Daily Papers

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.

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/.

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

Recent text-to-3D methods employing diffusion models have made significant advancements in 3D human generation. However, these approaches face challenges due to the limitations of the text-to-image diffusion model, which lacks an understanding of 3D structures. Consequently, these methods struggle to achieve high-quality human generation, resulting in smooth geometry and cartoon-like appearances. In this paper, we observed that fine-tuning text-to-image diffusion models with normal maps enables their adaptation into text-to-normal diffusion models, which enhances the 2D perception of 3D geometry while preserving the priors learned from large-scale datasets. Therefore, we propose HumanNorm, a novel approach for high-quality and realistic 3D human generation by learning the normal diffusion model including a normal-adapted diffusion model and a normal-aligned diffusion model. The normal-adapted diffusion model can generate high-fidelity normal maps corresponding to prompts with view-dependent text. The normal-aligned diffusion model learns to generate color images aligned with the normal maps, thereby transforming physical geometry details into realistic appearance. Leveraging the proposed normal diffusion model, we devise a progressive geometry generation strategy and coarse-to-fine texture generation strategy to enhance the efficiency and robustness of 3D human generation. Comprehensive experiments substantiate our method's ability to generate 3D humans with intricate geometry and realistic appearances, significantly outperforming existing text-to-3D methods in both geometry and texture quality. The project page of HumanNorm is https://humannorm.github.io/.

With advancements in satellite imaging technology, acquiring high-resolution multi-view satellite imagery has become increasingly accessible, enabling rapid and location-independent ground model reconstruction. However, traditional stereo matching methods struggle to capture fine details, and while neural radiance fields (NeRFs) achieve high-quality reconstructions, their training time is prohibitively long. Moreover, challenges such as low visibility of building facades, illumination and style differences between pixels, and weakly textured regions in satellite imagery further make it hard to reconstruct reasonable terrain geometry and detailed building facades. To address these issues, we propose Sat-DN, a novel framework leveraging a progressively trained multi-resolution hash grid reconstruction architecture with explicit depth guidance and surface normal consistency constraints to enhance reconstruction quality. The multi-resolution hash grid accelerates training, while the progressive strategy incrementally increases the learning frequency, using coarse low-frequency geometry to guide the reconstruction of fine high-frequency details. The depth and normal constraints ensure a clear building outline and correct planar distribution. Extensive experiments on the DFC2019 dataset demonstrate that Sat-DN outperforms existing methods, achieving state-of-the-art results in both qualitative and quantitative evaluations. The code is available at https://github.com/costune/SatDN.

In this paper, we present Surf-D, a novel method for generating high-quality 3D shapes as Surfaces with arbitrary topologies using Diffusion models. Specifically, we adopt Unsigned Distance Field (UDF) as the surface representation, as it excels in handling arbitrary topologies, enabling the generation of complex shapes. While the prior methods explored shape generation with different representations, they suffer from limited topologies and geometry details. Moreover, it's non-trivial to directly extend prior diffusion models to UDF because they lack spatial continuity due to the discrete volume structure. However, UDF requires accurate gradients for mesh extraction and learning. To tackle the issues, we first leverage a point-based auto-encoder to learn a compact latent space, which supports gradient querying for any input point through differentiation to effectively capture intricate geometry at a high resolution. Since the learning difficulty for various shapes can differ, a curriculum learning strategy is employed to efficiently embed various surfaces, enhancing the whole embedding process. With pretrained shape latent space, we employ a latent diffusion model to acquire the distribution of various shapes. Our approach demonstrates superior performance in shape generation across multiple modalities and conducts extensive experiments in unconditional generation, category conditional generation, 3D reconstruction from images, and text-to-shape tasks.

We propose a novel method called SHS-Net for oriented normal estimation of point clouds by learning signed hyper surfaces, which can accurately predict normals with global consistent orientation from various point clouds. Almost all existing methods estimate oriented normals through a two-stage pipeline, i.e., unoriented normal estimation and normal orientation, and each step is implemented by a separate algorithm. However, previous methods are sensitive to parameter settings, resulting in poor results from point clouds with noise, density variations and complex geometries. In this work, we introduce signed hyper surfaces (SHS), which are parameterized by multi-layer perceptron (MLP) layers, to learn to estimate oriented normals from point clouds in an end-to-end manner. The signed hyper surfaces are implicitly learned in a high-dimensional feature space where the local and global information is aggregated. Specifically, we introduce a patch encoding module and a shape encoding module to encode a 3D point cloud into a local latent code and a global latent code, respectively. Then, an attention-weighted normal prediction module is proposed as a decoder, which takes the local and global latent codes as input to predict oriented normals. Experimental results show that our SHS-Net outperforms the state-of-the-art methods in both unoriented and oriented normal estimation on the widely used benchmarks. The code, data and pretrained models are publicly available.

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

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

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

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

When learning simulations for modeling physical phenomena in industrial designs, geometrical variabilities are of prime interest. While classical regression techniques prove effective for parameterized geometries, practical scenarios often involve the absence of shape parametrization during the inference stage, leaving us with only mesh discretizations as available data. Learning simulations from such mesh-based representations poses significant challenges, with recent advances relying heavily on deep graph neural networks to overcome the limitations of conventional machine learning approaches. Despite their promising results, graph neural networks exhibit certain drawbacks, including their dependency on extensive datasets and limitations in providing built-in predictive uncertainties or handling large meshes. In this work, we propose a machine learning method that do not rely on graph neural networks. Complex geometrical shapes and variations with fixed topology are dealt with using well-known mesh morphing onto a common support, combined with classical dimensionality reduction techniques and Gaussian processes. The proposed methodology can easily deal with large meshes without the need for explicit shape parameterization and provides crucial predictive uncertainties, which are essential for informed decision-making. In the considered numerical experiments, the proposed method is competitive with respect to existing graph neural networks, regarding training efficiency and accuracy of the predictions.

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

For non-rigid objects, predicting the 3D shape from 2D keypoint observations is ill-posed due to occlusions, and the need to disentangle changes in viewpoint and changes in shape. This challenge has often been addressed by embedding low-rank constraints into specialized models. These models can be hard to train, as they depend on finding a canonical way of aligning observations, before they can learn detailed geometry. These constraints have limited the reconstruction quality. We show that generic, high capacity models, trained with an unsupervised loss, allow for more accurate predicted shapes. In particular, applying low-rank constraints to localized subsets of the full shape allows the high capacity to be suitably constrained. We reduce the state-of-the-art reconstruction error on the S-Up3D dataset by over 70%.

3D room layout estimation by a single panorama using deep neural networks has made great progress. However, previous approaches can not obtain efficient geometry awareness of room layout with the only latitude of boundaries or horizon-depth. We present that using horizon-depth along with room height can obtain omnidirectional-geometry awareness of room layout in both horizontal and vertical directions. In addition, we propose a planar-geometry aware loss function with normals and gradients of normals to supervise the planeness of walls and turning of corners. We propose an efficient network, LGT-Net, for room layout estimation, which contains a novel Transformer architecture called SWG-Transformer to model geometry relations. SWG-Transformer consists of (Shifted) Window Blocks and Global Blocks to combine the local and global geometry relations. Moreover, we design a novel relative position embedding of Transformer to enhance the spatial identification ability for the panorama. Experiments show that the proposed LGT-Net achieves better performance than current state-of-the-arts (SOTA) on benchmark datasets.

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

In this work, we introduce Wonder3D, a novel method for efficiently generating high-fidelity textured meshes from single-view images.Recent methods based on Score Distillation Sampling (SDS) have shown the potential to recover 3D geometry from 2D diffusion priors, but they typically suffer from time-consuming per-shape optimization and inconsistent geometry. In contrast, certain works directly produce 3D information via fast network inferences, but their results are often of low quality and lack geometric details. To holistically improve the quality, consistency, and efficiency of image-to-3D tasks, we propose a cross-domain diffusion model that generates multi-view normal maps and the corresponding color images. To ensure consistency, we employ a multi-view cross-domain attention mechanism that facilitates information exchange across views and modalities. Lastly, we introduce a geometry-aware normal fusion algorithm that extracts high-quality surfaces from the multi-view 2D representations. Our extensive evaluations demonstrate that our method achieves high-quality reconstruction results, robust generalization, and reasonably good efficiency compared to prior works.

Recent advances in discriminative and generative pretraining have yielded geometry estimation models with strong generalization capabilities. While discriminative monocular geometry estimation methods rely on large-scale fine-tuning data to achieve zero-shot generalization, several generative-based paradigms show the potential of achieving impressive generalization performance on unseen scenes by leveraging pre-trained diffusion models and fine-tuning on even a small scale of synthetic training data. Frustratingly, these models are trained with different recipes on different datasets, making it hard to find out the critical factors that determine the evaluation performance. Besides, current geometry evaluation benchmarks have two main drawbacks that may prevent the development of the field, i.e., limited scene diversity and unfavorable label quality. To resolve the above issues, (1) we build fair and strong baselines in a unified codebase for evaluating and analyzing the geometry estimation models; (2) we evaluate monocular geometry estimators on more challenging benchmarks for geometry estimation task with diverse scenes and high-quality annotations. Our results reveal that pre-trained using large data, discriminative models such as DINOv2, can outperform generative counterparts with a small amount of high-quality synthetic data under the same training configuration, which suggests that fine-tuning data quality is a more important factor than the data scale and model architecture. Our observation also raises a question: if simply fine-tuning a general vision model such as DINOv2 using a small amount of synthetic depth data produces SOTA results, do we really need complex generative models for depth estimation? We believe this work can propel advancements in geometry estimation tasks as well as a wide range of downstream applications.

