Daily Papers

Universal medical image segmentation seeks to use a single foundational model to handle diverse tasks across multiple imaging modalities. However, existing approaches often rely heavily on manual visual prompts or retrieved reference images, which limits their automation and robustness. In addition, naive joint training across modalities often fails to address large domain shifts. To address these limitations, we propose Concept-to-Pixel (C2P), a novel prompt-free universal segmentation framework. C2P explicitly separates anatomical knowledge into two components: Geometric and Semantic representations. It leverages Multimodal Large Language Models (MLLMs) to distill abstract, high-level medical concepts into learnable Semantic Tokens and introduces explicitly supervised Geometric Tokens to enforce universal physical and structural constraints. These disentangled tokens interact deeply with image features to generate input-specific dynamic kernels for precise mask prediction. Furthermore, we introduce a Geometry-Aware Inference Consensus mechanism, which utilizes the model's predicted geometric constraints to assess prediction reliability and suppress outliers. Extensive experiments and analysis on a unified benchmark comprising eight diverse datasets across seven modalities demonstrate the significant superiority of our jointly trained approach, compared to universe- or single-model approaches. Remarkably, our unified model demonstrates strong generalization, achieving impressive results not only on zero-shot tasks involving unseen cases but also in cross-modal transfers across similar tasks. Code is available at: https://github.com/Yundi218/Concept-to-Pixel

Localizing objects and parts from natural language in 3D space is essential for robotics, AR, and embodied AI, yet existing methods face a trade-off between the accuracy and geometric consistency of per-scene optimization and the efficiency of feed-forward inference. We present TrianguLang, a feed-forward framework for 3D localization that requires no camera calibration at inference. Unlike prior methods that treat views independently, we introduce Geometry-Aware Semantic Attention (GASA), which utilizes predicted geometry to gate cross-view feature correspondence, suppressing semantically plausible but geometrically inconsistent matches without requiring ground-truth poses. Validated on five benchmarks including ScanNet++ and uCO3D, TrianguLang achieves state-of-the-art feed-forward text-guided segmentation and localization, reducing user effort from O(N) clicks to a single text query. The model processes each frame at 1008x1008 resolution in sim57ms (sim18 FPS) without optimization, enabling practical deployment for interactive robotics and AR applications. Code and checkpoints are available at https://cwru-aism.github.io/triangulang/.

Spatial reasoning over three-dimensional scenes is a core capability for embodied intelligence, yet continuous model improvement remains bottlenecked by the cost of geometric annotation. The self-evolving paradigm offers a promising path, but its reliance on model consensus to construct pseudo-labels causes training to reinforce rather than correct the model's own geometric errors. We identify a property unique to 3D spatial reasoning that circumvents this limitation: ground truth is a deterministic consequence of the underlying geometry, computable exactly from point clouds and camera poses without any model involvement. Building on this insight, we present SpatialEvo, a self-evolving framework for 3D spatial reasoning, centered on the Deterministic Geometric Environment (DGE). The DGE formalizes 16 spatial reasoning task categories under explicit geometric validation rules and converts unannotated 3D scenes into zero-noise interactive oracles, replacing model consensus with objective physical feedback. A single shared-parameter policy co-evolves across questioner and solver roles under DGE constraints: the questioner generates physically valid spatial questions grounded in scene observations, while the solver derives precise answers against DGE-verified ground truth. A task-adaptive scheduler endogenously concentrates training on the model's weakest categories, producing a dynamic curriculum without manual design. Experiments across nine benchmarks demonstrate that SpatialEvo achieves the highest average score at both 3B and 7B scales, with consistent gains on spatial reasoning benchmarks and no degradation on general visual understanding.

Geometric foundation models hold promise for unconstrained dense geometry prediction from uncalibrated images. However, in current feed-forward designs, their predicted confidence scores are heuristic, lack probabilistic interpretation, and often fail to indicate where and how much the predicted geometry can be trusted. To address this gap, we present Trust3R, a lightweight evidential uncertainty framework for feed-forward 3D reconstruction. Trust3R combines gated residual mean refinement with a Normal-Inverse-Wishart evidential head, yielding a closed-form multivariate Student-t distribution for per-point geometric uncertainty. This design provides probabilistically grounded pointmap uncertainty estimates while adding moderate inference overhead. We evaluate on diverse indoor and outdoor benchmarks and compare against MASt3R's built-in confidence map as well as common uncertainty-aware baselines spanning single-pass heteroscedastic regression and sampling-based methods such as MC dropout and deep ensembles. Experimental results show that Trust3R consistently improves risk-coverage and sparsification, and generally improves geometric accuracy. These gains are reflected in stronger uncertainty ranking across benchmarks, with 25% lower AURC and 41% lower AUSE on ScanNet++, providing a practical reliability signal for uncertainty-aware weighting in downstream geometry pipelines. The project page and code are available at https://trust3r-z.github.io/.

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

Video spatial reasoning is essential for navigation-oriented perception and long-video question answering, where models must infer spatial relations across long horizons under changing viewpoints. However, existing multimodal large language models (MLLMs) remain largely semantic-centric, and often fail to reliably aggregate consistent spatial evidence from redundant video observations, leading to inefficient or unstable reasoning. To address these issues, we propose ConsiSpace, a geometry-consistency-aware framework for geometry-sensitive video spatial reasoning that turns spatial consistency into both an evidence organization principle and an explicit post-SFT learning signal. We build a geometry-consistent memory (GCM) including implicit evidence tokens and explicit geometric cues, and leverage efficient organization strategies to compactly preserve task-related spatial evidence. Furthermore, we utilize unified consistency self-supervised reinforcement learning (UC-SSRL) after supervised fine-tuning to improve cross-view stability, with answer-, metric-, and topology-consistency rewards. Extensive experiments on three spatial-reasoning benchmarks, VSI-Bench, OSI-Bench, and MMSI-Video-Bench, show consistent gains, improving the average score by 12.6 points over the strongest baselines.

Multi-view graph clustering (MGC) methods are increasingly being studied due to the explosion of multi-view data with graph structural information. The critical point of MGC is to better utilize view-specific and view-common information in features and graphs of multiple views. However, existing works have an inherent limitation that they are unable to concurrently utilize the consensus graph information across multiple graphs and the view-specific feature information. To address this issue, we propose Variational Graph Generator for Multi-View Graph Clustering (VGMGC). Specifically, a novel variational graph generator is proposed to extract common information among multiple graphs. This generator infers a reliable variational consensus graph based on a priori assumption over multiple graphs. Then a simple yet effective graph encoder in conjunction with the multi-view clustering objective is presented to learn the desired graph embeddings for clustering, which embeds the inferred view-common graph and view-specific graphs together with features. Finally, theoretical results illustrate the rationality of the VGMGC by analyzing the uncertainty of the inferred consensus graph with the information bottleneck principle.Extensive experiments demonstrate the superior performance of our VGMGC over SOTAs. The source code is publicly available at https://github.com/cjpcool/VGMGC.

Dense matching methods like DUSt3R regress pairwise pointmaps for 3D reconstruction. However, the reliance on pairwise prediction and the limited generalization capability inherently restrict the global geometric consistency. In this work, we introduce Test3R, a surprisingly simple test-time learning technique that significantly boosts geometric accuracy. Using image triplets (I_1,I_2,I_3), Test3R generates reconstructions from pairs (I_1,I_2) and (I_1,I_3). The core idea is to optimize the network at test time via a self-supervised objective: maximizing the geometric consistency between these two reconstructions relative to the common image I_1. This ensures the model produces cross-pair consistent outputs, regardless of the inputs. Extensive experiments demonstrate that our technique significantly outperforms previous state-of-the-art methods on the 3D reconstruction and multi-view depth estimation tasks. Moreover, it is universally applicable and nearly cost-free, making it easily applied to other models and implemented with minimal test-time training overhead and parameter footprint. Code is available at https://github.com/nopQAQ/Test3R.

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.

A key component of Visual Simultaneous Localization and Mapping (VSLAM) is estimating relative camera poses using matched keypoints. Accurate estimation is challenged by noisy correspondences. Classical methods rely on stochastic hypothesis sampling and iterative estimation, while learning-based methods often lack explicit geometric structure. In this work, we reformulate relative pose estimation as a relational inference problem over epipolar correspondence graphs, where matched keypoints are nodes and nearby ones are connected by edges. Graph operations such as pruning, message passing, and pooling estimate a quaternion rotation, translation vector, and the Essential Matrix (EM). Minimizing a loss comprising (i) L_2 differences with ground truth (GT), (ii) Frobenius norm between estimated and GT EMs, (iii) singular value differences, (iv) heading angle differences, and (v) scale differences, yields the relative pose between image pairs. The dense detector-free method LoFTR is used for matching. Experiments on indoor and outdoor benchmarks show improved robustness to dense noise and large baseline variation compared to classical and learning-guided approaches, highlighting the effectiveness of global relational consensus.

Feed-forward 3D reconstruction models are efficient but rigid: once trained, they perform inference in a zero-shot manner and cannot adapt to the test scene. As a result, visually plausible reconstructions often contain errors, particularly under occlusions, specularities, and ambiguous cues. To address this, we introduce Free Geometry, a framework that enables feed-forward 3D reconstruction models to self-evolve at test time without any 3D ground truth. Our key insight is that, when the model receives more views, it produces more reliable and view-consistent reconstructions. Leveraging this property, given a testing sequence, we mask a subset of frames to construct a self-supervised task. Free Geometry enforces cross-view feature consistency between representations from full and partial observations, while maintaining the pairwise relations implied by the held-out frames. This self-supervision allows for fast recalibration via lightweight LoRA updates, taking less than 2 minutes per dataset on a single GPU. Our approach consistently improves state-of-the-art foundation models, including Depth Anything 3 and VGGT, across 4 benchmark datasets, yielding an average improvement of 3.73% in camera pose accuracy and 2.88% in point map prediction. Code is available at https://github.com/hiteacherIamhumble/Free-Geometry .

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.

Large vision-language models have significantly advanced GUI agents, enabling executable interaction across web, mobile, and desktop interfaces. Yet these gains largely rely on a forgiving region-tolerant paradigm, where many nearby pixels inside the same component remain valid. Precise geometric construction breaks this assumption: actions must land on points in continuous canvas space rather than tolerant regions. Because geometric primitives carry ontological dependencies, a local coordinate error can induce cascading topological failures that distort downstream objects and invalidate the final construction. We identify this regime as precision-sensitive GUI tasks, requiring point-level accuracy, geometry-aware verification, and robustness to dependency-driven error propagation. To benchmark it, we introduce PAGE Bench, with 4,906 problems and over 224K process-supervised, pixel-level GUI actions. We further propose PAGER, a topology-aware agent that decomposes construction into dependency-structured planning and pixel-level execution. Pixel-grounded supervised tuning establishes executable action grammar, while precision-aligned reinforcement learning mitigates rollout-induced exposure bias through state-conditioned geometric feedback. Experiments reveal a pronounced Semantic-Execution Gap: general multimodal models can exceed 88% action type accuracy yet remain below 6% task success. PAGER closes this gap, delivering 4.1x higher task success than the strongest evaluated general baseline and raising step success rate from below 9% for GUI-specialized agents to over 62%, establishing a new state of the art for point-precise GUI control.

