Visual Geometry Grounded Transformer

Feed-forward 3D vision models such as VGGT have achieved remarkable progress, unifying camera estimation and dense scene reconstruction in a single pass. However, their quadratic global attention makes long image sequences expensive, while existing sparse methods may favor highly attended yet value-redundant regions. To address these limitations, we introduce VASC, a training-free sparse attention method combining value-aware block selection and execution-aware cross-layer memory. Our value-aware block selection integrates pooled query--key relevance with neighboring value contrast, reducing redundancy while preserving query-relevant and distinctive content. Cross-layer memory tracks unserved demand across layers and updates this state according to actual execution, enabling previously underserved blocks to compete under a fixed computation budget. Experiments on 7Scenes and NeuralRGB-D with VGGT and $π^3$ demonstrate improved pose estimation and reconstruction quality compared with FasterVGGT, together with up to $2.29\times$ faster inference than dense VGGT. Code is available at https://github.com/kosakayamahoo-design/VASC.

Recent advances in 3D reconstruction have progressed from per-scene optimization to feed-forward inference, and semantic scene understanding has followed suit -- yet existing methods remain confined to object-centric perception, neglecting spatial relations between objects. We formulate 3D spatial relation segmentation in a feed-forward, pose-free multi-view setting: given a visually specified subject and a relational text query, the model segments the target across views without receiving its category name. To this end, we propose RelationVGGT, a novel feed-forward framework that integrates semantic features from a visual foundation model with geometry-aware representations from a 3D geometry foundation model and leverages a relation transformer for subject-conditioned, cross-view relation prediction -- requiring neither per-scene optimization nor known camera poses. We additionally provide a fully automated annotation pipeline built on ScanNet++ with VLMs and LLMs, enabling scalable training data generation for this new task.

Learning partial differential equation (PDE) dynamics across varying domains is central to predictive modelling and data-driven discovery of governing equations. However, geometric variation alters both field representation and the governing differential operators, confounding geometric effects with intrinsic physical properties in the observed dynamics. This work identifies geometry-physics confounding as a unified failure mechanism for PDE learning across varying domains. In forward operator learning, this confounding increases the burden of inferring geometry-dependent operator changes from finite data, reducing data efficiency and generalisation. In equation discovery, omitting geometry-induced operators misspecifies the candidate library, leading to biased parameters, missed governing terms and spurious terms. We propose a de-confounding framework that makes the known geometry-to-operator transformation explicit. Geometry-induced coefficient fields improve prediction and data efficiency across five operator-learning benchmarks, while geometry-complete candidate libraries recover the generating equations and reduce held-out PDE residuals by more than two orders of magnitude in both evolving-domain systems. By separating known geometric action from intrinsic physics, the proposed framework supports more reliable and data-efficient PDE learning across scientific and engineering problems with varying geometries.

Recent event-based depth estimation methods successfully transfer geometric priors from vision foundation models via cross-modal distillation. However, their reliance on synchronized RGB-event pairs or depth annotations during training severely restricts practical deployment. To overcome this bottleneck, we propose SFE-VGGT, a novel source-free framework that distills the geometric priors of VGGT to the event domain without any paired RGB observations. Our core idea is to reconstruct surrogate frames directly from the target event stream to act as a frozen geometric teacher, entirely eliminating the need for genuine source RGB data. Crucially, as these surrogate frames inherently yield imperfect and spatially varying supervision, directly distilling from them propagates artifacts. To resolve this, we introduce a novel reliability-aware distillation strategy. This includes Density-Aware Feature Distillation to emphasize informative event regions, and Confidence-Weighted Depth Distillation to dynamically regulate supervision based on relative teacher-student prediction confidence. Meanwhile, we propose a Cross-Frame Relational Consistency loss that enforces temporal geometric stability using reliable inter-frame correspondences, bypassing the need for temporally consistent teacher's depth. Extensive experiments demonstrate that, despite source-free, our SFE-VGGT closely matches the accuracy of RGB-dependent baselines under standard conditions and significantly surpasses them in challenging nighttime scenarios. Across MVSEC nighttime sequences, SFE-VGGT reduces the average 10 m depth error by 15.3% compared with EventVGGT. Moreover, our method exhibits robust zero-shot generalization across real-world datasets, proving that highly effective geometric priors can be transferred to event cameras using strictly source-free supervision.

Which layers of a feed-forward geometry model are needed to preserve both camera poses and dense 3D structure? We study layer redundancy in VGGT, $π^3$, and VGGT-$Ω$: 3,018 pruned configurations, scored on seven camera-pose and dense-geometry metrics across four indoor and outdoor datasets. Four findings follow: (i) Removable layers cluster in two redundancy regions: a dominant early region and a narrower late one, while deletions spanning the intervening layers are consistently more disruptive. This recurring pattern holds across models, datasets, and metrics, and contrasts with the middle-to-late redundancy commonly reported in the literature. (ii) Within these regions, we observe that the joint degradation from deleting two intervals is approximately the sum of their individual degradations, reducing the number of model evaluations for pruning search from $O(L^4)$ to $O(L^2)$, where $L$ is the aggregator depth. (iii) We find that CKA provides a cheaper representation-based proxy for interval degradation, offering a practical trade-off between pruning quality and calibration cost. (iv) Closed-form linear calibration recovers accuracy after pruning without end-to-end retraining. A least-squares analysis shows that using a shared map for special and patch tokens generally incurs excess reconstruction loss, motivating token-aware recovery. Recovery maps fitted on just 100 calibration scenes generalize to held-out scenes and unseen datasets. The resulting models reduce aggregator parameters by up to 44% while maintaining accuracy comparable to their intact counterparts. Code and experimental results will be available at our project page: https://xian-bei.github.io/vggt-family-layer-redundancy/

3D vision transformers such as VGGT predict camera poses and scene geometry from multi-view images in a single forward pass, but their global attention over all concatenated view tokens dominates computation as the number of views grows. To reduce this cost, SparseVGGT and HeSS sparsify attention at the block level, and both retain blocks with high attention probability. However, we observe that attention probability poorly predicts how much the model's behavior actually changes when a block is removed, and we show that this mismatch is why performance collapses as sparsity increases. In this paper, we propose ReSS (ReSidual-ReStoring Sparse Attention), which recasts block selection from a problem of maximizing the retained attention mass to one of minimizing the drift that sparsification leaves in the residual stream. We introduce a drift score that quantifies how much each block shifts the residual, and, since the drift of a drop set depends on the directions of the contribution vectors rather than on their magnitudes alone, an iterative residual restoration procedure that refines the drop set as a whole. Across three backbones and five datasets, ReSS preserves dense performance better than prior methods at matched sparsity. Two further results support drift as the quantity that governs the cost of sparsification: maximizing drift degrades performance faster than random selection, and plotted against realized drift instead of sparsity, all methods fall approximately onto a single curve. Code is available at https://github.com/libary753/ReSS.

Visual grounding in remote sensing images aims to locate objects described by referring expressions. Most existing methods predict horizontal bounding boxes, which are often inaccurate for objects with arbitrary orientations. To address this limitation, we introduce O$^2$-VG, a family of models for oriented object visual grounding with three complementary designs. Specifically, O$^2$-VG-Trans is a cross-modality transformer for oriented object visual grounding. It establishes a strong discriminative foundation for the model family. Building upon it, O$^2$-VG-Uni predicts universal oriented proposals for possible foreground objects without specific text prompts. It also supports object retrieval through cached proposal embeddings. Using these universal oriented proposals as input prompts, O$^2$-VG-VLM is an autoregressive vision-language model. It generates oriented box token blocks in parallel through multi-token prediction. In addition, we construct DIOR-R-RSVG, a dataset for oriented object visual grounding in remote sensing images. It provides image, expression, and oriented box triplets for training and evaluation. Together, the O$^2$-VG family provides a flexible framework that spans discriminative transformers and generative vision-language models. It achieves superior performance across multiple benchmarks. Code is available at https://github.com/wokaikaixinxin/ai4rs.

Computing accurate geometry from multi-view images is a fundamental problem in computer vision. Recent feed-forward (FF) models jointly estimate 3D geometry and camera parameters, but they typically suffer from geometry distortion caused by reconstruction ambiguity, even when ground-truth camera parameters are supplied. In this paper, we study the multi-view stereo (MVS) problem with known camera parameters and propose a novel approach that bridges conventional MVS and FF methods. Rather than casting MVS as a sequence-to-one mapping that predicts depth only for a single reference view, we reformulate it as a sequence-to-sequence task, akin to FF models, that jointly predicts geometry for all input views. We introduce a global transformer-based architecture with two components that explicitly exploit camera-induced priors: ray-map embeddings that inject camera parameters into image patch tokens, making the transformer camera-aware, and a unified global cost volume that replaces conventional per-view cost volumes to jointly capture 3D structure across all views. Extensive experiments on multiple public benchmarks show our approach achieves state-of-the-art performance, surpassing both MVS and FF reconstruction baselines.