Recent advances in language and vision have demonstrated that scaling up model capacity consistently improves performance across diverse tasks. In 3D visual geometry reconstruction, large-scale training has likewise proven effective for learning versatile representations. However, further scaling of 3D models is challenging due to the complexity of geometric supervision and the diversity of 3D data. To overcome these limitations, we propose MoRE, a dense 3D visual foundation model based on a Mixture-of-Experts (MoE) architecture that dynamically routes features to task-specific experts, allowing them to specialize in complementary data aspects and enhance both scalability and adaptability. Aiming to improve robustness under real-world conditions, MoRE incorporates a confidence-based depth refinement module that stabilizes and refines geometric estimation. In addition, it integrates dense semantic features with globally aligned 3D backbone representations for high-fidelity surface normal prediction. MoRE is further optimized with tailored loss functions to ensure robust learning across diverse inputs and multiple geometric tasks. Extensive experiments demonstrate that MoRE achieves state-of-the-art performance across multiple benchmarks and supports effective downstream applications without extra computation.

3D plane reconstruction from a single image is a crucial yet challenging topic in 3D computer vision. Previous state-of-the-art (SOTA) methods have focused on training their system on a single dataset from either indoor or outdoor domain, limiting their generalizability across diverse testing data. In this work, we introduce a novel framework dubbed ZeroPlane, a Transformer-based model targeting zero-shot 3D plane detection and reconstruction from a single image, over diverse domains and environments. To enable data-driven models across multiple domains, we have curated a large-scale planar benchmark, comprising over 14 datasets and 560,000 high-resolution, dense planar annotations for diverse indoor and outdoor scenes. To address the challenge of achieving desirable planar geometry on multi-dataset training, we propose to disentangle the representation of plane normal and offset, and employ an exemplar-guided, classification-then-regression paradigm to learn plane and offset respectively. Additionally, we employ advanced backbones as image encoder, and present an effective pixel-geometry-enhanced plane embedding module to further facilitate planar reconstruction. Extensive experiments across multiple zero-shot evaluation datasets have demonstrated that our approach significantly outperforms previous methods on both reconstruction accuracy and generalizability, especially over in-the-wild data. Our code and data are available at: https://github.com/jcliu0428/ZeroPlane.

Polygon meshes are an efficient representation of 3D geometry, and are of central importance in computer graphics, robotics and games development. Existing learning-based approaches have avoided the challenges of working with 3D meshes, instead using alternative object representations that are more compatible with neural architectures and training approaches. We present an approach which models the mesh directly, predicting mesh vertices and faces sequentially using a Transformer-based architecture. Our model can condition on a range of inputs, including object classes, voxels, and images, and because the model is probabilistic it can produce samples that capture uncertainty in ambiguous scenarios. We show that the model is capable of producing high-quality, usable meshes, and establish log-likelihood benchmarks for the mesh-modelling task. We also evaluate the conditional models on surface reconstruction metrics against alternative methods, and demonstrate competitive performance despite not training directly on this task.

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.

Robust and efficient local feature matching plays a crucial role in applications such as SLAM and visual localization for robotics. Despite great progress, it is still very challenging to extract robust and discriminative visual features in scenarios with drastic lighting changes, low texture areas, or repetitive patterns. In this paper, we propose a new lightweight network called LiftFeat, which lifts the robustness of raw descriptor by aggregating 3D geometric feature. Specifically, we first adopt a pre-trained monocular depth estimation model to generate pseudo surface normal label, supervising the extraction of 3D geometric feature in terms of predicted surface normal. We then design a 3D geometry-aware feature lifting module to fuse surface normal feature with raw 2D descriptor feature. Integrating such 3D geometric feature enhances the discriminative ability of 2D feature description in extreme conditions. Extensive experimental results on relative pose estimation, homography estimation, and visual localization tasks, demonstrate that our LiftFeat outperforms some lightweight state-of-the-art methods. Code will be released at : https://github.com/lyp-deeplearning/LiftFeat.

Despite the growing demand for accurate surface normal estimation models, existing methods use general-purpose dense prediction models, adopting the same inductive biases as other tasks. In this paper, we discuss the inductive biases needed for surface normal estimation and propose to (1) utilize the per-pixel ray direction and (2) encode the relationship between neighboring surface normals by learning their relative rotation. The proposed method can generate crisp - yet, piecewise smooth - predictions for challenging in-the-wild images of arbitrary resolution and aspect ratio. Compared to a recent ViT-based state-of-the-art model, our method shows a stronger generalization ability, despite being trained on an orders of magnitude smaller dataset. The code is available at https://github.com/baegwangbin/DSINE.

Lifting 2D diffusion for 3D generation is a challenging problem due to the lack of geometric prior and the complex entanglement of materials and lighting in natural images. Existing methods have shown promise by first creating the geometry through score-distillation sampling (SDS) applied to rendered surface normals, followed by appearance modeling. However, relying on a 2D RGB diffusion model to optimize surface normals is suboptimal due to the distribution discrepancy between natural images and normals maps, leading to instability in optimization. In this paper, recognizing that the normal and depth information effectively describe scene geometry and be automatically estimated from images, we propose to learn a generalizable Normal-Depth diffusion model for 3D generation. We achieve this by training on the large-scale LAION dataset together with the generalizable image-to-depth and normal prior models. In an attempt to alleviate the mixed illumination effects in the generated materials, we introduce an albedo diffusion model to impose data-driven constraints on the albedo component. Our experiments show that when integrated into existing text-to-3D pipelines, our models significantly enhance the detail richness, achieving state-of-the-art results. Our project page is https://lingtengqiu.github.io/RichDreamer/.

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

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

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

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

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

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

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

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.

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

The rapid development of Large Multimodal Models (LMMs) has led to remarkable progress in 2D visual understanding; however, extending these capabilities to 3D scene understanding remains a significant challenge. Existing approaches predominantly rely on text-only supervision, which fails to provide the geometric constraints required for learning robust 3D spatial representations. In this paper, we introduce Reg3D, a novel Reconstructive Geometry Instruction Tuning framework that addresses this limitation by incorporating geometry-aware supervision directly into the training process. Our key insight is that effective 3D understanding necessitates reconstructing underlying geometric structures rather than merely describing them. Unlike existing methods that inject 3D information solely at the input level, Reg3D adopts a dual-supervision paradigm that leverages 3D geometric information both as input and as explicit learning targets. Specifically, we design complementary object-level and frame-level reconstruction tasks within a dual-encoder architecture, enforcing geometric consistency to encourage the development of spatial reasoning capabilities. Extensive experiments on ScanQA, Scan2Cap, ScanRefer, and SQA3D demonstrate that Reg3D delivers substantial performance improvements, establishing a new training paradigm for spatially aware multimodal models.

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.

We develop information geometric techniques to understand the representations learned by deep networks when they are trained on different tasks using supervised, meta-, semi-supervised and contrastive learning. We shed light on the following phenomena that relate to the structure of the space of tasks: (1) the manifold of probabilistic models trained on different tasks using different representation learning methods is effectively low-dimensional; (2) supervised learning on one task results in a surprising amount of progress even on seemingly dissimilar tasks; progress on other tasks is larger if the training task has diverse classes; (3) the structure of the space of tasks indicated by our analysis is consistent with parts of the Wordnet phylogenetic tree; (4) episodic meta-learning algorithms and supervised learning traverse different trajectories during training but they fit similar models eventually; (5) contrastive and semi-supervised learning methods traverse trajectories similar to those of supervised learning. We use classification tasks constructed from the CIFAR-10 and Imagenet datasets to study these phenomena.

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

The scarcity of large-scale 3D-text paired data poses a great challenge on open vocabulary 3D scene understanding, and hence it is popular to leverage internet-scale 2D data and transfer their open vocabulary capabilities to 3D models through knowledge distillation. However, the existing distillation-based 3D scene understanding approaches rely on the representation capacity of 2D models, disregarding the exploration of geometric priors and inherent representational advantages offered by 3D data. In this paper, we propose an effective approach, namely Geometry Guided Self-Distillation (GGSD), to learn superior 3D representations from 2D pre-trained models. Specifically, we first design a geometry guided distillation module to distill knowledge from 2D models, and then leverage the 3D geometric priors to alleviate the inherent noise in 2D models and enhance the representation learning process. Due to the advantages of 3D representation, the performance of the distilled 3D student model can significantly surpass that of the 2D teacher model. This motivates us to further leverage the representation advantages of 3D data through self-distillation. As a result, our proposed GGSD approach outperforms the existing open vocabulary 3D scene understanding methods by a large margin, as demonstrated by our experiments on both indoor and outdoor benchmark datasets.

