Daily Papers

Spider webs are incredible biological structures, comprising thin but strong silk filament and arranged into complex hierarchical architectures with striking mechanical properties (e.g., lightweight but high strength, achieving diverse mechanical responses). While simple 2D orb webs can easily be mimicked, the modeling and synthesis of 3D-based web structures remain challenging, partly due to the rich set of design features. Here we provide a detailed analysis of the heterogenous graph structures of spider webs, and use deep learning as a way to model and then synthesize artificial, bio-inspired 3D web structures. The generative AI models are conditioned based on key geometric parameters (including average edge length, number of nodes, average node degree, and others). To identify graph construction principles, we use inductive representation sampling of large experimentally determined spider web graphs, to yield a dataset that is used to train three conditional generative models: 1) An analog diffusion model inspired by nonequilibrium thermodynamics, with sparse neighbor representation, 2) a discrete diffusion model with full neighbor representation, and 3) an autoregressive transformer architecture with full neighbor representation. All three models are scalable, produce complex, de novo bio-inspired spider web mimics, and successfully construct graphs that meet the design objectives. We further propose algorithm that assembles web samples produced by the generative models into larger-scale structures based on a series of geometric design targets, including helical and parametric shapes, mimicking, and extending natural design principles towards integration with diverging engineering objectives. Several webs are manufactured using 3D printing and tested to assess mechanical properties.

We propose a two-stage deep learning framework for the inverse design of rectangular patch antennas. Our approach leverages generative modeling to learn a latent representation of antenna frequency response curves and conditions a subsequent generative model on these responses to produce feasible antenna geometries. We further demonstrate that leveraging search and optimization techniques at test-time improves the accuracy of the generated designs and enables consideration of auxiliary objectives such as manufacturability. Our approach generalizes naturally to different design criteria, and can be easily adapted to more complex geometric design spaces.

Machine learning approaches for solving partial differential equations require learning mappings between function spaces. While convolutional or graph neural networks are constrained to discretized functions, neural operators present a promising milestone toward mapping functions directly. Despite impressive results they still face challenges with respect to the domain geometry and typically rely on some form of discretization. In order to alleviate such limitations, we present CORAL, a new method that leverages coordinate-based networks for solving PDEs on general geometries. CORAL is designed to remove constraints on the input mesh, making it applicable to any spatial sampling and geometry. Its ability extends to diverse problem domains, including PDE solving, spatio-temporal forecasting, and inverse problems like geometric design. CORAL demonstrates robust performance across multiple resolutions and performs well in both convex and non-convex domains, surpassing or performing on par with state-of-the-art models.

Computational RNA design tasks are often posed as inverse problems, where sequences are designed based on adopting a single desired secondary structure without considering 3D geometry and conformational diversity. We introduce gRNAde, a geometric RNA design pipeline operating on 3D RNA backbones to design sequences that explicitly account for structure and dynamics. Under the hood, gRNAde is a multi-state Graph Neural Network that generates candidate RNA sequences conditioned on one or more 3D backbone structures where the identities of the bases are unknown. On a single-state fixed backbone re-design benchmark of 14 RNA structures from the PDB identified by Das et al. [2010], gRNAde obtains higher native sequence recovery rates (56% on average) compared to Rosetta (45% on average), taking under a second to produce designs compared to the reported hours for Rosetta. We further demonstrate the utility of gRNAde on a new benchmark of multi-state design for structurally flexible RNAs, as well as zero-shot ranking of mutational fitness landscapes in a retrospective analysis of a recent ribozyme. Open source code: https://github.com/chaitjo/geometric-rna-design

Denoising diffusion models have shown great potential in multiple research areas. Existing diffusion-based generative methods on de novo 3D molecule generation face two major challenges. Since majority heavy atoms in molecules allow connections to multiple atoms through single bonds, solely using pair-wise distance to model molecule geometries is insufficient. Therefore, the first one involves proposing an effective neural network as the denoising kernel that is capable to capture complex multi-body interatomic relationships and learn high-quality features. Due to the discrete nature of graphs, mainstream diffusion-based methods for molecules heavily rely on predefined rules and generate edges in an indirect manner. The second challenge involves accommodating molecule generation to diffusion and accurately predicting the existence of bonds. In our research, we view the iterative way of updating molecule conformations in diffusion process is consistent with molecular dynamics and introduce a novel molecule generation method named Geometric-Facilitated Molecular Diffusion (GFMDiff). For the first challenge, we introduce a Dual-Track Transformer Network (DTN) to fully excevate global spatial relationships and learn high quality representations which contribute to accurate predictions of features and geometries. As for the second challenge, we design Geometric-Facilitated Loss (GFLoss) which intervenes the formation of bonds during the training period, instead of directly embedding edges into the latent space. Comprehensive experiments on current benchmarks demonstrate the superiority of GFMDiff.

Modern 3D semantic instance segmentation approaches predominantly rely on specialized voting mechanisms followed by carefully designed geometric clustering techniques. Building on the successes of recent Transformer-based methods for object detection and image segmentation, we propose the first Transformer-based approach for 3D semantic instance segmentation. We show that we can leverage generic Transformer building blocks to directly predict instance masks from 3D point clouds. In our model called Mask3D each object instance is represented as an instance query. Using Transformer decoders, the instance queries are learned by iteratively attending to point cloud features at multiple scales. Combined with point features, the instance queries directly yield all instance masks in parallel. Mask3D has several advantages over current state-of-the-art approaches, since it neither relies on (1) voting schemes which require hand-selected geometric properties (such as centers) nor (2) geometric grouping mechanisms requiring manually-tuned hyper-parameters (e.g. radii) and (3) enables a loss that directly optimizes instance masks. Mask3D sets a new state-of-the-art on ScanNet test (+6.2 mAP), S3DIS 6-fold (+10.1 mAP), STPLS3D (+11.2 mAP) and ScanNet200 test (+12.4 mAP).

Innovations like protein diffusion have enabled significant progress in de novo protein design, which is a vital topic in life science. These methods typically depend on protein structure encoders to model residue backbone frames, where atoms do not exist. Most prior encoders rely on atom-wise features, such as angles and distances between atoms, which are not available in this context. Thus far, only several simple encoders, such as IPA, have been proposed for this scenario, exposing the frame modeling as a bottleneck. In this work, we proffer the Vector Field Network (VFN), which enables network layers to perform learnable vector computations between coordinates of frame-anchored virtual atoms, thus achieving a higher capability for modeling frames. The vector computation operates in a manner similar to a linear layer, with each input channel receiving 3D virtual atom coordinates instead of scalar values. The multiple feature vectors output by the vector computation are then used to update the residue representations and virtual atom coordinates via attention aggregation. Remarkably, VFN also excels in modeling both frames and atoms, as the real atoms can be treated as the virtual atoms for modeling, positioning VFN as a potential universal encoder. In protein diffusion (frame modeling), VFN exhibits an impressive performance advantage over IPA, excelling in terms of both designability (67.04% vs. 53.58%) and diversity (66.54% vs. 51.98%). In inverse folding (frame and atom modeling), VFN outperforms the previous SoTA model, PiFold (54.7% vs. 51.66%), on sequence recovery rate. We also propose a method of equipping VFN with the ESM model, which significantly surpasses the previous ESM-based SoTA (62.67% vs. 55.65%), LM-Design, by a substantial margin.

Despite their proficiency in general tasks, Multi-modal Large Language Models (MLLMs) struggle with automatic Geometry Problem Solving (GPS), which demands understanding diagrams, interpreting symbols, and performing complex reasoning. This limitation arises from their pre-training on natural images and texts, along with the lack of automated verification in the problem-solving process. Besides, current geometric specialists are limited by their task-specific designs, making them less effective for broader geometric problems. To this end, we present GeoX, a multi-modal large model focusing on geometric understanding and reasoning tasks. Given the significant differences between geometric diagram-symbol and natural image-text, we introduce unimodal pre-training to develop a diagram encoder and symbol decoder, enhancing the understanding of geometric images and corpora. Furthermore, we introduce geometry-language alignment, an effective pre-training paradigm that bridges the modality gap between unimodal geometric experts. We propose a Generator-And-Sampler Transformer (GS-Former) to generate discriminative queries and eliminate uninformative representations from unevenly distributed geometric signals. Finally, GeoX benefits from visual instruction tuning, empowering it to take geometric images and questions as input and generate verifiable solutions. Experiments show that GeoX outperforms both generalists and geometric specialists on publicly recognized benchmarks, such as GeoQA, UniGeo, Geometry3K, and PGPS9k.

LiDAR-based 3D panoptic segmentation often struggles with the inherent sparsity of data from LiDAR sensors, which makes it challenging to accurately recognize distant or small objects. Recently, a few studies have sought to overcome this challenge by integrating LiDAR inputs with camera images, leveraging the rich and dense texture information provided by the latter. While these approaches have shown promising results, they still face challenges, such as misalignment during data augmentation and the reliance on post-processing steps. To address these issues, we propose Image-Assists-LiDAR (IAL), a novel multi-modal 3D panoptic segmentation framework. In IAL, we first introduce a modality-synchronized data augmentation strategy, PieAug, to ensure alignment between LiDAR and image inputs from the start. Next, we adopt a transformer decoder to directly predict panoptic segmentation results. To effectively fuse LiDAR and image features into tokens for the decoder, we design a Geometric-guided Token Fusion (GTF) module. Additionally, we leverage the complementary strengths of each modality as priors for query initialization through a Prior-based Query Generation (PQG) module, enhancing the decoder's ability to generate accurate instance masks. Our IAL framework achieves state-of-the-art performance compared to previous multi-modal 3D panoptic segmentation methods on two widely used benchmarks. Code and models are publicly available at <https://github.com/IMPL-Lab/IAL.git>.

Depth-aware panoptic segmentation is an emerging topic in computer vision which combines semantic and geometric understanding for more robust scene interpretation. Recent works pursue unified frameworks to tackle this challenge but mostly still treat it as two individual learning tasks, which limits their potential for exploring cross-domain information. We propose a deeply unified framework for depth-aware panoptic segmentation, which performs joint segmentation and depth estimation both in a per-segment manner with identical object queries. To narrow the gap between the two tasks, we further design a geometric query enhancement method, which is able to integrate scene geometry into object queries using latent representations. In addition, we propose a bi-directional guidance learning approach to facilitate cross-task feature learning by taking advantage of their mutual relations. Our method sets the new state of the art for depth-aware panoptic segmentation on both Cityscapes-DVPS and SemKITTI-DVPS datasets. Moreover, our guidance learning approach is shown to deliver performance improvement even under incomplete supervision labels.

Computer-Aided Design (CAD) generative modeling is driving significant innovations across industrial applications. Recent works have shown remarkable progress in creating solid models from various inputs such as point clouds, meshes, and text descriptions. However, these methods fundamentally diverge from traditional industrial workflows that begin with 2D engineering drawings. The automatic generation of parametric CAD models from these 2D vector drawings remains underexplored despite being a critical step in engineering design. To address this gap, our key insight is to reframe CAD generation as a sequence-to-sequence learning problem where vector drawing primitives directly inform the generation of parametric CAD operations, preserving geometric precision and design intent throughout the transformation process. We propose Drawing2CAD, a framework with three key technical components: a network-friendly vector primitive representation that preserves precise geometric information, a dual-decoder transformer architecture that decouples command type and parameter generation while maintaining precise correspondence, and a soft target distribution loss function accommodating inherent flexibility in CAD parameters. To train and evaluate Drawing2CAD, we create CAD-VGDrawing, a dataset of paired engineering drawings and parametric CAD models, and conduct thorough experiments to demonstrate the effectiveness of our method. Code and dataset are available at https://github.com/lllssc/Drawing2CAD.

