Daily Papers

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enabled by reducing long-range dependencies on early frames through anchor-free relational modeling, thereby allowing outdated memory to be discarded on the fly.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

Current feed-forward 3D/4D reconstruction systems rely on dense geometry and pose supervision -- expensive to obtain at scale and particularly scarce for dynamic real-world scenes. We present Flow3r, a framework that augments visual geometry learning with dense 2D correspondences (`flow') as supervision, enabling scalable training from unlabeled monocular videos. Our key insight is that the flow prediction module should be factored: predicting flow between two images using geometry latents from one and pose latents from the other. This factorization directly guides the learning of both scene geometry and camera motion, and naturally extends to dynamic scenes. In controlled experiments, we show that factored flow prediction outperforms alternative designs and that performance scales consistently with unlabeled data. Integrating factored flow into existing visual geometry architectures and training with {sim}800K unlabeled videos, Flow3r achieves state-of-the-art results across eight benchmarks spanning static and dynamic scenes, with its largest gains on in-the-wild dynamic videos where labeled data is most scarce.

We introduce pi^3, a feed-forward neural network that offers a novel approach to visual geometry reconstruction, breaking the reliance on a conventional fixed reference view. Previous methods often anchor their reconstructions to a designated viewpoint, an inductive bias that can lead to instability and failures if the reference is suboptimal. In contrast, pi^3 employs a fully permutation-equivariant architecture to predict affine-invariant camera poses and scale-invariant local point maps without any reference frames. This design makes our model inherently robust to input ordering and highly scalable. These advantages enable our simple and bias-free approach to achieve state-of-the-art performance on a wide range of tasks, including camera pose estimation, monocular/video depth estimation, and dense point map reconstruction. Code and models are publicly available.

Feed-forward multi-frame 3D reconstruction models often degrade on videos with object motion. Global-reference becomes ambiguous under multiple motions, while the local pointmap relies heavily on estimated relative poses and can drift, causing cross-frame misalignment and duplicated structures. We propose TrajVG, a reconstruction framework that makes cross-frame 3D correspondence an explicit prediction by estimating camera-coordinate 3D trajectories. We couple sparse trajectories, per-frame local point maps, and relative camera poses with geometric consistency objectives: (i) bidirectional trajectory-pointmap consistency with controlled gradient flow, and (ii) a pose consistency objective driven by static track anchors that suppresses gradients from dynamic regions. To scale training to in-the-wild videos where 3D trajectory labels are scarce, we reformulate the same coupling constraints into self-supervised objectives using only pseudo 2D tracks, enabling unified training with mixed supervision. Extensive experiments across 3D tracking, pose estimation, pointmap reconstruction, and video depth show that TrajVG surpasses the current feedforward performance baseline.

Automatic 3D content creation has achieved rapid progress recently due to the availability of pre-trained, large language models and image diffusion models, forming the emerging topic of text-to-3D content creation. Existing text-to-3D methods commonly use implicit scene representations, which couple the geometry and appearance via volume rendering and are suboptimal in terms of recovering finer geometries and achieving photorealistic rendering; consequently, they are less effective for generating high-quality 3D assets. In this work, we propose a new method of Fantasia3D for high-quality text-to-3D content creation. Key to Fantasia3D is the disentangled modeling and learning of geometry and appearance. For geometry learning, we rely on a hybrid scene representation, and propose to encode surface normal extracted from the representation as the input of the image diffusion model. For appearance modeling, we introduce the spatially varying bidirectional reflectance distribution function (BRDF) into the text-to-3D task, and learn the surface material for photorealistic rendering of the generated surface. Our disentangled framework is more compatible with popular graphics engines, supporting relighting, editing, and physical simulation of the generated 3D assets. We conduct thorough experiments that show the advantages of our method over existing ones under different text-to-3D task settings. Project page and source codes: https://fantasia3d.github.io/.

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

We present MoGe, a powerful model for recovering 3D geometry from monocular open-domain images. Given a single image, our model directly predicts a 3D point map of the captured scene with an affine-invariant representation, which is agnostic to true global scale and shift. This new representation precludes ambiguous supervision in training and facilitate effective geometry learning. Furthermore, we propose a set of novel global and local geometry supervisions that empower the model to learn high-quality geometry. These include a robust, optimal, and efficient point cloud alignment solver for accurate global shape learning, and a multi-scale local geometry loss promoting precise local geometry supervision. We train our model on a large, mixed dataset and demonstrate its strong generalizability and high accuracy. In our comprehensive evaluation on diverse unseen datasets, our model significantly outperforms state-of-the-art methods across all tasks, including monocular estimation of 3D point map, depth map, and camera field of view. Code and models can be found on our project page.

With the growing demand for high-fidelity 3D models from 2D images, existing methods still face significant challenges in accurately reproducing fine-grained geometric details due to limitations in domain gaps and inherent ambiguities in RGB images. To address these issues, we propose Hi3DGen, a novel framework for generating high-fidelity 3D geometry from images via normal bridging. Hi3DGen consists of three key components: (1) an image-to-normal estimator that decouples the low-high frequency image pattern with noise injection and dual-stream training to achieve generalizable, stable, and sharp estimation; (2) a normal-to-geometry learning approach that uses normal-regularized latent diffusion learning to enhance 3D geometry generation fidelity; and (3) a 3D data synthesis pipeline that constructs a high-quality dataset to support training. Extensive experiments demonstrate the effectiveness and superiority of our framework in generating rich geometric details, outperforming state-of-the-art methods in terms of fidelity. Our work provides a new direction for high-fidelity 3D geometry generation from images by leveraging normal maps as an intermediate representation.

We present NeRFVS, a novel neural radiance fields (NeRF) based method to enable free navigation in a room. NeRF achieves impressive performance in rendering images for novel views similar to the input views while suffering for novel views that are significantly different from the training views. To address this issue, we utilize the holistic priors, including pseudo depth maps and view coverage information, from neural reconstruction to guide the learning of implicit neural representations of 3D indoor scenes. Concretely, an off-the-shelf neural reconstruction method is leveraged to generate a geometry scaffold. Then, two loss functions based on the holistic priors are proposed to improve the learning of NeRF: 1) A robust depth loss that can tolerate the error of the pseudo depth map to guide the geometry learning of NeRF; 2) A variance loss to regularize the variance of implicit neural representations to reduce the geometry and color ambiguity in the learning procedure. These two loss functions are modulated during NeRF optimization according to the view coverage information to reduce the negative influence brought by the view coverage imbalance. Extensive results demonstrate that our NeRFVS outperforms state-of-the-art view synthesis methods quantitatively and qualitatively on indoor scenes, achieving high-fidelity free navigation results.

3D modeling is shifting from static visual representations toward physical, articulated assets that can be directly used in simulation and interaction. However, most existing 3D generation methods overlook key physical and articulation properties, thereby limiting their utility in embodied AI. To bridge this gap, we introduce PhysX-Anything, the first simulation-ready physical 3D generative framework that, given a single in-the-wild image, produces high-quality sim-ready 3D assets with explicit geometry, articulation, and physical attributes. Specifically, we propose the first VLM-based physical 3D generative model, along with a new 3D representation that efficiently tokenizes geometry. It reduces the number of tokens by 193x, enabling explicit geometry learning within standard VLM token budgets without introducing any special tokens during fine-tuning and significantly improving generative quality. In addition, to overcome the limited diversity of existing physical 3D datasets, we construct a new dataset, PhysX-Mobility, which expands the object categories in prior physical 3D datasets by over 2x and includes more than 2K common real-world objects with rich physical annotations. Extensive experiments on PhysX-Mobility and in-the-wild images demonstrate that PhysX-Anything delivers strong generative performance and robust generalization. Furthermore, simulation-based experiments in a MuJoCo-style environment validate that our sim-ready assets can be directly used for contact-rich robotic policy learning. We believe PhysX-Anything can substantially empower a broad range of downstream applications, especially in embodied AI and physics-based simulation.

Open-world 3D reconstruction models have recently garnered significant attention. However, without sufficient 3D inductive bias, existing methods typically entail expensive training costs and struggle to extract high-quality 3D meshes. In this work, we introduce MeshFormer, a sparse-view reconstruction model that explicitly leverages 3D native structure, input guidance, and training supervision. Specifically, instead of using a triplane representation, we store features in 3D sparse voxels and combine transformers with 3D convolutions to leverage an explicit 3D structure and projective bias. In addition to sparse-view RGB input, we require the network to take input and generate corresponding normal maps. The input normal maps can be predicted by 2D diffusion models, significantly aiding in the guidance and refinement of the geometry's learning. Moreover, by combining Signed Distance Function (SDF) supervision with surface rendering, we directly learn to generate high-quality meshes without the need for complex multi-stage training processes. By incorporating these explicit 3D biases, MeshFormer can be trained efficiently and deliver high-quality textured meshes with fine-grained geometric details. It can also be integrated with 2D diffusion models to enable fast single-image-to-3D and text-to-3D tasks. Project page: https://meshformer3d.github.io

Talking head video generation aims to produce a synthetic human face video that contains the identity and pose information respectively from a given source image and a driving video.Existing works for this task heavily rely on 2D representations (e.g. appearance and motion) learned from the input images. However, dense 3D facial geometry (e.g. pixel-wise depth) is extremely important for this task as it is particularly beneficial for us to essentially generate accurate 3D face structures and distinguish noisy information from the possibly cluttered background. Nevertheless, dense 3D geometry annotations are prohibitively costly for videos and are typically not available for this video generation task. In this paper, we first introduce a self-supervised geometry learning method to automatically recover the dense 3D geometry (i.e.depth) from the face videos without the requirement of any expensive 3D annotation data. Based on the learned dense depth maps, we further propose to leverage them to estimate sparse facial keypoints that capture the critical movement of the human head. In a more dense way, the depth is also utilized to learn 3D-aware cross-modal (i.e. appearance and depth) attention to guide the generation of motion fields for warping source image representations. All these contributions compose a novel depth-aware generative adversarial network (DaGAN) for talking head generation. Extensive experiments conducted demonstrate that our proposed method can generate highly realistic faces, and achieve significant results on the unseen human faces.

Predominant techniques on talking head generation largely depend on 2D information, including facial appearances and motions from input face images. Nevertheless, dense 3D facial geometry, such as pixel-wise depth, plays a critical role in constructing accurate 3D facial structures and suppressing complex background noises for generation. However, dense 3D annotations for facial videos is prohibitively costly to obtain. In this work, firstly, we present a novel self-supervised method for learning dense 3D facial geometry (ie, depth) from face videos, without requiring camera parameters and 3D geometry annotations in training. We further propose a strategy to learn pixel-level uncertainties to perceive more reliable rigid-motion pixels for geometry learning. Secondly, we design an effective geometry-guided facial keypoint estimation module, providing accurate keypoints for generating motion fields. Lastly, we develop a 3D-aware cross-modal (ie, appearance and depth) attention mechanism, which can be applied to each generation layer, to capture facial geometries in a coarse-to-fine manner. Extensive experiments are conducted on three challenging benchmarks (ie, VoxCeleb1, VoxCeleb2, and HDTF). The results demonstrate that our proposed framework can generate highly realistic-looking reenacted talking videos, with new state-of-the-art performances established on these benchmarks. The codes and trained models are publicly available on the GitHub project page at https://github.com/harlanhong/CVPR2022-DaGAN

This paper addresses metric 3D reconstruction of indoor scenes by exploiting their inherent geometric regularities with compact representations. Using planar 3D primitives - a well-suited representation for man-made environments - we introduce PLANA3R, a pose-free framework for metric Planar 3D Reconstruction from unposed two-view images. Our approach employs Vision Transformers to extract a set of sparse planar primitives, estimate relative camera poses, and supervise geometry learning via planar splatting, where gradients are propagated through high-resolution rendered depth and normal maps of primitives. Unlike prior feedforward methods that require 3D plane annotations during training, PLANA3R learns planar 3D structures without explicit plane supervision, enabling scalable training on large-scale stereo datasets using only depth and normal annotations. We validate PLANA3R on multiple indoor-scene datasets with metric supervision and demonstrate strong generalization to out-of-domain indoor environments across diverse tasks under metric evaluation protocols, including 3D surface reconstruction, depth estimation, and relative pose estimation. Furthermore, by formulating with planar 3D representation, our method emerges with the ability for accurate plane segmentation. The project page is available at https://lck666666.github.io/plana3r

While current face animation methods can manipulate expressions individually, they suffer from several limitations. The expressions manipulated by some motion-based facial reenactment models are crude. Other ideas modeled with facial action units cannot generalize to arbitrary expressions not covered by annotations. In this paper, we introduce a novel Geometry-aware Facial Expression Translation (GaFET) framework, which is based on parametric 3D facial representations and can stably decoupled expression. Among them, a Multi-level Feature Aligned Transformer is proposed to complement non-geometric facial detail features while addressing the alignment challenge of spatial features. Further, we design a De-expression model based on StyleGAN, in order to reduce the learning difficulty of GaFET in unpaired "in-the-wild" images. Extensive qualitative and quantitative experiments demonstrate that we achieve higher-quality and more accurate facial expression transfer results compared to state-of-the-art methods, and demonstrate applicability of various poses and complex textures. Besides, videos or annotated training data are omitted, making our method easier to use and generalize.