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

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

With the advent of large-scale 3D datasets, feed-forward 3D generative models, such as the Large Reconstruction Model (LRM), have gained significant attention and achieved remarkable success. However, we observe that RGB images often lead to conflicting training objectives and lack the necessary clarity for geometry reconstruction. In this paper, we revisit the inductive biases associated with mesh reconstruction and introduce DiMeR, a novel disentangled dual-stream feed-forward model for sparse-view mesh reconstruction. The key idea is to disentangle both the input and framework into geometry and texture parts, thereby reducing the training difficulty for each part according to the Principle of Occam's Razor. Given that normal maps are strictly consistent with geometry and accurately capture surface variations, we utilize normal maps as exclusive input for the geometry branch to reduce the complexity between the network's input and output. Moreover, we improve the mesh extraction algorithm to introduce 3D ground truth supervision. As for texture branch, we use RGB images as input to obtain the textured mesh. Overall, DiMeR demonstrates robust capabilities across various tasks, including sparse-view reconstruction, single-image-to-3D, and text-to-3D. Numerous experiments show that DiMeR significantly outperforms previous methods, achieving over 30% improvement in Chamfer Distance on the GSO and OmniObject3D dataset.

We introduce GeoDANO, a geometric vision-language model (VLM) with a domain-agnostic vision encoder, for solving plane geometry problems. Although VLMs have been employed for solving geometry problems, their ability to recognize geometric features remains insufficiently analyzed. To address this gap, we propose a benchmark that evaluates the recognition of visual geometric features, including primitives such as dots and lines, and relations such as orthogonality. Our preliminary study shows that vision encoders often used in general-purpose VLMs, e.g., OpenCLIP, fail to detect these features and struggle to generalize across domains. We develop GeoCLIP, a CLIP based model trained on synthetic geometric diagram-caption pairs to overcome the limitation. Benchmark results show that GeoCLIP outperforms existing vision encoders in recognizing geometric features. We then propose our VLM, GeoDANO, which augments GeoCLIP with a domain adaptation strategy for unseen diagram styles. GeoDANO outperforms specialized methods for plane geometry problems and GPT-4o on MathVerse.

Novel view synthesis and 3D modeling using implicit neural field representation are shown to be very effective for calibrated multi-view cameras. Such representations are known to benefit from additional geometric and semantic supervision. Most existing methods that exploit additional supervision require dense pixel-wise labels or localized scene priors. These methods cannot benefit from high-level vague scene priors provided in terms of scenes' descriptions. In this work, we aim to leverage the geometric prior of Manhattan scenes to improve the implicit neural radiance field representations. More precisely, we assume that only the knowledge of the indoor scene (under investigation) being Manhattan is known -- with no additional information whatsoever -- with an unknown Manhattan coordinate frame. Such high-level prior is used to self-supervise the surface normals derived explicitly in the implicit neural fields. Our modeling allows us to cluster the derived normals and exploit their orthogonality constraints for self-supervision. Our exhaustive experiments on datasets of diverse indoor scenes demonstrate the significant benefit of the proposed method over the established baselines. The source code will be available at https://github.com/nikola3794/normal-clustering-nerf.

We present a neural architecture that takes as input a 2D or 3D shape and outputs a program that generates the shape. The instructions in our program are based on constructive solid geometry principles, i.e., a set of boolean operations on shape primitives defined recursively. Bottom-up techniques for this shape parsing task rely on primitive detection and are inherently slow since the search space over possible primitive combinations is large. In contrast, our model uses a recurrent neural network that parses the input shape in a top-down manner, which is significantly faster and yields a compact and easy-to-interpret sequence of modeling instructions. Our model is also more effective as a shape detector compared to existing state-of-the-art detection techniques. We finally demonstrate that our network can be trained on novel datasets without ground-truth program annotations through policy gradient techniques.

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

Deep neural networks are prone to adversarial examples that maliciously alter the network's outcome. Due to the increasing popularity of 3D sensors in safety-critical systems and the vast deployment of deep learning models for 3D point sets, there is a growing interest in adversarial attacks and defenses for such models. So far, the research has focused on the semantic level, namely, deep point cloud classifiers. However, point clouds are also widely used in a geometric-related form that includes encoding and reconstructing the geometry. In this work, we are the first to consider the problem of adversarial examples at a geometric level. In this setting, the question is how to craft a small change to a clean source point cloud that leads, after passing through an autoencoder model, to the reconstruction of a different target shape. Our attack is in sharp contrast to existing semantic attacks on 3D point clouds. While such works aim to modify the predicted label by a classifier, we alter the entire reconstructed geometry. Additionally, we demonstrate the robustness of our attack in the case of defense, where we show that remnant characteristics of the target shape are still present at the output after applying the defense to the adversarial input. Our code is publicly available at https://github.com/itailang/geometric_adv.

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.

Anomaly Detection (AD) in images is a fundamental computer vision problem and refers to identifying images and image substructures that deviate significantly from the norm. Popular AD algorithms commonly try to learn a model of normality from scratch using task specific datasets, but are limited to semi-supervised approaches employing mostly normal data due to the inaccessibility of anomalies on a large scale combined with the ambiguous nature of anomaly appearance. We follow an alternative approach and demonstrate that deep feature representations learned by discriminative models on large natural image datasets are well suited to describe normality and detect even subtle anomalies in a transfer learning setting. Our model of normality is established by fitting a multivariate Gaussian (MVG) to deep feature representations of classification networks trained on ImageNet using normal data only. By subsequently applying the Mahalanobis distance as the anomaly score we outperform the current state of the art on the public MVTec AD dataset, achieving an AUROC value of 95.8 pm 1.2 (mean pm SEM) over all 15 classes. We further investigate why the learned representations are discriminative to the AD task using Principal Component Analysis. We find that the principal components containing little variance in normal data are the ones crucial for discriminating between normal and anomalous instances. This gives a possible explanation to the often sub-par performance of AD approaches trained from scratch using normal data only. By selectively fitting a MVG to these most relevant components only, we are able to further reduce model complexity while retaining AD performance. We also investigate setting the working point by selecting acceptable False Positive Rate thresholds based on the MVG assumption. Code available at https://github.com/ORippler/gaussian-ad-mvtec

Auto-regressive models have achieved impressive results in 2D image generation by modeling joint distributions in grid space. In this paper, we extend auto-regressive models to 3D domains, and seek a stronger ability of 3D shape generation by improving auto-regressive models at capacity and scalability simultaneously. Firstly, we leverage an ensemble of publicly available 3D datasets to facilitate the training of large-scale models. It consists of a comprehensive collection of approximately 900,000 objects, with multiple properties of meshes, points, voxels, rendered images, and text captions. This diverse labeled dataset, termed Objaverse-Mix, empowers our model to learn from a wide range of object variations. However, directly applying 3D auto-regression encounters critical challenges of high computational demands on volumetric grids and ambiguous auto-regressive order along grid dimensions, resulting in inferior quality of 3D shapes. To this end, we then present a novel framework Argus3D in terms of capacity. Concretely, our approach introduces discrete representation learning based on a latent vector instead of volumetric grids, which not only reduces computational costs but also preserves essential geometric details by learning the joint distributions in a more tractable order. The capacity of conditional generation can thus be realized by simply concatenating various conditioning inputs to the latent vector, such as point clouds, categories, images, and texts. In addition, thanks to the simplicity of our model architecture, we naturally scale up our approach to a larger model with an impressive 3.6 billion parameters, further enhancing the quality of versatile 3D generation. Extensive experiments on four generation tasks demonstrate that Argus3D can synthesize diverse and faithful shapes across multiple categories, achieving remarkable performance.

Several first order stochastic optimization methods commonly used in the Euclidean domain such as stochastic gradient descent (SGD), accelerated gradient descent or variance reduced methods have already been adapted to certain Riemannian settings. However, some of the most popular of these optimization tools - namely Adam , Adagrad and the more recent Amsgrad - remain to be generalized to Riemannian manifolds. We discuss the difficulty of generalizing such adaptive schemes to the most agnostic Riemannian setting, and then provide algorithms and convergence proofs for geodesically convex objectives in the particular case of a product of Riemannian manifolds, in which adaptivity is implemented across manifolds in the cartesian product. Our generalization is tight in the sense that choosing the Euclidean space as Riemannian manifold yields the same algorithms and regret bounds as those that were already known for the standard algorithms. Experimentally, we show faster convergence and to a lower train loss value for Riemannian adaptive methods over their corresponding baselines on the realistic task of embedding the WordNet taxonomy in the Poincare ball.