Feed-forward visual geometry models such as the Visual Geometry Grounded Transformer (VGGT) have recently enabled direct 3D reconstruction from multi-view images. Despite their promising performance, these models scale quadratically with the number of input views due to their global attention mechanism, resulting in substantial latency for long sequence inputs. There have been some recent efforts to accelerate VGGT, but they primarily focus on reducing \emph{token redundancy} through token merging or key/value sparsification. Our work resolves this bottleneck from a different perspective by investigating \emph{architectural redundancy} in visual geometry transformers. We show that the multi-head attention modules in VGGT's global-attention layers contain substantial architectural redundancy, with only a subset of heads carrying critical geometric information. In light of this observation, we propose VGGT-Prime, a compute-adaptive mixture-of-heads model that resolves this redundancy to accelerate visual geometry transformers while maintaining competitive reconstruction quality. The key idea of VGGT-Prime is to estimate the appropriate computation level for each global-attention head using a lightweight router and then dynamically assign each head to different computation modes. Extensive experiments on multiple datasets demonstrate that VGGT-Prime can achieve an {$8\times$} inference speedup over VGGT while maintaining competitive performance on camera pose, depth, and point-cloud predictions. We further show that VGGT-Prime is complementary to existing acceleration methods, such as token merging, further improving inference speed by up to $14{\times}$ over VGGT. An overview of our work is available on our \href{https://vggt-prime.github.io}{project page}.

We present VGGT-GS SLAM, a monocular 3D Gaussian Splatting SLAM system designed for uncalibrated videos. Starting from feed-forward VGGT pose and depth priors, our system performs submap differentiable bundle adjustment that jointly refines camera poses and a 3D Gaussian map, while optimizing submap-shared intrinsics and radial--tangential distortion through analytic calibration Jacobians. To improve global consistency, we introduce Gaussian-native alignment (GNA) for camera-anchored scale refinement between sequential submaps and verification of loop-closure candidates. Extensive experiments on standard indoor benchmarks show consistent improvements in localization accuracy and strong rendering quality under uncalibrated settings, establishing a strong baseline for uncalibrated Gaussian SLAM.

We study relative position encoding for multi-view vision Transformers under camera heterogeneity, including varying fields of view (FoVs) or projection models. Existing rotary relative position encodings commonly use image-plane positional coordinates, producing projection-dependent relative phases and inconsistent geometric cues for cross-projection attention. We introduce G-ray, a ray-level relative position encoding whose rotary phases are parameterized by camera-local ray angles. The same camera-local ray pair induces the same relative phase across projections, providing projection-invariant positional consistency. G-ray can be used directly or integrated with existing encodings, retaining complementary geometric cues without additional learned parameters. We validate G-ray in three host encodings, RoPE, GTA, and RayRoPE, across 3D reconstruction and novel-view synthesis (NVS). Across three heterogeneous 3D reconstruction benchmarks at 50 views, G-ray leads all six averaged metrics and reduces mean pointmap relative error by 45.8% over MapAnything, with calibration supplied to both. Trained exclusively on homogeneous pinhole images, the 3D reconstruction model handles mixed pinhole and non-pinhole inputs without retraining and remains competitive on homogeneous pinhole 3D reconstruction protocols. For NVS, GTA and RayRoPE improve with G-ray under joint viewpoint and FoV variation. The project's webpage is available at https://g-ray-project.github.io/.

Geometry-conditioned multi-view diffusion enables high-quality 3D texture generation, but its repeated per-view denoiser evaluations introduce substantial computational cost. Existing training-free accelerators primarily exploit temporal redundancy by reusing computation across denoising steps. In multi-view texturing, however, skipping a step also removes the cross-view interaction that continually aligns different observations of the same surface, leading to rapidly degraded consistency and fidelity. Our analysis identifies a complementary source of redundancy: although intermediate features remain view-specific, geometrically corresponding surface points exhibit transferable evolution in their predicted clean signals. Based on this observation, we introduce \gc{}, a training-free plugin that evaluates a rotating subset of anchor views and transports their geometry-aligned per-step $\xz$ updates to the remaining views. Periodic full-view computation controls accumulated error, while sampler-consistent reconstruction preserves the denoising trajectory. \gc{} requires neither retraining nor architectural modification and uses the position maps already available in geometry-conditioned texturing pipelines. Across Hunyuan3D-2.1, SyncMVD, and MVPainter, \gc{} achieves a stronger speed--fidelity trade-off than temporal caches and step reduction at operating points above $2\times$. On Hunyuan3D-2.1, it delivers a $2.21\times$ denoiser-loop speedup with an MV-LPIPS of 0.0293 and an MV-PSNR of 33.60 dB, providing the best fidelity among all tested methods above $2\times$. The same transferred configuration reaches the highest speedup and lowest FLOPs on SyncMVD, while \gc{} achieves the lowest FLOPs and best fidelity among the accelerated methods on MVPainter. These results establish cross-view geometry as an effective acceleration axis for multi-view texture diffusion.

Geometry-aware video object scaling aims to anisotropically resize the object along object-centric axes while preserving geometric plausibility, temporal coherence, and background consistency. Existing text-guided methods mainly operate in the 2D image plane, while depth-guided approaches provide coarse control and mesh-based methods require costly 3D reconstruction. We present a progressive two-stage training framework that decouples geometry-aware foreground transformation from background preservation and realistic video composition, without mesh-pixel alignment and explicit 3D reconstruction at inference. In both stages, geometrically perturbed pseudo-sources are constructed from real videos, while the original complete videos are retained as reconstruction targets. The first stage uses planar transformations to learn robust foreground-background composition, whereas the second introduces object-centric 3D deformation guidance for geometry-aware scaling. This pseudo-source reconstruction formulation enables real-video synthesis without paired real-world scaling targets. We construct complementary paired-geometry and real-background benchmarks and further evaluate on in-the-wild videos. Extensive experiments demonstrate superior geometric consistency, foreground fidelity, and background preservation, together with faster and more practical inference than methods requiring explicit 3D reconstruction.

Transformer-based methods have achieved strong performance in monocular 3D human pose estimation, but most existing approaches organise spatial and temporal reasoning as separate stages, which may weaken unified spatial-temporal interdependencies inherent in human motion and compress frame-level structural information before temporal modelling. In this paper, we propose HSTGFormer, a graph-enhanced Transformer framework that reformulates spatial-temporal reasoning as localised coupled graph aggregation over joint-time nodes. Specifically, HSTGFormer introduces a Hyper Spatial-Temporal Graph (HSTG), which decomposes global spatial-temporal reasoning into local spatial-temporal receptive fields around individual joint-time nodes by extending per-frame skeleton graphs into temporal neighbourhoods, thereby enabling structure-aware coupled reasoning while preserving local structural motion information. It further incorporates an Adaptive Dual-Scale Temporal Graph (ADSTG) to capture joint-specific temporal dependencies over complementary short- and long-range windows. A lightweight node-wise fusion module further adaptively integrates the two graph representations for each joint-time node. Experiments on Human3.6M and MPI-INF-3DHP show that HSTGFormer achieves strong accuracy with high computational efficiency.

Single-frame surround-view reconstruction faces severe geometric instability and rendering artifacts due to minimal inter-camera overlap. While existing methods rely on complex decoders or auxiliary cues, they remain bottlenecked by the weak geometric capacity of upstream features. We argue that leveraging pretrained visual geometry priors strengthens upstream representations and alleviates the geometric ambiguity in sparse surround views. To this end, we propose VGGD, a visual geometry foundation-aware 3D Gaussian Splatting framework for feed-forward surround-view driving reconstruction, which shifts geometric modeling to the frontend and adapts foundation priors to the driving camera setting. First, VGGD leverages VGGT to provide transferable multi-view geometric prior tokens. Next, we introduce a Dual-Path Neck to decouple geometry-consistent and appearance-aware representations, improving appearance completion in weakly observed regions. We further apply Scale Warmup to stabilize early geometry learning and suppress scale drift under ego-pose changes. Finally, we use a hybrid pixel--volume Gaussian decoder to produce a renderable 3D Gaussian scene for novel-view synthesis. Experiments on the nuScenes single-frame benchmark show that VGGD achieves the best overall rendering quality among the compared methods and improves relative geometric consistency.