Video diffusion models lack explicit geometric supervision during training, leading to inconsistency artifacts such as object deformation, spatial drift, and depth violations in generated videos. To address this limitation, we propose a geometry-based reward model that leverages pretrained geometric foundation models to evaluate multi-view consistency through cross-frame reprojection error. Unlike previous geometric metrics that measure inconsistency in pixel space, where pixel intensity may introduce additional noise, our approach conducts error computation in a pointwise fashion, yielding a more physically grounded and robust error metric. Furthermore, we introduce a geometry-aware sampling strategy that filters out low-texture and non-semantic regions, focusing evaluation on geometrically meaningful areas with reliable correspondences to improve robustness. We apply this reward model to align video diffusion models through two complementary pathways: post-training of a bidirectional model via SFT or Reinforcement Learning and inference-time optimization of a Causal Video Model (e.g., Streaming video generator) via test-time scaling with our reward as a path verifier. Experimental results validate the effectiveness of our design, demonstrating that our geometry-based reward provides superior robustness compared to other variants. By enabling efficient inference-time scaling, our method offers a practical solution for enhancing open-source video models without requiring extensive computational resources for retraining.

Jigsaw puzzle solving requires jointly reasoning about visual content and geometric constraints, yet existing benchmarks use rectangular cuts that create ambiguous ground truth in texture-repeated regions. We introduce \ours{}, a benchmark with tab-and-blank interlocking pieces where geometric constraints provide strong local compatibility requirements that, combined with visual content, yield unambiguous ground truth. Across 95K instances at four grid densities (4times4 to 16times16), we find that zero-shot VLMs largely lack geometric reasoning: only one of five frontier models (GPT-5.5) exceeds random baseline on 4times4 puzzles, while all others perform at chance level. While supervised fine-tuning achieves >97\% on 4times4, all models collapse on larger grids: GPT-5.5 drops from 70\% to near-random on 8times8, and even fine-tuned models fall below 5\% on 12times12. This ``scaling cliff'' suggests current architectures cannot maintain consistent constraint satisfaction as the number of pieces increases. establishes scalable geometric reasoning as an open challenge for vision-language models.

Large-scale video diffusion models achieve impressive visual quality, yet often fail to preserve geometric consistency. Prior approaches improve consistency either by augmenting the generator with additional modules or applying geometry-aware alignment. However, architectural modifications can compromise the generalization of internet-scale pretrained models, while existing alignment methods are limited to static scenes and rely on RGB-space rewards that require repeated VAE decoding, incurring substantial compute overhead and failing to generalize to highly dynamic real-world scenes. To preserve the pretrained capacity while improving geometric consistency, we propose VGGRPO (Visual Geometry GRPO), a latent geometry-guided framework for geometry-aware video post-training. VGGRPO introduces a Latent Geometry Model (LGM) that stitches video diffusion latents to geometry foundation models, enabling direct decoding of scene geometry from the latent space. By constructing LGM from a geometry model with 4D reconstruction capability, VGGRPO naturally extends to dynamic scenes, overcoming the static-scene limitations of prior methods. Building on this, we perform latent-space Group Relative Policy Optimization with two complementary rewards: a camera motion smoothness reward that penalizes jittery trajectories, and a geometry reprojection consistency reward that enforces cross-view geometric coherence. Experiments on both static and dynamic benchmarks show that VGGRPO improves camera stability, geometry consistency, and overall quality while eliminating costly VAE decoding, making latent-space geometry-guided reinforcement an efficient and flexible approach to world-consistent video generation.

Sequential recommendation increasingly employs latent multi-step reasoning to enhance test-time computation. Despite empirical gains, existing approaches largely drive intermediate reasoning states via target-dominant objectives without imposing explicit feasibility constraints. This results in latent drift, where reasoning trajectories deviate into implausible regions. We argue that effective recommendation reasoning should instead be viewed as navigation on a collaborative manifold rather than free-form latent refinement. To this end, we propose ManCAR (Manifold-Constrained Adaptive Reasoning), a principled framework that grounds reasoning within the topology of a global interaction graph. ManCAR constructs a local intent prior from the collaborative neighborhood of a user's recent actions, represented as a distribution over the item simplex. During training, the model progressively aligns its latent predictive distribution with this prior, forcing the reasoning trajectory to remain within the valid manifold. At test time, reasoning proceeds adaptively until the predictive distribution stabilizes, avoiding over-refinement. We provide a variational interpretation of ManCAR to theoretically validate its drift-prevention and adaptive test-time stopping mechanisms. Experiments on seven benchmarks demonstrate that ManCAR consistently outperforms state-of-the-art baselines, achieving up to a 46.88% relative improvement w.r.t. NDCG@10. Our code is available at https://github.com/FuCongResearchSquad/ManCAR.

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

Vision-language models solve geometry problems with rising accuracy, yet their intermediate states remain latent and unverifiable: a relation expressed in textual reasoning or drawing code carries no guarantee that a constraint-satisfying configuration realizes it. We observe that existing externalization methods based on rendered pixels or one-shot scripts fail to provide exact, per-action geometric guarantees. Enforcing geometric relations by algebraic definition closes this gap: the workspace becomes a constraint-checked evolving canvas. We present Draw2Think, a framework that recasts geometric reasoning from latent spatial inference into agentic interaction with the GeoGebra constraint engine. In a Propose-Draw-Verify loop, Draw2Think externalizes hypotheses onto an executable canvas, measures exact geometric quantities, and feeds structured observations back to the model, so subsequent reasoning proceeds from checked canvas state grounded by the shared workspace. This externalization makes two properties separately auditable: model-level Construction Fidelity (whether the canvas realizes the intended configuration) and engine-level Measurement Faithfulness (exact values and relations from canvas constraints). Across construction, outcome, and rendering evaluations, Draw2Think builds canvases that pass 95.9% predicate-level and 84.0% strict problem-level construction checks on GeoGoal, improves outcome accuracy by up to 4.1%/16.4% on planar/solid benchmarks, and attains 68.2%/90.5% strict/relaxed rendering scores on GenExam-math. Project page is available at https://draw2think.github.io/

Predictive world models that simulate future observations under explicit camera control are fundamental to interactive AI. Despite rapid advances, current systems lack spatial persistence: they fail to maintain stable scene structures over long trajectories, frequently hallucinating details when cameras revisit previously observed locations. We identify that this geometric drift stems from reliance on screen-space positional embeddings, which conflict with the projective geometry required for 3D consistency. We introduce ViewRope, a geometry-aware encoding that injects camera-ray directions directly into video transformer self-attention layers. By parameterizing attention with relative ray geometry rather than pixel locality, ViewRope provides a model-native inductive bias for retrieving 3D-consistent content across temporal gaps. We further propose Geometry-Aware Frame-Sparse Attention, which exploits these geometric cues to selectively attend to relevant historical frames, improving efficiency without sacrificing memory consistency. We also present ViewBench, a diagnostic suite measuring loop-closure fidelity and geometric drift. Our results demonstrate that ViewRope substantially improves long-term consistency while reducing computational costs.

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

We introduce a unified framework for iterative reasoning that leverages non-Euclidean geometry via Bregman divergences, higher-order operator averaging, and adaptive feedback mechanisms. Our analysis establishes that, under mild smoothness and contractivity assumptions, a generalized update scheme not only unifies classical methods such as mirror descent and dynamic programming but also captures modern chain-of-thought reasoning processes in large language models. In particular, we prove that our accelerated iterative update achieves an O(1/t^2) convergence rate in the absence of persistent perturbations, and we further demonstrate that feedback (iterative) architectures are necessary to approximate certain fixed-point functions efficiently. These theoretical insights bridge classical acceleration techniques with contemporary applications in neural computation and optimization.

Classic 3D scene graph generation approaches fail to work in real-time due to the heavy computational cost of environment mapping and the need to generate intermediate point-cloud representations. To alleviate this issue, a recent work eschews point clouds in favor of a lightweight Gaussian distribution for each object. This approximation drastically speeds up inference and enables real-time 3D scene graph generation. However, the representation has two key weaknesses. 1) Each object is approximated by a single 3D Gaussian, which causes a severe loss of 3D geometric detail. 2) The discrepancy between this approximation and the true object geometry exacerbates the inaccurate merging of object candidates during online inference. To address these issues, we propose NoPA, which represents each object as a separate non-parametric distribution. This formulation retains 3D geometric information while preserving real-time inference of the parametric Gaussian formulation. To build upon our novel object representation, we propose a tailored merging strategy to recover coherent object instances. Specifically, we leverage maximum mean discrepancy on kernel density estimates to enable robust merging of object candidates during online exploration while minimizing added computational complexity. The key is to maintain a fixed particle set per object. Furthermore, to rectify the relation loss caused by misclassified objects, NoPA propagates relationships between objects with high affinity. Experiments show that NoPA substantially outperforms current methods without sacrificing real-time inference speed.

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.

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

Cross-modal Thermal Geo-localization (TG) provides a robust, all-weather solution for Unmanned Aerial Vehicles (UAVs) in Global Navigation Satellite System (GNSS)-denied environments. However, profound thermal-visible modality gaps introduce severe feature ambiguity, systematically corrupting conventional coarse-to-fine registration. To dismantle this bottleneck, we propose SCC-Loc, a unified Semantic-Cascade-Consensus localization framework. By sharing a single DINOv2 backbone across global retrieval and MINIMA_{RoMa} matching, it minimizes memory footprint and achieves zero-shot, highly accurate absolute position estimation. Specifically, we tackle modality ambiguity by introducing three cohesive components. First, we design the Semantic-Guided Viewport Alignment (SGVA) module to adaptively optimize satellite crop regions, effectively correcting initial spatial deviations. Second, we develop the Cascaded Spatial-Adaptive Texture-Structure Filtering (C-SATSF) mechanism to explicitly enforce geometric consistency, thereby eradicating dense cross-modal outliers. Finally, we propose the Consensus-Driven Reliability-Aware Position Selection (CD-RAPS) strategy to derive the optimal solution through a synergy of physically constrained pose optimization. To address data scarcity, we construct Thermal-UAV, a comprehensive dataset providing 11,890 diverse thermal queries referenced against a large-scale satellite ortho-photo and corresponding spatially aligned Digital Surface Model (DSM). Extensive experiments demonstrate that SCC-Loc establishes a new state-of-the-art, suppressing the mean localization error to 9.37 m and providing a 7.6-fold accuracy improvement within a strict 5-m threshold over the strongest baseline. Code and dataset are available at https://github.com/FloralHercules/SCC-Loc.

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

Sparse-view 3D modeling represents a fundamental tension between reconstruction fidelity and generative plausibility. While feed-forward reconstruction excels in efficiency and input alignment, it often lacks the global priors needed for structural completeness. Conversely, diffusion-based generation provides rich geometric details but struggles with multi-view consistency. We present UniRecGen, a unified framework that integrates these two paradigms into a single cooperative system. To overcome inherent conflicts in coordinate spaces, 3D representations, and training objectives, we align both models within a shared canonical space. We employ disentangled cooperative learning, which maintains stable training while enabling seamless collaboration during inference. Specifically, the reconstruction module is adapted to provide canonical geometric anchors, while the diffusion generator leverages latent-augmented conditioning to refine and complete the geometric structure. Experimental results demonstrate that UniRecGen achieves superior fidelity and robustness, outperforming existing methods in creating complete and consistent 3D models from sparse observations.