Vision-language models (VLMs) often struggle with geometric reasoning due to their limited perception of fundamental diagram elements. To tackle this challenge, we introduce GeoPerceive, a benchmark comprising diagram instances paired with domain-specific language (DSL) representations, along with an efficient automatic data generation pipeline. This design enables the isolated evaluation of geometric perception independently from reasoning. To exploit the data provided by GeoPerceive for enhancing the geometric perception capabilities of VLMs, we propose GeoDPO, a translator-guided reinforcement learning (RL) framework. GeoDPO employs an NL-to-DSL translator, which is trained on synthetic pairs generated by the data engine of GeoPerceive, to bridge natural language and DSL. This translator facilitates the computation of fine-grained, DSL-level scores, which serve as reward signals in reinforcement learning. We assess GeoDPO on both in-domain and out-of-domain datasets, spanning tasks in geometric perception as well as downstream reasoning. Experimental results demonstrate that, while supervised fine-tuning (SFT) offers only marginal improvements and may even impair performance in out-of-domain scenarios, GeoDPO achieves substantial gains: +26.5% on in-domain data, +8.0% on out-of-domain data, and +39.0% on downstream reasoning tasks. These findings underscore the superior performance and generalization ability of GeoDPO over SFT. All codes are released at https://github.com/Longin-Yu/GeoPerceive to ensure reproducibility.

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

Despite the impressive progress on understanding and generating images shown by the recent unified architectures, the integration of 3D tasks remains challenging and largely unexplored. In this paper, we introduce UniUGG, the first unified understanding and generation framework for 3D modalities. Our unified framework employs an LLM to comprehend and decode sentences and 3D representations. At its core, we propose a spatial decoder leveraging a latent diffusion model to generate high-quality 3D representations. This allows for the generation and imagination of 3D scenes based on a reference image and an arbitrary view transformation, while remaining supports for spatial visual question answering (VQA) tasks. Additionally, we propose a geometric-semantic learning strategy to pretrain the vision encoder. This design jointly captures the input's semantic and geometric cues, enhancing both spatial understanding and generation. Extensive experimental results demonstrate the superiority of our method in visual representation, spatial understanding, and 3D generation. The source code will be released upon paper acceptance.

The inference of topological principles is a key problem in structured reconstruction. We observe that wrongly predicted topological relationships are often incurred by the lack of holistic geometry clues in low-level features. Inspired by the fact that massive signals can be compactly described with frequency analysis, we experimentally explore the efficiency and tendency of learning structure geometry in the frequency domain. Accordingly, we propose a frequency-domain feature learning strategy (F-Learn) to fuse scattered geometric fragments holistically for topology-intact structure reasoning. Benefiting from the parsimonious design, the F-Learn strategy can be easily deployed into a deep reconstructor with a lightweight model modification. Experiments demonstrate that the F-Learn strategy can effectively introduce structure awareness into geometric primitive detection and topology inference, bringing significant performance improvement to final structured reconstruction. Code and pre-trained models are available at https://github.com/Geo-Tell/F-Learn.

Creating CAD digital twins from the physical world is crucial for manufacturing, design, and simulation. However, current methods typically rely on costly 3D scanning with labor-intensive post-processing. To provide a user-friendly design process, we explore the problem of reverse engineering from unconstrained real-world CAD images that can be easily captured by users of all experiences. However, the scarcity of real-world CAD data poses challenges in directly training such models. To tackle these challenges, we propose CADCrafter, an image-to-parametric CAD model generation framework that trains solely on synthetic textureless CAD data while testing on real-world images. To bridge the significant representation disparity between images and parametric CAD models, we introduce a geometry encoder to accurately capture diverse geometric features. Moreover, the texture-invariant properties of the geometric features can also facilitate the generalization to real-world scenarios. Since compiling CAD parameter sequences into explicit CAD models is a non-differentiable process, the network training inherently lacks explicit geometric supervision. To impose geometric validity constraints, we employ direct preference optimization (DPO) to fine-tune our model with the automatic code checker feedback on CAD sequence quality. Furthermore, we collected a real-world dataset, comprised of multi-view images and corresponding CAD command sequence pairs, to evaluate our method. Experimental results demonstrate that our approach can robustly handle real unconstrained CAD images, and even generalize to unseen general objects.

De novo 3D molecule generation is a pivotal task in drug discovery. However, many recent geometric generative models struggle to produce high-quality 3D structures, even if they maintain 2D validity and topological stability. To tackle this issue and enhance the learning of effective molecular generation dynamics, we present Megalodon-a family of scalable transformer models. These models are enhanced with basic equivariant layers and trained using a joint continuous and discrete denoising co-design objective. We assess Megalodon's performance on established molecule generation benchmarks and introduce new 3D structure benchmarks that evaluate a model's capability to generate realistic molecular structures, particularly focusing on energetics. We show that Megalodon achieves state-of-the-art results in 3D molecule generation, conditional structure generation, and structure energy benchmarks using diffusion and flow matching. Furthermore, doubling the number of parameters in Megalodon to 40M significantly enhances its performance, generating up to 49x more valid large molecules and achieving energy levels that are 2-10x lower than those of the best prior generative models.

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.

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.

The expressive power of Graph Neural Networks (GNNs) has been studied extensively through the Weisfeiler-Leman (WL) graph isomorphism test. However, standard GNNs and the WL framework are inapplicable for geometric graphs embedded in Euclidean space, such as biomolecules, materials, and other physical systems. In this work, we propose a geometric version of the WL test (GWL) for discriminating geometric graphs while respecting the underlying physical symmetries: permutations, rotation, reflection, and translation. We use GWL to characterise the expressive power of geometric GNNs that are invariant or equivariant to physical symmetries in terms of distinguishing geometric graphs. GWL unpacks how key design choices influence geometric GNN expressivity: (1) Invariant layers have limited expressivity as they cannot distinguish one-hop identical geometric graphs; (2) Equivariant layers distinguish a larger class of graphs by propagating geometric information beyond local neighbourhoods; (3) Higher order tensors and scalarisation enable maximally powerful geometric GNNs; and (4) GWL's discrimination-based perspective is equivalent to universal approximation. Synthetic experiments supplementing our results are available at https://github.com/chaitjo/geometric-gnn-dojo

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.

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.

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.

Recent advancements, such as Group Relative Policy Optimization (GRPO), have enhanced the reasoning capabilities of large language models by optimizing the arithmetic mean of token-level rewards. However, GRPO suffers from unstable policy updates when processing tokens with outlier importance-weighted rewards, which manifests as extreme importance sampling ratios during training, i.e., the ratio between the sampling probabilities assigned to a token by the current and old policies. In this work, we propose Geometric-Mean Policy Optimization (GMPO), a stabilized variant of GRPO. Instead of optimizing the arithmetic mean, GMPO maximizes the geometric mean of token-level rewards, which is inherently less sensitive to outliers and maintains a more stable range of importance sampling ratio. In addition, we provide comprehensive theoretical and experimental analysis to justify the design and stability benefits of GMPO. Beyond improved stability, GMPO-7B outperforms GRPO by an average of 4.1% on multiple mathematical benchmarks and 1.4% on multimodal reasoning benchmark, including AIME24, AMC, MATH500, OlympiadBench, Minerva, and Geometry3K. Code is available at https://github.com/callsys/GMPO.

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

Structure-Based Drug Design (SBDD) is crucial for identifying bioactive molecules. Recent deep generative models are faced with challenges in geometric structure modeling. A major bottleneck lies in the twisted probability path of multi-modalities -- continuous 3D positions and discrete 2D topologies -- which jointly determine molecular geometries. By establishing the fact that noise schedules decide the Variational Lower Bound (VLB) for the twisted probability path, we propose VLB-Optimal Scheduling (VOS) strategy in this under-explored area, which optimizes VLB as a path integral for SBDD. Our model effectively enhances molecular geometries and interaction modeling, achieving state-of-the-art PoseBusters passing rate of 95.9% on CrossDock, more than 10% improvement upon strong baselines, while maintaining high affinities and robust intramolecular validity evaluated on held-out test set. Code is available at https://github.com/AlgoMole/MolCRAFT.

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.

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.

The advent of Unified Multimodal Models (UMMs) signals a paradigm shift in artificial intelligence, moving from passive perception to active, cross-modal generation. Despite their unprecedented ability to synthesize information, a critical gap persists in evaluation: existing benchmarks primarily assess discriminative understanding or unconstrained image generation separately, failing to measure the integrated cognitive process of generative reasoning. To bridge this gap, we propose that geometric construction provides an ideal testbed as it inherently demands a fusion of language comprehension and precise visual generation. We introduce GGBench, a benchmark designed specifically to evaluate geometric generative reasoning. It provides a comprehensive framework for systematically diagnosing a model's ability to not only understand and reason but to actively construct a solution, thereby setting a more rigorous standard for the next generation of intelligent systems. Project website: https://opendatalab-raiser.github.io/GGBench/.

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.

We propose GGAvatar, a novel 3D avatar representation designed to robustly model dynamic head avatars with complex identities and deformations. GGAvatar employs a coarse-to-fine structure, featuring two core modules: Neutral Gaussian Initialization Module and Geometry Morph Adjuster. Neutral Gaussian Initialization Module pairs Gaussian primitives with deformable triangular meshes, employing an adaptive density control strategy to model the geometric structure of the target subject with neutral expressions. Geometry Morph Adjuster introduces deformation bases for each Gaussian in global space, creating fine-grained low-dimensional representations of deformation behaviors to address the Linear Blend Skinning formula's limitations effectively. Extensive experiments show that GGAvatar can produce high-fidelity renderings, outperforming state-of-the-art methods in visual quality and quantitative metrics.

Improving the quality of hyperspectral images (HSIs), such as through super-resolution, is a crucial research area. However, generative modeling for HSIs presents several challenges. Due to their high spectral dimensionality, HSIs are too memory-intensive for direct input into conventional diffusion models. Furthermore, general generative models lack an understanding of the topological and geometric structures of ground objects in remote sensing imagery. In addition, most diffusion models optimize loss functions at the noise level, leading to a non-intuitive convergence behavior and suboptimal generation quality for complex data. To address these challenges, we propose a Geometric Enhanced Wavelet-based Diffusion Model (GEWDiff), a novel framework for reconstructing hyperspectral images at 4-times super-resolution. A wavelet-based encoder-decoder is introduced that efficiently compresses HSIs into a latent space while preserving spectral-spatial information. To avoid distortion during generation, we incorporate a geometry-enhanced diffusion process that preserves the geometric features. Furthermore, a multi-level loss function was designed to guide the diffusion process, promoting stable convergence and improved reconstruction fidelity. Our model demonstrated state-of-the-art results across multiple dimensions, including fidelity, spectral accuracy, visual realism, and clarity.

Geometric Attention (GA) specifies an attention layer by four independent inputs: a finite carrier (what indices are addressable), an evidence-kernel rule (how masked proto-scores and a link induce nonnegative weights), a probe family (which observables are treated as admissible), and an anchor/update rule (which representative kernel is selected and how it is applied). Probe families induce an operational equivalence relation on kernels and therefore a gauge; anchors select representatives relative to that probe. Under a scalar relational-work representation and a multiplicative compositionality law for evidence, the admissible link family is exponential, yielding Gibbs weights; with row anchoring this includes the softmax kernel family as a subregime. After quotienting unary row/column score fields, the remaining interaction component admits a canonical rank-r normal form (Eckart-Young/SVD); dot-product score charts implement the corresponding low-rank interaction regime. Fixing the carrier and extensionalizing the update yields the standard fixed-token Transformer attention operator; allowing carrier updates yields adaptive-carrier and staged-depth regimes. The operator language also supports multihead/mixed kernels, plan-based anchors (e.g., entropic OT/Sinkhorn), and unary operators (e.g., FFN-style fields) as explicit regime choices. This separates invariant structure from modeling choice, enabling principled comparison and extension of attention mechanisms, and attention-based architectures.