Maps are a key component in image-based camera localization and visual SLAM systems: they are used to establish geometric constraints between images, correct drift in relative pose estimation, and relocalize cameras after lost tracking. The exact definitions of maps, however, are often application-specific and hand-crafted for different scenarios (e.g. 3D landmarks, lines, planes, bags of visual words). We propose to represent maps as a deep neural net called MapNet, which enables learning a data-driven map representation. Unlike prior work on learning maps, MapNet exploits cheap and ubiquitous sensory inputs like visual odometry and GPS in addition to images and fuses them together for camera localization. Geometric constraints expressed by these inputs, which have traditionally been used in bundle adjustment or pose-graph optimization, are formulated as loss terms in MapNet training and also used during inference. In addition to directly improving localization accuracy, this allows us to update the MapNet (i.e., maps) in a self-supervised manner using additional unlabeled video sequences from the scene. We also propose a novel parameterization for camera rotation which is better suited for deep-learning based camera pose regression. Experimental results on both the indoor 7-Scenes dataset and the outdoor Oxford RobotCar dataset show significant performance improvement over prior work. The MapNet project webpage is https://goo.gl/mRB3Au.

We present NeRF-Det, a novel method for indoor 3D detection with posed RGB images as input. Unlike existing indoor 3D detection methods that struggle to model scene geometry, our method makes novel use of NeRF in an end-to-end manner to explicitly estimate 3D geometry, thereby improving 3D detection performance. Specifically, to avoid the significant extra latency associated with per-scene optimization of NeRF, we introduce sufficient geometry priors to enhance the generalizability of NeRF-MLP. Furthermore, we subtly connect the detection and NeRF branches through a shared MLP, enabling an efficient adaptation of NeRF to detection and yielding geometry-aware volumetric representations for 3D detection. Our method outperforms state-of-the-arts by 3.9 mAP and 3.1 mAP on the ScanNet and ARKITScenes benchmarks, respectively. We provide extensive analysis to shed light on how NeRF-Det works. As a result of our joint-training design, NeRF-Det is able to generalize well to unseen scenes for object detection, view synthesis, and depth estimation tasks without requiring per-scene optimization. Code is available at https://github.com/facebookresearch/NeRF-Det.

Internet image collections containing photos captured by crowds of photographers show promise for enabling digital exploration of large-scale tourist landmarks. However, prior works focus primarily on geometric reconstruction and visualization, neglecting the key role of language in providing a semantic interface for navigation and fine-grained understanding. In constrained 3D domains, recent methods have leveraged vision-and-language models as a strong prior of 2D visual semantics. While these models display an excellent understanding of broad visual semantics, they struggle with unconstrained photo collections depicting such tourist landmarks, as they lack expert knowledge of the architectural domain. In this work, we present a localization system that connects neural representations of scenes depicting large-scale landmarks with text describing a semantic region within the scene, by harnessing the power of SOTA vision-and-language models with adaptations for understanding landmark scene semantics. To bolster such models with fine-grained knowledge, we leverage large-scale Internet data containing images of similar landmarks along with weakly-related textual information. Our approach is built upon the premise that images physically grounded in space can provide a powerful supervision signal for localizing new concepts, whose semantics may be unlocked from Internet textual metadata with large language models. We use correspondences between views of scenes to bootstrap spatial understanding of these semantics, providing guidance for 3D-compatible segmentation that ultimately lifts to a volumetric scene representation. Our results show that HaLo-NeRF can accurately localize a variety of semantic concepts related to architectural landmarks, surpassing the results of other 3D models as well as strong 2D segmentation baselines. Our project page is at https://tau-vailab.github.io/HaLo-NeRF/.

Vision-Language-Action (VLA) models achieve strong benchmark performance but still struggle in real-world deployment with unseen objects, background shifts, and different robot embodiments. We argue that this stems from the lack of a unified geometry-aware manipulation representation, leaving existing VLAs vulnerable to low-level trajectory supervision, misaligned 3D features, and embodiment differences. To address this, we propose GEAR-VLA, a VLA framework for learning unified geometry-aware action representations for generalizable robotic manipulation. GEAR-VLA adopts coarse-to-fine action learning, where multi-source embodied pretraining equips the VLM with embodied reasoning and discrete action understanding before latent action tokens connect action semantics to a gradient-decoupled DiT continuous action expert. It further performs semantic-aligned 3D integration by aligning a trainable 3D spatial backbone with the VLA representation while freezing the original VLM-aligned visual pathway. To share this representation across robots, GEAR-VLA uses embodiment canonicalization, where embodiment-aware states and embodiment-invariant actions confine robot differences to the low-level interface. Extensive simulation and real-world experiments demonstrate strong generalization: GEAR-VLA achieves state-of-the-art performance on LIBERO, zero-shot LIBERO-Plus, and RoboTwin 2.0, reaches 85.9% success on AgileX and 81.0% on the pretraining-unseen LDT-01 embodiment, and obtains 90.1% success on a 6,360-trial universal grasping benchmark with 212 unseen objects. Code and models will be released at https://github.com/babynabeauty/GEAR-VLA.

Bird's-Eye-View (BEV) perception serves as a cornerstone for autonomous driving, offering a unified spatial representation that fuses surrounding-view images to enable reasoning for various downstream tasks, such as semantic segmentation, 3D object detection, and motion prediction. However, most existing BEV perception frameworks adopt an end-to-end training paradigm, where image features are directly transformed into the BEV space and optimized solely through downstream task supervision. This formulation treats the entire perception process as a black box, often lacking explicit 3D geometric understanding and interpretability, leading to suboptimal performance. In this paper, we claim that an explicit 3D representation matters for accurate BEV perception, and we propose Splat2BEV, a Gaussian Splatting-assisted framework for BEV tasks. Splat2BEV aims to learn BEV feature representations that are both semantically rich and geometrically precise. We first pre-train a Gaussian generator that explicitly reconstructs 3D scenes from multi-view inputs, enabling the generation of geometry-aligned feature representations. These representations are then projected into the BEV space to serve as inputs for downstream tasks. Extensive experiments on nuScenes and argoverse dataset demonstrate that Splat2BEV achieves state-of-the-art performance and validate the effectiveness of incorporating explicit 3D reconstruction into BEV perception.

The ability of gaze estimation models to generalize is often significantly hindered by various factors unrelated to gaze, especially when the training dataset is limited. Current strategies aim to address this challenge through different domain generalization techniques, yet they have had limited success due to the risk of overfitting when solely relying on value labels for regression. Recent progress in pre-trained vision-language models has motivated us to capitalize on the abundant semantic information available. We propose a novel approach in this paper, reframing the gaze estimation task as a vision-language alignment issue. Our proposed framework, named Language-Guided Gaze Estimation (LG-Gaze), learns continuous and geometry-sensitive features for gaze estimation benefit from the rich prior knowledges of vision-language models. Specifically, LG-Gaze aligns gaze features with continuous linguistic features through our proposed multimodal contrastive regression loss, which customizes adaptive weights for different negative samples. Furthermore, to better adapt to the labels for gaze estimation task, we propose a geometry-aware interpolation method to obtain more precise gaze embeddings. Through extensive experiments, we validate the efficacy of our framework in four different cross-domain evaluation tasks.

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

Generalized few-shot object detection aims to achieve precise detection on both base classes with abundant annotations and novel classes with limited training data. Existing approaches enhance few-shot generalization with the sacrifice of base-class performance, or maintain high precision in base-class detection with limited improvement in novel-class adaptation. In this paper, we point out the reason is insufficient Discriminative feature learning for all of the classes. As such, we propose a new training framework, DiGeo, to learn Geometry-aware features of inter-class separation and intra-class compactness. To guide the separation of feature clusters, we derive an offline simplex equiangular tight frame (ETF) classifier whose weights serve as class centers and are maximally and equally separated. To tighten the cluster for each class, we include adaptive class-specific margins into the classification loss and encourage the features close to the class centers. Experimental studies on two few-shot benchmark datasets (VOC, COCO) and one long-tail dataset (LVIS) demonstrate that, with a single model, our method can effectively improve generalization on novel classes without hurting the detection of base classes.

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

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

In nature, symmetry governs regularities, while symmetry breaking brings texture. In artificial neural networks, symmetry has been a central design principle to efficiently capture regularities in the world, but the role of symmetry breaking is not well understood. Here, we develop a theoretical framework to study the "geometry of learning dynamics" in neural networks, and reveal a key mechanism of explicit symmetry breaking behind the efficiency and stability of modern neural networks. To build this understanding, we model the discrete learning dynamics of gradient descent using a continuous-time Lagrangian formulation, in which the learning rule corresponds to the kinetic energy and the loss function corresponds to the potential energy. Then, we identify "kinetic symmetry breaking" (KSB), the condition when the kinetic energy explicitly breaks the symmetry of the potential function. We generalize Noether's theorem known in physics to take into account KSB and derive the resulting motion of the Noether charge: "Noether's Learning Dynamics" (NLD). Finally, we apply NLD to neural networks with normalization layers and reveal how KSB introduces a mechanism of "implicit adaptive optimization", establishing an analogy between learning dynamics induced by normalization layers and RMSProp. Overall, through the lens of Lagrangian mechanics, we have established a theoretical foundation to discover geometric design principles for the learning dynamics of neural networks.

Recent advancements in human avatar synthesis have utilized radiance fields to reconstruct photo-realistic animatable human avatars. However, both NeRFs-based and 3DGS-based methods struggle with maintaining 3D consistency and exhibit suboptimal detail reconstruction, especially with sparse inputs. To address this challenge, we propose CHASE, which introduces supervision from intrinsic 3D consistency across poses and 3D geometry contrastive learning, achieving performance comparable with sparse inputs to that with full inputs. Following previous work, we first integrate a skeleton-driven rigid deformation and a non-rigid cloth dynamics deformation to coordinate the movements of individual Gaussians during animation, reconstructing basic avatar with coarse 3D consistency. To improve 3D consistency under sparse inputs, we design Dynamic Avatar Adjustment(DAA) to adjust deformed Gaussians based on a selected similar pose/image from the dataset. Minimizing the difference between the image rendered by adjusted Gaussians and the image with the similar pose serves as an additional form of supervision for avatar. Furthermore, we propose a 3D geometry contrastive learning strategy to maintain the 3D global consistency of generated avatars. Though CHASE is designed for sparse inputs, it surprisingly outperforms current SOTA methods in both full and sparse settings on the ZJU-MoCap and H36M datasets, demonstrating that our CHASE successfully maintains avatar's 3D consistency, hence improving rendering quality.

Shape optimization is essential in aerospace vehicle design, including reentry systems, and propulsion system components, as it directly influences aerodynamic efficiency, structural integrity, and overall mission success. Rapid and accurate prediction of external and internal flows accelerates design iterations. To this end, we develop a new variant of DeepONet, called Fusion-DeepONet as a fast surrogate model for geometry-dependent hypersonic and supersonic flow fields. We evaluated Fusion-DeepONet in learning two external hypersonic flows and a supersonic shape-dependent internal flow problem. First, we compare the performance of Fusion-DeepONet with state-of-the-art neural operators to learn inviscid hypersonic flow around semi-elliptic blunt bodies for two grid types: uniform Cartesian and irregular grids. Fusion-DeepONet provides comparable accuracy to parameter-conditioned U-Net on uniform grids while outperforming MeshGraphNet and Vanilla-DeepONet on irregular grids. Fusion-DeepONet requires significantly fewer trainable parameters than U-Net, MeshGraphNet, and FNO. For the second hypersonic problem, we set up Fusion-DeepONet to map from geometry and free stream Mach number to the temperature field around a reentry capsule traveling at hypersonic speed. This fast surrogate is then improved to predict the spatial derivative of the temperature, resulting in an accurate prediction of heat flux at the surfaces of the capsule. To enhance the accuracy of spatial derivative prediction, we introduce a derivative-enhanced loss term with the least computation overhead. For the third problem, we show that Fusion-DeepONet outperforms MeshGraphNet in learning geometry-dependent supersonic flow in a converging-diverging nozzle configuration. For all the problems, we used high-fidelity simulations with a high-order entropy-stable DGSEM solver to generate training datasets with limited samples.

We present SpatialTrackerV2, a feed-forward 3D point tracking method for monocular videos. Going beyond modular pipelines built on off-the-shelf components for 3D tracking, our approach unifies the intrinsic connections between point tracking, monocular depth, and camera pose estimation into a high-performing and feedforward 3D point tracker. It decomposes world-space 3D motion into scene geometry, camera ego-motion, and pixel-wise object motion, with a fully differentiable and end-to-end architecture, allowing scalable training across a wide range of datasets, including synthetic sequences, posed RGB-D videos, and unlabeled in-the-wild footage. By learning geometry and motion jointly from such heterogeneous data, SpatialTrackerV2 outperforms existing 3D tracking methods by 30%, and matches the accuracy of leading dynamic 3D reconstruction approaches while running 50times faster.

