent Open-vocabulary Semantic Scene understanding based on large-scale vision language models is effective in open-set settings because it can learn diverse concepts and categories. However, these prior methods fail to generalize across different camera views due to the lack of cross-view geometric modeling. At present, there are limited studies analyzing cross-view learning. To address this problem, we introduce a novel Unsupervised Cross-view Adaptation Learning approach to modeling the geometric structural change across views in Semantic Scene Understanding. First, we introduce a novel Cross-view Geometric Constraint on Unpaired Data to model structural changes in images and segmentation masks across cameras. Second, we present a new Geodesic Flow-based Correlation Metric to efficiently measure the geometric structural changes across camera views. Third, we introduce a novel view-condition prompting mechanism to enhance the view-information modeling of the open-vocabulary segmentation network in cross-view adaptation learning. The experiments on different cross-view adaptation benchmarks have shown the effectiveness of our approach in cross-view modeling, demonstrating that we achieve State-of-the-Art (SOTA) performance compared to prior unsupervised domain adaptation and open-vocabulary semantic segmentation methods.

Diffusion models (DMs) excel in photo-realistic image synthesis, but their adaptation to LiDAR scene generation poses a substantial hurdle. This is primarily because DMs operating in the point space struggle to preserve the curve-like patterns and 3D geometry of LiDAR scenes, which consumes much of their representation power. In this paper, we propose LiDAR Diffusion Models (LiDMs) to generate LiDAR-realistic scenes from a latent space tailored to capture the realism of LiDAR scenes by incorporating geometric priors into the learning pipeline. Our method targets three major desiderata: pattern realism, geometry realism, and object realism. Specifically, we introduce curve-wise compression to simulate real-world LiDAR patterns, point-wise coordinate supervision to learn scene geometry, and patch-wise encoding for a full 3D object context. With these three core designs, our method achieves competitive performance on unconditional LiDAR generation in 64-beam scenario and state of the art on conditional LiDAR generation, while maintaining high efficiency compared to point-based DMs (up to 107times faster). Furthermore, by compressing LiDAR scenes into a latent space, we enable the controllability of DMs with various conditions such as semantic maps, camera views, and text prompts.

We introduce CameraBench, a large-scale dataset and benchmark designed to assess and improve camera motion understanding. CameraBench consists of ~3,000 diverse internet videos, annotated by experts through a rigorous multi-stage quality control process. One of our contributions is a taxonomy of camera motion primitives, designed in collaboration with cinematographers. We find, for example, that some motions like "follow" (or tracking) require understanding scene content like moving subjects. We conduct a large-scale human study to quantify human annotation performance, revealing that domain expertise and tutorial-based training can significantly enhance accuracy. For example, a novice may confuse zoom-in (a change of intrinsics) with translating forward (a change of extrinsics), but can be trained to differentiate the two. Using CameraBench, we evaluate Structure-from-Motion (SfM) and Video-Language Models (VLMs), finding that SfM models struggle to capture semantic primitives that depend on scene content, while VLMs struggle to capture geometric primitives that require precise estimation of trajectories. We then fine-tune a generative VLM on CameraBench to achieve the best of both worlds and showcase its applications, including motion-augmented captioning, video question answering, and video-text retrieval. We hope our taxonomy, benchmark, and tutorials will drive future efforts towards the ultimate goal of understanding camera motions in any video.

Camera pose estimation is a long-standing computer vision problem that to date often relies on classical methods, such as handcrafted keypoint matching, RANSAC and bundle adjustment. In this paper, we propose to formulate the Structure from Motion (SfM) problem inside a probabilistic diffusion framework, modelling the conditional distribution of camera poses given input images. This novel view of an old problem has several advantages. (i) The nature of the diffusion framework mirrors the iterative procedure of bundle adjustment. (ii) The formulation allows a seamless integration of geometric constraints from epipolar geometry. (iii) It excels in typically difficult scenarios such as sparse views with wide baselines. (iv) The method can predict intrinsics and extrinsics for an arbitrary amount of images. We demonstrate that our method PoseDiffusion significantly improves over the classic SfM pipelines and the learned approaches on two real-world datasets. Finally, it is observed that our method can generalize across datasets without further training. Project page: https://posediffusion.github.io/

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

Gradient descent has proven to be a powerful and effective technique for optimization in numerous machine learning applications. Recent advances in computational neuroscience have shown that learning in standard gradient descent optimization formulation is not consistent with learning in biological systems. This has opened up interesting avenues for building biologically inspired learning techniques. One such approach is inspired by Dale's law, which states that inhibitory and excitatory synapses do not swap roles during the course of learning. The resulting exponential gradient descent optimization scheme leads to log-normally distributed synaptic weights. Interestingly, the density that satisfies the Fokker-Planck equation corresponding to the stochastic differential equation (SDE) with geometric Brownian motion (GBM) is the log-normal density. Leveraging this connection, we start with the SDE governing geometric Brownian motion, and show that discretizing the corresponding reverse-time SDE yields a multiplicative update rule, which surprisingly, coincides with the sampling equivalent of the exponential gradient descent update founded on Dale's law. Furthermore, we propose a new formalism for multiplicative denoising score-matching, subsuming the loss function proposed by Hyvaerinen for non-negative data. Indeed, log-normally distributed data is positive and the proposed score-matching formalism turns out to be a natural fit. This allows for training of score-based models for image data and results in a novel multiplicative update scheme for sample generation starting from a log-normal density. Experimental results on MNIST, Fashion MNIST, and Kuzushiji datasets demonstrate generative capability of the new scheme. To the best of our knowledge, this is the first instance of a biologically inspired generative model employing multiplicative updates, founded on geometric Brownian motion.