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.

Learning discriminative shape representations is a crucial issue for large-scale 3D shape retrieval. In this paper, we propose the Collaborative Inner Product Loss (CIP Loss) to obtain ideal shape embedding that discriminative among different categories and clustered within the same class. Utilizing simple inner product operation, CIP loss explicitly enforces the features of the same class to be clustered in a linear subspace, while inter-class subspaces are constrained to be at least orthogonal. Compared to previous metric loss functions, CIP loss could provide more clear geometric interpretation for the embedding than Euclidean margin, and is easy to implement without normalization operation referring to cosine margin. Moreover, our proposed loss term can combine with other commonly used loss functions and can be easily plugged into existing off-the-shelf architectures. Extensive experiments conducted on the two public 3D object retrieval datasets, ModelNet and ShapeNetCore 55, demonstrate the effectiveness of our proposal, and our method has achieved state-of-the-art results on both datasets.

Generative models have shown great promise in generating 3D geometric systems, which is a fundamental problem in many natural science domains such as molecule and protein design. However, existing approaches only operate on static structures, neglecting the fact that physical systems are always dynamic in nature. In this work, we propose geometric trajectory diffusion models (GeoTDM), the first diffusion model for modeling the temporal distribution of 3D geometric trajectories. Modeling such distribution is challenging as it requires capturing both the complex spatial interactions with physical symmetries and temporal correspondence encapsulated in the dynamics. We theoretically justify that diffusion models with equivariant temporal kernels can lead to density with desired symmetry, and develop a novel transition kernel leveraging SE(3)-equivariant spatial convolution and temporal attention. Furthermore, to induce an expressive trajectory distribution for conditional generation, we introduce a generalized learnable geometric prior into the forward diffusion process to enhance temporal conditioning. We conduct extensive experiments on both unconditional and conditional generation in various scenarios, including physical simulation, molecular dynamics, and pedestrian motion. Empirical results on a wide suite of metrics demonstrate that GeoTDM can generate realistic geometric trajectories with significantly higher quality.

Generative models, especially diffusion models (DMs), have achieved promising results for generating feature-rich geometries and advancing foundational science problems such as molecule design. Inspired by the recent huge success of Stable (latent) Diffusion models, we propose a novel and principled method for 3D molecule generation named Geometric Latent Diffusion Models (GeoLDM). GeoLDM is the first latent DM model for the molecular geometry domain, composed of autoencoders encoding structures into continuous latent codes and DMs operating in the latent space. Our key innovation is that for modeling the 3D molecular geometries, we capture its critical roto-translational equivariance constraints by building a point-structured latent space with both invariant scalars and equivariant tensors. Extensive experiments demonstrate that GeoLDM can consistently achieve better performance on multiple molecule generation benchmarks, with up to 7\% improvement for the valid percentage of large biomolecules. Results also demonstrate GeoLDM's higher capacity for controllable generation thanks to the latent modeling. Code is provided at https://github.com/MinkaiXu/GeoLDM.

Geometric methods for solving open-world off-road navigation tasks, by learning occupancy and metric maps, provide good generalization but can be brittle in outdoor environments that violate their assumptions (e.g., tall grass). Learning-based methods can directly learn collision-free behavior from raw observations, but are difficult to integrate with standard geometry-based pipelines. This creates an unfortunate conflict -- either use learning and lose out on well-understood geometric navigational components, or do not use it, in favor of extensively hand-tuned geometry-based cost maps. In this work, we reject this dichotomy by designing the learning and non-learning-based components in a way such that they can be effectively combined in a self-supervised manner. Both components contribute to a planning criterion: the learned component contributes predicted traversability as rewards, while the geometric component contributes obstacle cost information. We instantiate and comparatively evaluate our system in both in-distribution and out-of-distribution environments, showing that this approach inherits complementary gains from the learned and geometric components and significantly outperforms either of them. Videos of our results are hosted at https://sites.google.com/view/hybrid-imitative-planning

The last decade has witnessed an experimental revolution in data science and machine learning, epitomised by deep learning methods. Indeed, many high-dimensional learning tasks previously thought to be beyond reach -- such as computer vision, playing Go, or protein folding -- are in fact feasible with appropriate computational scale. Remarkably, the essence of deep learning is built from two simple algorithmic principles: first, the notion of representation or feature learning, whereby adapted, often hierarchical, features capture the appropriate notion of regularity for each task, and second, learning by local gradient-descent type methods, typically implemented as backpropagation. While learning generic functions in high dimensions is a cursed estimation problem, most tasks of interest are not generic, and come with essential pre-defined regularities arising from the underlying low-dimensionality and structure of the physical world. This text is concerned with exposing these regularities through unified geometric principles that can be applied throughout a wide spectrum of applications. Such a 'geometric unification' endeavour, in the spirit of Felix Klein's Erlangen Program, serves a dual purpose: on one hand, it provides a common mathematical framework to study the most successful neural network architectures, such as CNNs, RNNs, GNNs, and Transformers. On the other hand, it gives a constructive procedure to incorporate prior physical knowledge into neural architectures and provide principled way to build future architectures yet to be invented.

Recent advancements in reinforcement learning (RL) have enhanced the reasoning abilities of large language models (LLMs), yet the impact on multimodal LLMs (MLLMs) is limited. Particularly in vision-intensive tasks like geometric reasoning, MLLMs hallucinate frequently, leading to inaccurate reasoning. We attribute this to the perceptual bottleneck in MLLMs, which caps the benefits of reasoning training. To quantify this, we design a Geo-Perception Question-Answering (GeoPQA) benchmark, targeting basic geometric concepts and spatial relationships. Experiments on GeoPQA reveal significant shortcomings of MLLMs in visual perception, which constrain RL reward signals for effective training. To address this bottleneck, we propose a two-stage RL training framework by first enhancing the visual perception of geometric structures, then fostering reasoning capabilities. Applied to Qwen2.5-VL-3B-Instruct, our two-stage training improves geometric reasoning by 9.7% and geometric problem solving by 9.1%, compared to the direct reasoning training approach. Our method also generalizes to other vision-intensive domains like figure understanding, highlighting the importance of perceptual grounding in effective MLLM reasoning.

We introduce Talk2Move, a reinforcement learning (RL) based diffusion framework for text-instructed spatial transformation of objects within scenes. Spatially manipulating objects in a scene through natural language poses a challenge for multimodal generation systems. While existing text-based manipulation methods can adjust appearance or style, they struggle to perform object-level geometric transformations-such as translating, rotating, or resizing objects-due to scarce paired supervision and pixel-level optimization limits. Talk2Move employs Group Relative Policy Optimization (GRPO) to explore geometric actions through diverse rollouts generated from input images and lightweight textual variations, removing the need for costly paired data. A spatial reward guided model aligns geometric transformations with linguistic description, while off-policy step evaluation and active step sampling improve learning efficiency by focusing on informative transformation stages. Furthermore, we design object-centric spatial rewards that evaluate displacement, rotation, and scaling behaviors directly, enabling interpretable and coherent transformations. Experiments on curated benchmarks demonstrate that Talk2Move achieves precise, consistent, and semantically faithful object transformations, outperforming existing text-guided editing approaches in both spatial accuracy and scene coherence.

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.

Multi-view image generation holds significant application value in computer vision, particularly in domains like 3D reconstruction, virtual reality, and augmented reality. Most existing methods, which rely on extending single images, face notable computational challenges in maintaining cross-view consistency and generating high-resolution outputs. To address these issues, we propose the Geometry-guided Multi-View Diffusion Model, which incorporates mechanisms for extracting multi-view geometric information and adjusting the intensity of geometric features to generate images that are both consistent across views and rich in detail. Specifically, we design a multi-view geometry information extraction module that leverages depth maps, normal maps, and foreground segmentation masks to construct a shared geometric structure, ensuring shape and structural consistency across different views. To enhance consistency and detail restoration during generation, we develop a decoupled geometry-enhanced attention mechanism that strengthens feature focus on key geometric details, thereby improving overall image quality and detail preservation. Furthermore, we apply an adaptive learning strategy that fine-tunes the model to better capture spatial relationships and visual coherence between the generated views, ensuring realistic results. Our model also incorporates an iterative refinement process that progressively improves the output quality through multiple stages of image generation. Finally, a dynamic geometry information intensity adjustment mechanism is proposed to adaptively regulate the influence of geometric data, optimizing overall quality while ensuring the naturalness of generated images. More details can be found on the project page: https://sobeymil.github.io/GeoMVD.com.

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.

Sewing patterns, the essential blueprints for fabric cutting and tailoring, act as a crucial bridge between design concepts and producible garments. However, existing uni-modal sewing pattern generation models struggle to effectively encode complex design concepts with a multi-modal nature and correlate them with vectorized sewing patterns that possess precise geometric structures and intricate sewing relations. In this work, we propose a novel sewing pattern generation approach Design2GarmentCode based on Large Multimodal Models (LMMs), to generate parametric pattern-making programs from multi-modal design concepts. LMM offers an intuitive interface for interpreting diverse design inputs, while pattern-making programs could serve as well-structured and semantically meaningful representations of sewing patterns, and act as a robust bridge connecting the cross-domain pattern-making knowledge embedded in LMMs with vectorized sewing patterns. Experimental results demonstrate that our method can flexibly handle various complex design expressions such as images, textual descriptions, designer sketches, or their combinations, and convert them into size-precise sewing patterns with correct stitches. Compared to previous methods, our approach significantly enhances training efficiency, generation quality, and authoring flexibility.

This paper presents WorldPlay, a streaming video diffusion model that enables real-time, interactive world modeling with long-term geometric consistency, resolving the trade-off between speed and memory that limits current methods. WorldPlay draws power from three key innovations. 1) We use a Dual Action Representation to enable robust action control in response to the user's keyboard and mouse inputs. 2) To enforce long-term consistency, our Reconstituted Context Memory dynamically rebuilds context from past frames and uses temporal reframing to keep geometrically important but long-past frames accessible, effectively alleviating memory attenuation. 3) We also propose Context Forcing, a novel distillation method designed for memory-aware model. Aligning memory context between the teacher and student preserves the student's capacity to use long-range information, enabling real-time speeds while preventing error drift. Taken together, WorldPlay generates long-horizon streaming 720p video at 24 FPS with superior consistency, comparing favorably with existing techniques and showing strong generalization across diverse scenes. Project page and online demo can be found: https://3d-models.hunyuan.tencent.com/world/ and https://3d.hunyuan.tencent.com/sceneTo3D.

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.

Feedforward geometric foundation models achieve strong short-window reconstruction, yet scaling them to minutes-long videos is bottlenecked by quadratic attention complexity or limited effective memory in recurrent designs. We present LoGeR (Long-context Geometric Reconstruction), a novel architecture that scales dense 3D reconstruction to extremely long sequences without post-optimization. LoGeR processes video streams in chunks, leveraging strong bidirectional priors for high-fidelity intra-chunk reasoning. To manage the critical challenge of coherence across chunk boundaries, we propose a learning-based hybrid memory module. This dual-component system combines a parametric Test-Time Training (TTT) memory to anchor the global coordinate frame and prevent scale drift, alongside a non-parametric Sliding Window Attention (SWA) mechanism to preserve uncompressed context for high-precision adjacent alignment. Remarkably, this memory architecture enables LoGeR to be trained on sequences of 128 frames, and generalize up to thousands of frames during inference. Evaluated across standard benchmarks and a newly repurposed VBR dataset with sequences of up to 19k frames, LoGeR substantially outperforms prior state-of-the-art feedforward methods--reducing ATE on KITTI by over 74%--and achieves robust, globally consistent reconstruction over unprecedented horizons.