Real-time free-viewpoint rendering requires balancing multi-camera redundancy with the latency constraints of interactive applications. We address this challenge by combining lightweight geometry with learning and propose 3DTV, a feedforward network for real-time sparse-view interpolation. A Delaunay-based triplet selection ensures angular coverage for each target view. Building on this, we introduce a pose-aware depth module that estimates a coarse-to-fine depth pyramid, enabling efficient feature reprojection and occlusion-aware blending. Unlike methods that require scene-specific optimization, 3DTV runs feedforward without retraining, making it practical for AR/VR, telepresence, and interactive applications. Our experiments on challenging multi-view video datasets demonstrate that 3DTV consistently achieves a strong balance of quality and efficiency, outperforming recent real-time novel-view baselines. Crucially, 3DTV avoids explicit proxies, enabling robust rendering across diverse scenes. This makes it a practical solution for low-latency multi-view streaming and interactive rendering. Project Page: https://stefanmschulz.github.io/3DTV_webpage/

Neural operators have emerged as powerful data-driven solvers for PDEs, offering substantial acceleration over classical numerical methods. However, existing transformer-based operators still face critical challenges when modeling PDEs on complex geometries: directly processing over massive mesh points is computationally expensive, while operating in raw discretization coordinates may obscure the intrinsic geometry where physical interactions are more naturally expressed. To address these limitations, we introduce the Charted Axial Transformer Operator (CATO), a geometry-adaptive and derivative-aware neural operator for PDEs on general geometries. Instead of applying attention directly in the physical coordinate system, CATO learns a continuous latent chart that maps mesh coordinates into a learned chart space, where chart-conditioned axial attention efficiently captures long-range dependencies with reduced computational cost. In addition, CATO introduces a derivative-aware physics loss for steady-state PDEs that jointly supervises solution values, mesh-consistent gradients, and an auxiliary flux-like field, improving physical fidelity and reducing oversmoothing. We further provide a theoretical approximation result showing that, under a favorable chart, charted axial attention can represent low-rank axial solution operators with controlled error, and that small chart perturbations induce bounded approximation degradation. CATO achieves the best performance across all evaluated datasets, yielding an average improvement of approximately 26.76\% over the strongest competing baselines while reducing the number of parameters by 81.98\%. These results highlight the effectiveness of learning geometry-adaptive charts and derivative-aware physical supervision for accurate and efficient PDE operator learning.

Remote sensing (RS) visual grounding aims to use natural language expression to locate specific objects (in the form of the bounding box or segmentation mask) in RS images, enhancing human interaction with intelligent RS interpretation systems. Early research in this area was primarily based on horizontal bounding boxes (HBBs), but as more diverse RS datasets have become available, tasks involving oriented bounding boxes (OBBs) and segmentation masks have emerged. In practical applications, different targets require different grounding types: HBB can localize an object's position, OBB provides its orientation, and mask depicts its shape. However, existing specialized methods are typically tailored to a single type of RS visual grounding task and are hard to generalize across tasks. In contrast, large vision-language models (VLMs) exhibit powerful multi-task learning capabilities but struggle to handle dense prediction tasks like segmentation. This paper proposes GeoGround, a novel framework that unifies support for HBB, OBB, and mask RS visual grounding tasks, allowing flexible output selection. Rather than customizing the architecture of VLM, our work aims to elegantly support pixel-level visual grounding output through the Text-Mask technique. We define prompt-assisted and geometry-guided learning to enhance consistency across different signals. To support model training, we present refGeo, a large-scale RS visual instruction-following dataset containing 161k image-text pairs. Experimental results show that GeoGround demonstrates strong performance across four RS visual grounding tasks, matching or surpassing the performance of specialized methods on multiple benchmarks. Code available at https://github.com/zytx121/GeoGround

Most undeciphered lost languages exhibit two characteristics that pose significant decipherment challenges: (1) the scripts are not fully segmented into words; (2) the closest known language is not determined. We propose a decipherment model that handles both of these challenges by building on rich linguistic constraints reflecting consistent patterns in historical sound change. We capture the natural phonological geometry by learning character embeddings based on the International Phonetic Alphabet (IPA). The resulting generative framework jointly models word segmentation and cognate alignment, informed by phonological constraints. We evaluate the model on both deciphered languages (Gothic, Ugaritic) and an undeciphered one (Iberian). The experiments show that incorporating phonetic geometry leads to clear and consistent gains. Additionally, we propose a measure for language closeness which correctly identifies related languages for Gothic and Ugaritic. For Iberian, the method does not show strong evidence supporting Basque as a related language, concurring with the favored position by the current scholarship.

To achieve human-level dexterity, robots must infer spatial awareness from multimodal sensing to reason over contact interactions. During in-hand manipulation of novel objects, such spatial awareness involves estimating the object's pose and shape. The status quo for in-hand perception primarily employs vision, and restricts to tracking a priori known objects. Moreover, visual occlusion of objects in-hand is imminent during manipulation, preventing current systems to push beyond tasks without occlusion. We combine vision and touch sensing on a multi-fingered hand to estimate an object's pose and shape during in-hand manipulation. Our method, NeuralFeels, encodes object geometry by learning a neural field online and jointly tracks it by optimizing a pose graph problem. We study multimodal in-hand perception in simulation and the real-world, interacting with different objects via a proprioception-driven policy. Our experiments show final reconstruction F-scores of 81% and average pose drifts of 4.7,mm, further reduced to 2.3,mm with known CAD models. Additionally, we observe that under heavy visual occlusion we can achieve up to 94% improvements in tracking compared to vision-only methods. Our results demonstrate that touch, at the very least, refines and, at the very best, disambiguates visual estimates during in-hand manipulation. We release our evaluation dataset of 70 experiments, FeelSight, as a step towards benchmarking in this domain. Our neural representation driven by multimodal sensing can serve as a perception backbone towards advancing robot dexterity. Videos can be found on our project website https://suddhu.github.io/neural-feels/

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

Image-based 3D Virtual Try-ON (VTON) aims to sculpt the 3D human according to person and clothes images, which is data-efficient (i.e., getting rid of expensive 3D data) but challenging. Recent text-to-3D methods achieve remarkable improvement in high-fidelity 3D human generation, demonstrating its potential for 3D virtual try-on. Inspired by the impressive success of personalized diffusion models (e.g., Dreambooth and LoRA) for 2D VTON, it is straightforward to achieve 3D VTON by integrating the personalization technique into the diffusion-based text-to-3D framework. However, employing the personalized module in a pre-trained diffusion model (e.g., StableDiffusion (SD)) would degrade the model's capability for multi-view or multi-domain synthesis, which is detrimental to the geometry and texture optimization guided by Score Distillation Sampling (SDS) loss. In this work, we propose a novel customizing 3D human try-on model, named DreamVTON, to separately optimize the geometry and texture of the 3D human. Specifically, a personalized SD with multi-concept LoRA is proposed to provide the generative prior about the specific person and clothes, while a Densepose-guided ControlNet is exploited to guarantee consistent prior about body pose across various camera views. Besides, to avoid the inconsistent multi-view priors from the personalized SD dominating the optimization, DreamVTON introduces a template-based optimization mechanism, which employs mask templates for geometry shape learning and normal/RGB templates for geometry/texture details learning. Furthermore, for the geometry optimization phase, DreamVTON integrates a normal-style LoRA into personalized SD to enhance normal map generative prior, facilitating smooth geometry modeling.

Despite the rapid progress in data-driven 3D vision, aerial geometric 3D vision remains a formidable challenge due to the severe scarcity of large-scale, high-fidelity training data. Existing benchmarks, predominantly biased toward ground-level or object-centric views, do not account for complex viewpoint transformations and diverse environmental conditions in UAV-based sensing. To bridge this critical gap, we propose AirZoo, a unified large-scale dataset and benchmark for grounding aerial geometric 3D vision. AirZoo possesses three appealing properties: 1) Scalable Generation Pipeline: Leveraging freely available, world-scale photogrammetric 3D meshes, it renders vast outdoor environments with customizable UAV flight trajectories and configurable weather/illumination. 2) Comprehensive Scene Diversity: It provides the most extensive coverage of region types to date (spanning 378 regions across 22 countries), systematically encompassing both highly structured urban landscapes and complex unstructured natural environments. 3) Rich Geometric Annotations: Each frame provides synchronized, pixel-level metric depth and precise 6-DoF geo-referenced poses, essential for geometry-aware learning. Through three rigorous evaluation tracks -- aerial image retrieval, cross-view matching, and multi-view 3D reconstruction -- we demonstrate that AirZoo serves as a powerful pre-training engine. Extensive experiments on both public and newly collected real-world benchmarks reveal that fine-tuning on AirZoo yields substantial performance gains for SoTA models (e.g., MegaLoc, RoMa, VGGT, and Depth Anything 3), establishing a new performance upper bound for aerial spatial intelligence.

Recent monocular 3D shape reconstruction methods have shown promising zero-shot results on object-segmented images without any occlusions. However, their effectiveness is significantly compromised in real-world conditions, due to imperfect object segmentation by off-the-shelf models and the prevalence of occlusions. To effectively address these issues, we propose a unified regression model that integrates segmentation and reconstruction, specifically designed for occlusion-aware 3D shape reconstruction. To facilitate its reconstruction in the wild, we also introduce a scalable data synthesis pipeline that simulates a wide range of variations in objects, occluders, and backgrounds. Training on our synthetic data enables the proposed model to achieve state-of-the-art zero-shot results on real-world images, using significantly fewer parameters than competing approaches.

Leveraging the priors of 2D diffusion models for 3D editing has emerged as a promising paradigm. However, maintaining multi-view consistency in edited results remains challenging, and the extreme scarcity of 3D-consistent editing paired data renders supervised fine-tuning (SFT), the most effective training strategy for editing tasks, infeasible. In this paper, we observe that, while generating multi-view consistent 3D content is highly challenging, verifying 3D consistency is tractable, naturally positioning reinforcement learning (RL) as a feasible solution. Motivated by this, we propose RL3DEdit, a single-pass framework driven by RL optimization with novel rewards derived from the 3D foundation model, VGGT. Specifically, we leverage VGGT's robust priors learned from massive real-world data, feed the edited images, and utilize the output confidence maps and pose estimation errors as reward signals, effectively anchoring the 2D editing priors onto a 3D-consistent manifold via RL. Extensive experiments demonstrate that RL3DEdit achieves stable multi-view consistency and outperforms state-of-the-art methods in editing quality with high efficiency. To promote the development of 3D editing, we will release the code and model.

Geometry problem solving is a key area of mathematical reasoning, which is widely involved in many important fields such as education, mathematical ability assessment of artificial intelligence, and multimodal ability assessment. In recent years, the rapid development of deep learning technology, especially the rise of multimodal large language models, has triggered a widespread research boom. This paper provides a survey of the applications of deep learning in geometry problem solving, including (i) a comprehensive summary of the relevant tasks in geometry problem solving; (ii) a thorough review of related deep learning methods; (iii) a detailed analysis of evaluation metrics and methods; and (iv) a critical discussion of the current challenges and future directions that can be explored. Our goal is to provide a comprehensive and practical reference of deep learning for geometry problem solving to promote further developments in this field. We create a continuously updated list of papers on GitHub: https://github.com/majianz/dl4gps.

This paper tackles the intricate challenge of object removal to update the radiance field using the 3D Gaussian Splatting. The main challenges of this task lie in the preservation of geometric consistency and the maintenance of texture coherence in the presence of the substantial discrete nature of Gaussian primitives. We introduce a robust framework specifically designed to overcome these obstacles. The key insight of our approach is the enhancement of information exchange among visible and invisible areas, facilitating content restoration in terms of both geometry and texture. Our methodology begins with optimizing the positioning of Gaussian primitives to improve geometric consistency across both removed and visible areas, guided by an online registration process informed by monocular depth estimation. Following this, we employ a novel feature propagation mechanism to bolster texture coherence, leveraging a cross-attention design that bridges sampling Gaussians from both uncertain and certain areas. This innovative approach significantly refines the texture coherence within the final radiance field. Extensive experiments validate that our method not only elevates the quality of novel view synthesis for scenes undergoing object removal but also showcases notable efficiency gains in training and rendering speeds.

We review some recent applications of machine learning to algebraic geometry and physics. Since problems in algebraic geometry can typically be reformulated as mappings between tensors, this makes them particularly amenable to supervised learning. Additionally, unsupervised methods can provide insight into the structure of such geometrical data. At the heart of this programme is the question of how geometry can be machine learned, and indeed how AI helps one to do mathematics. This is a chapter contribution to the book Machine learning and Algebraic Geometry, edited by A. Kasprzyk et al.

6D pose estimation of rigid objects is a long-standing and challenging task in computer vision. Recently, the emergence of deep learning reveals the potential of Convolutional Neural Networks (CNNs) to predict reliable 6D poses. Given that direct pose regression networks currently exhibit suboptimal performance, most methods still resort to traditional techniques to varying degrees. For example, top-performing methods often adopt an indirect strategy by first establishing 2D-3D or 3D-3D correspondences followed by applying the RANSAC-based PnP or Kabsch algorithms, and further employing ICP for refinement. Despite the performance enhancement, the integration of traditional techniques makes the networks time-consuming and not end-to-end trainable. Orthogonal to them, this paper introduces a fully learning-based object pose estimator. In this work, we first perform an in-depth investigation of both direct and indirect methods and propose a simple yet effective Geometry-guided Direct Regression Network (GDRN) to learn the 6D pose from monocular images in an end-to-end manner. Afterwards, we introduce a geometry-guided pose refinement module, enhancing pose accuracy when extra depth data is available. Guided by the predicted coordinate map, we build an end-to-end differentiable architecture that establishes robust and accurate 3D-3D correspondences between the observed and rendered RGB-D images to refine the pose. Our enhanced pose estimation pipeline GDRNPP (GDRN Plus Plus) conquered the leaderboard of the BOP Challenge for two consecutive years, becoming the first to surpass all prior methods that relied on traditional techniques in both accuracy and speed. The code and models are available at https://github.com/shanice-l/gdrnpp_bop2022.

Large language models and deep neural networks achieve strong performance but suffer from reliability issues and high computational cost. This thesis proposes a unified framework based on spectral geometry and random matrix theory to address both problems by analyzing the eigenvalue structure of hidden activations. The first contribution, EigenTrack, is a real-time method for detecting hallucinations and out-of-distribution behavior in language and vision-language models using spectral features and their temporal dynamics. The second contribution, RMT-KD, is a principled compression method that identifies informative spectral components and applies iterative knowledge distillation to produce compact and efficient models while preserving accuracy. Together, these results show that spectral statistics provide interpretable and robust signals for monitoring uncertainty and guiding compression in large-scale neural networks.