Transformers have had a profound impact on the world of language processing and computer vision. As efforts to answer the million-dollar question of ``How does a Transformer learn?" have been increasing, existing interpretability studies primarily analyze representations at isolated layers or the network as a whole, while the developmental evolution of individual representations and its manifolds across transformer layers remains underexplored. With this work, we aim at providing a comprehensive analysis of the evolution of representations as the representation point cloud transforms across the layers; thereby attempting to isolate layers or establish a trend which comes closer to justifying how and when raw input representations evolve into task-relevant feature representations. Thus, Transformer Geometry Observatory-TGO-IV introduces a topological framework for analysing the evolution of Transformer representations through the lens of Persistent Homology. Rather than studying local geometric properties alone, TGO-IV constructs Vietoris--Rips simplicial complexes from token-level representation point clouds and investigates the evolution of their persistent topological signatures across Transformer layers. The proposed framework comprises complementary topological observatories including Persistence Diagrams, Barcode Diagrams, Betti Curves, Persistence Landscapes, Bottleneck Distance, and Wasserstein Distance, enabling a comprehensive analysis of how the global topology of representation point clouds develops throughout the forward pass.

With the widespread adoption of Vision Transformers in modern AI, the need to analyze their inherent representational behavior has become increasingly important. While most existing studies emphasize token geometries and training dynamics, the evolution of representational covariance structures and class-level geometric organization remains comparatively underexplored. In this work, we investigate semantic geometry and class separability as representations evolve across the layers of ViT-Small/16 through TGO-III: Semantic Geometry Observatory. It is a framework designed to analyze the emergence of semantic organization, feature evolution, and class-wise representation geometry throughout training. The framework employs multiple complementary observatories, including Linear Probe Accuracy, Fisher Ratio, Class Centroid Distances, Local Intrinsic Dimension, and Local PCA Rank, to quantify the progressive evolution of discriminative representations. Our analysis reveals that class representations become progressively more linearly separable, Fisher discriminability increases, class centroids move farther apart, and local representation manifolds exhibit structured class-dependent geometric complexity. These observations provide empirical evidence supporting the Semantic Expansion Hypothesis, suggesting that the manifold expansion observed in previous observatories is accompanied by the progressive organization of representations into increasingly discriminative semantic structures. Collectively, TGO-III extends the Transformer Geometry Observatory framework by establishing a direct connection between manifold geometry, covariance evolution, and semantic organization during Transformer training.

Visual imitation learning enables robots to acquire visuomotor skills directly from images, yet RGB observations lack explicit geometric cues, making learned policies brittle to camera perturbations. To address this, we propose \textbf{Ray-conditioned Vision Transformer Encoder (RayViT)}, a lightweight architecture that injects camera geometry into pretrained ViT backbones. RayViT represents camera geometry as a Plücker ray map, patchifies it into ray features, and uses gated cross-attention to produce a ray-conditioned class token. These ray features are added as dense positional embeddings, while the ray class token replaces the original ViT class token to provide a geometry-aware summary representation. We combine this approach with an auxiliary cosine similarity loss to consistently improve the performance and robustness for geometry-aware tokens. Experiments on sim- and real-robot tasks demonstrate that RayViT improves robustness by approximately 13 percentage points under camera perturbations in multi-task RoboCasa benchmark and by 1.78 average completed stages in real-world multi-task success rate compared to baselines.

Attribution methods are widely used to characterize the evidence underlying model predictions, yet their potential to improve model behavior remains underexplored. Attribution inconsistency under label-preserving geometric transformations may indicate transformation-sensitive evidence reliance, motivating attribution regularization. However, such supervision is valid only when attribution faithfully reflects the evidence driving predictions. Existing self-supervised methods typically align gradient-based maps such as Grad-CAM, whose limited faithfulness means that attribution consistency need not imply consistency of the underlying decision process, leaving transformation robustness unresolved. We propose an annotation-free attribution regularization framework based on submodular search over image regions. By measuring how candidate subsets affect model outputs, the search extracts compact, class-discriminative evidence as search-derived supervision. We further introduce a submodular ranking loss with path-consistency and termination-alignment terms that respectively align spatially corresponding candidate rankings along paired search trajectories and encourage the transformed trajectory to satisfy the stopping criterion at the target terminal step. The loss provides a differentiable surrogate for regularizing both final attributions and the otherwise discrete evidence-selection process. Experiments on ImageNet-100 show that our method substantially improves attribution stability, Insertion, and Deletion on ViT-B/16 with only a 0.28-point accuracy drop, with similar gains on ViT-L/16. On ImageNet-1K, it improves transformed-input accuracy on ResNet-50 and ConvNeXt-B while limiting the clean-accuracy drop to 0.30 points, demonstrating more consistent evidence reliance with minimal performance loss. Code will be released soon.

Geometry Foundation Models (GFMs) have substantially advanced monocular 3D reconstruction, yet extending this capability to 4D dynamic understanding remains a fundamental challenge. Most existing motion perception methods (e.g., sparse tracking, dense point-wise flow) treat motion as independent point-wise displacements, ignoring the structured nature of physical motion. However, real-world objects usually obey rigid-body kinematics, and points thus usually move collectively, not in isolation. Motion itself possesses geometric structure: physical objects undergo a set of rigid-body transformations governed by SE(3), rather than unstructured point-wise displacements. Building on this insight, we propose SM4RT, a Structured Motion 4D Reconstruction Transformer for end-to-end 3D reconstruction and structured motion perception. SM4RT introduces Structure-of-Motion to represent scene dynamics, where scene motion is decomposed into a compact set of motion bases, each represented as a temporal sequence of 6D twists in SE(3). Dense scene motion is then recovered by sparse, time-shared per-pixel assignment weights over these bases, ensuring points on the same object share a common rigid-body motion trajectory. SM4RT introduces a parallel motion geometry encoder and decoder that jointly infer 3D geometry, world-coordinate motion, and scene kinematic structure in a single forward pass from monocular RGB video. SM4RT achieves strong motion reconstruction performance while preserving the geometric structure of scene motion.

Real-world spatial intelligence requires agents to understand scenes from continuous video streams, where objects move, persist, disappear, and reappear over time. While recent spatial foundation models have enabled generalizable feed-forward 3D reconstruction, most streaming methods remain geometry-centric and lack temporally consistent object-level understanding. Meanwhile, existing semantic reconstruction and 3D-aware vision-language methods largely rely on externally extracted 2D semantic cues or loosely coupled geometry inputs, limiting unified geometry-instance learning in long dynamic scenes. In this paper, we propose IGGT4D, a streaming instance-grounded geometry Transformer for online 4D scene understanding. IGGT4D processes video frames sequentially, reuses historical context through causal spatial-temporal modeling, and incrementally updates a unified representation of camera motion, geometry, and object identity. This enables long-sequence feed-forward reconstruction with geometry-instance consistency in dynamic environments. To address the lack of high-quality 4D supervision, we further construct InsScene4D-147K, a large-scale dataset spanning real/synthetic and static/dynamic scenes, with RGB images, depth, poses, and temporally consistent instance masks generated by an automated geometry-guided annotation pipeline. Experiments on 3D reconstruction, pose estimation, instance spatial tracking, and open-vocabulary segmentation demonstrate that IGGT4D outperforms existing streaming baselines while maintaining scalable online inference for long dynamic sequences.

Geometric foundation models, such as the Visual Geometry Grounded Transformer (VGGT), provide strong 3D priors from unposed images. However, such models operate purely in a feed-forward, deterministic regime, \ie~they cannot generate plausible geometry beyond what the input views directly support. Generative models for 3D scenes, on the other hand, must rely on strong geometric priors to produce coherent outputs from sparse inputs. We bridge these two paradigms by performing flow matching directly in VGGT's latent space, leveraging its learned 3D priors without committing to any explicit downstream representation such as Gaussians, meshes, or video-VAE latents. This requires respecting the latent geometry: VGGT tokens occupy a product of high-dimensional hyperspheres on which standard Euclidean flow matching fails. We address this with a Riemannian Flow Matching framework defined on a product manifold of four hyperspheres, aligned with VGGT's multi-scale encoder, which keeps generated tokens on the valid data manifold required by the frozen decoding heads. On RealEstate10K, ScanNet++ and ETH3D, our method achieves strong performance against recent scene generation baselines in both per-view appearance and aggregated 3D geometry, establishing latent-space flow matching on geometric foundation models as a viable paradigm for 3D generation. The project page can be found $\href{https://lisaweijler.github.io/geometry-grounded-rfm/}{\text{here}}$.