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.

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.

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

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.

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.

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.

This paper presents the computational challenge on differential geometry and topology that happened within the ICLR 2021 workshop "Geometric and Topological Representation Learning". The competition asked participants to provide creative contributions to the fields of computational geometry and topology through the open-source repositories Geomstats and Giotto-TDA. The challenge attracted 16 teams in its two month duration. This paper describes the design of the challenge and summarizes its main findings.

Mathematical geometric reasoning is essential for scientific discovery and educational development, requiring precise logic and rigorous formal verification. While recent advances in Multimodal Large Language Models (MLLMs) have improved reasoning tasks, existing models typically struggle with formal geometric reasoning, particularly when dynamically constructing and verifying auxiliary geometric elements. To address these challenges, we introduce Geoint-R1, a multimodal reasoning framework designed to generate formally verifiable geometric solutions from textual descriptions and visual diagrams. Geoint-R1 uniquely integrates auxiliary elements construction, formal reasoning represented via Lean4, and interactive visualization. To systematically evaluate and advance formal geometric reasoning, we propose the Geoint benchmark, comprising 1,885 rigorously annotated geometry problems across diverse topics such as plane, spatial, and solid geometry. Each problem includes structured textual annotations, precise Lean4 code for auxiliary constructions, and detailed solution steps verified by experts. Extensive experiments demonstrate that Geoint-R1 significantly surpasses existing multimodal and math-specific reasoning models, particularly on challenging problems requiring explicit auxiliary element constructions.

Video Instance Segmentation (VIS) fundamentally struggles with pervasive challenges including object occlusions, motion blur, and appearance variations during temporal association. To overcome these limitations, this work introduces geometric awareness to enhance VIS robustness by strategically leveraging monocular depth estimation. We systematically investigate three distinct integration paradigms. Expanding Depth Channel (EDC) method concatenates the depth map as input channel to segmentation networks; Sharing ViT (SV) designs a uniform ViT backbone, shared between depth estimation and segmentation branches; Depth Supervision (DS) makes use of depth prediction as an auxiliary training guide for feature learning. Though DS exhibits limited effectiveness, benchmark evaluations demonstrate that EDC and SV significantly enhance the robustness of VIS. When with Swin-L backbone, our EDC method gets 56.2 AP, which sets a new state-of-the-art result on OVIS benchmark. This work conclusively establishes depth cues as critical enablers for robust video understanding.

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.

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.

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.

Text-to-3D generation by distilling pretrained large-scale text-to-image diffusion models has shown great promise but still suffers from inconsistent 3D geometric structures (Janus problems) and severe artifacts. The aforementioned problems mainly stem from 2D diffusion models lacking 3D awareness during the lifting. In this work, we present GeoDream, a novel method that incorporates explicit generalized 3D priors with 2D diffusion priors to enhance the capability of obtaining unambiguous 3D consistent geometric structures without sacrificing diversity or fidelity. Specifically, we first utilize a multi-view diffusion model to generate posed images and then construct cost volume from the predicted image, which serves as native 3D geometric priors, ensuring spatial consistency in 3D space. Subsequently, we further propose to harness 3D geometric priors to unlock the great potential of 3D awareness in 2D diffusion priors via a disentangled design. Notably, disentangling 2D and 3D priors allows us to refine 3D geometric priors further. We justify that the refined 3D geometric priors aid in the 3D-aware capability of 2D diffusion priors, which in turn provides superior guidance for the refinement of 3D geometric priors. Our numerical and visual comparisons demonstrate that GeoDream generates more 3D consistent textured meshes with high-resolution realistic renderings (i.e., 1024 times 1024) and adheres more closely to semantic coherence.

Recent advances in neural reconstruction using posed image sequences have made remarkable progress. However, due to the lack of depth information, existing volumetric-based techniques simply duplicate 2D image features of the object surface along the entire camera ray. We contend this duplication introduces noise in empty and occluded spaces, posing challenges for producing high-quality 3D geometry. Drawing inspiration from traditional multi-view stereo methods, we propose an end-to-end 3D neural reconstruction framework CVRecon, designed to exploit the rich geometric embedding in the cost volumes to facilitate 3D geometric feature learning. Furthermore, we present Ray-contextual Compensated Cost Volume (RCCV), a novel 3D geometric feature representation that encodes view-dependent information with improved integrity and robustness. Through comprehensive experiments, we demonstrate that our approach significantly improves the reconstruction quality in various metrics and recovers clear fine details of the 3D geometries. Our extensive ablation studies provide insights into the development of effective 3D geometric feature learning schemes. Project page: https://cvrecon.ziyue.cool/

Recently, "visual o1" began to enter people's vision, with expectations that this slow-thinking design can solve visual reasoning tasks, especially geometric math problems. However, the reality is that current LVLMs (Large Vision Language Models) can hardly even accurately copy a geometric figure, let alone truly understand the complex inherent logic and spatial relationships within geometric shapes. We believe accurate copying (strong perception) is the first step to visual o1. Accordingly, we introduce the concept of "slow perception" (SP), which guides the model to gradually perceive basic point-line combinations, as our humans, reconstruct complex geometric structures progressively. There are two-fold stages in SP: a) perception decomposition. Perception is not instantaneous. In this stage, complex geometric figures are broken down into basic simple units to unify geometry representation. b) perception flow, which acknowledges that accurately tracing a line is not an easy task. This stage aims to avoid "long visual jumps" in regressing line segments by using a proposed "perceptual ruler" to trace each line stroke-by-stroke. Surprisingly, such a human-like perception manner enjoys an inference time scaling law -- the slower, the better. Researchers strive to speed up the model's perception in the past, but we slow it down again, allowing the model to read the image step-by-step and carefully.

Graphic design forms the cornerstone of modern visual communication, serving as a vital medium for promoting cultural and commercial events. Recent advances have explored automating this process using Large Multimodal Models (LMMs), yet existing methods often produce geometrically inaccurate layouts and lack the iterative, layer-specific editing required in professional workflows. To address these limitations, we present PosterCopilot, a framework that advances layout reasoning and controllable editing for professional graphic design. Specifically, we introduce a progressive three-stage training strategy that equips LMMs with geometric understanding and aesthetic reasoning for layout design, consisting of Perturbed Supervised Fine-Tuning, Reinforcement Learning for Visual-Reality Alignment, and Reinforcement Learning from Aesthetic Feedback. Furthermore, we develop a complete workflow that couples the trained LMM-based design model with generative models, enabling layer-controllable, iterative editing for precise element refinement while maintaining global visual consistency. Extensive experiments demonstrate that PosterCopilot achieves geometrically accurate and aesthetically superior layouts, offering unprecedented controllability for professional iterative design.

Attention sink (AS) is a consistent pattern in transformer attention maps where certain tokens (often special tokens or positional anchors) disproportionately attract attention from other tokens. We show that in transformers, AS is not an architectural artifact, but it is the manifestation of a fundamental geometric principle: the establishment of reference frames that anchor representational spaces. We analyze several architectures and identify three distinct reference frame types, centralized, distributed, and bidirectional, that correlate with the attention sink phenomenon. We show that they emerge during the earliest stages of training as optimal solutions to the problem of establishing stable coordinate systems in high-dimensional spaces. We show the influence of architecture components, particularly position encoding implementations, on the specific type of reference frame. This perspective transforms our understanding of transformer attention mechanisms and provides insights for both architecture design and the relationship with AS.

Modern AI technologies for drug discovery are distributed across heterogeneous platforms-including web applications, desktop environments, and code libraries-leading to fragmented workflows, inconsistent interfaces, and high integration overhead. We present an agentic end-to-end drug design framework that leverages a Large Language Model (LLM) in conjunction with the Model Context Protocol (MCP) to dynamically coordinate access to biochemical databases, modular toolchains, and task-specific AI models. The system integrates four state-of-the-art components: MaSIF (MaSIF-site and MaSIF-seed-search) for geometric deep learning-based identification of protein-protein interaction (PPI) sites, Rosetta for grafting protein fragments onto protein backbones to form mini proteins, ProteinMPNN for amino acid sequences redesign, and AlphaFold3 for near-experimental accuracy in complex structure prediction. Starting from a target structure, the framework supports de novo binder generation via surface analysis, scaffold grafting and pose construction, sequence optimization, and structure prediction. Additionally, by replacing rigid, script-based workflows with a protocol-driven, LLM-coordinated architecture, the framework improves reproducibility, reduces manual overhead, and ensures extensibility, portability, and auditability across the entire drug design process.

We introduce DrugFlow, a generative model for structure-based drug design that integrates continuous flow matching with discrete Markov bridges, demonstrating state-of-the-art performance in learning chemical, geometric, and physical aspects of three-dimensional protein-ligand data. We endow DrugFlow with an uncertainty estimate that is able to detect out-of-distribution samples. To further enhance the sampling process towards distribution regions with desirable metric values, we propose a joint preference alignment scheme applicable to both flow matching and Markov bridge frameworks. Furthermore, we extend our model to also explore the conformational landscape of the protein by jointly sampling side chain angles and molecules.

Computer-aided design (CAD) is the digital construction of 2D and 3D objects, and is central to a wide range of engineering and manufacturing applications like automobile and aviation. Despite its importance, CAD modeling remains largely a time-intensive, manual task. Recent works have attempted to automate this process with small transformer-based models and handcrafted CAD sequence representations. However, there has been little effort to leverage the potential of large language models (LLMs) for sequential CAD design. In this work, we introduce a new large-scale dataset of more than 170k CAD models annotated with high-quality, human-like descriptions generated with our pipeline based on GPT-4.1. Using this dataset, we fine-tune powerful code-LLMs to generate CAD sequences represented in a JSON-based format from natural language descriptions, demonstrating the viability and effectiveness of this approach for text-conditioned CAD generation. Because simple metrics often fail to reflect the quality of generated objects, we introduce geometric and topological metrics based on sphericity, mean curvature, and Euler characteristic to provide richer structural insights. Our experiments and ablation studies on both synthetic and human-annotated data demonstrate that CADmium is able to automate CAD design, drastically speeding up the design of new objects. The dataset, code, and fine-tuned models are available online.

Realistic digital garment modeling remains a labor-intensive task due to the intricate process of translating 2D sewing patterns into high-fidelity, simulation-ready 3D garments. We introduce GarmageNet, a unified generative framework that automates the creation of 2D sewing patterns, the construction of sewing relationships, and the synthesis of 3D garment initializations compatible with physics-based simulation. Central to our approach is Garmage, a novel garment representation that encodes each panel as a structured geometry image, effectively bridging the semantic and geometric gap between 2D structural patterns and 3D garment shapes. GarmageNet employs a latent diffusion transformer to synthesize panel-wise geometry images and integrates GarmageJigsaw, a neural module for predicting point-to-point sewing connections along panel contours. To support training and evaluation, we build GarmageSet, a large-scale dataset comprising over 10,000 professionally designed garments with detailed structural and style annotations. Our method demonstrates versatility and efficacy across multiple application scenarios, including scalable garment generation from multi-modal design concepts (text prompts, sketches, photographs), automatic modeling from raw flat sewing patterns, pattern recovery from unstructured point clouds, and progressive garment editing using conventional instructions-laying the foundation for fully automated, production-ready pipelines in digital fashion. Project page: https://style3d.github.io/garmagenet.

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.

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.