Point cloud registration is the task of estimating the rigid transformation that aligns a pair of point cloud fragments. We present an efficient and robust framework for pairwise registration of real-world 3D scans, leveraging Hough voting in the 6D transformation parameter space. First, deep geometric features are extracted from a point cloud pair to compute putative correspondences. We then construct a set of triplets of correspondences to cast votes on the 6D Hough space, representing the transformation parameters in sparse tensors. Next, a fully convolutional refinement module is applied to refine the noisy votes. Finally, we identify the consensus among the correspondences from the Hough space, which we use to predict our final transformation parameters. Our method outperforms state-of-the-art methods on 3DMatch and 3DLoMatch benchmarks while achieving comparable performance on KITTI odometry dataset. We further demonstrate the generalizability of our approach by setting a new state-of-the-art on ICL-NUIM dataset, where we integrate our module into a multi-way registration pipeline.

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

Recovering the relative 6-DoF pose between two image groups underlies cross-sequence relocalization and multi-camera rig odometry. Each group carries known intra-group geometry from visual odometry or rig calibration, and pretrained multi-view backbones already fuse such geometry into visual features. Yet current models treat all views as an unstructured set, leaving cross-group reasoning as the missing piece. We introduce , which keeps the foundation model entirely frozen and adds three lightweight trainable modules to bridge the two groups: a perceiver resampler, a cross-group bridge with merged self-attention, and a multi-frame pose head. The trainable footprint totals about 32M parameters, under 6\% of the full model, and is supervised only by relative poses. Across four datasets that span indoor and outdoor simulation, real-world cross-season capture, and zero-shot sim-to-real transfer, attains state-of-the-art accuracy on both tasks, while every baseline is retrained with its full original supervision. Code is available at https://github.com/WeiYuFei0217/G2G.

Cross-view geo-localization for Unmanned Aerial Vehicles (UAVs) operating in GNSS-denied environments remains challenging due to the severe geometric discrepancy between oblique UAV imagery and orthogonal satellite maps. Most existing methods address this problem through a decoupled pipeline of place retrieval and pose estimation, implicitly treating perspective distortion as appearance noise rather than an explicit geometric transformation. In this work, we propose a geometry-aware UAV geo-localization framework that explicitly models the 3D scene geometry to unify coarse place recognition and fine-grained pose estimation within a single inference pipeline. Our approach reconstructs a local 3D scene from multi-view UAV image sequences using a Visual Geometry Grounded Transformer (VGGT), and renders a virtual Bird's-Eye View (BEV) representation that orthorectifies the UAV perspective to align with satellite imagery. This BEV serves as a geometric intermediary that enables robust cross-view retrieval and provides spatial priors for accurate 3 Degrees of Freedom (3-DoF) pose regression. To efficiently handle multiple location hypotheses, we introduce a Satellite-wise Attention Block that isolates the interaction between each satellite candidate and the reconstructed UAV scene, preventing inter-candidate interference while maintaining linear computational complexity. In addition, we release a recalibrated version of the University-1652 dataset with precise coordinate annotations and spatial overlap analysis, enabling rigorous evaluation of end-to-end localization accuracy. Extensive experiments on the refined University-1652 benchmark and SUES-200 demonstrate that our method significantly outperforms state-of-the-art baselines, achieving robust meter-level localization accuracy and improved generalization in complex urban environments.

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

Diffusion models excel at 2D outpainting, but extending them to 360^circ panoramic completion from unposed perspective images is challenging due to the geometric and topological mismatch between perspective projections and spherical panoramas. We present Gimbal360, a principled framework that explicitly bridges perspective observations and spherical panoramas. We introduce a Canonical Viewing Space that regularizes projective geometry and provides a consistent intermediate representation between the two domains. To anchor in-the-wild inputs to this space, we propose a Differentiable Auto-Leveling module that stabilizes feature orientation without requiring camera parameters at inference. Panoramic generation also introduces a topological challenge. Standard generative architectures assume a bounded Euclidean image plane, while Equirectangular Projection (ERP) panoramas exhibit intrinsic S^1 periodicity. Euclidean operations therefore break boundary continuity. We address this mismatch by enforcing topological equivariance in the latent space to preserve seamless periodic structure. To support this formulation, we introduce Horizon360, a curated large-scale dataset of gravity-aligned panoramic environments. Extensive experiments show that explicitly standardizing geometric and topological priors enables Gimbal360 to achieve state-of-the-art performance in structurally consistent 360^circ scene completion.

Multi-robot systems require scalable and federated methods to model complex environments under computational and communication constraints. Gaussian Processes (GPs) offer robust probabilistic modeling, but suffer from cubic computational complexity, limiting their applicability in large-scale deployments. To address this challenge, we introduce the pxpGP, a novel distributed GP framework tailored for both centralized and decentralized large-scale multi-robot networks. Our approach leverages sparse variational inference to generate a local compact pseudo-representation. We introduce a sparse variational optimization scheme that bounds local pseudo-datasets and formulate a global scaled proximal-inexact consensus alternating direction method of multipliers (ADMM) with adaptive parameter updates and warm-start initialization. Experiments on synthetic and real-world datasets demonstrate that pxpGP and its decentralized variant, dec-pxpGP, outperform existing distributed GP methods in hyperparameter estimation and prediction accuracy, particularly in large-scale networks.

We present UniScale, a unified, scale-aware multi-view 3D reconstruction framework for robotic applications that flexibly integrates geometric priors through a modular, semantically informed design. In vision-based robotic navigation, the accurate extraction of environmental structure from raw image sequences is critical for downstream tasks. UniScale addresses this challenge with a single feed-forward network that jointly estimates camera intrinsics and extrinsics, scale-invariant depth and point maps, and the metric scale of a scene from multi-view images, while optionally incorporating auxiliary geometric priors when available. By combining global contextual reasoning with camera-aware feature representations, UniScale is able to recover the metric-scale of the scene. In robotic settings where camera intrinsics are known, they can be easily incorporated to improve performance, with additional gains obtained when camera poses are also available. This co-design enables robust, metric-aware 3D reconstruction within a single unified model. Importantly, UniScale does not require training from scratch, and leverages world priors exhibited in pre-existing models without geometric encoding strategies, making it particularly suitable for resource-constrained robotic teams. We evaluate UniScale on multiple benchmarks, demonstrating strong generalization and consistent performance across diverse environments. We will release our implementation upon acceptance.

Plane geometry problem solving (PGPS) has recently gained significant attention as a benchmark to assess the multi-modal reasoning capabilities of large vision-language models. Despite the growing interest in PGPS, the research community still lacks a comprehensive overview that systematically synthesizes recent work in PGPS. To fill this gap, we present a survey of existing PGPS studies. We first categorize PGPS methods into an encoder-decoder framework and summarize the corresponding output formats used by their encoders and decoders. Subsequently, we classify and analyze these encoders and decoders according to their architectural designs. Finally, we outline major challenges and promising directions for future research. In particular, we discuss the hallucination issues arising during the encoding phase within encoder-decoder architectures, as well as the problem of data leakage in current PGPS benchmarks.

Stable Diffusion Models (SDMs) have shown remarkable proficiency in image synthesis. However, their broad application is impeded by their large model sizes and intensive computational requirements, which typically require expensive cloud servers for deployment. On the flip side, while there are many compact models tailored for edge devices that can reduce these demands, they often compromise on semantic integrity and visual quality when compared to full-sized SDMs. To bridge this gap, we introduce Hybrid SD, an innovative, training-free SDMs inference framework designed for edge-cloud collaborative inference. Hybrid SD distributes the early steps of the diffusion process to the large models deployed on cloud servers, enhancing semantic planning. Furthermore, small efficient models deployed on edge devices can be integrated for refining visual details in the later stages. Acknowledging the diversity of edge devices with differing computational and storage capacities, we employ structural pruning to the SDMs U-Net and train a lightweight VAE. Empirical evaluations demonstrate that our compressed models achieve state-of-the-art parameter efficiency (225.8M) on edge devices with competitive image quality. Additionally, Hybrid SD reduces the cloud cost by 66% with edge-cloud collaborative inference.

Geometry problem solving (GPS) represents a critical frontier in artificial intelligence, with profound applications in education, computer-aided design, and computational graphics. Despite its significance, automating GPS remains challenging due to the dual demands of spatial understanding and rigorous logical reasoning. Recent advances in large models have enabled notable breakthroughs, particularly for SAT-level problems, yet the field remains fragmented across methodologies, benchmarks, and evaluation frameworks. This survey systematically synthesizes GPS advancements through three core dimensions: (1) benchmark construction, (2) textual and diagrammatic parsing, and (3) reasoning paradigms. We further propose a unified analytical paradigm, assess current limitations, and identify emerging opportunities to guide future research toward human-level geometric reasoning, including automated benchmark generation and interpretable neuro-symbolic integration.

We present WorldMirror, an all-in-one, feed-forward model for versatile 3D geometric prediction tasks. Unlike existing methods constrained to image-only inputs or customized for a specific task, our framework flexibly integrates diverse geometric priors, including camera poses, intrinsics, and depth maps, while simultaneously generating multiple 3D representations: dense point clouds, multi-view depth maps, camera parameters, surface normals, and 3D Gaussians. This elegant and unified architecture leverages available prior information to resolve structural ambiguities and delivers geometrically consistent 3D outputs in a single forward pass. WorldMirror achieves state-of-the-art performance across diverse benchmarks from camera, point map, depth, and surface normal estimation to novel view synthesis, while maintaining the efficiency of feed-forward inference. Code and models will be publicly available soon.

Geometric Problem Solving (GPS) remains at the heart of enhancing mathematical reasoning in large language models because it requires the combination of diagrammatic understanding, symbolic manipulation and logical inference. In existing literature, researchers have chiefly focused on synchronising the diagram descriptions with text literals and solving the problem. In this vein, they have either taken a neural, symbolic or neuro-symbolic approach. But this solves only the first two of the requirements, namely diagrammatic understanding and symbolic manipulation, while leaving logical inference underdeveloped. The logical inference is often limited to one chain-of-thought (CoT). To address this weakness in hitherto existing models, this paper proposes MARS-GPS, that generates multiple parallel reasoning rollouts augmented with Python code execution for numerical verification, ranks them using token-level entropy as a confidence signal, and aggregates answers through a multi-stage voting and self-verification pipeline. Empirical results show that MARS-GPS with 8 parallel rollouts achieves 88.8% on Geometry3K, a nearly +11% improvement over the prior state-of-the-art, with accuracy scaling consistently as the number of rollouts increases from 1 to 16 (+6.0% on ablation subset). We provide our code and data in an anonymous repository: https://anonymous.4open.science/r/MARS-GPS-DE55.

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.

Multi-view 3D geometry networks offer a powerful prior but are prohibitively slow for real-time applications. We propose a novel way to adapt them for online use, enabling real-time 6-DoF pose tracking and online reconstruction of objects and scenes from monocular RGB videos. Our method rapidly selects and manages a set of images as keyframes to map a scene or object via π^3 with full bidirectional attention. We then cache the global self-attention block's key-value (KV) pairs and use them as the sole scene representation for online tracking. This allows for up to 15times speedup during inference without the fear of drift or catastrophic forgetting. Our caching strategy is model-agnostic and can be applied to other off-the-shelf multi-view networks without retraining. We demonstrate KV-Tracker on both scene-level tracking and the more challenging task of on-the-fly object tracking and reconstruction without depth measurements or object priors. Experiments on the TUM RGB-D, 7-Scenes, Arctic and OnePose datasets show the strong performance of our system while maintaining high frame-rates up to {sim}27 FPS.