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

This paper introduces an end-to-end residual network that operates entirely on the Poincar\'e ball model of hyperbolic space. Hyperbolic learning has recently shown great potential for visual understanding, but is currently only performed in the penultimate layer(s) of deep networks. All visual representations are still learned through standard Euclidean networks. In this paper we investigate how to learn hyperbolic representations of visual data directly from the pixel-level. We propose Poincar\'e ResNet, a hyperbolic counterpart of the celebrated residual network, starting from Poincar\'e 2D convolutions up to Poincar\'e residual connections. We identify three roadblocks for training convolutional networks entirely in hyperbolic space and propose a solution for each: (i) Current hyperbolic network initializations collapse to the origin, limiting their applicability in deeper networks. We provide an identity-based initialization that preserves norms over many layers. (ii) Residual networks rely heavily on batch normalization, which comes with expensive Fr\'echet mean calculations in hyperbolic space. We introduce Poincar\'e midpoint batch normalization as a faster and equally effective alternative. (iii) Due to the many intermediate operations in Poincar\'e layers, we lastly find that the computation graphs of deep learning libraries blow up, limiting our ability to train on deep hyperbolic networks. We provide manual backward derivations of core hyperbolic operations to maintain manageable computation graphs.

Existing RGB-based imitation learning approaches typically employ traditional vision encoders such as ResNet or ViT, which lack explicit 3D reasoning capabilities. Recent geometry-grounded vision models, such as VGGT~wang2025vggt, provide robust spatial understanding and are promising candidates to address this limitation. This work investigates the integration of geometry-aware visual representations into robotic manipulation. Our results suggest that incorporating the geometry-aware vision encoder into imitation learning frameworks, including ACT and DP, yields up to 6.5% improvement over standard vision encoders in success rate across single- and bi-manual manipulation tasks in both simulation and real-world settings. Despite these benefits, most geometry-grounded models require high computational cost, limiting their deployment in practical robotic systems. To address this challenge, we propose eVGGT, an efficient geometry-aware encoder distilled from VGGT. eVGGT is nearly 9 times faster and 5 times smaller than VGGT, while preserving strong 3D reasoning capabilities. Code and pretrained models will be released to facilitate further research in geometry-aware robotics.

We present a novel meta-learning approach for 6D pose estimation on unknown objects. In contrast to ``instance-level" and ``category-level" pose estimation methods, our algorithm learns object representation in a category-agnostic way, which endows it with strong generalization capabilities across object categories. Specifically, we employ a neural process-based meta-learning approach to train an encoder to capture texture and geometry of an object in a latent representation, based on very few RGB-D images and ground-truth keypoints. The latent representation is then used by a simultaneously meta-trained decoder to predict the 6D pose of the object in new images. Furthermore, we propose a novel geometry-aware decoder for the keypoint prediction using a Graph Neural Network (GNN), which explicitly takes geometric constraints specific to each object into consideration. To evaluate our algorithm, extensive experiments are conducted on the \linemod dataset, and on our new fully-annotated synthetic datasets generated from Multiple Categories in Multiple Scenes (MCMS). Experimental results demonstrate that our model performs well on unseen objects with very different shapes and appearances. Remarkably, our model also shows robust performance on occluded scenes although trained fully on data without occlusion. To our knowledge, this is the first work exploring cross-category level 6D pose estimation.

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

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

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

We introduce GeoWizard, a new generative foundation model designed for estimating geometric attributes, e.g., depth and normals, from single images. While significant research has already been conducted in this area, the progress has been substantially limited by the low diversity and poor quality of publicly available datasets. As a result, the prior works either are constrained to limited scenarios or suffer from the inability to capture geometric details. In this paper, we demonstrate that generative models, as opposed to traditional discriminative models (e.g., CNNs and Transformers), can effectively address the inherently ill-posed problem. We further show that leveraging diffusion priors can markedly improve generalization, detail preservation, and efficiency in resource usage. Specifically, we extend the original stable diffusion model to jointly predict depth and normal, allowing mutual information exchange and high consistency between the two representations. More importantly, we propose a simple yet effective strategy to segregate the complex data distribution of various scenes into distinct sub-distributions. This strategy enables our model to recognize different scene layouts, capturing 3D geometry with remarkable fidelity. GeoWizard sets new benchmarks for zero-shot depth and normal prediction, significantly enhancing many downstream applications such as 3D reconstruction, 2D content creation, and novel viewpoint synthesis.

3D anomaly detection and localization is of great significance for industrial inspection. Prior 3D anomaly detection and localization methods focus on the setting that the testing data share the same category as the training data which is normal. However, in real-world applications, the normal training data for the target 3D objects can be unavailable due to issues like data privacy or export control regulation. To tackle these challenges, we identify a new task -- zero-shot 3D anomaly detection and localization, where the training and testing classes do not overlap. To this end, we design 3DzAL, a novel patch-level contrastive learning framework based on pseudo anomalies generated using the inductive bias from task-irrelevant 3D xyz data to learn more representative feature representations. Furthermore, we train a normalcy classifier network to classify the normal patches and pseudo anomalies and utilize the classification result jointly with feature distance to design anomaly scores. Instead of directly using the patch point clouds, we introduce adversarial perturbations to the input patch xyz data before feeding into the 3D normalcy classifier for the classification-based anomaly score. We show that 3DzAL outperforms the state-of-the-art anomaly detection and localization performance.

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.

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

Learning visual representations with self-supervised learning has become popular in computer vision. The idea is to design auxiliary tasks where labels are free to obtain. Most of these tasks end up providing data to learn specific kinds of invariance useful for recognition. In this paper, we propose to exploit different self-supervised approaches to learn representations invariant to (i) inter-instance variations (two objects in the same class should have similar features) and (ii) intra-instance variations (viewpoint, pose, deformations, illumination, etc). Instead of combining two approaches with multi-task learning, we argue to organize and reason the data with multiple variations. Specifically, we propose to generate a graph with millions of objects mined from hundreds of thousands of videos. The objects are connected by two types of edges which correspond to two types of invariance: "different instances but a similar viewpoint and category" and "different viewpoints of the same instance". By applying simple transitivity on the graph with these edges, we can obtain pairs of images exhibiting richer visual invariance. We use this data to train a Triplet-Siamese network with VGG16 as the base architecture and apply the learned representations to different recognition tasks. For object detection, we achieve 63.2% mAP on PASCAL VOC 2007 using Fast R-CNN (compare to 67.3% with ImageNet pre-training). For the challenging COCO dataset, our method is surprisingly close (23.5%) to the ImageNet-supervised counterpart (24.4%) using the Faster R-CNN framework. We also show that our network can perform significantly better than the ImageNet network in the surface normal estimation task.

Self-supervised learning (SSL) for point cloud pre-training has become a cornerstone for many 3D vision tasks, enabling effective learning from large-scale unannotated data. At the scene level, existing SSL methods often incorporate volume rendering into the pre-training framework, using RGB-D images as reconstruction signals to facilitate cross-modal learning. This strategy promotes alignment between 2D and 3D modalities and enables the model to benefit from rich visual cues in the RGB-D inputs. However, these approaches are limited by their reliance on implicit scene representations and high memory demands. Furthermore, since their reconstruction objectives are applied only in 2D space, they often fail to capture underlying 3D geometric structures. To address these challenges, we propose Gaussian2Scene, a novel scene-level SSL framework that leverages the efficiency and explicit nature of 3D Gaussian Splatting (3DGS) for pre-training. The use of 3DGS not only alleviates the computational burden associated with volume rendering but also supports direct 3D scene reconstruction, thereby enhancing the geometric understanding of the backbone network. Our approach follows a progressive two-stage training strategy. In the first stage, a dual-branch masked autoencoder learns both 2D and 3D scene representations. In the second stage, we initialize training with reconstructed point clouds and further supervise learning using the geometric locations of Gaussian primitives and rendered RGB images. This process reinforces both geometric and cross-modal learning. We demonstrate the effectiveness of Gaussian2Scene across several downstream 3D object detection tasks, showing consistent improvements over existing pre-training methods.

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

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.

We present a class of novel optimisers for training neural networks that makes use of the Riemannian metric naturally induced when the loss landscape is embedded in higher-dimensional space. This is the same metric that underlies common visualisations of loss landscapes. By taking this geometric perspective literally and using the induced metric, we develop a new optimiser and compare it to existing methods, namely: SGD, Adam, AdamW, and Muon, across a range of tasks and architectures. Empirically, we conclude that this new class of optimisers is highly effective in low dimensional examples, and provides slight improvement over state-of-the-art methods for training neural networks. These new optimisers have theoretically desirable properties. In particular, the effective learning rate is automatically decreased in regions of high curvature acting as a smoothed out form of gradient clipping. Similarly, one variant of these optimisers can also be viewed as inducing an effective scheduled learning rate and decoupled weight decay is the natural choice from our geometric perspective. The basic method can be used to modify any existing preconditioning method. The new optimiser has a computational complexity comparable to that of Adam.

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.