Multi-view generation with camera pose control and prompt-based customization are both essential elements for achieving controllable generative models. However, existing multi-view generation models do not support customization with geometric consistency, whereas customization models lack explicit viewpoint control, making them challenging to unify. Motivated by these gaps, we introduce a novel task, multi-view customization, which aims to jointly achieve multi-view camera pose control and customization. Due to the scarcity of training data in customization, existing multi-view generation models, which inherently rely on large-scale datasets, struggle to generalize to diverse prompts. To address this, we propose MVCustom, a novel diffusion-based framework explicitly designed to achieve both multi-view consistency and customization fidelity. In the training stage, MVCustom learns the subject's identity and geometry using a feature-field representation, incorporating the text-to-video diffusion backbone enhanced with dense spatio-temporal attention, which leverages temporal coherence for multi-view consistency. In the inference stage, we introduce two novel techniques: depth-aware feature rendering explicitly enforces geometric consistency, and consistent-aware latent completion ensures accurate perspective alignment of the customized subject and surrounding backgrounds. Extensive experiments demonstrate that MVCustom is the only framework that simultaneously achieves faithful multi-view generation and customization.

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.

In this paper, we introduce Geometry-Inverse-Meet-Pixel-Insert, short for GEO, an exceptionally versatile image editing technique designed to cater to customized user requirements at both local and global scales. Our approach seamlessly integrates text prompts and image prompts to yield diverse and precise editing outcomes. Notably, our method operates without the need for training and is driven by two key contributions: (i) a novel geometric accumulation loss that enhances DDIM inversion to faithfully preserve pixel space geometry and layout, and (ii) an innovative boosted image prompt technique that combines pixel-level editing for text-only inversion with latent space geometry guidance for standard classifier-free reversion. Leveraging the publicly available Stable Diffusion model, our approach undergoes extensive evaluation across various image types and challenging prompt editing scenarios, consistently delivering high-fidelity editing results for real images.

We introduce AbBiBench (Antibody Binding Benchmarking), a benchmarking framework for antibody binding affinity maturation and design. Unlike previous strategies that evaluate antibodies in isolation, typically by comparing them to natural sequences with metrics such as amino acid recovery rate or structural RMSD, AbBiBench instead treats the antibody-antigen (Ab-Ag) complex as the fundamental unit. It evaluates an antibody design's binding potential by measuring how well a protein model scores the full Ab-Ag complex. We first curate, standardize, and share more than 184,500 experimental measurements of antibody mutants across 14 antibodies and 9 antigens-including influenza, lysozyme, HER2, VEGF, integrin, Ang2, and SARS-CoV-2-covering both heavy-chain and light-chain mutations. Using these datasets, we systematically compare 15 protein models including masked language models, autoregressive language models, inverse folding models, diffusion-based generative models, and geometric graph models by comparing the correlation between model likelihood and experimental affinity values. Additionally, to demonstrate AbBiBench's generative utility, we apply it to antibody F045-092 in order to introduce binding to influenza H1N1. We sample new antibody variants with the top-performing models, rank them by the structural integrity and biophysical properties of the Ab-Ag complex, and assess them with in vitro ELISA binding assays. Our findings show that structure-conditioned inverse folding models outperform others in both affinity correlation and generation tasks. Overall, AbBiBench provides a unified, biologically grounded evaluation framework to facilitate the development of more effective, function-aware antibody design models.

Cross-view geo-localization (CVGL) aims to establish spatial correspondences between images captured from significantly different viewpoints and constitutes a fundamental technique for visual localization in GNSS-denied environments. Nevertheless, CVGL remains challenging due to severe geometric asymmetry, texture inconsistency across imaging domains, and the progressive degradation of discriminative local information. Existing methods predominantly rely on spatial domain feature alignment, which is inherently sensitive to large scale viewpoint variations and local disturbances. To alleviate these limitations, this paper proposes the Spatial and Frequency Domain Enhancement Network (SFDE), which leverages complementary representations from spatial and frequency domains. SFDE adopts a three branch parallel architecture to model global semantic context, local geometric structure, and statistical stability in the frequency domain, respectively, thereby characterizing consistency across domains from the perspectives of scene topology, multiscale structural patterns, and frequency invariance. The resulting complementary features are jointly optimized in a unified embedding space via progressive enhancement and coupled constraints, enabling the learning of cross-view representations with consistency across multiple granularities. Comprehensive experiments show that SFDE achieves competitive performance and in many cases even surpasses state-of-the-art methods, while maintaining a lightweight and computationally efficient design. {Our code is available at https://github.com/Mashuaishuai669/SFDE

Dynamic view synthesis has seen significant advances, yet reconstructing scenes from uncalibrated, casual video remains challenging due to slow optimization and complex parameter estimation. In this work, we present Instant4D, a monocular reconstruction system that leverages native 4D representation to efficiently process casual video sequences within minutes, without calibrated cameras or depth sensors. Our method begins with geometric recovery through deep visual SLAM, followed by grid pruning to optimize scene representation. Our design significantly reduces redundancy while maintaining geometric integrity, cutting model size to under 10% of its original footprint. To handle temporal dynamics efficiently, we introduce a streamlined 4D Gaussian representation, achieving a 30x speed-up and reducing training time to within two minutes, while maintaining competitive performance across several benchmarks. Our method reconstruct a single video within 10 minutes on the Dycheck dataset or for a typical 200-frame video. We further apply our model to in-the-wild videos, showcasing its generalizability. Our project website is published at https://instant4d.github.io/.

High-quality molecular representations are essential for property prediction and molecular design, yet large labeled datasets remain scarce. While self-supervised pretraining on molecular graphs has shown promise, many existing approaches either depend on hand-crafted augmentations or complex generative objectives, and often rely solely on 2D topology, leaving valuable 3D structural information underutilized. To address this gap, we introduce C-FREE (Contrast-Free Representation learning on Ego-nets), a simple framework that integrates 2D graphs with ensembles of 3D conformers. C-FREE learns molecular representations by predicting subgraph embeddings from their complementary neighborhoods in the latent space, using fixed-radius ego-nets as modeling units across different conformers. This design allows us to integrate both geometric and topological information within a hybrid Graph Neural Network (GNN)-Transformer backbone, without negatives, positional encodings, or expensive pre-processing. Pretraining on the GEOM dataset, which provides rich 3D conformational diversity, C-FREE achieves state-of-the-art results on MoleculeNet, surpassing contrastive, generative, and other multimodal self-supervised methods. Fine-tuning across datasets with diverse sizes and molecule types further demonstrates that pretraining transfers effectively to new chemical domains, highlighting the importance of 3D-informed molecular representations.

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.

Unsupervised learning of depth and ego-motion, two fundamental 3D perception tasks, has made significant strides in recent years. However, most methods treat ego-motion as an auxiliary task, either mixing all motion types or excluding depth-independent rotational motions in supervision. Such designs limit the incorporation of strong geometric constraints, reducing reliability and robustness under diverse conditions. This study introduces a discriminative treatment of motion components, leveraging the geometric regularities of their respective rigid flows to benefit both depth and ego-motion estimation. Given consecutive video frames, network outputs first align the optical axes and imaging planes of the source and target cameras. Optical flows between frames are transformed through these alignments, and deviations are quantified to impose geometric constraints individually on each ego-motion component, enabling more targeted refinement. These alignments further reformulate the joint learning process into coaxial and coplanar forms, where depth and each translation component can be mutually derived through closed-form geometric relationships, introducing complementary constraints that improve depth robustness. DiMoDE, a general depth and ego-motion joint learning framework incorporating these designs, achieves state-of-the-art performance on multiple public datasets and a newly collected diverse real-world dataset, particularly under challenging conditions. Our source code will be publicly available at mias.group/DiMoDE upon publication.

Constructing drivable and photorealistic 3D head avatars has become a central task in AR/XR, enabling immersive and expressive user experiences. With the emergence of high-fidelity and efficient representations such as 3D Gaussians, recent works have pushed toward ultra-detailed head avatars. Existing approaches typically fall into two categories: rule-based analytic rigging or neural network-based deformation fields. While effective in constrained settings, both approaches often fail to generalize to unseen expressions and poses, particularly in extreme reenactment scenarios. Other methods constrain Gaussians to the global texel space of 3DMMs to reduce rendering complexity. However, these texel-based avatars tend to underutilize the underlying mesh structure. They apply minimal analytic deformation and rely heavily on neural regressors and heuristic regularization in UV space, which weakens geometric consistency and limits extrapolation to complex, out-of-distribution deformations. To address these limitations, we introduce TexAvatars, a hybrid avatar representation that combines the explicit geometric grounding of analytic rigging with the spatial continuity of texel space. Our approach predicts local geometric attributes in UV space via CNNs, but drives 3D deformation through mesh-aware Jacobians, enabling smooth and semantically meaningful transitions across triangle boundaries. This hybrid design separates semantic modeling from geometric control, resulting in improved generalization, interpretability, and stability. Furthermore, TexAvatars captures fine-grained expression effects, including muscle-induced wrinkles, glabellar lines, and realistic mouth cavity geometry, with high fidelity. Our method achieves state-of-the-art performance under extreme pose and expression variations, demonstrating strong generalization in challenging head reenactment settings.

Computer-Aided Design (CAD) relies on structured and editable geometric representations, yet existing generative methods are constrained by small annotated datasets with explicit design histories or boundary representation (BRep) labels. Meanwhile, millions of unannotated 3D meshes remain untapped, limiting progress in scalable CAD generation. To address this, we propose DreamCAD, a multi-modal generative framework that directly produces editable BReps from point-level supervision, without CAD-specific annotations. DreamCAD represents each BRep as a set of parametric patches (e.g., Bézier surfaces) and uses a differentiable tessellation method to generate meshes. This enables large-scale training on 3D datasets while reconstructing connected and editable surfaces. Furthermore, we introduce CADCap-1M, the largest CAD captioning dataset to date, with 1M+ descriptions generated using GPT-5 for advancing text-to-CAD research. DreamCAD achieves state-of-the-art performance on ABC and Objaverse benchmarks across text, image, and point modalities, improving geometric fidelity and surpassing 75% user preference. Code and dataset will be publicly available.

Implicit Neural Representations (INRs) have become an essential tool for modeling continuous 2D images, enabling high-fidelity reconstruction, super-resolution, and compression. Popular architectures such as SIREN, WIRE, and FINER demonstrate the potential of INR for capturing fine-grained image details. However, traditional INRs often lack explicit geometric structure and have limited capabilities for local editing or integration with physical simulation, restricting their applicability in dynamic or interactive settings. To address these limitations, we propose GaINeR: Geometry-Aware Implicit Network Representation, a novel framework for 2D images that combines trainable Gaussian distributions with a neural network-based INR. For a given image coordinate, the model retrieves the K nearest Gaussians, aggregates distance-weighted embeddings, and predicts the RGB value via a neural network. This design enables continuous image representation, interpretable geometric structure, and flexible local editing, providing a foundation for physically aware and interactive image manipulation. The official implementation of our method is publicly available at https://github.com/WJakubowska/GaINeR.

Design of neural networks that incorporate symmetry is crucial for geometric deep learning. Central to this effort is the development of invariant and equivariant operations. This works presents a systematic method for constructing valid invariant and equivariant operations. It can handle inputs and outputs in the form of Cartesian tensors with different rank, as well as spherical tensors with different types. In addition, our method features a graphical representation utilizing the symmetric tensor network, which simplifies both the proofs and constructions related to invariant and equivariant functions. We also apply this approach to design the equivariant interaction message for the geometry graph neural network, and equivariant machine learning model to learn the constitutive law of materials.