Recent advances in generative models highlight the power of geometry-aware modeling in manifold-constrained settings. Yet, for natural images, the field remains confined to Euclidean assumptions, failing to exploit the potential of intrinsic geometric structures within the data. In this work, we investigate the geometry of natural images and observe that semantic information is predominantly encoded in directional components, while norm components can be approximated by the global average. This property holds across both RGB and latent spaces, suggesting that natural images can be effectively modeled on a hypersphere. Building on this finding, we introduce Spherical Optimal Transport Flow Matching (SOT-CFM), which utilizes angular distance, and Spherical Flow Matching (SFM), which constrains dynamics directly on the manifold. Our experiments demonstrate that these geometry-aware methods achieve superior performance against Euclidean baselines. Ultimately, this work provides a novel perspective that bridges the gap between Riemannian manifold-based modeling and natural image generation.

Large language models (LLMs) are transforming society, powering applications from smartphone assistants to autonomous driving. Yet cloud-based LLM services alone cannot serve a growing class of applications, including those operating under intermittent connectivity, sub-second latency budgets, data-residency constraints, or sustained high-volume inference. On-device deployment is in turn constrained by limited computation and memory. No single endpoint can deliver high-quality service across this spectrum. This article focuses on collaborative intelligence, a paradigm in which multiple independent LLMs distributed across device and cloud endpoints collaborate at the task level through natural language or structured messages. Such collaboration strives for superior response quality under heterogeneous resource constraints spanning computation, memory, communication, and cost across network tiers. We present collaborative inference along two complementary and composable dimensions: vertical device-cloud collaboration and horizontal multi-agent collaboration, which can be combined into hybrid topologies in practice. We then examine learning to collaborate, addressing the training of routing policies and the development of cooperative capabilities among LLMs. Finally, we identify open research challenges including scaling under resource heterogeneity and trustworthy collaborative intelligence.

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

Geometry is a fundamental branch of mathematics and plays a crucial role in evaluating the reasoning capabilities of multimodal large language models (MLLMs). However, existing multimodal mathematics benchmarks mainly focus on plane geometry and largely ignore solid geometry, which requires spatial reasoning and is more challenging than plane geometry. To address this critical gap, we introduce SolidGeo, the first large-scale benchmark specifically designed to evaluate the performance of MLLMs on mathematical reasoning tasks in solid geometry. SolidGeo consists of 3,113 real-world K-12 and competition-level problems, each paired with visual context and annotated with difficulty levels and fine-grained solid geometry categories. Our benchmark covers a wide range of 3D reasoning subjects such as projection, unfolding, spatial measurement, and spatial vector, offering a rigorous testbed for assessing solid geometry. Through extensive experiments, we observe that MLLMs encounter substantial challenges in solid geometry math tasks, with a considerable performance gap relative to human capabilities on SolidGeo. Moreover, we analyze the performance, inference efficiency and error patterns of various models, offering insights into the solid geometric mathematical reasoning capabilities of MLLMs. We hope SolidGeo serves as a catalyst for advancing MLLMs toward deeper geometric reasoning and spatial intelligence.

Monocular and stereo depth estimation offer complementary strengths: monocular methods capture rich contextual priors but lack geometric precision, while stereo approaches leverage epipolar geometry yet struggle with ambiguities such as reflective or textureless surfaces. Despite post-hoc synergies, these paradigms remain largely disjoint in practice. We introduce a unified framework that bridges both through iterative bidirectional alignment of their latent representations. At its core, a novel cross-attentive alignment mechanism dynamically synchronizes monocular contextual cues with stereo hypothesis representations during stereo reasoning. This mutual alignment resolves stereo ambiguities (e.g., specular surfaces) by injecting monocular structure priors while refining monocular depth with stereo geometry within a single network. Extensive experiments demonstrate state-of-the-art results: it reduces zero-shot generalization error by !>!40% on Middlebury and ETH3D, while addressing longstanding failures on transparent and reflective surfaces. By harmonizing multi-view geometry with monocular context, our approach enables robust 3D perception that transcends modality-specific limitations. Codes available at https://github.com/aeolusguan/BridgeDepth.

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.

Belief Propagation (BP) is a powerful algorithm for distributed inference in probabilistic graphical models, however it quickly becomes infeasible for practical compute and memory budgets. Many efficient, non-parametric forms of BP have been developed, but the most popular is Gaussian Belief Propagation (GBP), a variant that assumes all distributions are locally Gaussian. GBP is widely used due to its efficiency and empirically strong performance in applications like computer vision or sensor networks - even when modelling non-Gaussian problems. In this paper, we seek to provide a theoretical guarantee for when Gaussian approximations are valid in highly non-Gaussian, sparsely-connected factor graphs performing BP (common in spatial AI). We leverage the Central Limit Theorem (CLT) to prove mathematically that variables' beliefs under BP converge to a Gaussian distribution in complex, loopy factor graphs obeying our 4 key assumptions. We then confirm experimentally that variable beliefs become increasingly Gaussian after just a few BP iterations in a stereo depth estimation task.

Geospatial reasoning requires models to resolve complex spatial semantics and user intent into precise target locations for Earth observation. Recent progress has liberated the reasoning path from manual curation, allowing models to generate their own inference chains. Yet a final dependency remains: they are still supervised by human-annotated ground-truth coordinates. This leaves the reasoning process autonomous, but not its spatial endpoint, and prevents true self-evolution on abundant unlabeled remote sensing data. To break this bottleneck, we introduce RemoteZero, a box-supervision-free framework for geospatial reasoning. RemoteZero is motivated by a simple asymmetry: an MLLM is typically better at verifying whether a region satisfies a query than at directly generating precise coordinates. Leveraging this stronger discriminative ability, RemoteZero replaces geometric supervision with intrinsic semantic verification and enables GRPO training without box annotations. The resulting framework further supports iterative self-evolution, allowing the model to improve from unlabeled remote sensing imagery through its own verification signal. Experiments show that RemoteZero achieves competitive performance against strong supervised methods, demonstrating the potential of self-verifying training for geospatial reasoning localization.

Recent feed-forward geometry foundation models have demonstrated impressive generalization by recovering depth and poses in a single forward pass. However, these models are typically constrained by a global coordinate frame assumption. This dependency becomes a significant bottleneck for long-context and streaming reconstruction, as it forces the network to maintain an arbitrary temporal origin and handle translation magnitudes that grow unbounded over time. Our solution, which we call R^3, employs relative regression. We employ a lightweight MLP to predict confidence-weighted relative constraints. These confidences serve as a unified anchor: weighting losses during training and guiding pose aggregation during inference. R^3 supports both full-context offline reconstruction and causal, bounded-memory streaming. Our evaluation in both offline and streaming settings validates the effectiveness of our relative mechanism. Project page: https://kevinxu02.github.io/r3-site

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

Recent studies of two-view correspondence learning usually establish an end-to-end network to jointly predict correspondence reliability and relative pose. We improve such a framework from two aspects. First, we propose a Local Feature Consensus (LFC) plugin block to augment the features of existing models. Given a correspondence feature, the block augments its neighboring features with mutual neighborhood consensus and aggregates them to produce an enhanced feature. As inliers obey a uniform cross-view transformation and share more consistent learned features than outliers, feature consensus strengthens inlier correlation and suppresses outlier distraction, which makes output features more discriminative for classifying inliers/outliers. Second, existing approaches supervise network training with the ground truth correspondences and essential matrix projecting one image to the other for an input image pair, without considering the information from the reverse mapping. We extend existing models to a Siamese network with a reciprocal loss that exploits the supervision of mutual projection, which considerably promotes the matching performance without introducing additional model parameters. Building upon MSA-Net, we implement the two proposals and experimentally achieve state-of-the-art performance on benchmark datasets.

Generating executable CAD programs from images requires alignment between visual geometry and symbolic program representations, a capability that current methods fail to learn reliably as design complexity increases. Existing fine-tuning approaches rely on either limited supervised datasets or expensive post-training pipelines, resulting in brittle systems that restrict progress in generative CAD design. We argue that the primary bottleneck lies not in model or algorithmic capacity, but in the scarcity of diverse training examples that align visual geometry with program syntax. This limitation is especially acute because the collection of diverse and verified engineering datasets is both expensive and difficult to scale, constraining the development of robust generative CAD models. We introduce Geometric Inference Feedback Tuning (GIFT), a data augmentation framework that leverages geometric feedback to turn test-time compute into a bootstrapped set of high-quality training samples. GIFT combines two mechanisms: Soft-Rejection Sampling (GIFT-REJECT), which retains diverse high-fidelity programs beyond exact ground-truth matches, and Failure-Driven Augmentation (GIFT-FAIL), which converts near-miss predictions into synthetic training examples that improve robustness on challenging geometries. By amortizing inference-time search into the model parameters, GIFT captures the benefits of test-time scaling while reducing inference compute by 80%. It improves mean IoU by 12% over a strong supervised baseline and remains competitive with more complex multimodal systems, without requiring additional human annotation or specialized architectures.

Conformal prediction is emerging as a popular paradigm for providing rigorous uncertainty quantification in machine learning since it can be easily applied as a post-processing step to already trained models. In this paper, we extend conformal prediction to the federated learning setting. The main challenge we face is data heterogeneity across the clients - this violates the fundamental tenet of exchangeability required for conformal prediction. We propose a weaker notion of partial exchangeability, better suited to the FL setting, and use it to develop the Federated Conformal Prediction (FCP) framework. We show FCP enjoys rigorous theoretical guarantees and excellent empirical performance on several computer vision and medical imaging datasets. Our results demonstrate a practical approach to incorporating meaningful uncertainty quantification in distributed and heterogeneous environments. We provide code used in our experiments https://github.com/clu5/federated-conformal.

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

Vision-Language Models (VLMs) often struggle with robust 3D spatial reasoning. Prevailing methods that rely on fine-tuning with 3D visual question-answering (VQA) datasets may overfit dataset-specific biases, while integrating specialized 3D visual encoders is often inflexible and cumbersome. In this paper, we argue that genuine spatial understanding should emerge from learning fundamental geometric priors, not only from high-level VQA supervision. We propose GASP (Geometric-Aware Spatial Priors), a framework that injects these priors directly into the LLM's transformer layers. GASP employs a small correspondence head, applied as a deep supervision signal across all layers, and is trained with a dual objective leveraging ground-truth geometry from large-scale video scenes: a contrastive loss on ground-truth point correspondences enforces 2D view-invariance, while a depth consistency supervision resolves 3D geometric ambiguities. Our analysis first provides a diagnostic showing that standard VLMs' internal correspondence matching accuracy is very low (often below 5%). We then demonstrate that our training substantially improves this behavior, boosting peak layer-wise correspondence to over 70% and maintaining over 85% temporal robustness while baselines remain below 5%. These internal improvements translate to significant gains on downstream spatial benchmarks including +18.2% on All-Angles Bench and +29.0% on VSI-Bench, all without training on any 3D VQA data. Our findings indicate that learning from fundamental geometric priors is a promising and generalizable pathway towards VLMs with more reliable 3D spatial reasoning.