We develop a continual learning method for pretrained models that requires no access to old-task data, addressing a practical barrier in foundation model adaptation where pretraining distributions are often unavailable. Our key observation is that pretrained networks exhibit substantial geometric redundancy, and that this redundancy can be exploited in two complementary ways. First, redundant neurons provide a proxy for dominant pretraining-era feature directions, enabling the construction of approximately protected update subspaces directly from pretrained weights. Second, redundancy offers a natural bias for where to place plasticity: by restricting updates to a subset of redundant neurons and constraining the remaining degrees of freedom, we obtain update families with reduced functional drift on the old-data distribution and improved worst-case retention guarantees. These insights lead to PLATE (Plasticity-Tunable Efficient Adapters), a continual learning method requiring no past-task data that provides explicit control over the plasticity-retention trade-off. PLATE parameterizes each layer with a structured low-rank update ΔW = B A Q^top, where B and Q are computed once from pretrained weights and kept frozen, and only A is trained on the new task. The code is available at https://github.com/SalesforceAIResearch/PLATE.

Learning Bird's Eye View (BEV) representation from surrounding-view cameras is of great importance for autonomous driving. In this work, we propose a Geometry-guided Kernel Transformer (GKT), a novel 2D-to-BEV representation learning mechanism. GKT leverages the geometric priors to guide the transformer to focus on discriminative regions and unfolds kernel features to generate BEV representation. For fast inference, we further introduce a look-up table (LUT) indexing method to get rid of the camera's calibrated parameters at runtime. GKT can run at 72.3 FPS on 3090 GPU / 45.6 FPS on 2080ti GPU and is robust to the camera deviation and the predefined BEV height. And GKT achieves the state-of-the-art real-time segmentation results, i.e., 38.0 mIoU (100mtimes100m perception range at a 0.5m resolution) on the nuScenes val set. Given the efficiency, effectiveness, and robustness, GKT has great practical values in autopilot scenarios, especially for real-time running systems. Code and models will be available at https://github.com/hustvl/GKT.

We propose a novel, object-agnostic method for learning a universal policy for dexterous object grasping from realistic point cloud observations and proprioceptive information under a table-top setting, namely UniDexGrasp++. To address the challenge of learning the vision-based policy across thousands of object instances, we propose Geometry-aware Curriculum Learning (GeoCurriculum) and Geometry-aware iterative Generalist-Specialist Learning (GiGSL) which leverage the geometry feature of the task and significantly improve the generalizability. With our proposed techniques, our final policy shows universal dexterous grasping on thousands of object instances with 85.4% and 78.2% success rate on the train set and test set which outperforms the state-of-the-art baseline UniDexGrasp by 11.7% and 11.3%, respectively.

We present a method for 3D object detection and pose estimation from a single image. In contrast to current techniques that only regress the 3D orientation of an object, our method first regresses relatively stable 3D object properties using a deep convolutional neural network and then combines these estimates with geometric constraints provided by a 2D object bounding box to produce a complete 3D bounding box. The first network output estimates the 3D object orientation using a novel hybrid discrete-continuous loss, which significantly outperforms the L2 loss. The second output regresses the 3D object dimensions, which have relatively little variance compared to alternatives and can often be predicted for many object types. These estimates, combined with the geometric constraints on translation imposed by the 2D bounding box, enable us to recover a stable and accurate 3D object pose. We evaluate our method on the challenging KITTI object detection benchmark both on the official metric of 3D orientation estimation and also on the accuracy of the obtained 3D bounding boxes. Although conceptually simple, our method outperforms more complex and computationally expensive approaches that leverage semantic segmentation, instance level segmentation and flat ground priors and sub-category detection. Our discrete-continuous loss also produces state of the art results for 3D viewpoint estimation on the Pascal 3D+ dataset.

Recently, world-action models (WAM) have emerged to bridge vision-language-action (VLA) models and world models, unifying their reasoning and instruction-following capabilities and spatio-temporal world modeling. However, existing WAM approaches often focus on modeling 2D appearance or latent representations, with limited geometric grounding-an essential element for embodied systems operating in the physical world. We present DriveDreamer-Policy, a unified driving world-action model that integrates depth generation, future video generation, and motion planning within a single modular architecture. The model employs a large language model to process language instructions, multi-view images, and actions, followed by three lightweight generators that produce depth, future video, and actions. By learning a geometry-aware world representation and using it to guide both future prediction and planning within a unified framework, the proposed model produces more coherent imagined futures and more informed driving actions, while maintaining modularity and controllable latency. Experiments on the Navsim v1 and v2 benchmarks demonstrate that DriveDreamer-Policy achieves strong performance on both closed-loop planning and world generation tasks. In particular, our model reaches 89.2 PDMS on Navsim v1 and 88.7 EPDMS on Navsim v2, outperforming existing world-model-based approaches while producing higher-quality future video and depth predictions. Ablation studies further show that explicit depth learning provides complementary benefits to video imagination and improves planning robustness.

Planetary exploration using aerial assets has the potential for unprecedented scientific discoveries on Mars. While NASA's Mars helicopter Ingenuity proved flight in Martian atmosphere is possible, future Mars rotorcraft will require advanced navigation capabilities for long-range flights. One such critical capability is Map-based Localization (MbL) which registers an onboard image to a reference map during flight to mitigate cumulative drift from visual odometry. However, significant illumination differences between rotorcraft observations and a reference map prove challenging for traditional MbL systems, restricting the operational window of the vehicle. In this work, we investigate a new MbL system and propose Geo-LoFTR, a geometry-aided deep learning model for image registration that is more robust under large illumination differences than prior models. The system is supported by a custom simulation framework that uses real orbital maps to produce large amounts of realistic images of the Martian terrain. Comprehensive evaluations show that our proposed system outperforms prior MbL efforts in terms of localization accuracy under significant lighting and scale variations. Furthermore, we demonstrate the validity of our approach across a simulated Martian day and on real Mars imagery. Code and datasets are available at: https://dpisanti.github.io/geo-loftr/.

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.

Reward hacking arises when a model improves a proxy reward by exploiting shortcuts rather than solving the intended task. We study this failure mode through the geometry of reinforcement learning updates in language models and argue that hacking emerges when optimization drifts away from a stable low-dimensional learning trajectory. We analyze this drift through dominant singular directions of parameter updates and show that reward-hacking runs exhibit substantially larger directional change than clean runs. Motivated by this observation, we introduce trusted-direction projection, which constrains gradients to remain within a clean reference subspace. Across reward-hacking experiments on mathematical reasoning, the proposed approach delays shortcut exploitation and better preserves task performance.

This work presents a modular and hierarchical approach to learn policies for exploring 3D environments, called `Active Neural SLAM'. Our approach leverages the strengths of both classical and learning-based methods, by using analytical path planners with learned SLAM module, and global and local policies. The use of learning provides flexibility with respect to input modalities (in the SLAM module), leverages structural regularities of the world (in global policies), and provides robustness to errors in state estimation (in local policies). Such use of learning within each module retains its benefits, while at the same time, hierarchical decomposition and modular training allow us to sidestep the high sample complexities associated with training end-to-end policies. Our experiments in visually and physically realistic simulated 3D environments demonstrate the effectiveness of our approach over past learning and geometry-based approaches. The proposed model can also be easily transferred to the PointGoal task and was the winning entry of the CVPR 2019 Habitat PointGoal Navigation Challenge.

Recent 3D generative models produce high-quality textures for 3D mesh objects. However, they commonly rely on the heavy assumption that input 3D meshes are accompanied by manual mesh parameterization (UV mapping), a manual task that requires both technical precision and artistic judgment. Industry surveys show that this process often accounts for a significant share of asset creation, creating a major bottleneck for 3D content creators. Moreover, existing automatic methods often ignore two perceptually important criteria: (1) semantic awareness (UV charts should align semantically similar 3D parts across shapes) and (2) visibility awareness (cutting seams should lie in regions unlikely to be seen). To overcome these shortcomings and to automate the mesh parameterization process, we present an unsupervised differentiable framework that augments standard geometry-preserving UV learning with semantic- and visibility-aware objectives. For semantic-awareness, our pipeline (i) segments the mesh into semantic 3D parts, (ii) applies an unsupervised learned per-part UV-parameterization backbone, and (iii) aggregates per-part charts into a unified UV atlas. For visibility-awareness, we use ambient occlusion (AO) as an exposure proxy and back-propagate a soft differentiable AO-weighted seam objective to steer cutting seams toward occluded regions. By conducting qualitative and quantitative evaluations against state-of-the-art methods, we show that the proposed method produces UV atlases that better support texture generation and reduce perceptible seam artifacts compared to recent baselines. Our implementation code is publicly available at: https://github.com/AHHHZ975/Semantic-Visibility-UV-Param.

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.

In this paper, we present a novel indoor 3D reconstruction method with occluded surface completion, given a sequence of depth readings. Prior state-of-the-art (SOTA) methods only focus on the reconstruction of the visible areas in a scene, neglecting the invisible areas due to the occlusions, e.g., the contact surface between furniture, occluded wall and floor. Our method tackles the task of completing the occluded scene surfaces, resulting in a complete 3D scene mesh. The core idea of our method is learning 3D geometry prior from various complete scenes to infer the occluded geometry of an unseen scene from solely depth measurements. We design a coarse-fine hierarchical octree representation coupled with a dual-decoder architecture, i.e., Geo-decoder and 3D Inpainter, which jointly reconstructs the complete 3D scene geometry. The Geo-decoder with detailed representation at fine levels is optimized online for each scene to reconstruct visible surfaces. The 3D Inpainter with abstract representation at coarse levels is trained offline using various scenes to complete occluded surfaces. As a result, while the Geo-decoder is specialized for an individual scene, the 3D Inpainter can be generally applied across different scenes. We evaluate the proposed method on the 3D Completed Room Scene (3D-CRS) and iTHOR datasets, significantly outperforming the SOTA methods by a gain of 16.8% and 24.2% in terms of the completeness of 3D reconstruction. 3D-CRS dataset including a complete 3D mesh of each scene is provided at project webpage.

3D scene reconstruction is a long-standing vision task. Existing approaches can be categorized into geometry-based and learning-based methods. The former leverages multi-view geometry but can face catastrophic failures due to the reliance on accurate pixel correspondence across views. The latter was proffered to mitigate these issues by learning 2D or 3D representation directly. However, without a large-scale video or 3D training data, it can hardly generalize to diverse real-world scenarios due to the presence of tens of millions or even billions of optimization parameters in the deep network. Recently, robust monocular depth estimation models trained with large-scale datasets have been proven to possess weak 3D geometry prior, but they are insufficient for reconstruction due to the unknown camera parameters, the affine-invariant property, and inter-frame inconsistency. Here, we propose a novel test-time optimization approach that can transfer the robustness of affine-invariant depth models such as LeReS to challenging diverse scenes while ensuring inter-frame consistency, with only dozens of parameters to optimize per video frame. Specifically, our approach involves freezing the pre-trained affine-invariant depth model's depth predictions, rectifying them by optimizing the unknown scale-shift values with a geometric consistency alignment module, and employing the resulting scale-consistent depth maps to robustly obtain camera poses and achieve dense scene reconstruction, even in low-texture regions. Experiments show that our method achieves state-of-the-art cross-dataset reconstruction on five zero-shot testing datasets.

Artificial neural networks (ANN) were inspired by the architecture and functions of the human brain and have revolutionised the field of artificial intelligence (AI). Inspired by studies on the latent geometry of the brain we posit that an increase in the research and application of hyperbolic geometry in machine learning will lead to increased accuracy, improved feature space representations and more efficient models across a range of tasks. We look at the structure and functions of the human brain, highlighting the alignment between the brain's hierarchical nature and hyperbolic geometry. By examining the brain's complex network of neuron connections and its cognitive processes, we illustrate how hyperbolic geometry plays a pivotal role in human intelligence. Empirical evidence indicates that hyperbolic neural networks outperform Euclidean models for tasks including natural language processing, computer vision and complex network analysis, requiring fewer parameters and exhibiting better generalisation. Despite its nascent adoption, hyperbolic geometry holds promise for improving machine learning models and advancing the field toward AGI.

4D head capture aims to generate dynamic topological meshes and corresponding texture maps from videos, which is widely utilized in movies and games for its ability to simulate facial muscle movements and recover dynamic textures in pore-squeezing. The industry often adopts the method involving multi-view stereo and non-rigid alignment. However, this approach is prone to errors and heavily reliant on time-consuming manual processing by artists. To simplify this process, we propose Topo4D, a novel framework for automatic geometry and texture generation, which optimizes densely aligned 4D heads and 8K texture maps directly from calibrated multi-view time-series images. Specifically, we first represent the time-series faces as a set of dynamic 3D Gaussians with fixed topology in which the Gaussian centers are bound to the mesh vertices. Afterward, we perform alternative geometry and texture optimization frame-by-frame for high-quality geometry and texture learning while maintaining temporal topology stability. Finally, we can extract dynamic facial meshes in regular wiring arrangement and high-fidelity textures with pore-level details from the learned Gaussians. Extensive experiments show that our method achieves superior results than the current SOTA face reconstruction methods both in the quality of meshes and textures. Project page: https://xuanchenli.github.io/Topo4D/.

