3D Gaussian Splatting

Recent single-view feed-forward 3D Gaussian Splatting (3DGS) generation predicts a fixed number of Gaussians per camera ray, introducing severe spatial redundancy. Most existing compaction strategies target multi-view setups to exploit cross-view consistency and are incompatible with single-image models. Instead of retraining the base feed-forward network to directly output compact representations, our insight is to keep the base models frozen and apply post-hoc pruning and recurrent refinement to the generated Gaussians. Consequently, we propose a backbone-agnostic compaction pipeline for single-view feed-forward 3DGS that couples an importance-score-based pruning mechanism with a trainable, lightweight recurrent refinement module, which iteratively updates the surviving primitives to restore image quality. Our results demonstrate seamless integration with existing baselines while preserving novel-view rendering fidelity and achieving high memory reduction. Furthermore, our method supports flexible inference-time keep ratios for application needs.

Referring scene understanding for embodied robots requires grounding object- and relation-centric language queries from a designated viewpoint. While a local semantic Gaussian map can support such grounding within one agent's observations, cooperative settings require this ability to remain effective after independently reconstructed maps are aligned and fused. In this setting, the referred target or its contextual landmark may come from another agent's observations, while spatial relations must still be interpreted from the querying robot's viewpoint. We formulate this problem as cooperative referring Gaussian grounding over fused maps, which requires geometric alignability, instance-level semantic comparability, and view-conditioned relation reasoning. Existing language-aware Gaussian methods mainly focus on single-map querying, whereas Gaussian registration methods optimize geometric or photometric alignment without preserving language-grounding-oriented semantic compatibility. We propose CoRef-GS, a cooperative referring Gaussian splatting framework. CoRef-GS constructs local open-vocabulary instance-aware Gaussian maps, then aligns partially overlapping maps with a cross-agent alignment module by geometric and semantic consistency, and grounds queries using a view-conditioned mask relation graph. We further introduce CoQuad-Ref, a dual-quadruped benchmark spanning both real-world and simulated indoor scenes. Experiments show that, on simulated scenes, CoRef-GS reduces the rotation error from 2.58° after coarse initialization to 0.15° after refinement, and improves real-world referring mIoU over ReferSplat from 52.6% to 68.8%. The established benchmark and source code will be publicly released at https://github.com/ruojiruoli17/CoRef-GS.git.

Conventional 3D Gaussian Splatting assumes a closed set of observations and long optimization schedules. Continual RGB-D mapping in contrast poses the problem that new observations arrive online, while previously reconstructed regions must be preserved. We present EliGSiR (Evidence-guided Load-adaptive Incremental Gaussian Splatting with Image Replay), a continual Gaussian mapper that controls how the available optimization budget is used as the reconstruction evolves. Map-Guided View Scheduling filters redundant incoming views and reconsiders retained views according to the current state of the map. Load-Adaptive Fidelity adjusts supervision resolution to the current mapping load instead of following a fixed resolution schedule. Targeted Geometry Growth separates depth supervision from Gaussian creation and adds geometric capacity only where repeated RGB-D observations indicate missing or misplaced structure. Together, these mechanisms adapt which views are optimized, how much image detail is used, and where the representation grows while mapping remains active. We evaluate EliGSiR on Replica, TUM RGB-D, ScanNet++, and real RGB-D sensor sequences, considering both the final reconstruction and the map available throughout acquisition. On TUM RGB-D fr3/long_office_household, EliGSiR reaches 21.52 dB with the same ground-truth mapping poses used by the controlled baselines, compared with 19.42 dB for SplaTAM. In the tracked-pose comparison, EliGSiR with live ORB-SLAM3 poses reaches 23.02 dB in 155.5 s, compared with 20.10 dB in 230.9 s for CaRtGS using its native tracker. We further evaluate reconstruction throughout acquisition and show how EliGSiR adaptive view scheduling, supervision fidelity, and geometry growth improve the use of the available mapping budget.

Gaussian Splatting (GS) excels at novel-view synthesis but encodes baked-in radiance, tightly entangling illumination with geometry and preventing seamless integration into physically based rendering (PBR) pipelines. Existing inverse-rendering methods attempt to disentangle materials via joint optimization, but often suffer from competing objectives that cause severe ambiguities and residual lighting artifacts. To overcome this, we present GS-PI, a novel optimization-decoupled framework that casts PBR material generation as a geometry-conditioned diffusion process on 3D point clouds. By operating directly in the 3D domain, our method inherently guarantees multi-view consistency, sidestepping the severe pixel correspondence issues that challenge 2D diffusion approaches. We introduce a multi-scale cross-view conditioning mechanism that integrates three complementary components: a global semantic prior, source-anchored photometric cues, and an absolute spatial learned view-direction conditioning signal. This design efficiently compresses complex multi-view evidence, mitigating cross-view projection misalignment and successfully preventing specular highlights from baking into intrinsic colors. By extracting a point cloud from a pre-trained Gaussian model, predicting PBR attributes via conditional diffusion, and distilling them back through differentiable rasterisation, we yield a fully relightable PBR-GS asset. GS-PI outperforms recent inverse-rendering baselines while replacing per-scene joint illumination/BRDF optimization with a learned diffusion pass followed by a short target-driven distillation, without requiring proxy meshes.