Computer-aided design (CAD) is crucial in prototyping 3D objects through geometric instructions (i.e., CAD programs). In practical design workflows, designers often engage in time-consuming reviews and refinements of these prototypes by comparing them with reference images. To bridge this gap, we introduce the CAD review task to automatically detect and correct potential errors, ensuring consistency between the constructed 3D objects and reference images. However, recent advanced multimodal large language models (MLLMs) struggle to recognize multiple geometric components and perform spatial geometric operations within the CAD program, leading to inaccurate reviews. In this paper, we propose the CAD program repairer (ReCAD) framework to effectively detect program errors and provide helpful feedback on error correction. Additionally, we create a dataset, CADReview, consisting of over 20K program-image pairs, with diverse errors for the CAD review task. Extensive experiments demonstrate that our ReCAD significantly outperforms existing MLLMs, which shows great potential in design applications.

Multi-object tracking aims to maintain object identities over time by associating detections across video frames. Two dominant paradigms exist in literature: tracking-by-detection methods, which are computationally efficient but rely on handcrafted association heuristics, and end-to-end approaches, which learn association from data at the cost of higher computational complexity. We propose Track-Detection Link Prediction (TDLP), a tracking-by-detection method that performs per-frame association via link prediction between tracks and detections, i.e., by predicting the correct continuation of each track at every frame. TDLP is architecturally designed primarily for geometric features such as bounding boxes, while optionally incorporating additional cues, including pose and appearance. Unlike heuristic-based methods, TDLP learns association directly from data without handcrafted rules, while remaining modular and computationally efficient compared to end-to-end trackers. Extensive experiments on multiple benchmarks demonstrate that TDLP consistently surpasses state-of-the-art performance across both tracking-by-detection and end-to-end methods. Finally, we provide a detailed analysis comparing link prediction with metric learning-based association and show that link prediction is more effective, particularly when handling heterogeneous features such as detection bounding boxes. Our code is available at https://github.com/Robotmurlock/TDLP{https://github.com/Robotmurlock/TDLP}.

3D visual grounding allows an embodied agent to understand visual information in real-world 3D environments based on human instructions, which is crucial for embodied intelligence. Existing 3D visual grounding methods typically rely on separate encoders for different modalities (e.g., RGB images, text, and 3D point clouds), resulting in large and complex models that are inefficient to train. While some approaches use pre-trained 2D multi-modal models like CLIP for 3D tasks, they still struggle with aligning point cloud data to 2D encoders. As a result, these methods continue to depend on 3D encoders for feature extraction, further increasing model complexity and training inefficiency. In this paper, we propose a unified 2D pre-trained multi-modal network to process all three modalities (RGB images, text, and point clouds), significantly simplifying the architecture. By leveraging a 2D CLIP bi-modal model with adapter-based fine-tuning, this framework effectively adapts to the tri-modal setting, improving both adaptability and performance across modalities. Our Geometric-Aware 2D-3D Feature Recovery and Fusion (GARF) module is designed to fuse geometric multi-scale features from point clouds and images. We then integrate textual features for final modality fusion and introduce a multi-modal decoder to facilitate deep cross-modal understanding. Together, our method achieves unified feature extraction and fusion across the three modalities, enabling an end-to-end 3D visual grounding model. Compared to the baseline, our method reduces the number of trainable parameters by approximately 58\%, while achieving a 6.52\% improvement in the 3D detection task and a 6.25\% improvement in the 3D visual grounding task.

Open-vocabulary semantic segmentation enables models to recognize and segment objects from arbitrary natural language descriptions, offering the flexibility to handle novel, fine-grained, or functionally defined categories beyond fixed label sets. While this capability is crucial for large-scale urban point clouds that support applications such as digital twins, smart city management, and urban analytics, it remains largely unexplored in this domain. The main obstacles are the frequent absence of high-quality, well-aligned multi-view imagery in large-scale urban point cloud datasets and the poor generalization of existing three-dimensional (3D) segmentation pipelines across diverse urban environments with substantial variation in geometry, scale, and appearance. To address these challenges, we present OpenUrban3D, the first 3D open-vocabulary semantic segmentation framework for large-scale urban scenes that operates without aligned multi-view images, pre-trained point cloud segmentation networks, or manual annotations. Our approach generates robust semantic features directly from raw point clouds through multi-view, multi-granularity rendering, mask-level vision-language feature extraction, and sample-balanced fusion, followed by distillation into a 3D backbone model. This design enables zero-shot segmentation for arbitrary text queries while capturing both semantic richness and geometric priors. Extensive experiments on large-scale urban benchmarks, including SensatUrban and SUM, show that OpenUrban3D achieves significant improvements in both segmentation accuracy and cross-scene generalization over existing methods, demonstrating its potential as a flexible and scalable solution for 3D urban scene understanding.

Synthesizing physically plausible articulated human-object interactions (HOI) without 3D/4D supervision remains a fundamental challenge. While recent zero-shot approaches leverage video diffusion models to synthesize human-object interactions, they are largely confined to rigid-object manipulation and lack explicit 4D geometric reasoning. To bridge this gap, we formulate articulated HOI synthesis as a 4D reconstruction problem from monocular video priors: given only a video generated by a diffusion model, we reconstruct a full 4D articulated scene without any 3D supervision. This reconstruction-based approach treats the generated 2D video as supervision for an inverse rendering problem, recovering geometrically consistent and physically plausible 4D scenes that naturally respect contact, articulation, and temporal coherence. We introduce ArtHOI, the first zero-shot framework for articulated human-object interaction synthesis via 4D reconstruction from video priors. Our key designs are: 1) Flow-based part segmentation: leveraging optical flow as a geometric cue to disentangle dynamic from static regions in monocular video; 2) Decoupled reconstruction pipeline: joint optimization of human motion and object articulation is unstable under monocular ambiguity, so we first recover object articulation, then synthesize human motion conditioned on the reconstructed object states. ArtHOI bridges video-based generation and geometry-aware reconstruction, producing interactions that are both semantically aligned and physically grounded. Across diverse articulated scenes (e.g., opening fridges, cabinets, microwaves), ArtHOI significantly outperforms prior methods in contact accuracy, penetration reduction, and articulation fidelity, extending zero-shot interaction synthesis beyond rigid manipulation through reconstruction-informed synthesis.

Many recent advances in robotic manipulation have come through imitation learning, yet these rely largely on mimicking a particularly hard-to-acquire form of demonstrations: those collected on the same robot in the same room with the same objects as the trained policy must handle at test time. In contrast, large pre-recorded human video datasets demonstrating manipulation skills in-the-wild already exist, which contain valuable information for robots. Is it possible to distill a repository of useful robotic skill policies out of such data without any additional requirements on robot-specific demonstrations or exploration? We present the first such system ZeroMimic, that generates immediately deployable image goal-conditioned skill policies for several common categories of manipulation tasks (opening, closing, pouring, pick&place, cutting, and stirring) each capable of acting upon diverse objects and across diverse unseen task setups. ZeroMimic is carefully designed to exploit recent advances in semantic and geometric visual understanding of human videos, together with modern grasp affordance detectors and imitation policy classes. After training ZeroMimic on the popular EpicKitchens dataset of ego-centric human videos, we evaluate its out-of-the-box performance in varied real-world and simulated kitchen settings with two different robot embodiments, demonstrating its impressive abilities to handle these varied tasks. To enable plug-and-play reuse of ZeroMimic policies on other task setups and robots, we release software and policy checkpoints of our skill policies.

Triangle meshes play a crucial role in 3D applications for efficient manipulation and rendering. While auto-regressive methods generate structured meshes by predicting discrete vertex tokens, they are often constrained by limited face counts and mesh incompleteness. To address these challenges, we propose DeepMesh, a framework that optimizes mesh generation through two key innovations: (1) an efficient pre-training strategy incorporating a novel tokenization algorithm, along with improvements in data curation and processing, and (2) the introduction of Reinforcement Learning (RL) into 3D mesh generation to achieve human preference alignment via Direct Preference Optimization (DPO). We design a scoring standard that combines human evaluation with 3D metrics to collect preference pairs for DPO, ensuring both visual appeal and geometric accuracy. Conditioned on point clouds and images, DeepMesh generates meshes with intricate details and precise topology, outperforming state-of-the-art methods in both precision and quality. Project page: https://zhaorw02.github.io/DeepMesh/

Depth Anything has achieved remarkable success in monocular depth estimation with strong generalization ability. However, it suffers from temporal inconsistency in videos, hindering its practical applications. Various methods have been proposed to alleviate this issue by leveraging video generation models or introducing priors from optical flow and camera poses. Nonetheless, these methods are only applicable to short videos (< 10 seconds) and require a trade-off between quality and computational efficiency. We propose Video Depth Anything for high-quality, consistent depth estimation in super-long videos (over several minutes) without sacrificing efficiency. We base our model on Depth Anything V2 and replace its head with an efficient spatial-temporal head. We design a straightforward yet effective temporal consistency loss by constraining the temporal depth gradient, eliminating the need for additional geometric priors. The model is trained on a joint dataset of video depth and unlabeled images, similar to Depth Anything V2. Moreover, a novel key-frame-based strategy is developed for long video inference. Experiments show that our model can be applied to arbitrarily long videos without compromising quality, consistency, or generalization ability. Comprehensive evaluations on multiple video benchmarks demonstrate that our approach sets a new state-of-the-art in zero-shot video depth estimation. We offer models of different scales to support a range of scenarios, with our smallest model capable of real-time performance at 30 FPS.

This paper presents Omni-View, which extends the unified multimodal understanding and generation to 3D scenes based on multiview images, exploring the principle that "generation facilitates understanding". Consisting of understanding model, texture module, and geometry module, Omni-View jointly models scene understanding, novel view synthesis, and geometry estimation, enabling synergistic interaction between 3D scene understanding and generation tasks. By design, it leverages the spatiotemporal modeling capabilities of its texture module responsible for appearance synthesis, alongside the explicit geometric constraints provided by its dedicated geometry module, thereby enriching the model's holistic understanding of 3D scenes. Trained with a two-stage strategy, Omni-View achieves a state-of-the-art score of 55.4 on the VSI-Bench benchmark, outperforming existing specialized 3D understanding models, while simultaneously delivering strong performance in both novel view synthesis and 3D scene generation.

We target a 3D generative model for general natural scenes that are typically unique and intricate. Lacking the necessary volumes of training data, along with the difficulties of having ad hoc designs in presence of varying scene characteristics, renders existing setups intractable. Inspired by classical patch-based image models, we advocate for synthesizing 3D scenes at the patch level, given a single example. At the core of this work lies important algorithmic designs w.r.t the scene representation and generative patch nearest-neighbor module, that address unique challenges arising from lifting classical 2D patch-based framework to 3D generation. These design choices, on a collective level, contribute to a robust, effective, and efficient model that can generate high-quality general natural scenes with both realistic geometric structure and visual appearance, in large quantities and varieties, as demonstrated upon a variety of exemplar scenes.

We introduce a new method of generating Computer Aided Design (CAD) profiles via a sequence of simple geometric constructions including curve offsetting, rotations and intersections. These sequences start with geometry provided by a designer and build up the points and curves of the final profile step by step. We demonstrate that adding construction steps between the designer's input geometry and the final profile improves generation quality in a similar way to the introduction of a chain of thought in language models. Similar to the constraints in a parametric CAD model, the construction sequences reduce the degrees of freedom in the modeled shape to a small set of parameter values which can be adjusted by the designer, allowing parametric editing with the constructed geometry evaluated to floating point precision. In addition we show that applying reinforcement learning to the construction sequences gives further improvements over a wide range of metrics, including some which were not explicitly optimized.