Learning surfaces from neural radiance field (NeRF) became a rising topic in Multi-View Stereo (MVS). Recent Signed Distance Function (SDF)-based methods demonstrated their ability to reconstruct accurate 3D shapes of Lambertian scenes. However, their results on reflective scenes are unsatisfactory due to the entanglement of specular radiance and complicated geometry. To address the challenges, we propose a Gaussian-based representation of normals in SDF fields. Supervised by polarization priors, this representation guides the learning of geometry behind the specular reflection and captures more details than existing methods. Moreover, we propose a reweighting strategy in the optimization process to alleviate the noise issue of polarization priors. To validate the effectiveness of our design, we capture polarimetric information, and ground truth meshes in additional reflective scenes with various geometry. We also evaluated our framework on the PANDORA dataset. Comparisons prove our method outperforms existing neural 3D reconstruction methods in reflective scenes by a large margin.

Monocular depth estimation has drawn widespread attention from the vision community due to its broad applications. In this paper, we propose a novel physics (geometry)-driven deep learning framework for monocular depth estimation by assuming that 3D scenes are constituted by piece-wise planes. Particularly, we introduce a new normal-distance head that outputs pixel-level surface normal and plane-to-origin distance for deriving depth at each position. Meanwhile, the normal and distance are regularized by a developed plane-aware consistency constraint. We further integrate an additional depth head to improve the robustness of the proposed framework. To fully exploit the strengths of these two heads, we develop an effective contrastive iterative refinement module that refines depth in a complementary manner according to the depth uncertainty. Extensive experiments indicate that the proposed method exceeds previous state-of-the-art competitors on the NYU-Depth-v2, KITTI and SUN RGB-D datasets. Notably, it ranks 1st among all submissions on the KITTI depth prediction online benchmark at the submission time.

Neural implicit fields are powerful for representing 3D scenes and generating high-quality novel views, but it remains challenging to use such implicit representations for creating a 3D human avatar with a specific identity and artistic style that can be easily animated. Our proposed method, AvatarCraft, addresses this challenge by using diffusion models to guide the learning of geometry and texture for a neural avatar based on a single text prompt. We carefully design the optimization framework of neural implicit fields, including a coarse-to-fine multi-bounding box training strategy, shape regularization, and diffusion-based constraints, to produce high-quality geometry and texture. Additionally, we make the human avatar animatable by deforming the neural implicit field with an explicit warping field that maps the target human mesh to a template human mesh, both represented using parametric human models. This simplifies animation and reshaping of the generated avatar by controlling pose and shape parameters. Extensive experiments on various text descriptions show that AvatarCraft is effective and robust in creating human avatars and rendering novel views, poses, and shapes. Our project page is: https://avatar-craft.github.io/.

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

We present GeoTransolver, a Multiscale Geometry-Aware Physics Attention Transformer for CAE that replaces standard attention with GALE, coupling physics-aware self-attention on learned state slices with cross-attention to a shared geometry/global/boundary-condition context computed from multi-scale ball queries (inspired by DoMINO) and reused in every block. Implemented and released in NVIDIA PhysicsNeMo, GeoTransolver persistently projects geometry, global and boundary condition parameters into physical state spaces to anchor latent computations to domain structure and operating regimes. We benchmark GeoTransolver on DrivAerML, Luminary SHIFT-SUV, and Luminary SHIFT-Wing, comparing against Domino, Transolver (as released in PhysicsNeMo), and literature-reported AB-UPT, and evaluate drag/lift R2 and Relative L1 errors for field variables. GeoTransolver delivers better accuracy, improved robustness to geometry/regime shifts, and favorable data efficiency; we include ablations on DrivAerML and qualitative results such as contour plots and design trends for the best GeoTransolver models. By unifying multiscale geometry-aware context with physics-based attention in a scalable transformer, GeoTransolver advances operator learning for high-fidelity surrogate modeling across complex, irregular domains and non-linear physical regimes.

Geometry-aware optimization algorithms, such as Muon, have achieved remarkable success in training deep neural networks (DNNs). These methods leverage the underlying geometry of DNNs by selecting appropriate norms for different layers and updating parameters via norm-constrained linear minimization oracles (LMOs). However, even within a group of layers associated with the same norm, the local curvature can be heterogeneous across layers and vary dynamically over the course of training. For example, recent work shows that sharpness varies substantially across transformer layers and throughout training, yet standard geometry-aware optimizers impose fixed learning rates to layers within the same group, which may be inefficient for DNN training. In this paper, we introduce a noise-adaptive layerwise learning rate scheme on top of geometry-aware optimization algorithms and substantially accelerate DNN training compared to methods that use fixed learning rates within each group. Our method estimates gradient variance in the dual norm induced by the chosen LMO on the fly, and uses it to assign time-varying noise-adaptive layerwise learning rates within each group. We provide a theoretical analysis showing that our algorithm achieves a sharp convergence rate. Empirical results on transformer architectures such as LLaMA and GPT demonstrate that our approach achieves faster convergence than state-of-the-art optimizers.

Foundation features from self-supervised vision models and text-to-image diffusion models have proven effective for semantic correspondence estimation. However, because these features are learned primarily from 2D image objectives, they lack explicit 3D awareness and often confuse symmetric object sides, repeated parts, and visually similar structures that are distinct in 3D. We introduce a 3D-aware post-training framework that goes beyond available 2D foundation features by incorporating priors from 3D foundation models. Given an image, our method uses SAM3D to estimate object geometry and pose, and refines the pose through render-and-compare optimization. Subsequently, we render PartField descriptors from the reconstructed geometry into the image plane based on the estimated object pose. The resulting geometry-aware feature maps complement DINO and Stable Diffusion features, while geodesic distances on the reconstructed shapes enable reliable filtering of candidate correspondences. We use the filtered matches as supervision to train a lightweight adapter on top of DINO and Stable Diffusion for semantic correspondence. In contrast to prior post-training approaches that require pose annotations and rely on coarse spherical geometry, our method automatically obtains instance-specific 3D structure and uses it to guide correspondence learning. Experiments show that our approach improves semantic correspondence over the prior methods while reducing manual geometric supervision. Code and model can be found at https:/github.com/GenIntel/3D-SC.

Understanding the physical world requires perceptual models grounded in physical laws rather than mere statistical correlations. However, existing multimodal learning frameworks, focused on vision and language, lack physical consistency and overlook the intrinsic causal relationships among an object's geometry, material, vibration modes, and the sounds it produces. We introduce VibraVerse, a large-scale geometry-acoustics alignment dataset that explicitly bridges the causal chain from 3D geometry -> physical attributes -> modal parameters -> acoustic signals. Each 3D model has explicit physical properties (density, Young's modulus, Poisson's ratio) and volumetric geometry, from which modal eigenfrequencies and eigenvectors are computed for impact sound synthesis under controlled excitations. To establish this coherence, we introduce CLASP, a contrastive learning framework for cross-modal alignment that preserves the causal correspondence between an object's physical structure and its acoustic response. This framework enforces physically consistent alignment across modalities, ensuring that every sample is coherent, traceable to the governing equations, and embedded within a unified representation space spanning shape, image, and sound. Built upon VibraVerse, we define a suite of benchmark tasks for geometry-to-sound prediction, sound-guided shape reconstruction, and cross-modal representation learning. Extensive validations on these tasks demonstrate that models trained on VibraVerse exhibit superior accuracy, interpretability, and generalization across modalities. These results establish VibraVerse as a benchmark for physically consistent and causally interpretable multimodal learning, providing a foundation for sound-guided embodied perception and a deeper understanding of the physical world. The dataset will be open-sourced.

Rapid growth of high-dimensional datasets in fields such as single-cell RNA sequencing and spatial genomics has led to unprecedented opportunities for scientific discovery, but it also presents unique computational and statistical challenges. Traditional methods struggle with geometry-aware data generation, interpolation along meaningful trajectories, and transporting populations via feasible paths. To address these issues, we introduce Geometry-Aware Generative Autoencoder (GAGA), a novel framework that combines extensible manifold learning with generative modeling. GAGA constructs a neural network embedding space that respects the intrinsic geometries discovered by manifold learning and learns a novel warped Riemannian metric on the data space. This warped metric is derived from both the points on the data manifold and negative samples off the manifold, allowing it to characterize a meaningful geometry across the entire latent space. Using this metric, GAGA can uniformly sample points on the manifold, generate points along geodesics, and interpolate between populations across the learned manifold using geodesic-guided flows. GAGA shows competitive performance in simulated and real-world datasets, including a 30% improvement over the state-of-the-art methods in single-cell population-level trajectory inference.

We introduce a framework for learning latent representations of 4D objects which are descriptive, faithfully capturing object geometry and appearance; compressive, aiding in downstream efficiency; and accessible, requiring minimal input, i.e., an unstructured dynamic point cloud, to construct. Specifically, Velox trains an encoder to compress spatiotemporal color point clouds into a set of dynamic shape tokens. These tokens are supervised using two complementary decoders: a 4D surface decoder, which models the time-varying surface distribution capturing the geometry; and a Gaussian decoder, which maps the tokens to 3D Gaussians, helping learn appearance. To demonstrate the utility of our representation, we evaluate it across three downstream tasks -- video-to-4D generation, 3D tracking, and cloth simulation via image-to-4D generation -- and observe strong performances in all settings.

Neural operators have become increasingly popular in solving partial differential equations (PDEs) due to their superior capability to capture intricate mappings between function spaces over complex domains. However, the data-hungry nature of operator learning inevitably poses a bottleneck for their widespread applications. At the core of the challenge lies the absence of transferability of neural operators to new geometries. To tackle this issue, we propose operator learning with domain decomposition, a local-to-global framework to solve PDEs on arbitrary geometries. Under this framework, we devise an iterative scheme Schwarz Neural Inference (SNI). This scheme allows for partitioning of the problem domain into smaller subdomains, on which local problems can be solved with neural operators, and stitching local solutions to construct a global solution. Additionally, we provide a theoretical analysis of the convergence rate and error bound. We conduct extensive experiments on several representative PDEs with diverse boundary conditions and achieve remarkable geometry generalization compared to alternative methods. These analysis and experiments demonstrate the proposed framework's potential in addressing challenges related to geometry generalization and data efficiency.

Reliable facial expression learning (FEL) involves the effective learning of distinctive facial expression characteristics for more reliable, unbiased and accurate predictions in real-life settings. However, current systems struggle with FEL tasks because of the variance in people's facial expressions due to their unique facial structures, movements, tones, and demographics. Biased and imbalanced datasets compound this challenge, leading to wrong and biased prediction labels. To tackle these, we introduce GReFEL, leveraging Vision Transformers and a facial geometry-aware anchor-based reliability balancing module to combat imbalanced data distributions, bias, and uncertainty in facial expression learning. Integrating local and global data with anchors that learn different facial data points and structural features, our approach adjusts biased and mislabeled emotions caused by intra-class disparity, inter-class similarity, and scale sensitivity, resulting in comprehensive, accurate, and reliable facial expression predictions. Our model outperforms current state-of-the-art methodologies, as demonstrated by extensive experiments on various datasets.

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

This paper presents an unpaired method for creating line drawings from photographs. Current methods often rely on high quality paired datasets to generate line drawings. However, these datasets often have limitations due to the subjects of the drawings belonging to a specific domain, or in the amount of data collected. Although recent work in unsupervised image-to-image translation has shown much progress, the latest methods still struggle to generate compelling line drawings. We observe that line drawings are encodings of scene information and seek to convey 3D shape and semantic meaning. We build these observations into a set of objectives and train an image translation to map photographs into line drawings. We introduce a geometry loss which predicts depth information from the image features of a line drawing, and a semantic loss which matches the CLIP features of a line drawing with its corresponding photograph. Our approach outperforms state-of-the-art unpaired image translation and line drawing generation methods on creating line drawings from arbitrary photographs. For code and demo visit our webpage carolineec.github.io/informative_drawings

Large language model (LLM) agents exhibit strong mathematical problem-solving abilities and can even solve International Mathematical Olympiad (IMO) level problems with the assistance of formal proof systems. However, due to weak heuristics for auxiliary constructions, AI for geometry problem solving remains dominated by expert models such as AlphaGeometry 2, which rely heavily on large-scale data synthesis and search for both training and evaluation. In this work, we make the first attempt to build a medalist-level LLM agent for geometry and present InternGeometry. InternGeometry overcomes the heuristic limitations in geometry by iteratively proposing propositions and auxiliary constructions, verifying them with a symbolic engine, and reflecting on the engine's feedback to guide subsequent proposals. A dynamic memory mechanism enables InternGeometry to conduct more than two hundred interactions with the symbolic engine per problem. To further accelerate learning, we introduce Complexity-Boosting Reinforcement Learning (CBRL), which gradually increases the complexity of synthesized problems across training stages. Built on InternThinker-32B, InternGeometry solves 44 of 50 IMO geometry problems (2000-2024), exceeding the average gold medalist score (40.9), using only 13K training examples, just 0.004% of the data used by AlphaGeometry 2, demonstrating the potential of LLM agents on expert-level geometry tasks. InternGeometry can also propose novel auxiliary constructions for IMO problems that do not appear in human solutions. We will release the model, data, and symbolic engine to support future research.

Previous research has investigated the application of Multimodal Large Language Models (MLLMs) in understanding 3D scenes by interpreting them as videos. These approaches generally depend on comprehensive 3D data inputs, such as point clouds or reconstructed Bird's-Eye View (BEV) maps. In our research, we advance this field by enhancing the capability of MLLMs to understand and reason in 3D spaces directly from video data, without the need for additional 3D input. We propose a novel and efficient method, the Video-3D Geometry Large Language Model (VG LLM). Our approach employs a 3D visual geometry encoder that extracts 3D prior information from video sequences. This information is integrated with visual tokens and fed into the MLLM. Extensive experiments have shown that our method has achieved substantial improvements in various tasks related to 3D scene understanding and spatial reasoning, all directly learned from video sources. Impressively, our 4B model, which does not rely on explicit 3D data inputs, achieves competitive results compared to existing state-of-the-art methods, and even surpasses the Gemini-1.5-Pro in the VSI-Bench evaluations.