We present a continuous geometric framework that models the discrete algebraic operations of the Transformer architecture as an integro-differential equation (IDE) on a semantic fiber bundle $\calE = \calM \times \R^d$. Beginning from a single geometric axiom -- that the token sequence forms a discrete $1$-manifold equipped with a canonical measure lattice -- we translate every core component of the modern Transformer (RMSNorm, RoPE, Softmax Attention, FFN, Residual Stream, SGD, Weight Decay) into a cohesive vocabulary of differential geometry, measure theory, and stochastic calculus. The resulting framework yields quantitative predictions spanning entropic optimal transport (Attention as a Schrödinger bridge) and non-equilibrium thermodynamics (SGD as Itô diffusion violating detailed balance). We conduct a six-part experimental campaign across five architectures (Qwen3, LLaMA\nobreakdash-3.1, Gemma\nobreakdash-3, GPT-2, Mistral) spanning $124$M to $8$B parameters. The empirical observables are quantitatively consistent with the geometric predictions: the $ε^{-1/2}$ Lipschitz scaling calibration at machine precision ($R^2 = 1.000$), the Lie--Trotter operator-splitting torsion, the symmetric ablation instability confirming the Dual-Law of Topological Stability, the $\calO(1/\sqrt{k})$ thermodynamic suppression of Poincaré recurrence on the RoPE torus, the thermodynamic context-limit phase transition, and the Non-Equilibrium Steady State parameter vortex -- verified across two optimizers (AdamW and Pure SGD) to exclude momentum artifacts. The results demonstrate that analyzing Transformers through the lens of continuous stochastic differential geometry provides a predictive descriptive vocabulary for the stability limits, context bounds, and optimization dynamics of Large Language Models.

A fundamental challenge in 3D reconstruction and robotic localization is co-visibility: determining which image pairs share overlapping visible surfaces, particularly in scenarios with minimal overlap. We demonstrate that VGGT implicitly encodes co-visibility as an emergent behavior: without any supervision for this task, its internal representations exhibit a clear hierarchical structure mirroring that of large language models, i.e. early layers build a 3D-aware scene representation, while late layers act as dedicated co-visibility reasoners. In particular, we identify layer L17 as a negative anchor that consistently routes non-co-visible pairs for this backbone, regardless of the evaluation setting, providing task-grounded evidence of layer specialization in a geometry-grounded foundation model. Building on this, we introduce Co-VGGT, which freezes VGGT and trains only a lightweight layer-wise mixture-of-experts head (less than 7.5M parameters) to classify co-visibility from RGB alone, treating each layer as a specialized expert whose geometric abstraction is adaptively weighted per input pair. On the Co-VisiON benchmark, Co-VGGT surpasses the human annotation baseline and improves over prior work by more than 25% pairwise and 10% multiview. Pairwise predictions are well-calibrated (ECE=0.030), enabling direct use as edge weights in visibility graphs for downstream SfM and SLAM pipelines without post-hoc correction. Code and data are available.

Geometry transformers such as VGGT achieve strong performance by jointly reasoning over multiple views with global attention. However, scaling them to large view collections remains challenging due to the quadratic cost of attention. Moreover, our empirical analysis reveals that the reconstruction quality in VGGT is sensitive to the distribution of viewpoints. Simply increasing the number of views without sufficient viewpoint diversity can even degrade performance, as redundant views introduce highly similar tokens that dilute informative geometric signals in the attention mechanism. Motivated by this observation, we propose a training-free and plug-and-play VGGT inference framework that organizes views into diversity-aware balanced chunks. The chunks are constructed through combinatorial graph partitioning over visual dissimilarity and spatial dispersion. This view organization allows the transformer to focus attention on geometrically informative views while reducing redundant attention interactions. To estimate spatial dispersion without full pose estimation, we approximate spatial relationships via a soft pose propagation strategy based on visual similarity from a small set of seed frames. Extensive experiments demonstrate improved performance in camera pose estimation, multi-view depth prediction, and 3D reconstruction while reducing memory usage and inference latency. Our framework also complements existing VGGT variants, enabling scalable multi-view reconstruction without sacrificing geometric fidelity.

Comprehensive 3D scene understanding from sparse, unposed images requires a model to recover renderable geometry, open-vocabulary semantics, and free/occupied 3D space without relying on external camera calibration. Recent feed-forward Gaussian methods improve pose-free reconstruction and semantic rendering, but their Gaussian primitives are mainly optimized through image-space objectives and remain weakly constrained in unobserved regions. We propose \textit{COVScene}, a pose-free semantic Gaussian framework that couples renderable Gaussian primitives with a dense semantic occupancy field through differentiable volumetric lifting. Instead of converting Gaussians to voxels only at evaluation time, COVScene lifts the predicted semantic Gaussians inside the training computation graph, so volumetric regularization provides gradients to Gaussian opacity, geometry, and semantic features. The framework combines a semantic-aware Geometry Transformer, multi-task Gaussian decoding, geometric foundation distillation, and occupancy entropy regularization to support novel view synthesis, open-vocabulary semantic querying, and semantic occupancy prediction within a single representation. Experiments on ScanNet and ScanNet++ show that COVScene maintains competitive rendering quality, improves open-vocabulary segmentation, and achieves stronger semantic occupancy prediction than the self-supervised baseline without direct voxel-level supervision.

We present RenderFormer++, a scalable and physically grounded feed-forward neural rendering framework for global illumination in mesh scenes. Existing Transformer-based neural rendering methods such as RenderFormer achieve promising cross-scene generalization, but suffer from limited physical consistency and poor scalability due to the quadratic attention complexity of triangle-level tokenization. To address these issues, we introduce Physics-Informed Transport Guidance (PITG), which embeds rendering-equation inductive biases into the attention mechanism and enforces transport consistency loss, enabling physically consistent light transport modeling. We further propose Hierarchical Object-Centric Tokenization (HOCT), which aggregates triangle-level features into compact object-level tokens via cross-attention with learnable queries, substantially reducing computational and memory costs while preserving geometric and radiometric information. Extensive experiments demonstrate that RenderFormer++ achieves scalable, stable, and generalizable feed-forward global illumination rendering across complex large-scale scenes with improved physical accuracy and efficiency over prior neural rendering methods.

Grounding deictic gestures in natural images is fundamental to AR and human-robot collaboration, providing a basis for seamless spatial interaction. While Transformer-based visual models have achieved significant progress in general object detection, their global attention mechanisms often neglect micro-geometric relationships, degrading orientation accuracy. In pointing tasks, this deficiency manifests as an inability to accurately capture the pointing ray implied by finger poses, which results in pointing drift and localization ambiguity when dealing with distant or densely packed objects. To address this, we propose VistaRef, a framework designed to explicitly enhance spatial orientation awareness. First, we develop the Local Hand Entity Modeling (LHEM) module, which incorporates hand-pose embeddings to strengthen the model's capability to capture subtle finger deviations. Second, drawing inspiration from multi-view geometry, we construct the Geometric Ray Modeling (GRM) module to transform implicit orientation information into explicit spatial geometric features, guiding feature aggregation and deep fusion via attention mechanisms. Furthermore, we introduce a novel Orientation-Consistent Alignment Loss (OCAL) to synergistically supervise hand presence and pointing consistency, ensuring that all architectural improvements collectively serve the core objective of spatial localization. Experimental results demonstrate that VistaRef significantly outperforms the baseline, achieving a 14-point absolute gain in grounding accuracy. Qualitative analysis further confirms that VistaRef effectively models the geometric correlation from hand to target, bridging the spatial perception gap inherent in traditional Transformers for complex scenarios. Code: https://github.com/lingli1724/VistaRef.

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$^3$VLA, 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 $π^3$X teacher predictions, requiring no depth sensors or manual annotations. Instantiated on $π_0$, G$^3$VLA 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

Text-driven Referring Video Object Segmentation (RVOS) aims to locate and segment target objects in videos given natural language. However, existing models are typically trained on 2D image or video datasets with naive segmentation losses, which overlooks the geometric consistency across frames and leads to weak spatial understanding. In this paper, we propose Geometry-enhanced Language-guided Video segmentation (GeoLaV), a two-stage framework that distills 3D geometric knowledge from images to enhance text-driven video segmentation. In the first stage, we perform monocular geometry pretraining with monocular novel-view synthesis, enabling the model to acquire geometry-consistent visual representations via spatial alignment on large-scale single-image datasets. In the second stage, we introduce geometry-aware distillation and fine-tune the model on video segmentation datasets, transferring 3D structural knowledge from a general 3D prior model. This process reinforces 3D awareness and improves both spatiotemporal coherence and language grounding in segmentation. Extensive experiments show that our method using only image segmentation data already provides notable zero-shot generalization in RVOS. When combined with geometry-aware distillation for fine-tuning on videos, our method achieves state-of-the-art performance across multiple RVOS benchmarks. The code is available at https://github.com/Tony1882880/GeoLaV.