We address the challenging problem of semi-supervised learning in the context of multiple visual interpretations of the world by finding consensus in a graph of neural networks. Each graph node is a scene interpretation layer, while each edge is a deep net that transforms one layer at one node into another from a different node. During the supervised phase edge networks are trained independently. During the next unsupervised stage edge nets are trained on the pseudo-ground truth provided by consensus among multiple paths that reach the nets' start and end nodes. These paths act as ensemble teachers for any given edge and strong consensus is used for high-confidence supervisory signal. The unsupervised learning process is repeated over several generations, in which each edge becomes a "student" and also part of different ensemble "teachers" for training other students. By optimizing such consensus between different paths, the graph reaches consistency and robustness over multiple interpretations and generations, in the face of unknown labels. We give theoretical justifications of the proposed idea and validate it on a large dataset. We show how prediction of different representations such as depth, semantic segmentation, surface normals and pose from RGB input could be effectively learned through self-supervised consensus in our graph. We also compare to state-of-the-art methods for multi-task and semi-supervised learning and show superior performance.

As a fundamental problem in computer vision, 3D point cloud registration (PCR) aims to seek the optimal pose to align a point cloud pair. In this paper, we present a 3D registration method with maximal cliques (MAC). The key insight is to loosen the previous maximum clique constraint, and mine more local consensus information in a graph for accurate pose hypotheses generation: 1) A compatibility graph is constructed to render the affinity relationship between initial correspondences. 2) We search for maximal cliques in the graph, each of which represents a consensus set. We perform node-guided clique selection then, where each node corresponds to the maximal clique with the greatest graph weight. 3) Transformation hypotheses are computed for the selected cliques by the SVD algorithm and the best hypothesis is used to perform registration. Extensive experiments on U3M, 3DMatch, 3DLoMatch and KITTI demonstrate that MAC effectively increases registration accuracy, outperforms various state-of-the-art methods and boosts the performance of deep-learned methods. MAC combined with deep-learned methods achieves state-of-the-art registration recall of 95.7% / 78.9% on 3DMatch / 3DLoMatch.

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

Large vision-language models (VLMs) still struggle with reliable 3D spatial reasoning, a core capability for embodied and physical AI systems. This limitation arises from their inability to capture fine-grained 3D geometry and spatial relationships. While recent efforts have introduced multi-view geometry transformers into VLMs, they typically fuse only the deep-layer features from vision and geometry encoders, discarding rich hierarchical signals and creating a fundamental bottleneck for spatial understanding. To overcome this, we propose SpatialStack, a general hierarchical fusion framework that progressively aligns vision, geometry, and language representations across the model hierarchy. Moving beyond conventional late-stage vision-geometry fusion, SpatialStack stacks and synchronizes multi-level geometric features with the language backbone, enabling the model to capture both local geometric precision and global contextual semantics. Building upon this framework, we develop VLM-SpatialStack, a model that achieves state-of-the-art performance on multiple 3D spatial reasoning benchmarks. Extensive experiments and ablations demonstrate that our multi-level fusion strategy consistently enhances 3D understanding and generalizes robustly across diverse spatial reasoning tasks, establishing SpatialStack as an effective and extensible design paradigm for vision-language-geometry integration in next-generation multimodal physical AI systems.

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

Open-Vocabulary 3D object affordance grounding aims to anticipate ``action possibilities'' regions on 3D objects with arbitrary instructions, which is crucial for robots to generically perceive real scenarios and respond to operational changes. Existing methods focus on combining images or languages that depict interactions with 3D geometries to introduce external interaction priors. However, they are still vulnerable to a limited semantic space by failing to leverage implied invariant geometries and potential interaction intentions. Normally, humans address complex tasks through multi-step reasoning and respond to diverse situations by leveraging associative and analogical thinking. In light of this, we propose GREAT (GeometRy-intEntion collAboraTive inference) for Open-Vocabulary 3D Object Affordance Grounding, a novel framework that mines the object invariant geometry attributes and performs analogically reason in potential interaction scenarios to form affordance knowledge, fully combining the knowledge with both geometries and visual contents to ground 3D object affordance. Besides, we introduce the Point Image Affordance Dataset v2 (PIADv2), the largest 3D object affordance dataset at present to support the task. Extensive experiments demonstrate the effectiveness and superiority of GREAT. The code and dataset are available at https://yawen-shao.github.io/GREAT/.

Multi-view visual reasoning is essential for intelligent systems that must understand complex environments from sparse and discrete viewpoints, yet existing research has largely focused on single-image or temporally dense video settings. In real-world scenarios, reasoning across views requires integrating partial observations without explicit guidance, while collecting large-scale multi-view data with accurate geometric and semantic annotations remains challenging. To address this gap, we leverage physically grounded simulation to construct diverse, high-fidelity 3D scenes with precise per-view metadata, enabling scalable data generation that remains transferable to real-world settings. Based on this engine, we introduce VIEW2SPACE, a multi-dimensional benchmark for sparse multi-view reasoning, together with a scalable, disjoint training split supporting millions of grounded question-answer pairs. Using this benchmark, a comprehensive evaluation of state-of-the-art vision-language and spatial models reveals that multi-view reasoning remains largely unsolved, with most models performing only marginally above random guessing. We further investigate whether training can bridge this gap. Our proposed Grounded Chain-of-Thought with Visual Evidence substantially improves performance under moderate difficulty, and generalizes to real-world data, outperforming existing approaches in cross-dataset evaluation. We further conduct difficulty-aware scaling analyses across model size, data scale, reasoning depth, and visibility constraints, indicating that while geometric perception can benefit from scaling under sufficient visibility, deep compositional reasoning across sparse views remains a fundamental challenge.

Driving world models serve as a pivotal technology for autonomous driving by simulating environmental dynamics. However, existing approaches predominantly focus on future scene generation, often overlooking comprehensive 3D scene understanding. Conversely, while Large Language Models (LLMs) demonstrate impressive reasoning capabilities, they lack the capacity to predict future geometric evolution, creating a significant disparity between semantic interpretation and physical simulation. To bridge this gap, we propose HERMES++, a unified driving world model that integrates 3D scene understanding and future geometry prediction within a single framework. Our approach addresses the distinct requirements of these tasks through synergistic designs. First, a BEV representation consolidates multi-view spatial information into a structure compatible with LLMs. Second, we introduce LLM-enhanced world queries to facilitate knowledge transfer from the understanding branch. Third, a Current-to-Future Link is designed to bridge the temporal gap, conditioning geometric evolution on semantic context. Finally, to enforce structural integrity, we employ a Joint Geometric Optimization strategy that integrates explicit geometric constraints with implicit latent regularization to align internal representations with geometry-aware priors. Extensive evaluations on multiple benchmarks validate the effectiveness of our method. HERMES++ achieves strong performance, outperforming specialist approaches in both future point cloud prediction and 3D scene understanding tasks. The model and code will be publicly released at https://github.com/H-EmbodVis/HERMESV2.

Self-supervised surround-view depth estimation enables dense, low-cost 3D perception with a 360° field of view from multiple minimally overlapping images. Yet, most existing methods suffer from depth estimates that are inconsistent across overlapping images. To address this limitation, we propose a novel geometry-guided method for calibrated, time-synchronized multi-camera rigs that predicts dense metric depth. Our approach targets two main sources of inconsistency: the limited receptive field in border regions of single-image depth estimation, and the difficulty of correspondence matching. We mitigate these two issues by extending the receptive field across views and restricting cross-view attention to a small neighborhood. To this end, we establish the neighborhood relationships between images by mapping the image-specific feature positions onto a shared cylinder. Based on the cylindrical positions, we apply an explicit spatial attention mechanism, with non-learned weighting, that aggregates features across images according to their distances on the cylinder. The modulated features are then decoded into a depth map for each view. Evaluated on the DDAD and nuScenes datasets, our method improves both cross-view depth consistency and overall depth accuracy compared with state-of-the-art approaches. Code is available at https://abualhanud.github.io/CylinderDepthPage.

We address the challenge of knowledge composition in Vision-Language Models (VLMs), where accumulating expertise across multiple domains or tasks typically leads to catastrophic forgetting. We introduce GeoStack (Geometric Stacking), a modular framework that allows independently trained domain experts to be composed into a unified model. By imposing geometric and structural constraints on the adapter manifold, GeoStack ensures the foundational knowledge of the base model is preserved. Furthermore, we mathematically demonstrate a weight-folding property that achieves constant-time inference complexity (O(1)), regardless of the number of integrated experts. Experimental results across multi-domain adaptation and class-incremental learning show that GeoStack provides an efficient mechanism for long-term knowledge composition while significantly mitigating catastrophic forgetting. Code is available at https://github.com/QuantitativeImagingLaboratory/GeoStack.

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

Multimodal Large Language Models (MLLMs) excel at 2D semantic understanding but lack intrinsic 3D awareness, resulting in representations that fail to maintain geometric and spatial consistency across video frames. Given the scarcity of large-scale 3D data, we present GeoVR, a novel framework that learns geometric representations using purely 2D video sequences. This approach effectively restructures the semantic latent space within MLLMs to unlock spatial intelligence. Rather than employing superficial feature mixing, GeoVR reshapes the internal representations of the MLLM by distilling geometry knowledge from pre-trained 3D foundation models. This is accomplished through a multi-objective learning strategy driven by four complementary geometric targets: (1) estimating inter-frame camera poses to embed varying viewpoint dynamics, (2) regressing dense depth maps to anchor physical distances, (3) predicting a metric scale factor for real-world calibration, and (4) distilling multi-scale 3D features to align the intermediate feature space. Guided by these explicit physical and geometric constraints, the model's internal representations naturally develop strong 3D awareness. Extensive experiments on spatial reasoning benchmarks demonstrate that GeoVR achieves state-of-the-art performance, establishing a new paradigm for endowing foundation models with spatial intelligence.

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

We introduce StereoSpace, a diffusion-based framework for monocular-to-stereo synthesis that models geometry purely through viewpoint conditioning, without explicit depth or warping. A canonical rectified space and the conditioning guide the generator to infer correspondences and fill disocclusions end-to-end. To ensure fair and leakage-free evaluation, we introduce an end-to-end protocol that excludes any ground truth or proxy geometry estimates at test time. The protocol emphasizes metrics reflecting downstream relevance: iSQoE for perceptual comfort and MEt3R for geometric consistency. StereoSpace surpasses other methods from the warp & inpaint, latent-warping, and warped-conditioning categories, achieving sharp parallax and strong robustness on layered and non-Lambertian scenes. This establishes viewpoint-conditioned diffusion as a scalable, depth-free solution for stereo generation.

The Platonic Representation Hypothesis suggests that independently trained neural networks converge to increasingly similar latent spaces. However, current strategies for mapping these representations are inherently pairwise, scaling quadratically with the number of models and failing to yield a consistent global reference. In this paper, we study the alignment of M ge 3 models. We first adapt Generalized Procrustes Analysis (GPA) to construct a shared orthogonal universe that preserves the internal geometry essential for tasks like model stitching. We then show that strict isometric alignment is suboptimal for retrieval, where agreement-maximizing methods like Canonical Correlation Analysis (CCA) typically prevail. To bridge this gap, we finally propose Geometry-Corrected Procrustes Alignment (GCPA), which establishes a robust GPA-based universe followed by a post-hoc correction for directional mismatch. Extensive experiments demonstrate that GCPA consistently improves any-to-any retrieval while retaining a practical shared reference space.