Novel view acoustic synthesis (NVAS) aims to render binaural audio at any target viewpoint, given a mono audio emitted by a sound source at a 3D scene. Existing methods have proposed NeRF-based implicit models to exploit visual cues as a condition for synthesizing binaural audio. However, in addition to low efficiency originating from heavy NeRF rendering, these methods all have a limited ability of characterizing the entire scene environment such as room geometry, material properties, and the spatial relation between the listener and sound source. To address these issues, we propose a novel Audio-Visual Gaussian Splatting (AV-GS) model. To obtain a material-aware and geometry-aware condition for audio synthesis, we learn an explicit point-based scene representation with an audio-guidance parameter on locally initialized Gaussian points, taking into account the space relation from the listener and sound source. To make the visual scene model audio adaptive, we propose a point densification and pruning strategy to optimally distribute the Gaussian points, with the per-point contribution in sound propagation (e.g., more points needed for texture-less wall surfaces as they affect sound path diversion). Extensive experiments validate the superiority of our AV-GS over existing alternatives on the real-world RWAS and simulation-based SoundSpaces datasets.

Reinforcement learning (RL) is a central approach for improving reasoning capabilities in large language models (LLMs), where training efficiency depends critically on how problems are sampled during optimization. Existing adaptive curriculum learning methods typically prioritize prompts of intermediate difficulty, treating problem selection as a standard bandit problem with independent arms and overlooking the structured, heterogeneous nature of the task space. In this work, we frame problem sampling as a manifold-structured bandit problem with endogenous non-stationarity: problems are related through the model's latent representation space, and sampling decisions can steer how learning signals evolve across that space. To operationalize this perspective, we introduce Bayesian Manifold Curriculum (BMC), a structure-aware framework that organizes problems into a hierarchical task tree and applies Bayesian learning to guide sampling. Empirically, we find that different sampling strategies induce non-trivial tradeoffs between productivity (learning signal), diversity (coverage of the task manifold), and utility (evaluation relevance). These results show that prioritizing difficulty alone is insufficient for strong downstream performance, highlighting the importance of incorporating structure and type-awareness into problem sampling.

Vision-language models (VLMs) can couple visual perception with open-ended clinical reasoning, making them attractive for computational histopathology. However, fine-tuning billions of parameters on scarce, expert-annotated pathology data is prohibitive, while in-context learning (ICL), which conditions the VLM on demonstrative image-text pairs without parameter updates, suffers from high sensitivity to which examples are selected and how the query is phrased, producing unreliable diagnostics. Existing selection strategies rely on query-dependent nearest-neighbour retrieval that ignores global data structure, require costly parameter updates, or disregard the joint vision-text embedding geometry of VLMs. We propose GAUC, a training-free coreset selection method operating directly in the pre-trained multimodal embedding space. GAUC jointly optimises three objectives: (1) a Maximum Mean Discrepancy term enforcing distributional fidelity between coreset and full dataset, (2) an Effective Mutual Information Difference regulariser bounding performance degradation under prompt paraphrases by exploiting the VLM's joint vision-text alignment, and (3) a predictive-variance penalty suppressing overconfident, unstable outputs. On CRC-100K and MHIST across multiple open-source VLM architectures, GAUC consistently improves accuracy, calibration, and prompt robustness over recent ICL selection methods and dataset-distillation baselines, all without a single gradient update.

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.

We introduce the Information-Estimation Metric (IEM), a novel form of distance function derived from an underlying continuous probability density over a domain of signals. The IEM is rooted in a fundamental relationship between information theory and estimation theory, which links the log-probability of a signal with the errors of an optimal denoiser, applied to noisy observations of the signal. In particular, the IEM between a pair of signals is obtained by comparing their denoising error vectors over a range of noise amplitudes. Geometrically, this amounts to comparing the score vector fields of the blurred density around the signals over a range of blur levels. We prove that the IEM is a valid global distance metric and derive a closed-form expression for its local second-order approximation, which yields a Riemannian metric. For Gaussian-distributed signals, the IEM coincides with the Mahalanobis distance. But for more complex distributions, it adapts, both locally and globally, to the geometry of the distribution. In practice, the IEM can be computed using a learned denoiser (analogous to generative diffusion models) and solving a one-dimensional integral. To demonstrate the value of our framework, we learn an IEM on the ImageNet database. Experiments show that this IEM is competitive with or outperforms state-of-the-art supervised image quality metrics in predicting human perceptual judgments.

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

This paper introduces a novel hierarchical autoencoder that maps 3D models into a highly compressed latent space. The hierarchical autoencoder is specifically designed to tackle the challenges arising from large-scale datasets and generative modeling using diffusion. Different from previous approaches that only work on a regular image or volume grid, our hierarchical autoencoder operates on unordered sets of vectors. Each level of the autoencoder controls different geometric levels of detail. We show that the model can be used to represent a wide range of 3D models while faithfully representing high-resolution geometry details. The training of the new architecture takes 0.70x time and 0.58x memory compared to the baseline. We also explore how the new representation can be used for generative modeling. Specifically, we propose a cascaded diffusion framework where each stage is conditioned on the previous stage. Our design extends existing cascaded designs for image and volume grids to vector sets.

Deep neural networks can approximate functions on different types of data, from images to graphs, with varied underlying structure. This underlying structure can be viewed as the geometry of the data manifold. By extending recent advances in the theoretical understanding of neural networks, we study how a randomly initialized neural network with piece-wise linear activation splits the data manifold into regions where the neural network behaves as a linear function. We derive bounds on the density of boundary of linear regions and the distance to these boundaries on the data manifold. This leads to insights into the expressivity of randomly initialized deep neural networks on non-Euclidean data sets. We empirically corroborate our theoretical results using a toy supervised learning problem. Our experiments demonstrate that number of linear regions varies across manifolds and the results hold with changing neural network architectures. We further demonstrate how the complexity of linear regions is different on the low dimensional manifold of images as compared to the Euclidean space, using the MetFaces dataset.

Training accurate 3D human pose estimators requires large amount of 3D ground-truth data which is costly to collect. Various weakly or self supervised pose estimation methods have been proposed due to lack of 3D data. Nevertheless, these methods, in addition to 2D ground-truth poses, require either additional supervision in various forms (e.g. unpaired 3D ground truth data, a small subset of labels) or the camera parameters in multiview settings. To address these problems, we present EpipolarPose, a self-supervised learning method for 3D human pose estimation, which does not need any 3D ground-truth data or camera extrinsics. During training, EpipolarPose estimates 2D poses from multi-view images, and then, utilizes epipolar geometry to obtain a 3D pose and camera geometry which are subsequently used to train a 3D pose estimator. We demonstrate the effectiveness of our approach on standard benchmark datasets i.e. Human3.6M and MPI-INF-3DHP where we set the new state-of-the-art among weakly/self-supervised methods. Furthermore, we propose a new performance measure Pose Structure Score (PSS) which is a scale invariant, structure aware measure to evaluate the structural plausibility of a pose with respect to its ground truth. Code and pretrained models are available at https://github.com/mkocabas/EpipolarPose

Numerous deep learning applications benefit from multi-task learning with multiple regression and classification objectives. In this paper we make the observation that the performance of such systems is strongly dependent on the relative weighting between each task's loss. Tuning these weights by hand is a difficult and expensive process, making multi-task learning prohibitive in practice. We propose a principled approach to multi-task deep learning which weighs multiple loss functions by considering the homoscedastic uncertainty of each task. This allows us to simultaneously learn various quantities with different units or scales in both classification and regression settings. We demonstrate our model learning per-pixel depth regression, semantic and instance segmentation from a monocular input image. Perhaps surprisingly, we show our model can learn multi-task weightings and outperform separate models trained individually on each task.

Human-object interaction (HOI) video generation has garnered increasing attention due to its promising applications in digital humans, e-commerce, advertising, and robotics imitation learning. However, existing methods face two critical limitations: (1) a lack of effective mechanisms to inject multi-view information of the object into the model, leading to poor cross-view consistency, and (2) heavy reliance on fine-grained hand mesh annotations for modeling interaction occlusions. To address these challenges, we introduce ByteLoom, a Diffusion Transformer (DiT)-based framework that generates realistic HOI videos with geometrically consistent object illustration, using simplified human conditioning and 3D object inputs. We first propose an RCM-cache mechanism that leverages Relative Coordinate Maps (RCM) as a universal representation to maintain object's geometry consistency and precisely control 6-DoF object transformations in the meantime. To compensate HOI dataset scarcity and leverage existing datasets, we further design a training curriculum that enhances model capabilities in a progressive style and relaxes the demand of hand mesh. Extensive experiments demonstrate that our method faithfully preserves human identity and the object's multi-view geometry, while maintaining smooth motion and object manipulation.

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

In machine learning, there is a long history of trying to build neural networks that can learn from fewer example data by baking in strong geometric priors. However, it is not always clear a priori what geometric constraints are appropriate for a given task. Here, we explore the possibility that one can uncover useful geometric inductive biases by studying how training molds the Riemannian geometry induced by unconstrained neural network feature maps. We first show that at infinite width, neural networks with random parameters induce highly symmetric metrics on input space. This symmetry is broken by feature learning: networks trained to perform classification tasks learn to magnify local areas along decision boundaries. This holds in deep networks trained on high-dimensional image classification tasks, and even in self-supervised representation learning. These results begin to elucidate how training shapes the geometry induced by unconstrained neural network feature maps, laying the groundwork for an understanding of this richly nonlinear form of feature learning.

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

Imitation Learning has become a fundamental approach in robotic manipulation. However, collecting large-scale real-world robot demonstrations is prohibitively expensive. Simulators offer a cost-effective alternative, but the sim-to-real gap make it extremely challenging to scale. Therefore, we introduce RoboTransfer, a diffusion-based video generation framework for robotic data synthesis. Unlike previous methods, RoboTransfer integrates multi-view geometry with explicit control over scene components, such as background and object attributes. By incorporating cross-view feature interactions and global depth/normal conditions, RoboTransfer ensures geometry consistency across views. This framework allows fine-grained control, including background edits and object swaps. Experiments demonstrate that RoboTransfer is capable of generating multi-view videos with enhanced geometric consistency and visual fidelity. In addition, policies trained on the data generated by RoboTransfer achieve a 33.3% relative improvement in the success rate in the DIFF-OBJ setting and a substantial 251% relative improvement in the more challenging DIFF-ALL scenario. Explore more demos on our project page: https://horizonrobotics.github.io/robot_lab/robotransfer

Predicting flows that occur both through and around porous bodies is challenging due to coupled physics across fluid and porous regions and the need to generalize across diverse geometries and boundary conditions. We address this problem using two Physics Informed learning approaches: Physics Informed PointNets (PIPN) and Physics Informed Geometry Aware Neural Operator (P-IGANO). We enforce the incompressible Navier Stokes equations in the free-flow region and a Darcy Forchheimer extension in the porous region within a unified loss and condition the networks on geometry and material parameters. Datasets are generated with OpenFOAM on 2D ducts containing porous obstacles and on 3D windbreak scenarios with tree canopies and buildings. We first verify the pipeline via the method of manufactured solutions, then assess generalization to unseen shapes, and for PI-GANO, to variable boundary conditions and parameter settings. The results show consistently low velocity and pressure errors in both seen and unseen cases, with accurate reproduction of the wake structures. Performance degrades primarily near sharp interfaces and in regions with large gradients. Overall, the study provides a first systematic evaluation of PIPN/PI-GANO for simultaneous through-and-around porous flows and shows their potential to accelerate design studies without retraining per geometry.

Manipulating objects with varying geometries and deformable objects is a major challenge in robotics. Tasks such as insertion with different objects or cloth hanging require precise control and effective modelling of complex dynamics. In this work, we frame this problem through the lens of a heterogeneous graph that comprises smaller sub-graphs, such as actuators and objects, accompanied by different edge types describing their interactions. This graph representation serves as a unified structure for both rigid and deformable objects tasks, and can be extended further to tasks comprising multiple actuators. To evaluate this setup, we present a novel and challenging reinforcement learning benchmark, including rigid insertion of diverse objects, as well as rope and cloth manipulation with multiple end-effectors. These tasks present a large search space, as both the initial and target configurations are uniformly sampled in 3D space. To address this issue, we propose a novel graph-based policy model, dubbed Heterogeneous Equivariant Policy (HEPi), utilizing SE(3) equivariant message passing networks as the main backbone to exploit the geometric symmetry. In addition, by modeling explicit heterogeneity, HEPi can outperform Transformer-based and non-heterogeneous equivariant policies in terms of average returns, sample efficiency, and generalization to unseen objects. Our project page is available at https://thobotics.github.io/hepi.

Text-to-3D generation has recently seen significant progress. To enhance its practicality in real-world applications, it is crucial to generate multiple independent objects with interactions, similar to layer-compositing in 2D image editing. However, existing text-to-3D methods struggle with this task, as they are designed to generate either non-independent objects or independent objects lacking spatially plausible interactions. Addressing this, we propose DreamDissector, a text-to-3D method capable of generating multiple independent objects with interactions. DreamDissector accepts a multi-object text-to-3D NeRF as input and produces independent textured meshes. To achieve this, we introduce the Neural Category Field (NeCF) for disentangling the input NeRF. Additionally, we present the Category Score Distillation Sampling (CSDS), facilitated by a Deep Concept Mining (DCM) module, to tackle the concept gap issue in diffusion models. By leveraging NeCF and CSDS, we can effectively derive sub-NeRFs from the original scene. Further refinement enhances geometry and texture. Our experimental results validate the effectiveness of DreamDissector, providing users with novel means to control 3D synthesis at the object level and potentially opening avenues for various creative applications in the future.