Current end-to-end multi-view 3D reconstruction methods achieve impressive results, but rely on a restrictive static assumption: the scenes is entire distractor-free with perfect cross-view geometry. This reliance on idealized inputs causes even the most advanced methods to fail in real-world settings, where transient distractors and occlusions present. To address this, we propose Visual Geometry Transformer in the Wild (VGTW), an end-to-end framework for robust reconstruction from inconsistent views. At its core, we isolate and suppress distractor-affected regions while preserving the consistent components across views. Specifically, we introduce a Distractor-aware Training (DAT) strategy that separates clean features from distractor-contaminated ones in the attention mechanism while enforcing feature consistency across images. To enable this, we train the model with an auxiliary mask prediction head, using supervision from a new dataset we collected with pixel-level distractor masks. The resulting VGTW model is a feed-forward network that directly outputs clean, distractor-free point clouds. Remarkably, it requires no additional 3D supervision, remains computationally efficient, and is compatible with existing pipelines. Extensive experiments validate our approach, demonstrating state-of-the-art performance and robust generalization in diverse, real-world scenarios.

Despite the widespread adoption of Vision Transformers (ViTs) and their success across numerous computer vision applications, the fundamental understanding of their dimensional and representational geometry remains relatively underexplored. To address this gap, we introduce Transformer Geometry Observatory (TGO), a systematic framework of experiments and analysis pipelines designed to investigate the representational geometry and dynamics of Vision Transformers. TGO-I, the first installment of the framework, focuses on the spectral geometry of ViT representations. Using a ViT-Small/16 model trained on ImageNet-100, we analyze Effective Rank, Stable Rank, Participation Ratio, Spectral Entropy, Spectral Flatness, Spectral Anisotropy, covariance structure, eigenspectra, and singular value spectra throughout training. Our results reveal a consistent increase in dimensional utilization, accompanied by decreasing anisotropy, increasing spectral entropy, increasing participation ratio, and progressively flatter eigenspectra. Contrary to the common intuition that training should concentrate information into a small number of dominant directions, we observe a progressive redistribution of variance across representational dimensions. This phenomenon is particularly pronounced in the final CLS token representation, which exhibits the highest effective dimensionality and lowest anisotropy within the network.

Visual Geometry Grounded Transformer (VGGT) recovers dense 3D scene structure from multi-view images in one forward pass, but quadratic cross-frame attention limits its scalability. Existing training-free accelerators reduce computation uniformly along one axis, missing layer heterogeneity. Our spectral, probing, and causal analyses reveal three regimes: shallow layers lack cross-view structure, middle layers drive cross-view alignment, and deep layers are redundant for dense geometry yet their cross-frame attention remains essential for pose. RegimeVGGT applies layer-wise U-shaped compression along two axes: Saliency-Guided Banded Merging protects geometry- and edge-salient tokens, while Selectively Protected K/V Downsampling preserves cross-frame spatial coverage and the pose-critical path through a phase-shifted spatial grid, a reference-frame anchor, and uncompressed camera/register tokens. Training-free, RegimeVGGT achieves a 6.7x speedup over VGGT* at matched reconstruction quality.

3D object reconstruction, and camera pose estimation in industrial applications are challenging tasks, as errors are costly while the computation time is often limited. The complexity of typical industrial objects further complicates these tasks. Most of the existing datasets in this context do not depict realistic industrial scenarios. Therefore, we introduce the Machine Vision Metrology Industrial Object Dataset (MVM-IOD). Images of typical industrial objects are captured systematically, by moving a camera, mounted at the end effector of an industrial robot arm, on a hemisphere around the objects. MVM-IOD contains reference camera poses and reference 3D point clouds, the acquired RGB images of 9 objects and 2 background choices resulting in 18 scenes, which allows evaluation of all image based methods that compute a 3D reconstruction, camera poses, or novel views of a scene. Based on MVM-IOD, we extensively evaluate current SOTA 3D reconstruction and camera pose estimation methods, such as Structure from Motion, Multi-View Stereo, recent feed forward methods (Visual Geometry Grounded Transformer, π3), and 2D Gaussian Splatting and report our findings as a baseline for future research. The experiments show that capture setups like ours generate out-of distribution images for feed forward methods, leading to suboptimal point clouds and camera poses. However, these out-of-distribution images can be shifted closer to the training distribution by applying simple preprocessing steps. Consequently, in certain industrial applications, feed forward methods should be used with caution.

Visual Geometry Grounded Transformer (VGGT) has already attracted a great deal of attention in a short period of time, not least due to the Best Paper Award at CVPR-2025. Similar to DUSt3R and MASt3R, VGGT aims to bring about a paradigm shift by replacing established methods like bundle adjustment and feature matching with a simple, unified, feed-forward neural network that predicts camera poses, depth maps, and dense 3D structure directly from multiple images of a scene in a few seconds. A key aspect is its ability to process an arbitrary number of views consistently in a single forward pass without any post-processing or iterative optimization. For photogrammetry, this opens new possibilities for real-time, scalable, and accessible 3D reconstruction. In this context, not only high reconstruction accuracy but also high-quality uncertainty estimates are crucial, as they foster trust and enable robust quality assurance. This paper therefore investigates the quality of VGGT's uncertainty predictions. The analysis identifies an effective confidence threshold for filtering VGGT's raw output and demonstrates that enhancing uncertainty quality holds strong potential for improving the accuracy of its 3D reconstructions.

In this paper, we propose SGFormer++, a novel Semantic Graph Transformer for 3D scene graph generation (SGG), which aims to parse point cloud scenes into semantic structural graphs, where nodes denote detected object instances and edges encode their pairwise relationships, with the core challenge lying in modeling complex global scene structure. While existing graph convolutional network (GCN)-based methods suffer from over-smoothing and limited receptive fields, SGFormer++ leverages Transformer layers as its backbone to enable global message passing. Specifically, we introduce two key components tailored for 3D SGG: (1) a Graph Embedding Layer++ that efficiently integrates edge-aware global context with linear computational complexity, and (2) a Semantic Injection Layer++ that enriches visual features with linguistic priors from large language models (LLMs) and vision-language models (VLMs), boosting semantic representation without introducing extra trainable parameters. To further address the practical challenge of incremental SGG (I-SGG), where new relationship categories arrive sequentially, we equip SGFormer++ with a novel Spatial-guided Feature Adapter, which calibrates predicate features using subject-object spatial geometry to counter scale variation, and a Cascaded Binary Prediction Head that mitigates catastrophic forgetting via task-incremental classifier expansion and logit distillation. Extensive experiments on the 3DSSG benchmark demonstrate that SGFormer++ achieves state-of-the-art performance in both standard and incremental settings: it yields a significant 4.49% absolute improvement in Predicate A@1 under the incremental setting. Code and data are available at: https://github.com/Andy20178/SGFormer.

Partial-to-full registration remains challenging due to varying overlap ratios, fluctuating point densities, and the presence of noise. While transformers have shown strong potential for point cloud processing, prior methods typically confine them to global context aggregation, overlooking fine-grained local geometry crucial for accurate correspondence. We propose \emph{GAPR-Net}, a learning-based point cloud registration framework with a coarse-to-fine architecture that combines convolution and transformer modules, in which local and global information is fused between the partial and full point clouds using a cross-attention mechanism. To achieve this, a transformation-invariant point-wise geometric feature representation is proposed, which can robustly capture relative geometric features for individual points with respect to their neighboring points. To evaluate the effectiveness of the proposed approach, experiments are conducted on four geometrically distinct bones, including the tibia, femur, pelvis, and thoracic cartilage. The overall registration recall reaches 94.2%, the method results in a low RMSE of 1.992 mm and $R^2$ values of 0.908 and 0.974 for rotation and translation, respectively. The results demonstrate that the proposed method effectively addresses the partial-to-full point cloud registration problem. The proposed method enables highly accurate 3D point cloud registration using partial observation, providing a critical foundation for precise surgical navigation and robotic interventions in computer-assisted surgery. The code will be accessed after the double-blind review process.

Point cloud semantic segmentation requires architectures that capture both fine-grained local geometry and broad global scene structure. Transformer-based networks have demonstrated strong performance by focusing on detailed local feature aggregation; however, global context is conveyed primarily through skip connections across encoder-decoder stages, which we argue is insufficient for full scene understanding. We hypothesize that augmenting skip connections with a learnable global feature extraction module allows the network to acquire scene-level knowledge before descending into local detail, leading to richer and more contextually grounded representations. To this end, we propose Point Transformer with Wavelet Neural Operato (PT-WNO), which integrates a shared Wavelet Neural Operator (WNO) branch alongside the skip connections of a point cloud transformer backbone. At each encoder-decoder transition, point features are projected onto a dense 3D volumetric grid where the WNO captures multi-scale global spectral context through learnable wavelet decomposition and reconstruction. These global features are fused back into the network via lightweight adapters, complementing rather than replacing the existing skip connections. Experiments on four large-scale 3D point cloud benchmarks demonstrate the effectiveness of PT-WNO. On S3DIS (Area 5), PT-WNO achieves 71.59% mIoU, outperforming the Point Transformer v3 (PTv3) baseline by +1.03 points. On DALES it achieves 81.05% mIoU (+1.47 over the baseline). On ScanNet~v2, PT-WNO obtains 76.19% mIoU, remaining competitive with the baseline (76.36%).