As centralized AI hits compute ceilings and diminishing returns from ever-larger training runs, meeting demand requires an inference layer that scales horizontally in both capacity and capability. We present Fortytwo, a novel protocol that leverages swarm intelligence principles and distributed pairwise ranking consensus to achieve superior performance in AI inference. Our approach reimagines collaboration among AI nodes using swarm inference: a peer-ranked, reputation-weighted consensus across heterogeneous models that surfaces the highest-quality responses. Using pairwise ranking with a custom Bradley-Terry-style aggregation model, we demonstrate that swarm inference substantially outperforms majority voting, achieving 85.90% on GPQA Diamond versus 68.69% for majority voting with the same model set - an improvement of +17.21 percentage points (approximately +25.1% relative). The protocol incorporates on-chain reputation so node influence adapts to demonstrated accuracy over time, yielding a meritocratic consensus that filters low-quality or malicious participants. To resist Sybil attacks, Fortytwo employs proof-of-capability in its consensus: nodes must successfully complete calibration/test requests and stake reputation to enter ranking rounds, making multi-identity attacks economically unattractive while preserving openness. Across six challenging benchmarks, including GPQA Diamond, LiveCodeBench, and AIME, our evaluation indicates higher accuracy and strong resilience to adversarial and noisy free-form prompting (e.g., prompt-injection degradation of only 0.12% versus 6.20% for a monolithic single-model baseline), while retaining practical deployability. Together, these results establish a foundation for decentralized AI systems - democratizing access to high-quality inference through collective intelligence without sacrificing reliability or security.

Vision-centric autonomous driving requires accurate metric geometry and ego-motion estimation from synchronized multi-camera observations. Recent visual geometry models show strong performance in pose estimation, depth prediction, and 3D reconstruction, but are not tailored to rigid multi-camera driving systems. They often encode camera poses as entangled representations, in which time-varying ego-motion and static camera-rig geometry are jointly modeled, limiting the utilization of vehicle-side geometric priors. We propose Trajectory-Rig Decoupled Metric Geometry Learning (TRIG), a geometry perception framework for autonomous driving. TRIG factorizes camera poses into ego-trajectory and camera-rig components, enabling separate modeling of ego-motion and static multi-camera topology. We introduce decoupled pose encoding and supervision, which separately constrain trajectory evolution and rig geometry for metric-consistent learning. Moreover, sparse Temporal--Spatial attention separates cross-camera interaction from temporal aggregation, reducing global attention cost while preserving geometric reasoning. Experiments on five autonomous driving benchmarks show that TRIG achieves state-of-the-art performance in pose estimation, metric depth prediction, and 3D reconstruction.

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

Recent advances in vision foundation models have revolutionized geometry reconstruction and semantic understanding. Yet, most of the existing approaches treat these capabilities in isolation, leading to redundant pipelines and compounded errors. This paper introduces FF3R, a fully annotation-free feed-forward framework that unifies geometric and semantic reasoning from unconstrained multi-view image sequences. Unlike previous methods, FF3R does not require camera poses, depth maps, or semantic labels, relying solely on rendering supervision for RGB and feature maps, establishing a scalable paradigm for unified 3D reasoning. In addition, we address two critical challenges in feedforward feature reconstruction pipelines, namely global semantic inconsistency and local structural inconsistency, through two key innovations: (i) a Token-wise Fusion Module that enriches geometry tokens with semantic context via cross-attention, and (ii) a Semantic-Geometry Mutual Boosting mechanism combining geometry-guided feature warping for global consistency with semantic-aware voxelization for local coherence. Extensive experiments on ScanNet and DL3DV-10K demonstrate FF3R's superior performance in novel-view synthesis, open-vocabulary semantic segmentation, and depth estimation, with strong generalization to in-the-wild scenarios, paving the way for embodied intelligence systems that demand both spatial and semantic understanding.

While Multimodal Large Language Models (MLLMs) excel in semantic tasks, they frequently lack the "spatial sense" essential for sophisticated geometric reasoning. Current models typically suffer from exorbitant modality-alignment costs and deficiency in fine-grained structural modeling precision.We introduce SSR, a framework designed for Structured Scene Reasoning that seamlessly integrates 2D and 3D representations via a lightweight alignment mechanism. To minimize training overhead, our framework anchors 3D geometric features to the large language model's pre-aligned 2D visual semantics through cross-modal addition and token interleaving, effectively obviating the necessity for large-scale alignment pre-training. To underpin complex spatial reasoning, we propose a novel scene graph generation pipeline that represents global layouts as a chain of independent local triplets defined by relative coordinates. This is complemented by an incremental generation algorithm, enabling the model to construct "language-model-friendly" structural scaffolds for complex environments. Furthermore, we extend these capabilities to global-scale 3D global grounding task, achieving absolute metric precision across heterogeneous data sources. At a 7B parameter scale, SSR achieves state-of-the-art performance on multiple spatial intelligence benchmarks, notably scoring 73.9 on VSI-Bench. Our approach significantly outperforms much larger models, demonstrating that efficient feature alignment and structured scene reasoning are the cornerstones of authentic spatial intelligence.

We propose 3D Congealing, a novel problem of 3D-aware alignment for 2D images capturing semantically similar objects. Given a collection of unlabeled Internet images, our goal is to associate the shared semantic parts from the inputs and aggregate the knowledge from 2D images to a shared 3D canonical space. We introduce a general framework that tackles the task without assuming shape templates, poses, or any camera parameters. At its core is a canonical 3D representation that encapsulates geometric and semantic information. The framework optimizes for the canonical representation together with the pose for each input image, and a per-image coordinate map that warps 2D pixel coordinates to the 3D canonical frame to account for the shape matching. The optimization procedure fuses prior knowledge from a pre-trained image generative model and semantic information from input images. The former provides strong knowledge guidance for this under-constraint task, while the latter provides the necessary information to mitigate the training data bias from the pre-trained model. Our framework can be used for various tasks such as correspondence matching, pose estimation, and image editing, achieving strong results on real-world image datasets under challenging illumination conditions and on in-the-wild online image collections.

We introduce `dualGNN', an autoregressive message-passing GNN for sampling fine, regular triangulations (FRTs) of convex polytopes. dualGNN operates on a generalization of the dual graph of a triangulation, with edges labeled by `signed circuits' -- combinatorial invariants from oriented matroid theory which we show are both necessary and sufficient for exposing regularity. The model is independent of the number of points in the polytope and invariant under the polytope's orientation-preserving symmetries (SL(d,Z) ltimes Z^d). When implemented with a certain masking procedure, one can also guarantee that every rollout produces a fine triangulation (in 2D). On unseen polygons with N_pts leq 40, dualGNN is the most uniform FRT sampler we tested, and even a model trained on a single polygon generalizes well to other polygons. The model is small (sim92k parameters), trains in sim7.5 hours on a single consumer GPU, and runs without modification on an M1 MacBook Pro. We apply dualGNN to string theory, uniformly sampling Calabi-Yau threefolds at h^{1,1}=86 and consistent with uniformity at h^{1,1}=128. This is an order of magnitude beyond previous learned methods with a model sim1000times smaller. Code, training scripts, and pretrained models are available at https://github.com/natemacfadden/dualGNN .

Stream networks, a unique class of spatiotemporal graphs, exhibit complex directional flow constraints and evolving dependencies, making uncertainty quantification a critical yet challenging task. Traditional conformal prediction methods struggle in this setting due to the need for joint predictions across multiple interdependent locations and the intricate spatio-temporal dependencies inherent in stream networks. Existing approaches either neglect dependencies, leading to overly conservative predictions, or rely solely on data-driven estimations, failing to capture the rich topological structure of the network. To address these challenges, we propose Spatio-Temporal Adaptive Conformal Inference (STACI), a novel framework that integrates network topology and temporal dynamics into the conformal prediction framework. STACI introduces a topology-aware nonconformity score that respects directional flow constraints and dynamically adjusts prediction sets to account for temporal distributional shifts. We provide theoretical guarantees on the validity of our approach and demonstrate its superior performance on both synthetic and real-world datasets. Our results show that STACI effectively balances prediction efficiency and coverage, outperforming existing conformal prediction methods for stream networks.

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

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.

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.

Prior methods that tackle the problem of generalizable object pose estimation highly rely on having dense views of the unseen object. By contrast, we address the scenario where only a single reference view of the object is available. Our goal then is to estimate the relative object pose between this reference view and a query image that depicts the object in a different pose. In this scenario, robust generalization is imperative due to the presence of unseen objects during testing and the large-scale object pose variation between the reference and the query. To this end, we present a new hypothesis-and-verification framework, in which we generate and evaluate multiple pose hypotheses, ultimately selecting the most reliable one as the relative object pose. To measure reliability, we introduce a 3D-aware verification that explicitly applies 3D transformations to the 3D object representations learned from the two input images. Our comprehensive experiments on the Objaverse, LINEMOD, and CO3D datasets evidence the superior accuracy of our approach in relative pose estimation and its robustness in large-scale pose variations, when dealing with unseen objects.

Reconstructing 3D geometry from streaming video requires continuous inference under bounded resources. Recent geometric foundation models achieve impressive reconstruction quality through all-to-all attention, yet their quadratic cost confines them to short, offline sequences. Causal-attention variants such as StreamVGGT enable single-pass streaming but accumulate an ever-growing KV cache, exhausting GPU memory within hundreds of frames and precluding the long-horizon deployment that motivates streaming inference in the first place. We present OVGGT, a training-free framework that bounds both memory and compute to a fixed budget regardless of sequence length. Our approach combines Self-Selective Caching, which leverages FFN residual magnitudes to compress the KV cache while remaining fully compatible with FlashAttention, with Dynamic Anchor Protection, which shields coordinate-critical tokens from eviction to suppress geometric drift over extended trajectories. Extensive experiments on indoor, outdoor, and ultra-long sequence benchmarks demonstrate that OVGGT processes arbitrarily long videos within a constant VRAM envelope while achieving state-of-the-art 3D geometric accuracy.

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.

In this paper, we introduce a novel geometry-aware self-training framework for room layout estimation models on unseen scenes with unlabeled data. Our approach utilizes a ray-casting formulation to aggregate multiple estimates from different viewing positions, enabling the computation of reliable pseudo-labels for self-training. In particular, our ray-casting approach enforces multi-view consistency along all ray directions and prioritizes spatial proximity to the camera view for geometry reasoning. As a result, our geometry-aware pseudo-labels effectively handle complex room geometries and occluded walls without relying on assumptions such as Manhattan World or planar room walls. Evaluation on publicly available datasets, including synthetic and real-world scenarios, demonstrates significant improvements in current state-of-the-art layout models without using any human annotation.