The development of aerial holistic scene understanding algorithms is hindered by the scarcity of comprehensive datasets that enable both semantic and geometric reconstruction. While synthetic datasets offer an alternative, existing options exhibit task-specific limitations, unrealistic scene compositions, and rendering artifacts that compromise real-world applicability. We introduce ClaraVid, a synthetic aerial dataset specifically designed to overcome these limitations. Comprising 16,917 high-resolution images captured at 4032x3024 from multiple viewpoints across diverse landscapes, ClaraVid provides dense depth maps, panoptic segmentation, sparse point clouds, and dynamic object masks, while mitigating common rendering artifacts. To further advance neural reconstruction, we introduce the Delentropic Scene Profile (DSP), a novel complexity metric derived from differential entropy analysis, designed to quantitatively assess scene difficulty and inform reconstruction tasks. Utilizing DSP, we systematically benchmark neural reconstruction methods, uncovering a consistent, measurable correlation between scene complexity and reconstruction accuracy. Empirical results indicate that higher delentropy strongly correlates with increased reconstruction errors, validating DSP as a reliable complexity prior. Currently under review, upon acceptance the data and code will be available at https://rdbch.github.io/claravid{rdbch.github.io/ClaraVid}.

Text logo design heavily relies on the creativity and expertise of professional designers, in which arranging element layouts is one of the most important procedures. However, few attention has been paid to this specific task which needs to take precise textural details and user constraints into consideration, but only on the broader tasks such as document/poster layout generation. In this paper, we propose a VLM-based framework that generates content-aware text logo layouts by integrating multi-modal inputs with user constraints, supporting a more flexible and stable layout design in real-world applications. We introduce two model techniques to reduce the computation for processing multiple glyph images simultaneously, while does not face performance degradation. To support instruction-tuning of out model, we construct two extensive text logo datasets, which are 5x more larger than the existing public dataset. Except for the geometric annotations (e.g. text masks and character recognition), we also compliment with comprehensive layout descriptions in natural language format, for more effective training to have reasoning ability when dealing with complex layouts and custom user constraints. Experimental studies demonstrate the effectiveness of our proposed model and datasets, when comparing with previous methods in various benchmarks to evaluate geometric aesthetics and human preferences. The code and datasets will be publicly available.

We present Diffusion Soup, a compartmentalization method for Text-to-Image Generation that averages the weights of diffusion models trained on sharded data. By construction, our approach enables training-free continual learning and unlearning with no additional memory or inference costs, since models corresponding to data shards can be added or removed by re-averaging. We show that Diffusion Soup samples from a point in weight space that approximates the geometric mean of the distributions of constituent datasets, which offers anti-memorization guarantees and enables zero-shot style mixing. Empirically, Diffusion Soup outperforms a paragon model trained on the union of all data shards and achieves a 30% improvement in Image Reward (.34 to .44) on domain sharded data, and a 59% improvement in IR (.37 to .59) on aesthetic data. In both cases, souping also prevails in TIFA score (respectively, 85.5 to 86.5 and 85.6 to 86.8). We demonstrate robust unlearning -- removing any individual domain shard only lowers performance by 1% in IR (.45 to .44) -- and validate our theoretical insights on anti-memorization using real data. Finally, we showcase Diffusion Soup's ability to blend the distinct styles of models finetuned on different shards, resulting in the zero-shot generation of hybrid styles.

Image captioning models typically follow an encoder-decoder architecture which uses abstract image feature vectors as input to the encoder. One of the most successful algorithms uses feature vectors extracted from the region proposals obtained from an object detector. In this work we introduce the Object Relation Transformer, that builds upon this approach by explicitly incorporating information about the spatial relationship between input detected objects through geometric attention. Quantitative and qualitative results demonstrate the importance of such geometric attention for image captioning, leading to improvements on all common captioning metrics on the MS-COCO dataset.

We present UP2You, the first tuning-free solution for reconstructing high-fidelity 3D clothed portraits from extremely unconstrained in-the-wild 2D photos. Unlike previous approaches that require "clean" inputs (e.g., full-body images with minimal occlusions, or well-calibrated cross-view captures), UP2You directly processes raw, unstructured photographs, which may vary significantly in pose, viewpoint, cropping, and occlusion. Instead of compressing data into tokens for slow online text-to-3D optimization, we introduce a data rectifier paradigm that efficiently converts unconstrained inputs into clean, orthogonal multi-view images in a single forward pass within seconds, simplifying the 3D reconstruction. Central to UP2You is a pose-correlated feature aggregation module (PCFA), that selectively fuses information from multiple reference images w.r.t. target poses, enabling better identity preservation and nearly constant memory footprint, with more observations. We also introduce a perceiver-based multi-reference shape predictor, removing the need for pre-captured body templates. Extensive experiments on 4D-Dress, PuzzleIOI, and in-the-wild captures demonstrate that UP2You consistently surpasses previous methods in both geometric accuracy (Chamfer-15%, P2S-18% on PuzzleIOI) and texture fidelity (PSNR-21%, LPIPS-46% on 4D-Dress). UP2You is efficient (1.5 minutes per person), and versatile (supports arbitrary pose control, and training-free multi-garment 3D virtual try-on), making it practical for real-world scenarios where humans are casually captured. Both models and code will be released to facilitate future research on this underexplored task. Project Page: https://zcai0612.github.io/UP2You