Multi-modal novel view synthesis (NVS) combining RGB and thermal imagery enables precise 3D scene reconstruction with visual and thermal information. However, existing methods typically rely on precisely calibrated RGB-thermal image pairs or stereo setups, limiting scalability and practical deployment. To address this, we introduce a framework for unpaired RGB-thermal NVS that leverages VGGT, a 3D feed-forward transformer architecture, to independently estimate camera poses for each modality. The pose sets are then aligned using the Procrustes algorithm with a cross-modal feature matcher, enabling joint registration without paired calibration. Building on this alignment, we further propose a multi-modal 3D Gaussian Splatting approach that learns directly from unpaired RGB and thermal images. Experiments on diverse scenes demonstrate that our method achieves competitive performance in thermal view synthesis while maintaining RGB fidelity. Moreover, we show that existing reconstruction approaches can produce modality-specific reconstructions that lack cross-modal consistency. We thus introduce a benchmarking framework to rigorously evaluate both per-modality image synthesis and the multi-modal coherence of reconstructed scenes.

Gaussian splatting has shown strong potential for 3D reconstruction and novel view synthesis. However, most existing methods require accurate camera parameters and per-scene optimization, while feed-forward methods with pixel-aligned Gaussian primitives often suffer from artifacts and non-uniform primitives. In this paper, we propose $\text{VG}^2$GT, a Voxel-Gaussian Splatting Visual Geometry-Grounded Transformer. $\text{VG}^2$GT leverages a frozen pretrained visual foundation model (VFM), incorporates a multi-scale differentiable voxel module to enhance geometric understanding, and directly splits and regresses Gaussian primitive parameters from voxel features. During training, depth maps are supervised through stochastic solid volume rendering, enabling geometrically accurate Gaussian scene reconstruction while keeping the visual foundation model fully frozen. This design enables $\text{VG}^2$GT to be seamlessly plugged into any patch-feature-based VFM, while substantially reducing the required training cost. $\text{VG}^2$GT outperforms current state-of-the-art methods on widely used DTU, Replica, TAT, and ScanNet datasets.

Estimating 3D attributes directly from images has advanced rapidly with the Visual Geometry Grounded Transformer (VGGT), which predicts camera parameters, depth maps, and point clouds in a single forward pass. However, its 1.2B-parameter scale severely limits deployment on resource-constrained platforms such as UAVs and mobile AR devices. To address this limitation, we introduce QVGGT, a tailored quantization framework designed to compress VGGT. Our approach starts from the observation that transformer blocks within VGGT exhibit heterogeneous sensitivity to quantization. We thus analyze per-block quantization sensitivity and propose a selective mixed-precision strategy that allocates higher precision to the most fragile transformer blocks. To address the amplification of quantization error caused by high-variance camera and register tokens, we further introduce token filtering with camera information compensation, which removes these outliers from activation calibration and restores their geometric cues using a PCA-derived global compensation token. Finally, we develop a task-aware scale search mechanism that evaluates candidate quantization scales not only through layer reconstruction but also through multi-head supervision and cross-head geometric consistency among camera poses, depth maps, and point maps. Extensive experiments on multiple geometry perception benchmarks demonstrate that QVGGT achieves near-lossless W4A16 quantization, preserving the accuracy of all 3D prediction heads while delivering 3$\sim$4.9$\times$ memory reduction and up to 2.8$\times$ real hardware speedup over FP32. Our approach makes high-fidelity 3D perception feasible on edge devices, enabling practical deployment of feed-forward 3D reconstruction models in real-world constrained environments.

Video Motion Magnification (VMM) reveals imperceptible dynamics but often suffers from structural inconsistencies under complex geometric transformations. Existing learning-based methods generally face a trade-off between the limited global context of CNNs and the high computational cost of Transformers. In addition, current training protocols, largely dominated by simple linear motion, fail to capture the geometric and imaging complexities encountered in real-world videos. To address these issues, we propose GeoMag, a geometric-aware VMM framework built upon State Space Models to achieve globally consistent motion amplification with linear complexity. We further construct Geo-200K, a large-scale synthetic dataset that introduces rich geometric transformations together with sensor-realistic degradations, improving the diversity and realism of training signals. Extensive experiments on synthetic and real-world benchmarks show that GeoMag consistently outperforms prior methods in visual fidelity and computational efficiency, while producing fewer artifacts and better structural consistency.

We propose Kan Extension Transformers (KETs) as a unifying categorical framework for a diverse group of Transformer implementations. The core claim is that a Transformer layer can be viewed as a weighted structured extension operator: standard attention is the singleton-neighborhood case, Geometric Transformer style incidence mixing is a sparse edge-restricted case, and KET is the higher-order simplicial case. This lens also clarifies a bridge to diffusion-style completion. When the extension operator acts on detached predictive carriers instead of teacher-forced hidden states, it becomes a valid self-conditioning mechanism that exposes noncausal structure without leaking gold future tokens. We include a comprehensive experimental validation of 12 different Transformer implementations varying across strict-causal and predict-detach regimes on Penn Treebank, WikiText-2, and WikiText-103. In the strict-causal setting, quadratic KET is the strongest model among the compared causal architectures on WikiText-2 and WikiText-103. Across all datasets, however, the largest gains come from the predict-detach regime rather than from changing the neighborhood family alone.

Recent work explores new opportunities at the intersection of vision-language-action models (VLAs) and geometric foundation models (GFMs) for 3D reconstruction, such as VGGT. While the resulting geometric VLAs often show improved performance, it remains unclear (i) if modern VLAs already have sufficient geometric understanding to start with, (ii) what is the best architecture to inject geometric understanding into a VLA, and (iii) what is the effect of other design choices that affect geometric VLAs. In this paper we provide a rigorous experimental analysis to shed light on these questions, for a specific choice of VLA (GR00T-N1.5) and GFM (VGGT). Our first contribution is to formalize prior work's intuition that current VLAs lack geometric understanding, by providing a rigorous analysis based on linear probing. The analysis quantifies, for the first time, the "geometric gap" between VLAs and GFMs. Our second contribution is to identify and compare different strategies to bridge GFMs with VLAs. We implement three different architectures, which differ in the way they inject geometry in the VLA, while keeping low-level implementation details as similar as possible, to ensure a fair comparison. Finally, we analyze the impact of non-architectural choices (e.g., training data, number of cameras, reconstruction quality) on the performance of the geometric VLAs.

Visual geometry transformers have become powerful architectures for multi-view 3D reconstruction, enabling joint prediction of multiple 3D attributes in a feed-forward manner. However, their computational cost grows quadratically with the input sequence length due to the global attention layers inside these models. This limits both their scalability and efficiency. In this work, we address this challenge with a simple yet general strategy: restricting the number of key/value tokens that each query interacts with during global attention. To achieve effective token selection, we introduce a two-stage framework. First, an inter-frame selection step operates at the frame level to identify frames that should be preserved. Second, an intra-frame selection step further discards more redundant tokens within the selected frames. Our analysis highlights the advantage of a diversity-based strategy for inter-frame selection, which ensures broad coverage of the scene. For intra-frame selection, we show that layer-aware sparsification is necessary, with the selection process guided by the entropy of the global attention pattern. Our approach offers a superior speed-accuracy trade-off compared to existing solutions. Extensive experiments show that it accelerates visual geometry transformers by over 85% for scenes with 500 images while maintaining, or even improving, baseline performance, which hints that how our token selection strategy can play a crucial role in future applications of visual geometry transformers. Our project website is available at https://zsh2000.github.io/good-token-hunting.github.io.

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.