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 present ParticleSplat, a self-supervised object-centric learning method that decomposes scenes into a set of latent ''particles'' representing semantic entities through feedforward 3D Gaussian Splatting. Building on the Deep Latent Particles (DLP) framework, which represents images as a set of particles with attributes such as position, scale, and visual appearance, we address a key limitation of DLP: its inherently 2D nature, which prevents explicit 3D spatial and geometric reasoning that are critical for downstream tasks such as robotic manipulation. Leveraging the structural similarity between latent particles and 3D Gaussian primitives, we introduce a 3D latent particle space trained with a novel view synthesis objective. Our model jointly encodes multiple views with camera poses into a shared 3D object-centric latent space, then transforms particles into particle-aligned 3D Gaussians whose composition reconstructs the full scene. On simulated and real-world datasets, we show that this formulation inherently learns object masks without supervision and supports controllable 3D scene editing, such as moving objects by modifying particles in the latent space. We further establish that the learned 3D representation improves downstream performance on robotic manipulation tasks.

Gaussian Splatting has significantly improved the quality of novel view synthesis with explicit Gaussian representation. However, we observed that existing 3D Gaussian Splatting methods (3DGS) often suffer from surface collapse issues on reflective regions, and thus produce inferior geometry and low-quality specular. In this work, we propose a physically-based deferred rendering framework, named Reflection-aware Gaussian Splatting (RGS), that can accurately model specular regions and improve novel view synthesis performance. Specifically, we found that a powerful 3D foundation model can provide a strong 3D geometric prior to foster correct geometric modeling. Based on this, we propose a cross-view shape consistency regularization to regularize the geometry surface with the large model prior and cross-view constraints. In this manner, our RGS can produce smoother geometric surfaces on reflective regions while reducing geometric hollows. To further improve rendering results on reflective regions, we present a reflection-aware densification strategy that is designed to capture specular variations across various views. With this strategy, our RGS is able to render novel views of objects in higher quality. Extensive experiments demonstrate our method consistently renders high-quality reflective objects, achieving state-of-the-art performance.

Autonomous robots operating in partially observed environments must navigate safely while acquiring observations that improve future planning. Existing safety formulations generally reason primarily about geometry. Consequently, geometrically similar scene elements may induce comparable control responses despite having different semantic consequences. We present a semantic risk aware safe-active perception framework for navigation in attributed 3D Gaussian maps. Semantic attributes modulate an Average Value-at-Risk collision clearance model through class dependent risk weights, allowing safety-critical Gaussian primitives to receive greater influence in the composite barrier. The resulting weighted clearances are aggregated into a control barrier function, while a trajectory-relevant active perception barrier promotes observations that reduce geometric map uncertainty along the robot's anticipated motion. Both objectives are integrated in a unified CBF-QP that enforces semantic risk-aware collision avoidance as a hard constraint while relaxing information acquisition when it conflicts with safety or task progress. Experiments demonstrate efficient safety constraint, improved navigation through active perception, semantic dependent trajectory adaptation, and real-robot execution under Ackermann dynamics.

Real-time dense SLAM is a core capability for robotics applications that require robust localization and high- quality mapping in dynamic or fast-changing environments. Recent 3D Gaussian Splatting (3DGS)-based SLAM methods have shown promising performance, but most are designed for narrow-FoV pinhole cameras, where limited angular coverage weakens pose observability and often leads to unstable photo- metric optimization under rapid motion and large viewpoint changes. We present PanoGS-SLAM, the first panoramic dense SLAM system built on 3D Gaussian Splatting. Our method per- forms differentiable rendering and pose optimization directly in the spherical domain, enabling omnidirectional photometric constraints for more stable tracking. To improve geometric consistency and robustness, we introduce (1) a sphere-consistent photometric loss that compensates for the area distortion of equirectangular projection, and (2) a depth-guided Gaussian initialization strategy that stabilizes incremental mapping in newly observed regions. Extensive experiments on both real and synthetic panoramic benchmarks (PALVIO and SynPano) show that PanoGS-SLAM consistently outperforms geometric and GS-based baselines in tracking accuracy and rendering quality, while achieving fast front-end convergence and real-time perfor- mance. In addition, controlled field-of-view experiments reveal a clear monotonic improvement in optimization conditioning and convergence stability as angular coverage increases, high- lighting the fundamental role of sensing geometry in shaping the optimization landscape of differentiable Gaussian-based SLAM. The source code will be made publicly available.