Adversarial threats against LLMs are escalating faster than current defenses can adapt. We expose a critical geometric blind spot in alignment: adversarial prompts exploit latent camouflage, embedding perilously close to the safe representation manifold while encoding unsafe intent thereby evading surface level defenses like Direct Preference Optimization (DPO), which remain blind to the latent geometry. We introduce ALKALI, the first rigorously curated adversarial benchmark and the most comprehensive to date spanning 9,000 prompts across three macro categories, six subtypes, and fifteen attack families. Evaluation of 21 leading LLMs reveals alarmingly high Attack Success Rates (ASRs) across both open and closed source models, exposing an underlying vulnerability we term latent camouflage, a structural blind spot where adversarial completions mimic the latent geometry of safe ones. To mitigate this vulnerability, we introduce GRACE - Geometric Representation Aware Contrastive Enhancement, an alignment framework coupling preference learning with latent space regularization. GRACE enforces two constraints: latent separation between safe and adversarial completions, and adversarial cohesion among unsafe and jailbreak behaviors. These operate over layerwise pooled embeddings guided by a learned attention profile, reshaping internal geometry without modifying the base model, and achieve up to 39% ASR reduction. Moreover, we introduce AVQI, a geometry aware metric that quantifies latent alignment failure via cluster separation and compactness. AVQI reveals when unsafe completions mimic the geometry of safe ones, offering a principled lens into how models internally encode safety. We make the code publicly available at https://anonymous.4open.science/r/alkali-B416/README.md.

Large Language Models (LLMs) are increasingly deployed in applications that interact with the physical world, such as navigation, robotics, or mapping, making robust geospatial reasoning a critical capability. Despite that, LLMs' ability to reason about GPS coordinates and real-world geography remains underexplored. We introduce GPSBench, a dataset of 57,800 samples across 17 tasks for evaluating geospatial reasoning in LLMs, spanning geometric coordinate operations (e.g., distance and bearing computation) and reasoning that integrates coordinates with world knowledge. Focusing on intrinsic model capabilities rather than tool use, we evaluate 14 state-of-the-art LLMs and find that GPS reasoning remains challenging, with substantial variation across tasks: models are generally more reliable at real-world geographic reasoning than at geometric computations. Geographic knowledge degrades hierarchically, with strong country-level performance but weak city-level localization, while robustness to coordinate noise suggests genuine coordinate understanding rather than memorization. We further show that GPS-coordinate augmentation can improve in downstream geospatial tasks, and that finetuning induces trade-offs between gains in geometric computation and degradation in world knowledge. Our dataset and reproducible code are available at https://github.com/joey234/gpsbench

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

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

3D shape completion methods typically assume scans are pre-aligned to a canonical frame. This leaks pose and scale cues that networks may exploit to memorize absolute positions rather than inferring intrinsic geometry. When such alignment is absent in real data, performance collapses. We argue that robust generalization demands architectural equivariance to the similarity group, SIM(3), so the model remains agnostic to pose and scale. Following this principle, we introduce the first SIM(3)-equivariant shape completion network, whose modular layers successively canonicalize features, reason over similarity-invariant geometry, and restore the original frame. Under a de-biased evaluation protocol that removes the hidden cues, our model outperforms both equivariant and augmentation baselines on the PCN benchmark. It also sets new cross-domain records on real driving and indoor scans, lowering minimal matching distance on KITTI by 17% and Chamfer distance ell1 on OmniObject3D by 14%. Perhaps surprisingly, ours under the stricter protocol still outperforms competitors under their biased settings. These results establish full SIM(3) equivariance as an effective route to truly generalizable shape completion. Project page: https://sime-completion.github.io.

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

Large Language model (LLM)-based Multi-Agent Systems (MAS) are prone to cascading risks, where early-stage interactions remain semantically fluent and policy-compliant, yet the underlying interaction dynamics begin to distort in ways that amplify latent instability or misalignment. Traditional auditing methods that focus on per-message semantic content are inherently reactive and lagging, failing to capture these early structural precursors. In this paper, we propose a principled framework for cascading-risk detection grounded in semantic--geometric co-evolution. We model MAS interactions as dynamic graphs and introduce Ollivier--Ricci Curvature (ORC) -- a discrete geometric measure -- to characterize information redundancy and bottleneck formation in communication topologies. By coupling semantic flow signals with graph geometry, the framework learns the normal co-evolutionary dynamics of trusted collaboration and treats deviations from this coupled manifold as early-warning signals. Experiments on a suite of cascading-risk scenarios aligned with the risk category demonstrate that curvature anomalies systematically precede explicit semantic violations by several interaction turns, enabling proactive intervention. Furthermore, the local nature of Ricci curvature provides principled interpretability for root-cause attribution, identifying specific agents or links that precipitate the collapse of trustworthy collaboration.

Reliable odometry is essential for mobile robots as they increasingly enter more challenging environments, which often contain little information to constrain point cloud registration, resulting in degraded LiDAR-Inertial Odometry (LIO) accuracy or even divergence. To address this, we present BIEVR-LIO, a novel approach designed specifically to exploit subtle variations in the available geometry for improved robustness. We propose a high-resolution map representation that stores surfaces as compact voxel-wise oriented height images. This representation can directly be used for registration without the calculation of intermediate geometric primitives while still supporting efficient updates. Since informative geometry is often sparsely distributed in the environment, we further propose a map-informed point sampling strategy to focus registration on geometrically informative regions, improving robustness in uninformative environments while reducing computational cost compared to global high-resolution sampling. Experiments across multiple sensors, platforms, and environments demonstrates state-of-the-art performance in well-constrained scenes and substantial improvements in challenging scenarios where baseline methods diverge. Additionally, we demonstrate that the fine-grained geometry captured by BIEVR-LIO can be used for downstream tasks such as elevation mapping for robot locomotion.

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

We introduce Rectified Point Flow, a unified parameterization that formulates pairwise point cloud registration and multi-part shape assembly as a single conditional generative problem. Given unposed point clouds, our method learns a continuous point-wise velocity field that transports noisy points toward their target positions, from which part poses are recovered. In contrast to prior work that regresses part-wise poses with ad-hoc symmetry handling, our method intrinsically learns assembly symmetries without symmetry labels. Together with a self-supervised encoder focused on overlapping points, our method achieves a new state-of-the-art performance on six benchmarks spanning pairwise registration and shape assembly. Notably, our unified formulation enables effective joint training on diverse datasets, facilitating the learning of shared geometric priors and consequently boosting accuracy. Project page: https://rectified-pointflow.github.io/.

Vision Language Models (VLMs) exhibit a fundamental semantic-to-geometric gap in spatial reasoning: they excel at qualitative semantic inference but their reasoning operates within a lossy semantic space, misaligned with high-fidelity geometry. Current paradigms fail to bridge this gap. Training-based methods suffer from an ``oracle paradox,'' learning flawed spatial logic from imperfect oracles. Tool-integrated methods constrain the final computation but critically leave the VLM's planning process unconstrained, resulting in geometrically flawed plans. In this work, we propose Geometrically-Constrained Agent (GCA), a training-free agentic paradigm that resolves this gap by introducing a formal task constraint. Specifically, we strategically decouples the VLM's role into two stages. First, acting as a semantic analyst, the VLM translates the user's ambiguous query into the formal, verifiable task constraint, which defines the reference frame and objective. Second, acting as a task solver, the VLM generates and executes tool calls strictly within the deterministic bounds defined by the constraint. This geometrically-constrained reasoning strategy successfully resolve the semantic-to-geometric gap, yielding a robust and verifiable reasoning pathway for spatial reasoning. Comprehensive experiments demonstrate that GCA achieves SOTA performance on multiple spatial reasoning benchmarks, surpassing existing training-based and tool-integrated methods by ~27%. Please see our homepage at https://gca-spatial-reasoning.github.io.

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

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

World models serve as essential building blocks toward Artificial General Intelligence (AGI), enabling intelligent agents to predict future states and plan actions by simulating complex physical interactions. However, existing interactive models primarily predict visual observations, thereby neglecting crucial hidden states like geometric structures and spatial coherence. This leads to rapid error accumulation and temporal inconsistency. To address these limitations, we introduce DeepVerse, a novel 4D interactive world model explicitly incorporating geometric predictions from previous timesteps into current predictions conditioned on actions. Experiments demonstrate that by incorporating explicit geometric constraints, DeepVerse captures richer spatio-temporal relationships and underlying physical dynamics. This capability significantly reduces drift and enhances temporal consistency, enabling the model to reliably generate extended future sequences and achieve substantial improvements in prediction accuracy, visual realism, and scene rationality. Furthermore, our method provides an effective solution for geometry-aware memory retrieval, effectively preserving long-term spatial consistency. We validate the effectiveness of DeepVerse across diverse scenarios, establishing its capacity for high-fidelity, long-horizon predictions grounded in geometry-aware dynamics.

We present a differentiable optimization framework for multi-agent coordination. An input is decomposed into overlapping local views, each processed by an agent that solves a convex subproblem parameterized by a neural encoder. Agents coordinate through the Alternating Direction Method of Multipliers (ADMM) with inter-agent constraints specified by a cellular sheaf. The sheaf specifies which aspects of neighboring solutions must agree, allowing for heterogeneous notions of global consensus. Backpropagating through the unrolled optimization jointly trains all components of the multi-agent system. We evaluate on maze pathfinding, image classification, and Sudoku, where agents with individually insufficient local views learn to coordinate to produce correct global outputs. On MNIST, the local-view decomposition yields improved robustness to distribution shifts relative to a standard CNN. On Sudoku, the optimization-derived structure yields markedly higher solve rates than parameter-matched MPNN baselines. Finally, the ADMM structure exposes distinct primal, consensus, and dual state variables, opening the coordination dynamics to direct analysis and intervention -- a property unavailable in standard message-passing architectures.

A deep understanding of kinematic structures and movable components is essential for enabling robots to manipulate objects and model their own articulated forms. Such understanding is captured through articulated objects, which are essential for tasks such as physical simulation, motion planning, and policy learning. However, creating these models, particularly for objects with high degrees of freedom (DoF), remains a significant challenge. Existing methods typically rely on motion sequences or strong assumptions from hand-curated datasets, which hinders scalability. In this paper, we introduce Kinematify, an automated framework that synthesizes articulated objects directly from arbitrary RGB images or textual descriptions. Our method addresses two core challenges: (i) inferring kinematic topologies for high-DoF objects and (ii) estimating joint parameters from static geometry. To achieve this, we combine MCTS search for structural inference with geometry-driven optimization for joint reasoning, producing physically consistent and functionally valid descriptions. We evaluate Kinematify on diverse inputs from both synthetic and real-world environments, demonstrating improvements in registration and kinematic topology accuracy over prior work.

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

Despite recent advances in leveraging generative prior from pre-trained diffusion models for 3D scene reconstruction, existing methods still face two critical limitations. First, due to the lack of reliable geometric supervision, they struggle to produce high-quality reconstructions even in observed regions, let alone in unobserved areas. Second, they lack effective mechanisms to mitigate multi-view inconsistencies in the generated images, leading to severe shape-appearance ambiguities and degraded scene geometry. In this paper, we identify accurate geometry as the fundamental prerequisite for effectively exploiting generative models to enhance 3D scene reconstruction. We first propose to leverage the prevalence of planar structures to derive accurate metric-scale depth maps, providing reliable supervision in both observed and unobserved regions. Furthermore, we incorporate this geometry guidance throughout the generative pipeline to improve visibility mask estimation, guide novel view selection, and enhance multi-view consistency when inpainting with video diffusion models, resulting in accurate and consistent scene completion. Extensive experiments on Replica, ScanNet++, and DeepBlending show that our method consistently outperforms existing baselines in both geometry and appearance reconstruction, particularly for unobserved regions. Moreover, our method naturally supports single-view inputs and unposed videos, with strong generalizability in both indoor and outdoor scenarios with practical real-world applicability. The project page is available at https://dali-jack.github.io/g4splat-web/.