Multi-task learning (MTL) is an inductive transfer mechanism designed to leverage useful information from multiple tasks to improve generalization performance compared to single-task learning. It has been extensively explored in traditional machine learning to address issues such as data sparsity and overfitting in neural networks. In this work, we apply MTL to problems in science and engineering governed by partial differential equations (PDEs). However, implementing MTL in this context is complex, as it requires task-specific modifications to accommodate various scenarios representing different physical processes. To this end, we present a multi-task deep operator network (MT-DeepONet) to learn solutions across various functional forms of source terms in a PDE and multiple geometries in a single concurrent training session. We introduce modifications in the branch network of the vanilla DeepONet to account for various functional forms of a parameterized coefficient in a PDE. Additionally, we handle parameterized geometries by introducing a binary mask in the branch network and incorporating it into the loss term to improve convergence and generalization to new geometry tasks. Our approach is demonstrated on three benchmark problems: (1) learning different functional forms of the source term in the Fisher equation; (2) learning multiple geometries in a 2D Darcy Flow problem and showcasing better transfer learning capabilities to new geometries; and (3) learning 3D parameterized geometries for a heat transfer problem and demonstrate the ability to predict on new but similar geometries. Our MT-DeepONet framework offers a novel approach to solving PDE problems in engineering and science under a unified umbrella based on synergistic learning that reduces the overall training cost for neural operators.

In this work, we focus on the task of learning and representing dense correspondences in deformable object categories. While this problem has been considered before, solutions so far have been rather ad-hoc for specific object types (i.e., humans), often with significant manual work involved. However, scaling the geometry understanding to all objects in nature requires more automated approaches that can also express correspondences between related, but geometrically different objects. To this end, we propose a new, learnable image-based representation of dense correspondences. Our model predicts, for each pixel in a 2D image, an embedding vector of the corresponding vertex in the object mesh, therefore establishing dense correspondences between image pixels and 3D object geometry. We demonstrate that the proposed approach performs on par or better than the state-of-the-art methods for dense pose estimation for humans, while being conceptually simpler. We also collect a new in-the-wild dataset of dense correspondences for animal classes and demonstrate that our framework scales naturally to the new deformable object categories.

Normalization layers are crucial for deep learning, but their Euclidean formulations are inadequate for data on manifolds. On the other hand, many Riemannian manifolds in machine learning admit gyro-structures, enabling principled extensions of Euclidean neural networks to non-Euclidean domains. Inspired by this, we introduce GyroBN, a principled Riemannian batch normalization framework for gyrogroups. We establish two necessary conditions, namely pseudo-reduction and gyroisometric gyrations, that guarantee GyroBN with theoretical control over sample statistics, and show that these conditions hold for all known gyrogroups in machine learning. Our framework also incorporates several existing Riemannian normalization methods as special cases. We further instantiate GyroBN on seven representative geometries, including the Grassmannian, five constant curvature spaces, and the correlation manifold, and derive novel gyro and Riemannian structures to enable these instantiations. Experiments across these geometries demonstrate the effectiveness of GyroBN. The code is available at https://github.com/GitZH-Chen/GyroBN.git.

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

In this paper, we present DV-Matcher, a novel learning-based framework for estimating dense correspondences between non-rigidly deformable point clouds. Learning directly from unstructured point clouds without meshing or manual labelling, our framework delivers high-quality dense correspondences, which is of significant practical utility in point cloud processing. Our key contributions are two-fold: First, we propose a scheme to inject prior knowledge from pre-trained vision models into geometric feature learning, which effectively complements the local nature of geometric features with global and semantic information; Second, we propose a novel deformation-based module to promote the extrinsic alignment induced by the learned correspondences, which effectively enhances the feature learning. Experimental results show that our method achieves state-of-the-art results in matching non-rigid point clouds in both near-isometric and heterogeneous shape collection as well as more realistic partial and noisy data.

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

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

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.

We introduce a new neural architecture to learn the conditional probability of an output sequence with elements that are discrete tokens corresponding to positions in an input sequence. Such problems cannot be trivially addressed by existent approaches such as sequence-to-sequence and Neural Turing Machines, because the number of target classes in each step of the output depends on the length of the input, which is variable. Problems such as sorting variable sized sequences, and various combinatorial optimization problems belong to this class. Our model solves the problem of variable size output dictionaries using a recently proposed mechanism of neural attention. It differs from the previous attention attempts in that, instead of using attention to blend hidden units of an encoder to a context vector at each decoder step, it uses attention as a pointer to select a member of the input sequence as the output. We call this architecture a Pointer Net (Ptr-Net). We show Ptr-Nets can be used to learn approximate solutions to three challenging geometric problems -- finding planar convex hulls, computing Delaunay triangulations, and the planar Travelling Salesman Problem -- using training examples alone. Ptr-Nets not only improve over sequence-to-sequence with input attention, but also allow us to generalize to variable size output dictionaries. We show that the learnt models generalize beyond the maximum lengths they were trained on. We hope our results on these tasks will encourage a broader exploration of neural learning for discrete problems.

Normalizing Flows explicitly maximize a full-dimensional likelihood on the training data. However, real data is typically only supported on a lower-dimensional manifold leading the model to expend significant compute on modeling noise. Injective Flows fix this by jointly learning a manifold and the distribution on it. So far, they have been limited by restrictive architectures and/or high computational cost. We lift both constraints by a new efficient estimator for the maximum likelihood loss, compatible with free-form bottleneck architectures. We further show that naively learning both the data manifold and the distribution on it can lead to divergent solutions, and use this insight to motivate a stable maximum likelihood training objective. We perform extensive experiments on toy, tabular and image data, demonstrating the competitive performance of the resulting model.

Text-to-3D generation represents an exciting field that has seen rapid advancements, facilitating the transformation of textual descriptions into detailed 3D models. However, current progress often neglects the intricate high-order correlation of geometry and texture within 3D objects, leading to challenges such as over-smoothness, over-saturation and the Janus problem. In this work, we propose a method named ``3D Gaussian Generation via Hypergraph (Hyper-3DG)'', designed to capture the sophisticated high-order correlations present within 3D objects. Our framework is anchored by a well-established mainflow and an essential module, named ``Geometry and Texture Hypergraph Refiner (HGRefiner)''. This module not only refines the representation of 3D Gaussians but also accelerates the update process of these 3D Gaussians by conducting the Patch-3DGS Hypergraph Learning on both explicit attributes and latent visual features. Our framework allows for the production of finely generated 3D objects within a cohesive optimization, effectively circumventing degradation. Extensive experimentation has shown that our proposed method significantly enhances the quality of 3D generation while incurring no additional computational overhead for the underlying framework. (Project code: https://github.com/yjhboy/Hyper3DG)

It has been observed that representations learned by distinct neural networks conceal structural similarities when the models are trained under similar inductive biases. From a geometric perspective, identifying the classes of transformations and the related invariances that connect these representations is fundamental to unlocking applications, such as merging, stitching, and reusing different neural modules. However, estimating task-specific transformations a priori can be challenging and expensive due to several factors (e.g., weights initialization, training hyperparameters, or data modality). To this end, we introduce a versatile method to directly incorporate a set of invariances into the representations, constructing a product space of invariant components on top of the latent representations without requiring prior knowledge about the optimal invariance to infuse. We validate our solution on classification and reconstruction tasks, observing consistent latent similarity and downstream performance improvements in a zero-shot stitching setting. The experimental analysis comprises three modalities (vision, text, and graphs), twelve pretrained foundational models, nine benchmarks, and several architectures trained from scratch.

We propose Riemannian Flow Matching (RFM), a simple yet powerful framework for training continuous normalizing flows on manifolds. Existing methods for generative modeling on manifolds either require expensive simulation, are inherently unable to scale to high dimensions, or use approximations for limiting quantities that result in biased training objectives. Riemannian Flow Matching bypasses these limitations and offers several advantages over previous approaches: it is simulation-free on simple geometries, does not require divergence computation, and computes its target vector field in closed-form. The key ingredient behind RFM is the construction of a relatively simple premetric for defining target vector fields, which encompasses the existing Euclidean case. To extend to general geometries, we rely on the use of spectral decompositions to efficiently compute premetrics on the fly. Our method achieves state-of-the-art performance on many real-world non-Euclidean datasets, and we demonstrate tractable training on general geometries, including triangular meshes with highly non-trivial curvature and boundaries.

Recent advances in dense 3D reconstruction have led to significant progress, yet achieving accurate unified geometric prediction remains a major challenge. Most existing methods are limited to predicting a single geometry quantity from input images. However, geometric quantities such as depth, surface normals, and point maps are inherently correlated, and estimating them in isolation often fails to ensure consistency, thereby limiting both accuracy and practical applicability. This motivates us to explore a unified framework that explicitly models the structural coupling among different geometric properties to enable joint regression. In this paper, we present Dens3R, a 3D foundation model designed for joint geometric dense prediction and adaptable to a wide range of downstream tasks. Dens3R adopts a two-stage training framework to progressively build a pointmap representation that is both generalizable and intrinsically invariant. Specifically, we design a lightweight shared encoder-decoder backbone and introduce position-interpolated rotary positional encoding to maintain expressive power while enhancing robustness to high-resolution inputs. By integrating image-pair matching features with intrinsic invariance modeling, Dens3R accurately regresses multiple geometric quantities such as surface normals and depth, achieving consistent geometry perception from single-view to multi-view inputs. Additionally, we propose a post-processing pipeline that supports geometrically consistent multi-view inference. Extensive experiments demonstrate the superior performance of Dens3R across various dense 3D prediction tasks and highlight its potential for broader applications.