Visual Geometry Grounded Transformers (VGGT) have set new benchmarks in high-fidelity 3D scene reconstruction. However, as the sequence length increases, these models suffer from catastrophic geometric forgetting and accumulation drift, primarily due to the quadratic complexity of global attention which necessitates truncated temporal windows. To overcome the resulting geometric drift, we present Mamba-VGGT, an enhanced VGGT framework capable of persistent long-range reasoning. Our key contribution is a Sliding Window Mamba (SWM) memory module that maintains an explicit external memory token across temporal windows. This module leverages selective state-space modeling to distill and propagate global geometric priors, effectively bypassing the memory constraints of traditional transformers. To integrate these long-term temporal cues without disrupting the highly optimized spatial features of the pre-trained VGGT, we propose a Zero-Init Spatial Memory Injector. Utilizing zero-convolutional layers, this injector adaptively fuses persistent memory into the patch token stream, ensuring structural stability and seamless feature alignment. Extensive experiments demonstrate that our approach significantly outperforms existing VGGT-based methods in maintaining spatial consistency and reducing trajectory accumulation errors. Our work provides a scalable, linear-complexity solution for geometry-grounded world modeling in extensive 3D environments.

Reconstructing coherent 3D geometry and appearance from unposed multi-view images is a fundamental yet challenging problem in computer vision. Most existing visual geometry foundation models predict explicit geometry by regressing pixel-aligned pointmaps, often suffering from redundancy and limited geometric continuity. We propose IVGT, an Implicit Visual Geometry Transformer that implicitly models continuous and coherent geometry from pose-free multi-view images. This formulation learns a continuous neural scene representation in a canonical coordinate system and supports continuous spatial queries at any 3D positions, retrieving local features to predict signed distance (SDF) values and colors using lightweight decoders. It allows direct extraction of continuous and coherent surface geometry, enabling rendering of RGB images, depth maps, and surface normal maps from arbitrary viewpoints. We train IVGT via multi-dataset joint optimization with 2D supervision and 3D geometric regularization. IVGT demonstrates generalization across scenes and achieves strong performance on various tasks, including mesh and point cloud reconstruction, novel view synthesis, depth and surface normal estimation, and camera pose estimation.

Feed-forward 3D reconstruction models, represented by Visual Geometry Grounded Transformer (VGGT), jointly predict multiple visual geometry tasks such as depth estimation, camera pose prediction, and point cloud reconstruction in a single forward pass. They have been widely adopted in 3D vision applications, but their billion-scale parameters bring substantial memory and computation overhead, posing challenges for on-device deployment. Post-Training Quantization (PTQ) is an effective technique to reduce this overhead. Existing PTQ methods for feed-forward 3D models mainly focus on handling heavy-tailed activation distributions and constructing diverse calibration datasets. However, we observe that feed-forward 3D models predict multiple geometric attributes through a shared backbone, where different transformer blocks and hidden channels contribute distinctly to each task, resulting in substantially different sensitivities to quantization errors across tasks, blocks, and channels. Consequently, treating all tasks equally over-emphasizes insensitive tasks and causes significant accuracy loss on the sensitive ones. To address this issue, we propose Fisher-Guided Quantization (FGQ) for feed-forward 3D reconstruction models. Specifically, FGQ uses the diagonal Fisher information matrix to quantify the different sensitivities across tasks, blocks, and channels, and incorporates these sensitivities into the Learnable Affine Transformation during calibration to better preserve the channels and blocks most critical to each task. Extensive experiments across camera pose estimation, point map reconstruction, and depth estimation show that FGQ consistently outperforms state-of-the-art quantization baselines on VGGT, achieving up to 39% relative improvement under the 4-bit quantization. Code is available at https://github.com/ypzhng/FGQ.

Recent feed-forward reconstruction models, such as VGGT, have proven competitive with traditional optimization-based reconstructors while also providing geometry-aware features useful for other tasks. Here, we show that the quality of these models scales predictably with model and data size. We do so by introducing VGGT-$Ω$, which substantially improves reconstruction accuracy, efficiency, and capabilities for both static and dynamic scenes. To enable training this model at an unprecedented scale, we introduce architectural changes that improve training efficiency, a high-quality data annotation pipeline that supports dynamic scenes, and a self-supervised learning protocol. We simplify VGGT's architecture by using a single dense prediction head with multi-task supervision and removing the expensive high-resolution convolutional layers. We also use registers to aggregate scene information into a compact representation and introduce register attention, which restricts inter-frame information exchange to these registers, in part replacing global attention. In this way, during training, VGGT-$Ω$ uses only about 30% of the GPU memory of its predecessor, allowing us to train with 15x more supervised data than prior work and to leverage vast amounts of unlabeled video data. VGGT-$Ω$ achieves strong results for reconstruction of static and dynamic scenes across multiple benchmarks, for example, improving over the previous best camera estimation accuracy on Sintel by 77%. We also show that the learned registers can improve vision-language-action models and support alignment with language, suggesting that reconstruction can be a powerful and scalable proxy task for spatial understanding. Project Page: http://vggt-omega.github.io/

Recent feed-forward 3D reconstruction methods, such as visual geometry transformers, have substantially advanced the traditional per-scene optimization paradigm by enabling effective multi-view reconstruction in a single forward pass. However, most existing methods struggle to achieve a balance between reconstruction quality and computational efficiency, which limits their scalability and efficiency. Although some efficient visual geometry transformers have recently emerged, they typically use the same sparsity ratio across layers and frames and lack mechanisms to adaptively learn representative tokens to capture global relationships, leading to suboptimal performance. In this work, we propose TurboVGGT, a novel approach that employs an efficient visual geometry transformer with adaptive alternating attention for fast multi-view 3D reconstruction. Specifically, TurboVGGT employs an end-to-end trainable framework with adaptive sparse global attention guided by adaptive sparsity selection to capture global relationships across frames and frame attention to aggregate local details within each frame. In the adaptive sparse global attention, TurboVGGT adaptively learns representative tokens with varying sparsity levels for global geometry modeling, considering that token importance varies across frames, attention layers operate tokens at different levels of abstraction, and global dependencies rely on structurally informative regions. Extensive experiments on multiple 3D reconstruction benchmarks demonstrate that TurboVGGT achieves fast multi-view reconstruction while maintaining competitive reconstruction quality compared with state-of-the-art methods. Project page: https://turbovggt.github.io/.

Modern SMILES-based chemical language models obtain strong MoleculeNet performance by treating SMILES as generic text and compensating with multi-million-molecule self-supervised pretraining. We ask: when a domain carries structural priors as rich as chemistry's, does it warrant a domain-native transformer rather than a generic one rescued by scale? We answer affirmatively with \textbf{GM-Net} (Geometric Measure Network), a transformer family in which every module is replaced by a sphere-native counterpart, and instantiate it as \textbf{Chem-GMNet}. Three blocks follow: SH-Embedding (tokens as learnable directions on $S^{k-1}$ lifted through a Gegenbauer feature map); DualSKA (a per-head fusion of a linear-time gated Sphere-Flow recurrence whose persistent state we prove is the truncated multipole expansion of the input distribution, and a softmax Sphere-Kernel branch over the same Schoenberg-valid kernel); and SH-FFN (sphere projection $\to$ Gegenbauer lift $\to$ moment readout). On canonical DeepChem scaffold splits, against same-shape ChemBERTa-2 baselines under the chemberta3-faithful protocol: (i) random-initialised, Chem-GMNet wins on 7 of 10 MoleculeNet endpoints at $\sim\!35\%$ fewer parameters; (ii) pretrained on the same 10M-SMILES ZINC corpus as ChemBERTa-2 MLM-10M, it matches or beats the public release on 6 of 8 shared endpoints (5/7 excluding a known ClinTox release anomaly). A $(k,L)$ ablation shows that increasing the sphere dimension from $k\!=\!8$ to $k\!=\!10$ at fixed $L\!=\!3$ lowers ESOL RMSE to $0.938$ at scratch, beating pretrained ChemBERTa-2 MLM-10M on this endpoint without any pretraining at all.

Reconstructing dynamic 4D scenes from monocular videos is a fundamental yet challenging task. While recent 3D foundation models provide strong geometric priors, their performance significantly degrades in dynamic environments. This degradation stems from a fundamental tension: the inherent coupling of camera ego-motion and object motion within global attention mechanisms. In this paper, we propose a novel, training-free progressive decoupling framework that disentangles dynamics from statics in a principled, coarse-to-fine manner. Our core insight is to resolve the tension by first stabilizing the camera pose, followed by geometric refinement. Specifically, our approach consists of three synergistic components: (1) a Dynamic-Mask-Guided Pose Decoupling module that isolates pose estimation from dynamic interference, yielding a stable motion-free reference frame; (2) a Topological Subspace Surgery mechanism that orthogonally decomposes the depth manifold, safely preserving dynamic objects while injecting refined, mask-aware geometry into static regions; and (3) an Information-Theoretic Confidence-Aware Fusion strategy that formulates depth integration as a heteroscedastic Bayesian inference problem, adaptively blending multi-pass predictions via inverse-variance weighting. Extensive experiments on standard 4D reconstruction benchmarks demonstrate that our method achieves consistent and substantial improvements across principal point-cloud metrics. Notably, our approach shows competitive performance in robust 4D scene reconstruction without requiring fine-tuning, suggesting the potential of mathematically grounded dynamic-static disentanglement.