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

SLAM methods based on 3D Gaussian Splatting (3DGS) have demonstrated impressive tracking and mapping performance, but typically require additional geometric information from external depth sensors. Meanwhile, recent SLAM systems that leverage geometric priors from pre-trained feed-forward models enable real-time dense reconstruction, yet often discard original RGB information during optimization, thus degrading overall reconstruction quality. We present GeoGS-SLAM, an online monocular dense reconstruction system that combines the 3DGS-based map representation with learned geometric priors. Given uncalibrated RGB input, we first employ a feed-forward visual geometry model to predict camera and scene priors. The Gaussian scene map is then expanded by directly sampling Gaussian primitives from both RGB input and geometric priors. Camera poses and the scene map are jointly optimized through a coarse-to-fine strategy that minimizes both photometric and geometric losses. To ensure global consistency, we further incorporate online loop closure detection and pose graph optimization. Extensive experiments across indoor and outdoor benchmarks demonstrate that GeoGS-SLAM achieves superior rendering quality and tracking accuracy compared to state-of-the-art methods while maintaining online real-time performance. Project page: https://rlgao.github.io/geogs_slam.

Consistent 3D geometry estimation from streaming RGB input is crucial for real-world applications such as autonomous driving, embodied AI, and large-scale reconstruction. While modern monocular geometry foundation models achieve strong single-image accuracy, they exhibit severe temporal inconsistency on continuous input, notably dominated by scale--shift drifting. Through targeted empirical analysis, we trace this instability to its root cause: fluctuations in latent feature statistics, whose mean and variance directly determine the predicted depth's scale and shift. Building on this insight, we introduce Dynamic Feature Normalization (DyFN), a lightweight, causal recurrent module that dynamically and robustly modulates feature statistics to maintain stable geometry over time. We adapt powerful pretrained monocular geometry models for streaming by finetuning only DyFN, a mere 2\% additional parameters, while keeping the backbone frozen, thereby achieving temporal consistency without compromising single-image accuracy. Extensive experiments across four benchmarks show that DyFN effectively eliminates temporal artifacts such as disjointed layering and positional jitter, and achieves state-of-the-art temporal stability, improving over prior streaming methods by up to 14\% and even outperforming heavier non-causal video baselines. Project Page: https://shawlyu.github.io/DyFN

Large Multimodal Models (LMMs) have achieved remarkable success on images and short videos, yet scaling them to long videos remains challenging due to frame-centric tokenization and limited context windows. 3D geometry provides a natural compression mechanism for visual streams: depth and camera pose enable observations from multiple views and time steps to be fused into a persistent, world-aligned representation. While recent 3D LMMs leverage geometry-aware representations to improve spatial reasoning, they continue to lag behind specialist 3D perception systems on grounding and segmentation tasks. We argue that a key limitation is geometry-aware decoding: existing methods communicate 3D predictions through language tokens, proposal selection, or lightweight grounding queries, creating a bottleneck between language reasoning and dense geometric prediction. Building on these insights, we introduce Qwen-3D, a geometry-aware LMM that compresses visual information within the Qwen backbone using multi-view geometric cues, enabling efficient long-horizon visual reasoning over static scenes. Qwen-3D augments visual tokens with 3D Rotary Positional Embeddings, allowing attention to operate directly in 3D scene space rather than across independent image frames and thereby facilitating scalable cross-view and temporal reasoning. To bridge language and geometry, Qwen-3D incorporates a query-based segmentation decoder that grounds language directly in the underlying 3D scene representation, unifying referential grounding, instance segmentation, and visual question answering across both images and videos. Across a diverse set of benchmarks, Qwen-3D surpasses existing 3D LMMs and outperforms several large proprietary 2D models. Notably, Qwen-3D achieves these improvements while maintaining strong performance on standard 2D vision-language benchmarks by jointly training on 2D and 3D data.

Effective robotic manipulation relies on a precise understanding of 3D scene geometry, and one of the most straightforward ways to acquire such geometry is through multi-view observations. Motivated by this, we present GP3 -- a 3D geometry-aware robotic manipulation policy that leverages multi-view input. GP3 employs a spatial encoder to infer dense spatial features from RGB observations, which enable the estimation of depth and camera parameters, leading to a compact yet expressive 3D scene representation tailored for manipulation. This representation is fused with language instructions and translated into continuous actions via a lightweight policy head. Comprehensive experiments demonstrate that GP3 consistently outperforms state-of-the-art methods on simulated benchmarks. Furthermore, GP3 transfers effectively to real-world robots without depth sensors or pre-mapped environments, requiring only minimal fine-tuning. These results highlight GP3 as a practical, sensor-agnostic solution for geometry-aware robotic manipulation.

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

Multi-agent LLM committees replicate the same model under different role prompts and aggregate outputs by majority vote, implicitly assuming that agents contribute complementary evidence. We embed each agent's chain-of-thought rationale and measure pairwise similarity: across 100 GSM8K questions with three Qwen2.5-14B agents, mean cosine similarity is 0.888 and effective rank is 2.17 out of 3.0, a failure mode we term representational collapse. DALC, a training-free consensus protocol that computes diversity weights from embedding geometry, reaches 87% on GSM8K versus 84% for self-consistency at 26% lower token cost. Ablation experiments reveal 1-3 point per-protocol run-to-run variance, confirm that hint sharing contributes more than diversity weighting alone, and show that encoder choice strongly modulates collapse severity (cosine 0.908 with mxbai versus 0.888 with nomic) and downstream accuracy. The more robust finding is that collapse is measurable, worsens on harder tasks, and that the choice of embedding proxy is a first-order design decision for any latent communication protocol.

Multi-agent systems powered by large language models exhibit strong capabilities in collaborative problem-solving. However, these systems suffer from substantial knowledge redundancy. Agents duplicate efforts in retrieval and reasoning processes. This inefficiency stems from a deeper issue: current architectures lack mechanisms to ensure agents share minimal sufficient information at each operational stage. Empirical analysis reveals an average knowledge duplication rate of 47.3\% across agent communications. We propose D3MAS (Decompose, Deduce, and Distribute), a hierarchical coordination framework addressing redundancy through structural design rather than explicit optimization. The framework organizes collaboration across three coordinated layers. Task decomposition filters irrelevant sub-problems early. Collaborative reasoning captures complementary inference paths across agents. Distributed memory provides access to non-redundant knowledge. These layers coordinate through structured message passing in a unified heterogeneous graph. This cross-layer alignment ensures information remains aligned with actual task needs. Experiments on four challenging datasets show that D3MAS consistently improves reasoning accuracy by 8.7\% to 15.6\% and reduces knowledge redundancy by 46\% on average.

Spatial reasoning from egocentric videos is inherently challenging because the observable evidence is constrained by the camera trajectory. Existing methods rely on single-turn inference, forcing models to resolve geometric ambiguity through semantic priors rather than verifiable evidence. We argue that spatial reasoning should be revisitable: conclusions formed under limited evidence should remain open to revision when complementary viewpoints become available. Building on this insight, we propose Reason, then Re-reason (ReRe), a training-free, inference-time framework with two phases: in the Reason Phase, an MLLM forms a spatial hypothesis from the original video; in the Re-reason Phase, it verifies or revises the hypothesis by observing a synthesized novel-view video. To enable effective cross-view revisiting, we design a Geometry-to-Video pipeline that renders strategically complementary novel views from predicted 3D geometry. These views feature an elevated, oblique perspective with scene-spanning coverage, while preserving the MLLM's native video interface without architectural modifications. Extensive evaluations on VSI-Bench and STI-Bench demonstrate that ReRe substantially boosts open-source MLLMs to rival proprietary state-of-the-art performance. Project page: https://zhenjiemao.github.io/ReRe/

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

Generative novel view synthesis faces a fundamental dilemma: geometric priors provide spatial alignment but become sparse and inaccurate under view changes, while appearance priors offer visual fidelity but lack geometric correspondence. Existing methods either propagate geometric errors throughout generation or suffer from signal conflicts when fusing both statically. We introduce MoCam, which employs structured denoising dynamics to orchestrate a coordinated progression from geometry to appearance within the diffusion process.MoCam first leverages geometric priors in early stages to anchor coarse structures and tolerate their incompleteness, then switches to appearance priors in later stages to actively correct geometric errors and refine details. This design naturally unifies static and dynamic view synthesis by temporally decoupling geometric alignment and appearance refinement within the diffusion process.Experiments demonstrate that MoCam significantly outperforms prior methods, particularly when point clouds contain severe holes or distortions, achieving robust geometry-appearance disentanglement.

Vision-language-action (VLA) models have made rapid progress in generalist robot manipulation by harnessing semantic knowledge from pretrained vision-language backbones, but their visual tokens remain grounded in 2D image coordinates rather than the calibrated geometry of the robot's cameras -- a mismatch especially pronounced in multi-camera setups, where views are coupled by known intrinsics and extrinsics yet processed as independent images. We propose G^3VLA, a camera-aware geometric module that injects calibrated structure into the visual-token stream of a pretrained VLA without altering its action space or imitation objective, combining intrinsic-conditioned ray embeddings, projective positional encoding (PRoPE), and bidirectional cross-view fusion. Geometric supervision is provided either from ground-truth point maps when available, or from confidence-gated π^3X teacher predictions, requiring no depth sensors or manual annotations. Instantiated on π_0, G^3VLA yields consistent gains across the LIBERO suites, RoboCasa24, RoboTwin2.0, and real-robot settings, with the largest improvements on spatially and object-sensitive tasks. We further validate on π_{0.5} and GR00T 1.5, with results suggesting that geometric transfer is most effective when geometry-aware tokens have direct access to the action generation pathway. Our project page is at https://sites.google.com/view/g3vla

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

Recent feed-forward networks have achieved remarkable progress in sparse-view 3D reconstruction by predicting dense point maps directly from RGB images. However, they often suffer from geometric inconsistencies and limited fine-grained accuracy due to the absence of explicit multi-view constraints. We introduce the Geometry-Grounded Point Transformer (GGPT), a framework that augments feed-forward reconstruction with reliable sparse geometric guidance. We first propose an improved Structure-from-Motion pipeline based on dense feature matching and lightweight geometric optimisation to efficiently estimate accurate camera poses and partial 3D point clouds from sparse input views. Building on this foundation, we propose a geometry-guided 3D point transformer that refines dense point maps under explicit partial-geometry supervision using an optimised guidance encoding. Extensive experiments demonstrate that our method provides a principled mechanism for integrating geometric priors with dense feed-forward predictions, producing reconstructions that are both geometrically consistent and spatially complete, recovering fine structures and filling gaps in textureless areas. Trained solely on ScanNet++ with VGGT predictions, GGPT generalises across architectures and datasets, substantially outperforming state-of-the-art feed-forward 3D reconstruction models in both in-domain and out-of-domain settings.