Recent progress in neural rendering has brought forth pioneering methods, such as NeRF and Gaussian Splatting, which revolutionize view rendering across various domains like AR/VR, gaming, and content creation. While these methods excel at interpolating {\em within the training data}, the challenge of generalizing to new scenes and objects from very sparse views persists. Specifically, modeling 3D humans from sparse views presents formidable hurdles due to the inherent complexity of human geometry, resulting in inaccurate reconstructions of geometry and textures. To tackle this challenge, this paper leverages recent advancements in Gaussian Splatting and introduces a new method to learn generalizable human Gaussians that allows photorealistic and accurate view-rendering of a new human subject from a limited set of sparse views in a feed-forward manner. A pivotal innovation of our approach involves reformulating the learning of 3D Gaussian parameters into a regression process defined on the 2D UV space of a human template, which allows leveraging the strong geometry prior and the advantages of 2D convolutions. In addition, a multi-scaffold is proposed to effectively represent the offset details. Our method outperforms recent methods on both within-dataset generalization as well as cross-dataset generalization settings.

We propose Hyper-Dimensional Function Encoding (HDFE). Given samples of a continuous object (e.g. a function), HDFE produces an explicit vector representation of the given object, invariant to the sample distribution and density. Sample distribution and density invariance enables HDFE to consistently encode continuous objects regardless of their sampling, and therefore allows neural networks to receive continuous objects as inputs for machine learning tasks, such as classification and regression. Besides, HDFE does not require any training and is proved to map the object into an organized embedding space, which facilitates the training of the downstream tasks. In addition, the encoding is decodable, which enables neural networks to regress continuous objects by regressing their encodings. Therefore, HDFE serves as an interface for processing continuous objects. We apply HDFE to function-to-function mapping, where vanilla HDFE achieves competitive performance as the state-of-the-art algorithm. We apply HDFE to point cloud surface normal estimation, where a simple replacement from PointNet to HDFE leads to immediate 12% and 15% error reductions in two benchmarks. In addition, by integrating HDFE into the PointNet-based SOTA network, we improve the SOTA baseline by 2.5% and 1.7% in the same benchmarks.

We present PVSeRF, a learning framework that reconstructs neural radiance fields from single-view RGB images, for novel view synthesis. Previous solutions, such as pixelNeRF, rely only on pixel-aligned features and suffer from feature ambiguity issues. As a result, they struggle with the disentanglement of geometry and appearance, leading to implausible geometries and blurry results. To address this challenge, we propose to incorporate explicit geometry reasoning and combine it with pixel-aligned features for radiance field prediction. Specifically, in addition to pixel-aligned features, we further constrain the radiance field learning to be conditioned on i) voxel-aligned features learned from a coarse volumetric grid and ii) fine surface-aligned features extracted from a regressed point cloud. We show that the introduction of such geometry-aware features helps to achieve a better disentanglement between appearance and geometry, i.e. recovering more accurate geometries and synthesizing higher quality images of novel views. Extensive experiments against state-of-the-art methods on ShapeNet benchmarks demonstrate the superiority of our approach for single-image novel view synthesis.

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

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.

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

Vision-Language Models (VLMs) have shown remarkable performance on diverse visual and linguistic tasks, yet they remain fundamentally limited in their understanding of 3D spatial structures. We propose Geometric Distillation, a lightweight, annotation-free fine-tuning framework that injects human-inspired geometric cues into pretrained VLMs without modifying their architecture. By distilling (1) sparse correspondences, (2) relative depth relations, and (3) dense cost volumes from off-the-shelf 3D foundation models (e.g., MASt3R, VGGT), our method shapes representations to be geometry-aware while remaining compatible with natural image-text inputs. Through extensive evaluations on 3D vision-language reasoning and 3D perception benchmarks, our method consistently outperforms prior approaches, achieving improved 3D spatial reasoning with significantly lower computational cost. Our work demonstrates a scalable and efficient path to bridge 2D-trained VLMs with 3D understanding, opening up wider use in spatially grounded multimodal tasks.

Recently, there has been growing interest in developing learning-based methods to detect and utilize salient semi-global or global structures, such as junctions, lines, planes, cuboids, smooth surfaces, and all types of symmetries, for 3D scene modeling and understanding. However, the ground truth annotations are often obtained via human labor, which is particularly challenging and inefficient for such tasks due to the large number of 3D structure instances (e.g., line segments) and other factors such as viewpoints and occlusions. In this paper, we present a new synthetic dataset, Structured3D, with the aim of providing large-scale photo-realistic images with rich 3D structure annotations for a wide spectrum of structured 3D modeling tasks. We take advantage of the availability of professional interior designs and automatically extract 3D structures from them. We generate high-quality images with an industry-leading rendering engine. We use our synthetic dataset in combination with real images to train deep networks for room layout estimation and demonstrate improved performance on benchmark datasets.

Deep learning models have become increasingly useful in many different industries. On the domain of image classification, convolutional neural networks proved the ability to learn robust features for the closed set problem, as shown in many different datasets, such as MNIST FASHIONMNIST, CIFAR10, CIFAR100, and IMAGENET. These approaches use deep neural networks with dense layers with softmax activation functions in order to learn features that can separate classes in a latent space. However, this traditional approach is not useful for identifying classes unseen on the training set, known as the open set problem. A similar problem occurs in scenarios involving learning on small data. To tackle both problems, few-shot learning has been proposed. In particular, metric learning learns features that obey constraints of a metric distance in the latent space in order to perform classification. However, while this approach proves to be useful for the open set problem, current implementation requires pair-wise training, where both positive and negative examples of similar images are presented during the training phase, which limits the applicability of these approaches in large data or large class scenarios given the combinatorial nature of the possible inputs.In this paper, we present a constraint-based approach applied to the representations in the latent space under the normalized softmax loss, proposed by[18]. We experimentally validate the proposed approach for the classification of unseen classes on different datasets using both metric learning and the normalized softmax loss, on disjoint and joint scenarios. Our results show that not only our proposed strategy can be efficiently trained on larger set of classes, as it does not require pairwise learning, but also present better classification results than the metric learning strategies surpassing its accuracy by a significant margin.

Neural volume rendering became increasingly popular recently due to its success in synthesizing novel views of a scene from a sparse set of input images. So far, the geometry learned by neural volume rendering techniques was modeled using a generic density function. Furthermore, the geometry itself was extracted using an arbitrary level set of the density function leading to a noisy, often low fidelity reconstruction. The goal of this paper is to improve geometry representation and reconstruction in neural volume rendering. We achieve that by modeling the volume density as a function of the geometry. This is in contrast to previous work modeling the geometry as a function of the volume density. In more detail, we define the volume density function as Laplace's cumulative distribution function (CDF) applied to a signed distance function (SDF) representation. This simple density representation has three benefits: (i) it provides a useful inductive bias to the geometry learned in the neural volume rendering process; (ii) it facilitates a bound on the opacity approximation error, leading to an accurate sampling of the viewing ray. Accurate sampling is important to provide a precise coupling of geometry and radiance; and (iii) it allows efficient unsupervised disentanglement of shape and appearance in volume rendering. Applying this new density representation to challenging scene multiview datasets produced high quality geometry reconstructions, outperforming relevant baselines. Furthermore, switching shape and appearance between scenes is possible due to the disentanglement of the two.

Since real-world training datasets cannot properly sample the long tail of the underlying data distribution, corner cases and rare out-of-domain samples can severely hinder the performance of state-of-the-art models. This problem becomes even more severe for dense tasks, such as 3D semantic segmentation, where points of non-standard objects can be confidently associated to the wrong class. In this work, we focus on improving the generalization to out-of-domain data. We achieve this by augmenting the training set with adversarial examples. First, we learn a set of vectors that deform the objects in an adversarial fashion. To prevent the adversarial examples from being too far from the existing data distribution, we preserve their plausibility through a series of constraints, ensuring sensor-awareness and shapes smoothness. Then, we perform adversarial augmentation by applying the learned sample-independent vectors to the available objects when training a model. We conduct extensive experiments across a variety of scenarios on data from KITTI, Waymo, and CrashD for 3D object detection, and on data from SemanticKITTI, Waymo, and nuScenes for 3D semantic segmentation. Despite training on a standard single dataset, our approach substantially improves the robustness and generalization of both 3D object detection and 3D semantic segmentation methods to out-of-domain data.