Visual Geometry Grounded Transformer (VGGT) advances 3D reconstruction via scalable Transformer architecture, but the quadratic complexity of global attention prevents long context application. StreamVGGT enables streaming with causal attention, yet its KV cache grows linearly with frames, causing memory overflow and quality degradation. We present RetrieveVGGT, a training-free framework, which formulates context construction for VGGT as a retrieval problem. By retrieving a fixed number of relevant frames at each step, VGGT maintains a controllable memory budget, which is close to its training context length. Interestingly, we find that the similarity between current frame queries and cached history frame keys at the first global attention layer of VGGT is already a strong indicator of relevance, eliminating the need for additional learned scoring. To enhance information diversity similar to a recommender system, we propose Segment Sampling so that the retrieval spans distinct relevant segments rather than a single high-similarity region. We design a pose-aware spatial memory mechanism that organizes history frames according to their already estimated camera poses, enabling location-aware retrieval. Extensive experiments demonstrate that RetrieveVGGT achieves state-of-the-art performance, outperforming StreamVGGT, TTT3R, and InfiniteVGGT while maintaining constant memory usage regardless of sequence length. Code is available at https://github.com/zzctmd/RetrieveVGGT.

Post-training alignment algorithms are predominantly evaluated as black boxes, obscuring how they reshape language models' internal computations. We present a systematic mechanistic analysis of six preference-optimization methods: PPO, DPO, SimPO, ORPO, GRPO, and KTO across three open-weight model families. By integrating layer-wise linear probing, Sparse Autoencoders, and crosscoders, we localize preference representations and quantify alignment-induced geometric transformations in latent space. We find that preference signals consistently concentrate in early--mid or mid--late layers, but different objectives induce qualitatively distinct representational shifts. KTO and GRPO enhance linear separability through constructive feature sharing and sparse, high-salience recruitment. In contrast, DPO and ORPO degrade separability via non-constructive geometric rotation and feature attenuation, while PPO and SimPO largely preserve baseline geometry. These transformations exhibit architecture-dependent variability, demonstrating that behavioral alignment does not imply uniform internal restructuring. Our findings establish alignment as a heterogeneous intervention, motivate standardized feature-level auditing for safety and interpretability, and highlight the need for mechanism-aware optimization objectives.

Multi-view geometry transformers are feed-forward 3D foundation models that jointly predict depth maps, point maps, and camera poses for N images in a single forward pass. Most of them build on an alternating-attention (AA) stack whose cross-view attention runs over the patch tokens of all N views in every block, so its cost grows quadratically in N: on 300-frame ScanNetv2 clips, VGGT peaks at 72.3 GiB, and MapAnything does not fit on a 93 GiB card. Existing methods reduce tokens or attention inside the AA stack, so the full patch grid still enters it, and the pre-AA interface, where the encoder hands its tokens to the first AA block, has been overlooked. We propose PrePARE, which prunes patch tokens once at the pre-AA interface and restores the dense grid once after the last AA block. Every block of the frozen AA stack then runs on the reduced tokens, while the prediction heads receive the full grid. A Token Scorer, supervised by how the unpruned AA stack uses each token, and a Feature-guided Restoration module are the only trained parts. The Token Routing module is rule-based. On ScanNetv2 at N = 300, PrePARE reduces the peak memory of VGGT by 80%, from 72.3 to 14.4 GiB, below every in-AA method we ran, and runs 5.4 times faster, while its per-scene Chamfer distance is lower than the unpruned model's on 34 of 50 scenes (sign test p = 0.015). On pi^3 and Depth Anything 3 it saves 15% and 20% of peak memory, where the in-AA methods save at most 9%, and at 1000 frames it is the only method we ran that fits Depth Anything 3 and MapAnything on one GPU.

Modern visual world modeling systems increasingly rely on high-capacity architectures and large-scale data to produce plausible motion, yet they often fail to preserve underlying 3D geometry or physically consistent camera dynamics. A key limitation lies not only in model capacity, but in the latent representations used to encode geometric structure. We propose S$^2$VAE, a geometry-first latent learning framework that focuses on compressing and representing the latent 3D state of a scene, including camera motion, depth, and point-level structure, rather than modeling appearance alone. Building on representations from a Visual Geometry Grounded Transformer (VGGT), we introduce a novel type of variational autoencoder using a product of Power Spherical latent distributions, explicitly enforcing hyperspherical structure in the bottleneck to preserve directional and geometric semantics under strong compression. Across depth estimation, camera pose recovery, and point cloud reconstruction, we show that geometry-aligned hyperspherical latents consistently outperform conventional Gaussian bottlenecks, particularly in high-compression regimes. Our results highlight latent geometry as a first-class design choice for physically grounded visual and world models.

Transformers have become a common foundation across deep learning, yet 3D scene understanding still relies on specialized backbones with strong domain priors. This keeps the field isolated from the broader Transformer ecosystem, limiting the transfer of new advances as well as the benefits of increasingly optimized software and hardware stacks. To bridge this gap, we adapt the vanilla Transformer encoder to 3D scenes with minimal modifications. Given an input 3D scene, we partition it into volumetric patch tokens, process them with full global self-attention, and inject positional information via a 3D extension of rotary positional embeddings. We call the resulting model the Volume Transformer (Volt) and apply it to 3D semantic segmentation. Naively training Volt on standard 3D benchmarks leads to shortcut learning, highlighting the limited scale of current 3D supervision. To overcome this, we introduce a data-efficient training recipe based on strong 3D augmentations, regularization, and distillation from a convolutional teacher, making Volt competitive with state-of-the-art methods. We then scale supervision through joint training on multiple datasets and show that Volt benefits more from increased scale than domain-specific 3D backbones, achieving state-of-the-art results across indoor and outdoor datasets. Finally, when used as a drop-in backbone in a standard 3D instance segmentation pipeline, Volt again sets a new state of the art, highlighting its potential as a simple, scalable, general-purpose backbone for 3D scene understanding.

Relative position embedding has become a standard mechanism for encoding positional information in Transformers. However, existing formulations are typically limited to a fixed geometric space, namely 1D sequences or regular 2D/3D grids, which restricts their applicability to many computer vision tasks that require geometric reasoning across camera views or between 2D and 3D spaces. To address this limitation, we propose URoPE, a universal extension of Rotary Position Embedding (RoPE) to cross-view or cross-dimensional geometric spaces. For each key/value image patch, URoPE samples 3D points along the corresponding camera ray at predefined depth anchors and projects them into the query image plane. Standard 2D RoPE can then be applied using the projected pixel coordinates. URoPE is a parameter-free and intrinsics-aware relative position embedding that is invariant to the choice of global coordinate systems, while remaining fully compatible with existing RoPE-optimized attention kernels. We evaluate URoPE as a plug-in positional encoding for transformer architectures across a diverse set of tasks, including novel view synthesis, 3D object detection, object tracking, and depth estimation, covering 2D-2D, 2D-3D, and temporal scenarios. Experiments show that URoPE consistently improves the performance of transformer-based models across all tasks, demonstrating its effectiveness and generality for geometric reasoning. Our code is available on our project website: https://urope-pe.github.io/.

3D human pose estimation is a classic and important research direction in the field of computer vision. In recent years, Transformer-based methods have made significant progress in lifting 2D to 3D human pose estimation. However, these methods primarily focus on modeling global temporal and spatial relationships, neglecting local skeletal relationships and the information interaction between different channels. Therefore, we have proposed a novel method,the Dual-stream Spatio-temporal GCN-Transformer Network (MixTGFormer). This method models the spatial and temporal relationships of human skeletons simultaneously through two parallel channels, achieving effective fusion of global and local features. The core of MixTGFormer is composed of stacked Mixformers. Specifically, the Mixformer includes the Mixformer Block and the Squeeze-and-Excitation Layer ( SE Layer). It first extracts and fuses various information of human skeletons through two parallel Mixformer Blocks with different modes. Then, it further supplements the fused information through the SE Layer. The Mixformer Block integrates Graph Convolutional Networks (GCN) into the Transformer, enhancing both local and global information utilization. Additionally, we further implement its temporal and spatial forms to extract both spatial and temporal relationships. We extensively evaluated our model on two benchmark datasets (Human3.6M and MPI-INF-3DHP). The experimental results showed that, compared to other methods, our MixTGFormer achieved state-of-the-art results, with P1 errors of 37.6mm and 15.7mm on these datasets, respectively.