Producing long, coherent video sequences with stable 3D structure remains a major challenge, particularly in streaming scenarios. Motivated by this, we introduce Endless World, a real-time framework for infinite, 3D-consistent video generation.To support infinite video generation, we introduce a conditional autoregressive training strategy that aligns newly generated content with existing video frames. This design preserves long-range dependencies while remaining computationally efficient, enabling real-time inference on a single GPU without additional training overhead.Moreover, our Endless World integrates global 3D-aware attention to provide continuous geometric guidance across time. Our 3D injection mechanism enforces physical plausibility and geometric consistency throughout extended sequences, addressing key challenges in long-horizon and dynamic scene synthesis.Extensive experiments demonstrate that Endless World produces long, stable, and visually coherent videos, achieving competitive or superior performance to existing methods in both visual fidelity and spatial consistency. Our project has been available on https://bwgzk-keke.github.io/EndlessWorld/.

Generative 3D reconstruction shows strong potential in incomplete observations. While sparse-view and single-image reconstruction are well-researched, partial observation remains underexplored. In this context, dense views are accessible only from a specific angular range, with other perspectives remaining inaccessible. This task presents two main challenges: (i) limited View Range: observations confined to a narrow angular scope prevent effective traditional interpolation techniques that require evenly distributed perspectives. (ii) inconsistent Generation: views created for invisible regions often lack coherence with both visible regions and each other, compromising reconstruction consistency. To address these challenges, we propose \method, a novel training-free approach that integrates the local dense observations and multi-source priors for reconstruction. Our method introduces a fusion-based strategy to effectively align these priors in DDIM sampling, thereby generating multi-view consistent images to supervise invisible views. We further design an iterative refinement strategy, which uses the geometric structures of the object to enhance reconstruction quality. Extensive experiments on multiple datasets show the superiority of our method over SOTAs, especially in invisible regions.

We propose a novel test-time optimization approach for efficiently and robustly tracking any pixel at any time in a video. The latest state-of-the-art optimization-based tracking technique, OmniMotion, requires a prohibitively long optimization time, rendering it impractical for downstream applications. OmniMotion is sensitive to the choice of random seeds, leading to unstable convergence. To improve efficiency and robustness, we introduce a novel invertible deformation network, CaDeX++, which factorizes the function representation into a local spatial-temporal feature grid and enhances the expressivity of the coupling blocks with non-linear functions. While CaDeX++ incorporates a stronger geometric bias within its architectural design, it also takes advantage of the inductive bias provided by the vision foundation models. Our system utilizes monocular depth estimation to represent scene geometry and enhances the objective by incorporating DINOv2 long-term semantics to regulate the optimization process. Our experiments demonstrate a substantial improvement in training speed (more than 10 times faster), robustness, and accuracy in tracking over the SoTA optimization-based method OmniMotion.

3D printing or additive manufacturing is a revolutionary technology that enables the creation of physical objects from digital models. However, the quality and accuracy of 3D printing depend on the correctness and efficiency of the G-code, a low-level numerical control programming language that instructs 3D printers how to move and extrude material. Debugging G-code is a challenging task that requires a syntactic and semantic understanding of the G-code format and the geometry of the part to be printed. In this paper, we present the first extensive evaluation of six state-of-the-art foundational large language models (LLMs) for comprehending and debugging G-code files for 3D printing. We design effective prompts to enable pre-trained LLMs to understand and manipulate G-code and test their performance on various aspects of G-code debugging and manipulation, including detection and correction of common errors and the ability to perform geometric transformations. We analyze their strengths and weaknesses for understanding complete G-code files. We also discuss the implications and limitations of using LLMs for G-code comprehension.

Sonification -- the mapping of data to non-speech audio -- offers an underexplored channel for representing complex dynamical systems. We treat El Niño-Southern Oscillation (ENSO), a canonical example of low-dimensional climate chaos, as a test case for culturally-situated sonification evaluated through complex systems diagnostics. Using parameter-mapping sonification of the Niño 3.4 sea surface temperature anomaly index (1870--2024), we encode ENSO variability into two traditional Javanese gamelan pentatonic systems (pelog and slendro) across four composition strategies, then analyze the resulting audio as trajectories in a two-dimensional acoustic phase space. Recurrence-based diagnostics, convex hull geometry, and coupling analysis reveal that the sonification pipeline preserves key dynamical signatures: alternating modes produce the highest trajectory recurrence rates, echoing ENSO's quasi-periodicity; layered polyphonic modes explore the broadest phase space regions; and the two scale families induce qualitatively distinct coupling regimes between spectral brightness and energy -- predominantly anti-phase in pelog but near-independent in slendro. Phase space trajectory analysis provides a rigorous geometric framework for comparing sonification designs within a complex systems context. Perceptual validation remains necessary; we contribute the dynamical systems methodology for evaluating such mappings.

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.

Recent developments in Multimodal Large Language Models (MLLMs) have significantly improved Vision-Language (VL) reasoning in 2D domains. However, extending these capabilities to 3D scene understanding remains a major challenge. Existing 3D Multimodal Large Language Models (3D-MLLMs) often depend on 3D data inputs, which limits scalability and generalization. To address this limitation, we propose Vid-LLM, a video-based 3D-MLLM that directly processes video inputs without requiring external 3D data, making it practical for real-world deployment. In our method, the geometric prior are directly used to improve the performance of the sceen perception. To integrate the geometric cues into the MLLM compactly, we design a Cross-Task Adapter (CTA) module to align the 3D geometric priors with the vision-language representations. To ensure geometric consistency and integrity, we introduce a Metric Depth Model that recovers real-scale geometry from the reconstruction outputs. Finally, the model is fine-tuned with a two-stage distillation optimization strategy, realizing fast convergence and stabilizes training. Extensive experiments across diverse benchmarks verified the effectiveness of our method on 3D Question Answering, 3D Dense Captioning and 3D Visual Grounding tasks, demonstrating the superior multi-task capabilities.

For human-centric large-scale scenes, fine-grained modeling for 3D human global pose and shape is significant for scene understanding and can benefit many real-world applications. In this paper, we present LiveHPS, a novel single-LiDAR-based approach for scene-level human pose and shape estimation without any limitation of light conditions and wearable devices. In particular, we design a distillation mechanism to mitigate the distribution-varying effect of LiDAR point clouds and exploit the temporal-spatial geometric and dynamic information existing in consecutive frames to solve the occlusion and noise disturbance. LiveHPS, with its efficient configuration and high-quality output, is well-suited for real-world applications. Moreover, we propose a huge human motion dataset, named FreeMotion, which is collected in various scenarios with diverse human poses, shapes and translations. It consists of multi-modal and multi-view acquisition data from calibrated and synchronized LiDARs, cameras, and IMUs. Extensive experiments on our new dataset and other public datasets demonstrate the SOTA performance and robustness of our approach. We will release our code and dataset soon.

Parametric computer-aided design (CAD) tools are the predominant way that engineers specify physical structures, from bicycle pedals to airplanes to printed circuit boards. The key characteristic of parametric CAD is that design intent is encoded not only via geometric primitives, but also by parameterized constraints between the elements. This relational specification can be viewed as the construction of a constraint program, allowing edits to coherently propagate to other parts of the design. Machine learning offers the intriguing possibility of accelerating the design process via generative modeling of these structures, enabling new tools such as autocompletion, constraint inference, and conditional synthesis. In this work, we present such an approach to generative modeling of parametric CAD sketches, which constitute the basic computational building blocks of modern mechanical design. Our model, trained on real-world designs from the SketchGraphs dataset, autoregressively synthesizes sketches as sequences of primitives, with initial coordinates, and constraints that reference back to the sampled primitives. As samples from the model match the constraint graph representation used in standard CAD software, they may be directly imported, solved, and edited according to downstream design tasks. In addition, we condition the model on various contexts, including partial sketches (primers) and images of hand-drawn sketches. Evaluation of the proposed approach demonstrates its ability to synthesize realistic CAD sketches and its potential to aid the mechanical design workflow.

Dynamic and static components in scenes often exhibit distinct properties, yet most 4D reconstruction methods treat them indiscriminately, leading to suboptimal performance in both cases. This work introduces SDD-4DGS, the first framework for static-dynamic decoupled 4D scene reconstruction based on Gaussian Splatting. Our approach is built upon a novel probabilistic dynamic perception coefficient that is naturally integrated into the Gaussian reconstruction pipeline, enabling adaptive separation of static and dynamic components. With carefully designed implementation strategies to realize this theoretical framework, our method effectively facilitates explicit learning of motion patterns for dynamic elements while maintaining geometric stability for static structures. Extensive experiments on five benchmark datasets demonstrate that SDD-4DGS consistently outperforms state-of-the-art methods in reconstruction fidelity, with enhanced detail restoration for static structures and precise modeling of dynamic motions. The code will be released.

We present our position on the elusive quest for a general-purpose framework for specifying and studying deep learning architectures. Our opinion is that the key attempts made so far lack a coherent bridge between specifying constraints which models must satisfy and specifying their implementations. Focusing on building a such a bridge, we propose to apply category theory -- precisely, the universal algebra of monads valued in a 2-category of parametric maps -- as a single theory elegantly subsuming both of these flavours of neural network design. To defend our position, we show how this theory recovers constraints induced by geometric deep learning, as well as implementations of many architectures drawn from the diverse landscape of neural networks, such as RNNs. We also illustrate how the theory naturally encodes many standard constructs in computer science and automata theory.

Visual navigation, a fundamental challenge in mobile robotics, demands versatile policies to handle diverse environments. Classical methods leverage geometric solutions to minimize specific costs, offering adaptability to new scenarios but are prone to system errors due to their multi-modular design and reliance on hand-crafted rules. Learning-based methods, while achieving high planning success rates, face difficulties in generalizing to unseen environments beyond the training data and often require extensive training. To address these limitations, we propose a hybrid approach that combines the strengths of learning-based methods and classical approaches for RGB-only visual navigation. Our method first trains a conditional diffusion model on diverse path-RGB observation pairs. During inference, it integrates the gradients of differentiable scene-specific and task-level costs, guiding the diffusion model to generate valid paths that meet the constraints. This approach alleviates the need for retraining, offering a plug-and-play solution. Extensive experiments in both indoor and outdoor settings, across simulated and real-world scenarios, demonstrate zero-shot transfer capability of our approach, achieving higher success rates and fewer collisions compared to baseline methods. Code will be released at https://github.com/SYSU-RoboticsLab/NaviD.

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.

Existing multi-view image generation methods often make invasive modifications to pre-trained text-to-image (T2I) models and require full fine-tuning, leading to (1) high computational costs, especially with large base models and high-resolution images, and (2) degradation in image quality due to optimization difficulties and scarce high-quality 3D data. In this paper, we propose the first adapter-based solution for multi-view image generation, and introduce MV-Adapter, a versatile plug-and-play adapter that enhances T2I models and their derivatives without altering the original network structure or feature space. By updating fewer parameters, MV-Adapter enables efficient training and preserves the prior knowledge embedded in pre-trained models, mitigating overfitting risks. To efficiently model the 3D geometric knowledge within the adapter, we introduce innovative designs that include duplicated self-attention layers and parallel attention architecture, enabling the adapter to inherit the powerful priors of the pre-trained models to model the novel 3D knowledge. Moreover, we present a unified condition encoder that seamlessly integrates camera parameters and geometric information, facilitating applications such as text- and image-based 3D generation and texturing. MV-Adapter achieves multi-view generation at 768 resolution on Stable Diffusion XL (SDXL), and demonstrates adaptability and versatility. It can also be extended to arbitrary view generation, enabling broader applications. We demonstrate that MV-Adapter sets a new quality standard for multi-view image generation, and opens up new possibilities due to its efficiency, adaptability and versatility.