We propose a novel neural network architecture, the normalized Transformer (nGPT) with representation learning on the hypersphere. In nGPT, all vectors forming the embeddings, MLP, attention matrices and hidden states are unit norm normalized. The input stream of tokens travels on the surface of a hypersphere, with each layer contributing a displacement towards the target output predictions. These displacements are defined by the MLP and attention blocks, whose vector components also reside on the same hypersphere. Experiments show that nGPT learns much faster, reducing the number of training steps required to achieve the same accuracy by a factor of 4 to 20, depending on the sequence length.

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

We introduce PartGlot, a neural framework and associated architectures for learning semantic part segmentation of 3D shape geometry, based solely on part referential language. We exploit the fact that linguistic descriptions of a shape can provide priors on the shape's parts -- as natural language has evolved to reflect human perception of the compositional structure of objects, essential to their recognition and use. For training, we use the paired geometry / language data collected in the ShapeGlot work for their reference game, where a speaker creates an utterance to differentiate a target shape from two distractors and the listener has to find the target based on this utterance. Our network is designed to solve this target discrimination problem, carefully incorporating a Transformer-based attention module so that the output attention can precisely highlight the semantic part or parts described in the language. Furthermore, the network operates without any direct supervision on the 3D geometry itself. Surprisingly, we further demonstrate that the learned part information is generalizable to shape classes unseen during training. Our approach opens the possibility of learning 3D shape parts from language alone, without the need for large-scale part geometry annotations, thus facilitating annotation acquisition.

Transfer learning is a crucial technique for handling a small amount of data that is potentially related to other abundant data. However, most of the existing methods are focused on classification tasks using images and language datasets. Therefore, in order to expand the transfer learning scheme to regression tasks, we propose a novel transfer technique based on differential geometry, namely the Geometrically Aligned Transfer Encoder (GATE). In this method, we interpret the latent vectors from the model to exist on a Riemannian curved manifold. We find a proper diffeomorphism between pairs of tasks to ensure that every arbitrary point maps to a locally flat coordinate in the overlapping region, allowing the transfer of knowledge from the source to the target data. This also serves as an effective regularizer for the model to behave in extrapolation regions. In this article, we demonstrate that GATE outperforms conventional methods and exhibits stable behavior in both the latent space and extrapolation regions for various molecular graph datasets.

While surface normals are widely used to analyse 3D scene geometry, surface normal estimation from LiDAR point clouds remains severely underexplored. This is caused by the lack of large-scale annotated datasets on the one hand, and lack of methods that can robustly handle the sparse and often noisy LiDAR data in a reasonable time on the other hand. We address these limitations using a traffic simulation engine and present LiSu, the first large-scale, synthetic LiDAR point cloud dataset with ground truth surface normal annotations, eliminating the need for tedious manual labeling. Additionally, we propose a novel method that exploits the spatiotemporal characteristics of autonomous driving data to enhance surface normal estimation accuracy. By incorporating two regularization terms, we enforce spatial consistency among neighboring points and temporal smoothness across consecutive LiDAR frames. These regularizers are particularly effective in self-training settings, where they mitigate the impact of noisy pseudo-labels, enabling robust real-world deployment. We demonstrate the effectiveness of our method on LiSu, achieving state-of-the-art performance in LiDAR surface normal estimation. Moreover, we showcase its full potential in addressing the challenging task of synthetic-to-real domain adaptation, leading to improved neural surface reconstruction on real-world data.

Real-world visual data exhibit intrinsic hierarchical structures that can be represented effectively in hyperbolic spaces. Hyperbolic neural networks (HNNs) are a promising approach for learning feature representations in such spaces. However, current HNNs in computer vision rely on Euclidean backbones and only project features to the hyperbolic space in the task heads, limiting their ability to fully leverage the benefits of hyperbolic geometry. To address this, we present HCNN, a fully hyperbolic convolutional neural network (CNN) designed for computer vision tasks. Based on the Lorentz model, we generalize fundamental components of CNNs and propose novel formulations of the convolutional layer, batch normalization, and multinomial logistic regression. {Experiments on standard vision tasks demonstrate the promising performance of our HCNN framework in both hybrid and fully hyperbolic settings.} Overall, we believe our contributions provide a foundation for developing more powerful HNNs that can better represent complex structures found in image data. Our code is publicly available at https://github.com/kschwethelm/HyperbolicCV.

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.

Self-supervised learning has emerged as a promising approach for acquiring transferable 3D representations from unlabeled 3D point clouds. Unlike 2D images, which are widely accessible, acquiring 3D assets requires specialized expertise or professional 3D scanning equipment, making it difficult to scale and raising copyright concerns. To address these challenges, we propose learning 3D representations from procedural 3D programs that automatically generate 3D shapes using simple primitives and augmentations. Remarkably, despite lacking semantic content, the 3D representations learned from this synthesized dataset perform on par with state-of-the-art representations learned from semantically recognizable 3D models (e.g., airplanes) across various downstream 3D tasks, including shape classification, part segmentation, and masked point cloud completion. Our analysis further suggests that current self-supervised learning methods primarily capture geometric structures rather than high-level semantics.

The popularity of pre-trained large models has revolutionized downstream tasks across diverse fields, such as language, vision, and multi-modality. To minimize the adaption cost for downstream tasks, many Parameter-Efficient Fine-Tuning (PEFT) techniques are proposed for language and 2D image pre-trained models. However, the specialized PEFT method for 3D pre-trained models is still under-explored. To this end, we introduce Point-PEFT, a novel framework for adapting point cloud pre-trained models with minimal learnable parameters. Specifically, for a pre-trained 3D model, we freeze most of its parameters, and only tune the newly added PEFT modules on downstream tasks, which consist of a Point-prior Prompt and a Geometry-aware Adapter. The Point-prior Prompt adopts a set of learnable prompt tokens, for which we propose to construct a memory bank with domain-specific knowledge, and utilize a parameter-free attention to enhance the prompt tokens. The Geometry-aware Adapter aims to aggregate point cloud features within spatial neighborhoods to capture fine-grained geometric information through local interactions. Extensive experiments indicate that our Point-PEFT can achieve better performance than the full fine-tuning on various downstream tasks, while using only 5% of the trainable parameters, demonstrating the efficiency and effectiveness of our approach. Code is released at https://github.com/Ivan-Tang-3D/Point-PEFT.

Self-supervised learning (SSL) has emerged as a powerful paradigm for learning representations without labeled data. Most SSL approaches rely on strong, well-established, handcrafted data augmentations to generate diverse views for representation learning. However, designing such augmentations requires domain-specific knowledge and implicitly imposes representational invariances on the model, which can limit generalization. In this work, we propose an unsupervised representation learning method that replaces augmentations by generating views using orthonormal bases and overcomplete frames. We show that embeddings learned from orthonormal and overcomplete spaces reside on distinct manifolds, shaped by the geometric biases introduced by representing samples in different spaces. By jointly leveraging the complementary geometry of these distinct manifolds, our approach achieves superior performance without artificially increasing data diversity through strong augmentations. We demonstrate the effectiveness of our method on nine datasets across five temporal sequence tasks, where signal-specific characteristics make data augmentations particularly challenging. Without relying on augmentation-induced diversity, our method achieves performance gains of up to 15--20\% over existing self-supervised approaches. Source code: https://github.com/eth-siplab/Learning-with-FrameProjections

We introduce an unsupervised feature learning approach that embeds 3D shape information into a single-view image representation. The main idea is a self-supervised training objective that, given only a single 2D image, requires all unseen views of the object to be predictable from learned features. We implement this idea as an encoder-decoder convolutional neural network. The network maps an input image of an unknown category and unknown viewpoint to a latent space, from which a deconvolutional decoder can best "lift" the image to its complete viewgrid showing the object from all viewing angles. Our class-agnostic training procedure encourages the representation to capture fundamental shape primitives and semantic regularities in a data-driven manner---without manual semantic labels. Our results on two widely-used shape datasets show 1) our approach successfully learns to perform "mental rotation" even for objects unseen during training, and 2) the learned latent space is a powerful representation for object recognition, outperforming several existing unsupervised feature learning methods.

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

Riemannian submanifold optimization with momentum is computationally challenging because, to ensure that the iterates remain on the submanifold, we often need to solve difficult differential equations. Here, we simplify such difficulties for a class of structured symmetric positive-definite matrices with the affine-invariant metric. We do so by proposing a generalized version of the Riemannian normal coordinates that dynamically orthonormalizes the metric and locally converts the problem into an unconstrained problem in the Euclidean space. We use our approach to simplify existing approaches for structured covariances and develop matrix-inverse-free 2^nd-order optimizers for deep learning in low precision settings. Code: https://github.com/yorkerlin/StructuredNGD-DL

Transformers have been recently explored for 3D point cloud understanding with impressive progress achieved. A large number of points, over 0.1 million, make the global self-attention infeasible for point cloud data. Thus, most methods propose to apply the transformer in a local region, e.g., spherical or cubic window. However, it still contains a large number of Query-Key pairs, which requires high computational costs. In addition, previous methods usually learn the query, key, and value using a linear projection without modeling the local 3D geometric structure. In this paper, we attempt to reduce the costs and model the local geometry prior by developing a new transformer block, named ConDaFormer. Technically, ConDaFormer disassembles the cubic window into three orthogonal 2D planes, leading to fewer points when modeling the attention in a similar range. The disassembling operation is beneficial to enlarging the range of attention without increasing the computational complexity, but ignores some contexts. To provide a remedy, we develop a local structure enhancement strategy that introduces a depth-wise convolution before and after the attention. This scheme can also capture the local geometric information. Taking advantage of these designs, ConDaFormer captures both long-range contextual information and local priors. The effectiveness is demonstrated by experimental results on several 3D point cloud understanding benchmarks. Code is available at https://github.com/LHDuan/ConDaFormer .