Modeling the mechanics of fluid in complex scenes is vital to applications in design, graphics, and robotics. Learning-based methods provide fast and differentiable fluid simulators, however most prior work is unable to accurately model how fluids interact with genuinely novel surfaces not seen during training. We introduce SURFSUP, a framework that represents objects implicitly using signed distance functions (SDFs), rather than an explicit representation of meshes or particles. This continuous representation of geometry enables more accurate simulation of fluid-object interactions over long time periods while simultaneously making computation more efficient. Moreover, SURFSUP trained on simple shape primitives generalizes considerably out-of-distribution, even to complex real-world scenes and objects. Finally, we show we can invert our model to design simple objects to manipulate fluid flow.

StyleGAN has achieved great progress in 2D face reconstruction and semantic editing via image inversion and latent editing. While studies over extending 2D StyleGAN to 3D faces have emerged, a corresponding generic 3D GAN inversion framework is still missing, limiting the applications of 3D face reconstruction and semantic editing. In this paper, we study the challenging problem of 3D GAN inversion where a latent code is predicted given a single face image to faithfully recover its 3D shapes and detailed textures. The problem is ill-posed: innumerable compositions of shape and texture could be rendered to the current image. Furthermore, with the limited capacity of a global latent code, 2D inversion methods cannot preserve faithful shape and texture at the same time when applied to 3D models. To solve this problem, we devise an effective self-training scheme to constrain the learning of inversion. The learning is done efficiently without any real-world 2D-3D training pairs but proxy samples generated from a 3D GAN. In addition, apart from a global latent code that captures the coarse shape and texture information, we augment the generation network with a local branch, where pixel-aligned features are added to faithfully reconstruct face details. We further consider a new pipeline to perform 3D view-consistent editing. Extensive experiments show that our method outperforms state-of-the-art inversion methods in both shape and texture reconstruction quality. Code and data will be released.

We introduce VEGA, an approach for training navigation VisionLanguage-Action (VLA) models from unlabeled egocentric navigation videos. Internet-scale egocentric videos provide a scalable source of navigation-relevant visual observations, capturing cluttered scenes, close-range obstacles, and natural human motion through real-world spaces. However, these videos are not directly usable for policy learning because they do not provide obstacle-aware trajectories conditioned on explicit navigation goals in the robot's coordinate frame. VEGA addresses this gap by reconstructing local scene geometry from monocular video, sampling navigation goals (represented as text, image, or spatial waypoints) and generating obstacle-aware trajectories using the constructed geometry. The resulting trajectory distribution is then used to train a flow-matching VLA navigation policy. By using geometry exclusively during training, VEGA distills obstacle-aware planning directly into a vision-based policy. Furthermore, we introduce VEGA-Bench, a benchmark containing 250k scenes and approximately 5 million navigation goals paired with scene geometry, designed to evaluate goal progress, collision avoidance, and obstacle clearance of VLAs. Our evaluation shows that VEGA achieves competitive goal progress while reducing collisions by 33.0% and improving obstacle clearance by 17.9% over the strongest baseline on VEGABench, while improving success by at least 150.0%, reducing collisions by at least 66.7%, and improving obstacle clearance by at least 60.0% in real-world trials. Ultimately, we demonstrate that video-derived geometric supervision provides a scalable and effective signal for training obstacle-aware navigation VLAs. The code and benchmark will be released at the time of publication.

We propose a Geometry-aware Policy Imitation (GPI) approach that rethinks imitation learning by treating demonstrations as geometric curves rather than collections of state-action samples. From these curves, GPI derives distance fields that give rise to two complementary control primitives: a progression flow that advances along expert trajectories and an attraction flow that corrects deviations. Their combination defines a controllable, non-parametric vector field that directly guides robot behavior. This formulation decouples metric learning from policy synthesis, enabling modular adaptation across low-dimensional robot states and high-dimensional perceptual inputs. GPI naturally supports multimodality by preserving distinct demonstrations as separate models and allows efficient composition of new demonstrations through simple additions to the distance field. We evaluate GPI in simulation and on real robots across diverse tasks. Experiments show that GPI achieves higher success rates than diffusion-based policies while running 20 times faster, requiring less memory, and remaining robust to perturbations. These results establish GPI as an efficient, interpretable, and scalable alternative to generative approaches for robotic imitation learning. Project website: https://yimingli1998.github.io/projects/GPI/

The very challenging task of learning solution operators of PDEs on arbitrary domains accurately and efficiently is of vital importance to engineering and industrial simulations. Despite the existence of many operator learning algorithms to approximate such PDEs, we find that accurate models are not necessarily computationally efficient and vice versa. We address this issue by proposing a geometry aware operator transformer (GAOT) for learning PDEs on arbitrary domains. GAOT combines novel multiscale attentional graph neural operator encoders and decoders, together with geometry embeddings and (vision) transformer processors to accurately map information about the domain and the inputs into a robust approximation of the PDE solution. Multiple innovations in the implementation of GAOT also ensure computational efficiency and scalability. We demonstrate this significant gain in both accuracy and efficiency of GAOT over several baselines on a large number of learning tasks from a diverse set of PDEs, including achieving state of the art performance on a large scale three-dimensional industrial CFD dataset.

Understanding the 3D geometry and semantics of driving scenes is critical for safe autonomous driving. Recent advances in 3D occupancy prediction have improved scene representation but often suffer from spatial inconsistencies, leading to floating artifacts and poor surface localization. Existing voxel-wise losses (e.g., cross-entropy) fail to enforce geometric coherence. In this paper, we propose GaussRender, a module that improves 3D occupancy learning by enforcing projective consistency. Our key idea is to project both predicted and ground-truth 3D occupancy into 2D camera views, where we apply supervision. Our method penalizes 3D configurations that produce inconsistent 2D projections, thereby enforcing a more coherent 3D structure. To achieve this efficiently, we leverage differentiable rendering with Gaussian splatting. GaussRender seamlessly integrates with existing architectures while maintaining efficiency and requiring no inference-time modifications. Extensive evaluations on multiple benchmarks (SurroundOcc-nuScenes, Occ3D-nuScenes, SSCBench-KITTI360) demonstrate that GaussRender significantly improves geometric fidelity across various 3D occupancy models (TPVFormer, SurroundOcc, Symphonies), achieving state-of-the-art results, particularly on surface-sensitive metrics. The code is open-sourced at https://github.com/valeoai/GaussRender.

In this study, we address the challenge of 3D scene structure recovery from monocular depth estimation. While traditional depth estimation methods leverage labeled datasets to directly predict absolute depth, recent advancements advocate for mix-dataset training, enhancing generalization across diverse scenes. However, such mixed dataset training yields depth predictions only up to an unknown scale and shift, hindering accurate 3D reconstructions. Existing solutions necessitate extra 3D datasets or geometry-complete depth annotations, constraints that limit their versatility. In this paper, we propose a learning framework that trains models to predict geometry-preserving depth without requiring extra data or annotations. To produce realistic 3D structures, we render novel views of the reconstructed scenes and design loss functions to promote depth estimation consistency across different views. Comprehensive experiments underscore our framework's superior generalization capabilities, surpassing existing state-of-the-art methods on several benchmark datasets without leveraging extra training information. Moreover, our innovative loss functions empower the model to autonomously recover domain-specific scale-and-shift coefficients using solely unlabeled images.

Geometry diagram parsing plays a key role in geometry problem solving, wherein the primitive extraction and relation parsing remain challenging due to the complex layout and between-primitive relationship. In this paper, we propose a powerful diagram parser based on deep learning and graph reasoning. Specifically, a modified instance segmentation method is proposed to extract geometric primitives, and the graph neural network (GNN) is leveraged to realize relation parsing and primitive classification incorporating geometric features and prior knowledge. All the modules are integrated into an end-to-end model called PGDPNet to perform all the sub-tasks simultaneously. In addition, we build a new large-scale geometry diagram dataset named PGDP5K with primitive level annotations. Experiments on PGDP5K and an existing dataset IMP-Geometry3K show that our model outperforms state-of-the-art methods in four sub-tasks remarkably. Our code, dataset and appendix material are available at https://github.com/mingliangzhang2018/PGDP.

Learning-based 3D reconstruction models, represented by Visual Geometry Grounded Transformers (VGGTs), have made remarkable progress with the use of large-scale transformers. Their prohibitive computational and memory costs severely hinder real-world deployment. Post-Training Quantization (PTQ) has become a common practice for compressing and accelerating models. However, we empirically observe that PTQ faces unique obstacles when compressing billion-scale VGGTs: the data-independent special tokens induce heavy-tailed activation distributions, while the multi-view nature of 3D data makes calibration sample selection highly unstable. This paper proposes the first Quantization framework for VGGTs, namely QuantVGGT. This mainly relies on two technical contributions: First, we introduce Dual-Smoothed Fine-Grained Quantization, which integrates pre-global Hadamard rotation and post-local channel smoothing to mitigate heavy-tailed distributions and inter-channel variance robustly. Second, we design Noise-Filtered Diverse Sampling, which filters outliers via deep-layer statistics and constructs frame-aware diverse calibration clusters to ensure stable quantization ranges. Comprehensive experiments demonstrate that QuantVGGT achieves the state-of-the-art results across different benchmarks and bit-width, surpassing the previous state-of-the-art generic quantization method with a great margin. We highlight that our 4-bit QuantVGGT can deliver a 3.7times memory reduction and 2.5times acceleration in real-hardware inference, while maintaining reconstruction accuracy above 98\% of its full-precision counterpart. This demonstrates the vast advantages and practicality of QuantVGGT in resource-constrained scenarios. Our code is released in https://github.com/wlfeng0509/QuantVGGT.

Learning-based multi-view stereo (MVS) methods deal with predicting accurate depth maps to achieve an accurate and complete 3D representation. Despite the excellent performance, existing methods ignore the fact that a suitable depth geometry is also critical in MVS. In this paper, we demonstrate that different depth geometries have significant performance gaps, even using the same depth prediction error. Therefore, we introduce an ideal depth geometry composed of Saddle-Shaped Cells, whose predicted depth map oscillates upward and downward around the ground-truth surface, rather than maintaining a continuous and smooth depth plane. To achieve it, we develop a coarse-to-fine framework called Dual-MVSNet (DMVSNet), which can produce an oscillating depth plane. Technically, we predict two depth values for each pixel (Dual-Depth), and propose a novel loss function and a checkerboard-shaped selecting strategy to constrain the predicted depth geometry. Compared to existing methods,DMVSNet achieves a high rank on the DTU benchmark and obtains the top performance on challenging scenes of Tanks and Temples, demonstrating its strong performance and generalization ability. Our method also points to a new research direction for considering depth geometry in MVS.

This work addresses cross-view camera pose estimation, i.e., determining the 3-Degrees-of-Freedom camera pose of a given ground-level image w.r.t. an aerial image of the local area. We propose SliceMatch, which consists of ground and aerial feature extractors, feature aggregators, and a pose predictor. The feature extractors extract dense features from the ground and aerial images. Given a set of candidate camera poses, the feature aggregators construct a single ground descriptor and a set of pose-dependent aerial descriptors. Notably, our novel aerial feature aggregator has a cross-view attention module for ground-view guided aerial feature selection and utilizes the geometric projection of the ground camera's viewing frustum on the aerial image to pool features. The efficient construction of aerial descriptors is achieved using precomputed masks. SliceMatch is trained using contrastive learning and pose estimation is formulated as a similarity comparison between the ground descriptor and the aerial descriptors. Compared to the state-of-the-art, SliceMatch achieves a 19% lower median localization error on the VIGOR benchmark using the same VGG16 backbone at 150 frames per second, and a 50% lower error when using a ResNet50 backbone.

Large Language Models (LLMs) often produce fluent yet factually incorrect statements-a phenomenon known as hallucination-posing serious risks in high-stakes domains. We present Layer-wise Semantic Dynamics (LSD), a geometric framework for hallucination detection that analyzes the evolution of hidden-state semantics across transformer layers. Unlike prior methods that rely on multiple sampling passes or external verification sources, LSD operates intrinsically within the model's representational space. Using margin-based contrastive learning, LSD aligns hidden activations with ground-truth embeddings derived from a factual encoder, revealing a distinct separation in semantic trajectories: factual responses preserve stable alignment, while hallucinations exhibit pronounced semantic drift across depth. Evaluated on the TruthfulQA and synthetic factual-hallucination datasets, LSD achieves an F1-score of 0.92, AUROC of 0.96, and clustering accuracy of 0.89, outperforming SelfCheckGPT and Semantic Entropy baselines while requiring only a single forward pass. This efficiency yields a 5-20x speedup over sampling-based methods without sacrificing precision or interpretability. LSD offers a scalable, model-agnostic mechanism for real-time hallucination monitoring and provides new insights into the geometry of factual consistency within large language models.