3D occupancy prediction plays a pivotal role in the realm of autonomous driving, as it provides a comprehensive understanding of the driving environment. Most existing methods construct dense scene representations for occupancy prediction, overlooking the inherent sparsity of real-world driving scenes. Recently, 3D superquadric representation has emerged as a promising sparse alternative to dense scene representations due to the strong geometric expressiveness of superquadrics. However, existing superquadric frameworks still suffer from insufficient temporal modeling, a challenging trade-off between query sparsity and geometric expressiveness, and inefficient superquadric-to-voxel splatting. To address these issues, we propose SuperOcc, a novel framework for superquadric-based 3D occupancy prediction. SuperOcc incorporates three key designs: (1) a cohesive temporal modeling mechanism to simultaneously exploit view-centric and object-centric temporal cues; (2) a multi-superquadric decoding strategy to enhance geometric expressiveness without sacrificing query sparsity; and (3) an efficient superquadric-to-voxel splatting scheme to improve computational efficiency. Extensive experiments on the SurroundOcc and Occ3D benchmarks demonstrate that SuperOcc achieves state-of-the-art performance while maintaining superior efficiency. The code is available at https://github.com/Yzichen/SuperOcc.

Spatial perception and reasoning are crucial for Vision-Language-Action (VLA) models to accomplish fine-grained manipulation tasks. However, existing approaches often lack the ability to understand and reason over the essential 3D structures necessary for precise control. To address this limitation, we propose QDepth-VLA, a general framework that augments VLA models with an auxiliary depth prediction task. A dedicated depth expert is designed to predict quantized latent tokens of depth maps obtained from a VQ-VAE encoder, enabling the model to learn depth-aware representations that capture critical geometric cues. Experimental results on the simulation benchmarks and real-world tasks demonstrate that QDepth-VLA yields strong spatial reasoning and competitive performance on manipulation tasks.

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

This paper presents the first photo-realistic LiDAR-Inertial-Camera Gaussian Splatting SLAM system that simultaneously addresses visual quality, geometric accuracy, and real-time performance. The proposed method performs robust and accurate pose estimation within a continuous-time trajectory optimization framework, while incrementally reconstructing a 3D Gaussian map using camera and LiDAR data, all in real time. The resulting map enables high-quality, real-time novel view rendering of both RGB images and depth maps. To effectively address under-reconstruction in regions not covered by the LiDAR, we employ a lightweight zero-shot depth model that synergistically combines RGB appearance cues with sparse LiDAR measurements to generate dense depth maps. The depth completion enables reliable Gaussian initialization in LiDAR-blind areas, significantly improving system applicability for sparse LiDAR sensors. To enhance geometric accuracy, we use sparse but precise LiDAR depths to supervise Gaussian map optimization and accelerate it with carefully designed CUDA-accelerated strategies. Furthermore, we explore how the incrementally reconstructed Gaussian map can improve the robustness of odometry. By tightly incorporating photometric constraints from the Gaussian map into the continuous-time factor graph optimization, we demonstrate improved pose estimation under LiDAR degradation scenarios. We also showcase downstream applications via extending our elaborate system, including video frame interpolation and fast 3D mesh extraction. To support rigorous evaluation, we construct a dedicated LiDAR-Inertial-Camera dataset featuring ground-truth poses, depth maps, and extrapolated trajectories for assessing out-of-sequence novel view synthesis. Both the dataset and code will be made publicly available on project page https://xingxingzuo.github.io/gaussian_lic2.

Recently, image-to-3D approaches have achieved significant results with a natural image as input. However, it is not always possible to access these enriched color input samples in practical applications, where only sketches are available. Existing sketch-to-3D researches suffer from limitations in broad applications due to the challenges of lacking color information and multi-view content. To overcome them, this paper proposes a novel generation paradigm Sketch3D to generate realistic 3D assets with shape aligned with the input sketch and color matching the textual description. Concretely, Sketch3D first instantiates the given sketch in the reference image through the shape-preserving generation process. Second, the reference image is leveraged to deduce a coarse 3D Gaussian prior, and multi-view style-consistent guidance images are generated based on the renderings of the 3D Gaussians. Finally, three strategies are designed to optimize 3D Gaussians, i.e., structural optimization via a distribution transfer mechanism, color optimization with a straightforward MSE loss and sketch similarity optimization with a CLIP-based geometric similarity loss. Extensive visual comparisons and quantitative analysis illustrate the advantage of our Sketch3D in generating realistic 3D assets while preserving consistency with the input.

Endeavors have been recently made to transfer knowledge from the labeled pinhole image domain to the unlabeled panoramic image domain via Unsupervised Domain Adaptation (UDA). The aim is to tackle the domain gaps caused by the style disparities and distortion problem from the non-uniformly distributed pixels of equirectangular projection (ERP). Previous works typically focus on transferring knowledge based on geometric priors with specially designed multi-branch network architectures. As a result, considerable computational costs are induced, and meanwhile, their generalization abilities are profoundly hindered by the variation of distortion among pixels. In this paper, we find that the pixels' neighborhood regions of the ERP indeed introduce less distortion. Intuitively, we propose a novel UDA framework that can effectively address the distortion problems for panoramic semantic segmentation. In comparison, our method is simpler, easier to implement, and more computationally efficient. Specifically, we propose distortion-aware attention (DA) capturing the neighboring pixel distribution without using any geometric constraints. Moreover, we propose a class-wise feature aggregation (CFA) module to iteratively update the feature representations with a memory bank. As such, the feature similarity between two domains can be consistently optimized. Extensive experiments show that our method achieves new state-of-the-art performance while remarkably reducing 80% parameters.

Referring Video Object Segmentation (RVOS) requires segmenting specific objects in a video guided by a natural language description. The core challenge of RVOS is to anchor abstract linguistic concepts onto a specific set of pixels and continuously segment them through the complex dynamics of a video. Faced with this difficulty, prior work has often decomposed the task into a pragmatic `locate-then-segment' pipeline. However, this cascaded design creates an information bottleneck by simplifying semantics into coarse geometric prompts (e.g, point), and struggles to maintain temporal consistency as the segmenting process is often decoupled from the initial language grounding. To overcome these fundamental limitations, we propose FlowRVS, a novel framework that reconceptualizes RVOS as a conditional continuous flow problem. This allows us to harness the inherent strengths of pretrained T2V models, fine-grained pixel control, text-video semantic alignment, and temporal coherence. Instead of conventional generating from noise to mask or directly predicting mask, we reformulate the task by learning a direct, language-guided deformation from a video's holistic representation to its target mask. Our one-stage, generative approach achieves new state-of-the-art results across all major RVOS benchmarks. Specifically, achieving a J&F of 51.1 in MeViS (+1.6 over prior SOTA) and 73.3 in the zero shot Ref-DAVIS17 (+2.7), demonstrating the significant potential of modeling video understanding tasks as continuous deformation processes.

Computer-aided design (CAD) is vital to modern manufacturing, yet model creation remains labor-intensive and expertise-heavy. To enable non-experts to translate intuitive design intent into manufacturable artifacts, recent large language models-based text-to-CAD efforts focus on command sequences or script-based formats like CadQuery. However, these formats are kernel-dependent and lack universality for manufacturing. In contrast, the Standard for the Exchange of Product Data (STEP, ISO 10303) file is a widely adopted, neutral boundary representation (B-rep) format directly compatible with manufacturing, but its graph-structured, cross-referenced nature poses unique challenges for auto-regressive LLMs. To address this, we curate a dataset of ~40K STEP-caption pairs and introduce novel preprocessing tailored for the graph-structured format of STEP, including a depth-first search-based reserialization that linearizes cross-references while preserving locality and chain-of-thought(CoT)-style structural annotations that guide global coherence. We integrate retrieval-augmented generation to ground predictions in relevant examples for supervised fine-tuning, and refine generation quality through reinforcement learning with a specific Chamfer Distance-based geometric reward. Experiments demonstrate consistent gains of our STEP-LLM in geometric fidelity over the Text2CAD baseline, with improvements arising from multiple stages of our framework: the RAG module substantially enhances completeness and renderability, the DFS-based reserialization strengthens overall accuracy, and the RL further reduces geometric discrepancy. Both metrics and visual comparisons confirm that STEP-LLM generates shapes with higher fidelity than Text2CAD. These results show the feasibility of LLM-driven STEP model generation from natural language, showing its potential to democratize CAD design for manufacturing.

Accurate monocular 3D object detection (M3OD) is pivotal for safety-critical applications like autonomous driving, yet its reliability deteriorates significantly under real-world domain shifts caused by environmental or sensor variations. To address these shifts, Test-Time Adaptation (TTA) methods have emerged, enabling models to adapt to target distributions during inference. While prior TTA approaches recognize the positive correlation between low uncertainty and high generalization ability, they fail to address the dual uncertainty inherent to M3OD: semantic uncertainty (ambiguous class predictions) and geometric uncertainty (unstable spatial localization). To bridge this gap, we propose Dual Uncertainty Optimization (DUO), the first TTA framework designed to jointly minimize both uncertainties for robust M3OD. Through a convex optimization lens, we introduce an innovative convex structure of the focal loss and further derive a novel unsupervised version, enabling label-agnostic uncertainty weighting and balanced learning for high-uncertainty objects. In parallel, we design a semantic-aware normal field constraint that preserves geometric coherence in regions with clear semantic cues, reducing uncertainty from the unstable 3D representation. This dual-branch mechanism forms a complementary loop: enhanced spatial perception improves semantic classification, and robust semantic predictions further refine spatial understanding. Extensive experiments demonstrate the superiority of DUO over existing methods across various datasets and domain shift types.

Humans have the ability to reason about geometric patterns in images and scenes from a young age. However, developing large multimodal models (LMMs) capable of similar reasoning remains a challenge, highlighting the need for robust evaluation methods to assess these capabilities. We introduce \Turtle, a benchmark designed to evaluate LMMs' capacity to interpret geometric patterns -- given visual examples, textual instructions, or both -- and generate precise code outputs. Inspired by turtle geometry, a notion used to teach children foundational coding and geometric concepts, TurtleBench features tasks with patterned shapes that have underlying algorithmic logic. Our evaluation reveals that leading LMMs struggle significantly with these tasks, with GPT-4o achieving only 19\% accuracy on the simplest tasks and few-shot prompting only marginally improves their performance (<2%). \Turtle highlights the gap between human and AI performance in intuitive and visual geometrical understanding, setting the stage for future research in this area. \Turtle stands as one of the few benchmarks to evaluate the integration of visual understanding and code generation capabilities in LMMs, setting the stage for future research. Code and Dataset for this paper is provided here: https://github.com/sinaris76/TurtleBench{https://github.com/sinaris76/TurtleBench}

In this work, we aim to improve the 3D reasoning ability of Transformers in multi-view 3D human pose estimation. Recent works have focused on end-to-end learning-based transformer designs, which struggle to resolve geometric information accurately, particularly during occlusion. Instead, we propose a novel hybrid model, MVGFormer, which has a series of geometric and appearance modules organized in an iterative manner. The geometry modules are learning-free and handle all viewpoint-dependent 3D tasks geometrically which notably improves the model's generalization ability. The appearance modules are learnable and are dedicated to estimating 2D poses from image signals end-to-end which enables them to achieve accurate estimates even when occlusion occurs, leading to a model that is both accurate and generalizable to new cameras and geometries. We evaluate our approach for both in-domain and out-of-domain settings, where our model consistently outperforms state-of-the-art methods, and especially does so by a significant margin in the out-of-domain setting. We will release the code and models: https://github.com/XunshanMan/MVGFormer.