We propose a new sampler for robust estimators that always selects the sample with the highest probability of consisting only of inliers. After every unsuccessful iteration, the inlier probabilities are updated in a principled way via a Bayesian approach. The probabilities obtained by the deep network are used as prior (so-called neural guidance) inside the sampler. Moreover, we introduce a new loss that exploits, in a geometrically justifiable manner, the orientation and scale that can be estimated for any type of feature, e.g., SIFT or SuperPoint, to estimate two-view geometry. The new loss helps to learn higher-order information about the underlying scene geometry. Benefiting from the new sampler and the proposed loss, we combine the neural guidance with the state-of-the-art MAGSAC++. Adaptive Reordering Sampler with Neurally Guided MAGSAC (ARS-MAGSAC) is superior to the state-of-the-art in terms of accuracy and run-time on the PhotoTourism and KITTI datasets for essential and fundamental matrix estimation. The code and trained models are available at https://github.com/weitong8591/ars_magsac.

One-class learning is the classic problem of fitting a model to data for which annotations are available only for a single class. In this paper, we propose a novel objective for one-class learning. Our key idea is to use a pair of orthonormal frames -- as subspaces -- to "sandwich" the labeled data via optimizing for two objectives jointly: i) minimize the distance between the origins of the two subspaces, and ii) to maximize the margin between the hyperplanes and the data, either subspace demanding the data to be in its positive and negative orthant respectively. Our proposed objective however leads to a non-convex optimization problem, to which we resort to Riemannian optimization schemes and derive an efficient conjugate gradient scheme on the Stiefel manifold. To study the effectiveness of our scheme, we propose a new dataset~Dash-Cam-Pose, consisting of clips with skeleton poses of humans seated in a car, the task being to classify the clips as normal or abnormal; the latter is when any human pose is out-of-position with regard to say an airbag deployment. Our experiments on the proposed Dash-Cam-Pose dataset, as well as several other standard anomaly/novelty detection benchmarks demonstrate the benefits of our scheme, achieving state-of-the-art one-class accuracy.

This paper introduces the point-axis representation for oriented object detection, emphasizing its flexibility and geometrically intuitive nature with two key components: points and axes. 1) Points delineate the spatial extent and contours of objects, providing detailed shape descriptions. 2) Axes define the primary directionalities of objects, providing essential orientation cues crucial for precise detection. The point-axis representation decouples location and rotation, addressing the loss discontinuity issues commonly encountered in traditional bounding box-based approaches. For effective optimization without introducing additional annotations, we propose the max-projection loss to supervise point set learning and the cross-axis loss for robust axis representation learning. Further, leveraging this representation, we present the Oriented DETR model, seamlessly integrating the DETR framework for precise point-axis prediction and end-to-end detection. Experimental results demonstrate significant performance improvements in oriented object detection tasks.

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

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

Estimating the pose of an object from a monocular image is an inverse problem fundamental in computer vision. The ill-posed nature of this problem requires incorporating deformation priors to solve it. In practice, many materials do not perceptibly shrink or extend when manipulated, constituting a powerful and well-known prior. Mathematically, this translates to the preservation of the Riemannian metric. Neural networks offer the perfect playground to solve the surface reconstruction problem as they can approximate surfaces with arbitrary precision and allow the computation of differential geometry quantities. This paper presents an approach to inferring continuous deformable surfaces from a sequence of images, which is benchmarked against several techniques and obtains state-of-the-art performance without the need for offline training.

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

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

Learning implicit representations has been a widely used solution for surface reconstruction from 3D point clouds. The latest methods infer a distance or occupancy field by overfitting a neural network on a single point cloud. However, these methods suffer from a slow inference due to the slow convergence of neural networks and the extensive calculation of distances to surface points, which limits them to small scale points. To resolve the scalability issue in surface reconstruction, we propose GridPull to improve the efficiency of learning implicit representations from large scale point clouds. Our novelty lies in the fast inference of a discrete distance field defined on grids without using any neural components. To remedy the lack of continuousness brought by neural networks, we introduce a loss function to encourage continuous distances and consistent gradients in the field during pulling queries onto the surface in grids near to the surface. We use uniform grids for a fast grid search to localize sampled queries, and organize surface points in a tree structure to speed up the calculation of distances to the surface. We do not rely on learning priors or normal supervision during optimization, and achieve superiority over the latest methods in terms of complexity and accuracy. We evaluate our method on shape and scene benchmarks, and report numerical and visual comparisons with the latest methods to justify our effectiveness and superiority. The code is available at https://github.com/chenchao15/GridPull.

Recently, methods leveraging diffusion model priors to assist monocular geometric estimation (e.g., depth and normal) have gained significant attention due to their strong generalization ability. However, most existing works focus on estimating geometric properties within the camera coordinate system of individual video frames, neglecting the inherent ability of diffusion models to determine inter-frame correspondence. In this work, we demonstrate that, through appropriate design and fine-tuning, the intrinsic consistency of video generation models can be effectively harnessed for consistent geometric estimation. Specifically, we 1) select geometric attributes in the global coordinate system that share the same correspondence with video frames as the prediction targets, 2) introduce a novel and efficient conditioning method by reusing positional encodings, and 3) enhance performance through joint training on multiple geometric attributes that share the same correspondence. Our results achieve superior performance in predicting global geometric attributes in videos and can be directly applied to reconstruction tasks. Even when trained solely on static video data, our approach exhibits the potential to generalize to dynamic video scenes.

Surface reconstruction with preservation of geometric features is a challenging computer vision task. Despite significant progress in implicit shape reconstruction, state-of-the-art mesh extraction methods often produce aliased, perceptually distorted surfaces and lack scalability to high-resolution 3D shapes. We present a data-driven approach for automatic feature detection and remeshing that requires only a coarse, aliased mesh as input and scales to arbitrary resolution reconstructions. We define and learn a collection of surface-based fields to (1) capture sharp geometric features in the shape with an implicit vertexwise model and (2) approximate improvements in normals alignment obtained by applying edge-flips with an edgewise model. To support scaling to arbitrary complexity shapes, we learn our fields using local triangulated patches, fusing estimates on complete surface meshes. Our feature remeshing algorithm integrates the learned fields as sharp feature priors and optimizes vertex placement and mesh connectivity for maximum expected surface improvement. On a challenging collection of high-resolution shape reconstructions in the ABC dataset, our algorithm improves over state-of-the-art by 26% normals F-score and 42% perceptual RMSE_{v}.

Generalist Anomaly Detection (GAD) aims to train a unified model on an original domain that can detect anomalies in new target domains. Previous GAD methods primarily use only normal samples as references, overlooking the valuable information contained in anomalous samples that are often available in real-world scenarios. To address this limitation, we propose a more practical approach: normal-abnormal-guided generalist anomaly detection, which leverages both normal and anomalous samples as references to guide anomaly detection across diverse domains. We introduce the Normal-Abnormal Generalist Learning (NAGL) framework, consisting of two key components: Residual Mining (RM) and Anomaly Feature Learning (AFL). RM extracts abnormal patterns from normal-abnormal reference residuals to establish transferable anomaly representations, while AFL adaptively learns anomaly features in query images through residual mapping to identify instance-aware anomalies. Our approach effectively utilizes both normal and anomalous references for more accurate and efficient cross-domain anomaly detection. Extensive experiments across multiple benchmarks demonstrate that our method significantly outperforms existing GAD approaches. This work represents the first to adopt a mixture of normal and abnormal samples as references in generalist anomaly detection. The code and datasets are available at https://github.com/JasonKyng/NAGL.

We introduce RealmDreamer, a technique for generation of general forward-facing 3D scenes from text descriptions. Our technique optimizes a 3D Gaussian Splatting representation to match complex text prompts. We initialize these splats by utilizing the state-of-the-art text-to-image generators, lifting their samples into 3D, and computing the occlusion volume. We then optimize this representation across multiple views as a 3D inpainting task with image-conditional diffusion models. To learn correct geometric structure, we incorporate a depth diffusion model by conditioning on the samples from the inpainting model, giving rich geometric structure. Finally, we finetune the model using sharpened samples from image generators. Notably, our technique does not require video or multi-view data and can synthesize a variety of high-quality 3D scenes in different styles, consisting of multiple objects. Its generality additionally allows 3D synthesis from a single image.