Learning-based 3D visual geometry models have benefited substantially from large-scale transformers. Among these, StreamVGGT leverages frame-wise causal attention for strong streaming reconstruction, but suffers from unbounded KV cache growth, leading to escalating memory consumption and inference latency as input frames accumulate. We propose XStreamVGGT, a tuning-free approach that systematically compresses the KV cache through joint pruning and quantization, enabling extremely memory-efficient streaming inference. Specifically, redundant KVs originating from multi-view inputs are pruned through efficient token importance identification, enabling a fixed memory budget. Leveraging the unique distribution of KV tensors, we incorporate KV quantization to further reduce memory consumption. Extensive evaluations show that XStreamVGGT achieves mostly negligible performance degradation while substantially reducing memory usage by 4.42times and accelerating inference by 5.48times, enabling scalable and practical streaming 3D applications. The code is available at https://github.com/ywh187/XStreamVGGT/.

Structure-from-motion (SfM) is a long-standing problem in the computer vision community, which aims to reconstruct the camera poses and 3D structure of a scene from a set of unconstrained 2D images. Classical frameworks solve this problem in an incremental manner by detecting and matching keypoints, registering images, triangulating 3D points, and conducting bundle adjustment. Recent research efforts have predominantly revolved around harnessing the power of deep learning techniques to enhance specific elements (e.g., keypoint matching), but are still based on the original, non-differentiable pipeline. Instead, we propose a new deep pipeline VGGSfM, where each component is fully differentiable and thus can be trained in an end-to-end manner. To this end, we introduce new mechanisms and simplifications. First, we build on recent advances in deep 2D point tracking to extract reliable pixel-accurate tracks, which eliminates the need for chaining pairwise matches. Furthermore, we recover all cameras simultaneously based on the image and track features instead of gradually registering cameras. Finally, we optimise the cameras and triangulate 3D points via a differentiable bundle adjustment layer. We attain state-of-the-art performance on three popular datasets, CO3D, IMC Phototourism, and ETH3D.

Geometry problem solving has attracted much attention in the NLP community recently. The task is challenging as it requires abstract problem understanding and symbolic reasoning with axiomatic knowledge. However, current datasets are either small in scale or not publicly available. Thus, we construct a new large-scale benchmark, Geometry3K, consisting of 3,002 geometry problems with dense annotation in formal language. We further propose a novel geometry solving approach with formal language and symbolic reasoning, called Interpretable Geometry Problem Solver (Inter-GPS). Inter-GPS first parses the problem text and diagram into formal language automatically via rule-based text parsing and neural object detecting, respectively. Unlike implicit learning in existing methods, Inter-GPS incorporates theorem knowledge as conditional rules and performs symbolic reasoning step by step. Also, a theorem predictor is designed to infer the theorem application sequence fed to the symbolic solver for the more efficient and reasonable searching path. Extensive experiments on the Geometry3K and GEOS datasets demonstrate that Inter-GPS achieves significant improvements over existing methods. The project with code and data is available at https://lupantech.github.io/inter-gps.

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

An open problem in mobile manipulation is how to represent objects and scenes in a unified manner, so that robots can use it both for navigating in the environment and manipulating objects. The latter requires capturing intricate geometry while understanding fine-grained semantics, whereas the former involves capturing the complexity inherit to an expansive physical scale. In this work, we present GeFF (Generalizable Feature Fields), a scene-level generalizable neural feature field that acts as a unified representation for both navigation and manipulation that performs in real-time. To do so, we treat generative novel view synthesis as a pre-training task, and then align the resulting rich scene priors with natural language via CLIP feature distillation. We demonstrate the effectiveness of this approach by deploying GeFF on a quadrupedal robot equipped with a manipulator. We evaluate GeFF's ability to generalize to open-set objects as well as running time, when performing open-vocabulary mobile manipulation in dynamic scenes.

The aerodynamic coefficients of aircrafts are significantly impacted by its geometry, especially when the angle of attack (AoA) is large. In the field of aerodynamics, traditional polynomial-based parameterization uses as few parameters as possible to describe the geometry of an airfoil. However, because the 3D geometry of a wing is more complicated than the 2D airfoil, polynomial-based parameterizations have difficulty in accurately representing the entire shape of a wing in 3D space. Existing deep learning-based methods can extract massive latent neural representations for the shape of 2D airfoils or 2D slices of wings. Recent studies highlight that directly taking geometric features as inputs to the neural networks can improve the accuracy of predicted aerodynamic coefficients. Motivated by geometry theory, we propose to incorporate Riemannian geometric features for learning Coefficient of Pressure (CP) distributions on wing surfaces. Our method calculates geometric features (Riemannian metric, connection, and curvature) and further inputs the geometric features, coordinates and flight conditions into a deep learning model to predict the CP distribution. Experimental results show that our method, compared to state-of-the-art Deep Attention Network (DAN), reduces the predicted mean square error (MSE) of CP by an average of 8.41% for the DLR-F11 aircraft test set.

Significant advancements have been made in developing parametric models for digital humans, with various approaches concentrating on parts such as the human body, hand, or face. Nevertheless, connectors such as the neck have been overlooked in these models, with rich anatomical priors often unutilized. In this paper, we introduce HACK (Head-And-neCK), a novel parametric model for constructing the head and cervical region of digital humans. Our model seeks to disentangle the full spectrum of neck and larynx motions, facial expressions, and appearance variations, providing personalized and anatomically consistent controls, particularly for the neck regions. To build our HACK model, we acquire a comprehensive multi-modal dataset of the head and neck under various facial expressions. We employ a 3D ultrasound imaging scheme to extract the inner biomechanical structures, namely the precise 3D rotation information of the seven vertebrae of the cervical spine. We then adopt a multi-view photometric approach to capture the geometry and physically-based textures of diverse subjects, who exhibit a diverse range of static expressions as well as sequential head-and-neck movements. Using the multi-modal dataset, we train the parametric HACK model by separating the 3D head and neck depiction into various shape, pose, expression, and larynx blendshapes from the neutral expression and the rest skeletal pose. We adopt an anatomically-consistent skeletal design for the cervical region, and the expression is linked to facial action units for artist-friendly controls. HACK addresses the head and neck as a unified entity, offering more accurate and expressive controls, with a new level of realism, particularly for the neck regions. This approach has significant benefits for numerous applications and enables inter-correlation analysis between head and neck for fine-grained motion synthesis and transfer.

Profile extrusion is a continuous production process for manufacturing plastic profiles from molten polymer. Especially interesting is the design of the die, through which the melt is pressed to attain the desired shape. However, due to an inhomogeneous velocity distribution at the die exit or residual stresses inside the extrudate, the final shape of the manufactured part often deviates from the desired one. To avoid these deviations, the shape of the die can be computationally optimized, which has already been investigated in the literature using classical optimization approaches. A new approach in the field of shape optimization is the utilization of Reinforcement Learning (RL) as a learning-based optimization algorithm. RL is based on trial-and-error interactions of an agent with an environment. For each action, the agent is rewarded and informed about the subsequent state of the environment. While not necessarily superior to classical, e.g., gradient-based or evolutionary, optimization algorithms for one single problem, RL techniques are expected to perform especially well when similar optimization tasks are repeated since the agent learns a more general strategy for generating optimal shapes instead of concentrating on just one single problem. In this work, we investigate this approach by applying it to two 2D test cases. The flow-channel geometry can be modified by the RL agent using so-called Free-Form Deformation, a method where the computational mesh is embedded into a transformation spline, which is then manipulated based on the control-point positions. In particular, we investigate the impact of utilizing different agents on the training progress and the potential of wall time saving by utilizing multiple environments during training.

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

Affordance, defined as the potential actions that an object offers, is crucial for robotic manipulation tasks. A deep understanding of affordance can lead to more intelligent AI systems. For example, such knowledge directs an agent to grasp a knife by the handle for cutting and by the blade when passing it to someone. In this paper, we present a streamlined affordance learning system that encompasses data collection, effective model training, and robot deployment. First, we collect training data from egocentric videos in an automatic manner. Different from previous methods that focus only on the object graspable affordance and represent it as coarse heatmaps, we cover both graspable (e.g., object handles) and functional affordances (e.g., knife blades, hammer heads) and extract data with precise segmentation masks. We then propose an effective model, termed Geometry-guided Affordance Transformer (GKT), to train on the collected data. GKT integrates an innovative Depth Feature Injector (DFI) to incorporate 3D shape and geometric priors, enhancing the model's understanding of affordances. To enable affordance-oriented manipulation, we further introduce Aff-Grasp, a framework that combines GKT with a grasp generation model. For comprehensive evaluation, we create an affordance evaluation dataset with pixel-wise annotations, and design real-world tasks for robot experiments. The results show that GKT surpasses the state-of-the-art by 15.9% in mIoU, and Aff-Grasp achieves high success rates of 95.5% in affordance prediction and 77.1% in successful grasping among 179 trials, including evaluations with seen, unseen objects, and cluttered scenes.

Simulating physical systems governed by Lagrangian dynamics often entails solving partial differential equations (PDEs) over high-resolution spatial domains, leading to significant computational expense. Reduced-order modeling (ROM) mitigates this cost by evolving low-dimensional latent representations of the underlying system. While neural ROMs enable querying solutions from latent states at arbitrary spatial points, their latent states typically represent the global domain and struggle to capture localized, highly dynamic behaviors such as fluids. We propose a sampling-based reduction framework that evolves Lagrangian systems directly in physical space over the particles themselves, reducing the number of active degrees of freedom via data-driven neural PDE operators. To enable querying at arbitrary spatial locations, we introduce a learnable kernel parameterization that uses local spatial information from time-evolved sample particles to infer the underlying solution manifold. Empirically, our approach achieves a 6.6x to 32x reduction in input dimensionality while maintaining high-fidelity evaluations across diverse Lagrangian regimes, including fluid flows, granular media, and elastoplastic dynamics. We refer to this framework as GIOROM (Geometry-Informed Reduced-Order Modeling). All code and data are available at: https://github.com/HrishikeshVish/GIOROM

Novel view synthesis aims to render unseen views given a set of calibrated images. In practical applications, the coverage, appearance or geometry of the scene may change over time, with new images continuously being captured. Efficiently incorporating such continuous change is an open challenge. Standard NeRF benchmarks only involve scene coverage expansion. To study other practical scene changes, we propose a new dataset, World Across Time (WAT), consisting of scenes that change in appearance and geometry over time. We also propose a simple yet effective method, CLNeRF, which introduces continual learning (CL) to Neural Radiance Fields (NeRFs). CLNeRF combines generative replay and the Instant Neural Graphics Primitives (NGP) architecture to effectively prevent catastrophic forgetting and efficiently update the model when new data arrives. We also add trainable appearance and geometry embeddings to NGP, allowing a single compact model to handle complex scene changes. Without the need to store historical images, CLNeRF trained sequentially over multiple scans of a changing scene performs on-par with the upper bound model trained on all scans at once. Compared to other CL baselines CLNeRF performs much better across standard benchmarks and WAT. The source code, and the WAT dataset are available at https://github.com/IntelLabs/CLNeRF. Video presentation is available at: https://youtu.be/nLRt6OoDGq0?si=8yD6k-8MMBJInQPs

Geometry and color information provided by the point clouds are both crucial for 3D scene understanding. Two pieces of information characterize the different aspects of point clouds, but existing methods lack an elaborate design for the discrimination and relevance. Hence we explore a 3D self-supervised paradigm that can better utilize the relations of point cloud information. Specifically, we propose a universal 3D scene pre-training framework via Geometry-Color Contrast (Point-GCC), which aligns geometry and color information using a Siamese network. To take care of actual application tasks, we design (i) hierarchical supervision with point-level contrast and reconstruct and object-level contrast based on the novel deep clustering module to close the gap between pre-training and downstream tasks; (ii) architecture-agnostic backbone to adapt for various downstream models. Benefiting from the object-level representation associated with downstream tasks, Point-GCC can directly evaluate model performance and the result demonstrates the effectiveness of our methods. Transfer learning results on a wide range of tasks also show consistent improvements across all datasets. e.g., new state-of-the-art object detection results on SUN RGB-D and S3DIS datasets. Codes will be released at https://github.com/Asterisci/Point-GCC.

Automated assembly of 3D fractures is essential in orthopedics, archaeology, and our daily life. This paper presents Jigsaw, a novel framework for assembling physically broken 3D objects from multiple pieces. Our approach leverages hierarchical features of global and local geometry to match and align the fracture surfaces. Our framework consists of four components: (1) front-end point feature extractor with attention layers, (2) surface segmentation to separate fracture and original parts, (3) multi-parts matching to find correspondences among fracture surface points, and (4) robust global alignment to recover the global poses of the pieces. We show how to jointly learn segmentation and matching and seamlessly integrate feature matching and rigidity constraints. We evaluate Jigsaw on the Breaking Bad dataset and achieve superior performance compared to state-of-the-art methods. Our method also generalizes well to diverse fracture modes, objects, and unseen instances. To the best of our knowledge, this is the first learning-based method designed specifically for 3D fracture assembly over multiple pieces. Our code is available at https://jiaxin-lu.github.io/Jigsaw/.

We propose a method to learn a high-quality implicit 3D head avatar from a monocular RGB video captured in the wild. The learnt avatar is driven by a parametric face model to achieve user-controlled facial expressions and head poses. Our hybrid pipeline combines the geometry prior and dynamic tracking of a 3DMM with a neural radiance field to achieve fine-grained control and photorealism. To reduce over-smoothing and improve out-of-model expressions synthesis, we propose to predict local features anchored on the 3DMM geometry. These learnt features are driven by 3DMM deformation and interpolated in 3D space to yield the volumetric radiance at a designated query point. We further show that using a Convolutional Neural Network in the UV space is critical in incorporating spatial context and producing representative local features. Extensive experiments show that we are able to reconstruct high-quality avatars, with more accurate expression-dependent details, good generalization to out-of-training expressions, and quantitatively superior renderings compared to other state-of-the-art approaches.