Robot teams that learn a common environment model exchange belief summaries and plan by the expected information gain of their actions. Under conjugate exponential-family beliefs the shared belief is counted once per robot at two points: at fusion, the product of local posteriors counts the common prior $n$ times, and at planning, every robot scores its plan under the same belief and the team converges on the same unknown. Both errors are removed by adding evidence increments to the shared natural parameter, realized increments at fusion and expected increments at planning. The expected increment of a committed teammate gives the next robot its conditional gain; corrected gains sum to the joint gain, the redundancy removed equals the total correlation of the planned observation streams, and sequential commitment keeps the $1/2$ greedy guarantee. The expected increment is exact for Gaussian beliefs with fixed sampling paths and for Dirichlet beliefs under the novelty approximation of discrete active inference, whose team objective has a closed concave form within an explicit bound of the exact mutual information, and fails for finite hypothesis classes, where a short exact enumeration replaces it. Experiments on cooperative RockSample, foraging, and field monitoring show that fusion correction leaves exploration redundancy unchanged, anticipated evidence removes it, and sequential commitment recovers most of the value of centralized joint planning at cost linear in the team size.

Streaming 3D reconstruction demands both speed and temporal fidelity, goals that existing methods undermine by updating every Gaussian every frame, even in static regions. We present DecoGS, a method for efficient online training of 3D Gaussians from streaming videos. Unlike prior methods that update the entire scene indiscriminately, DecoGS introduces an adaptive mechanism that selectively focuses optimization on spatiotemporal regions exhibiting motion or photometric changes. This targeted training strategy eliminates redundant updates that cause flickering and drift in nominally static regions, while enabling fast, high-fidelity scene updates. The pipeline further integrates region-aware Gaussian management through gradient gating and efficient visibility filtering to maintain temporal coherence and a compact memory footprint. On N3DV and MeetRoom, DecoGS achieves 34.55 and 31.60 dB PSNR respectively, outperforming all streaming and offline baselines, while rendering at 261 FPS with $70\times$ lower temporal flicker than the best prior method, requiring no large-scale pretraining.

Detecting and grasping small objects remains a significant challenge in robotics. Active vision, where the robot moves closer to the object, is an intuitive solution, yet comparing approaches on common ground is difficult since identical physical scene setups are required. Hence, we introduce BRAVE-6D, a benchmark designed to evaluate robotic active vision systems for object pose estimation, a crucial first step in grasping objects. BRAVE-6D leverages view synthesis based on Gaussian Splats (3DGS) to provide scenes and tools for benchmarking active vision systems. We show baseline solutions performing visual servoing within the scene and accurately estimating the poses of small objects.

Sparse-view 3D scene reconstruction with 3D Gaussian Splatting (3DGS) is inherently underconstrained. Plausible renderings can also coexist with erroneous Gaussian geometry, as errors in positions or depths may be concealed by opacity, scale, and appearance; we term this failure mode Geometry Cheating. Existing regularization methods constrain geometry but remain limited to observed views, while video-diffusion-based methods complete unseen views yet mainly use them as RGB pseudo-supervision, underusing motion and temporal priors and lacking explicit geometry supervision. We present Bi-FlowGS, which uses optical flow to bridge generative view completion and Gaussian geometry regularization. Our plug-and-play Video-to-Geometry Flow Distillation (V2G) distills temporal correspondence priors from restored videos into Gaussian geometry to alleviate Geometry Cheating. Conversely, Geometry-to-Video Flow-Guided Restoration (G2V) uses the current 3DGS geometry to guide temporally consistent video restoration, providing more reliable generative supervision. Together, V2G and G2V form an implicit bidirectional co-refinement process, enabling restored videos and the optimized 3DGS scene to iteratively improve each other. Experiments demonstrate improved rendering quality and geometric consistency across wide-baseline and unbounded 360° benchmarks.

A Digital Surface Model (DSM) is a fundamental geospatial data product for representing the elevation of the Earth's surface. Recently, 3D Gaussian Splatting (3DGS) has shown considerable potential for DSM reconstruction from multi-view optical satellite imagery due to its explicit scene representation and efficient optimization. However, in 3DGS-based DSM generation, alpha-weighted aggregation of Gaussian altitudes may blend splats from different height layers at the same rendered pixel or DSM sampling location, producing non-physical intermediate elevations and height-layer mixing errors. To address this problem, we propose HLC-GS, a risk-map-guided height-layer consistency Gaussian Splatting method for DSM reconstruction from optical satellite imagery. HLC-GS consists of a risk map module, a dominant-layer reliability correction module, and a secondary-layer suppression module. The risk map localizes high-risk pixels with abnormal height dispersion and unreliable dominant-layer responses, while the latter two modules regularize unreliable dominant-layer responses and suppress weakly supported far secondary-layer responses. Extensive experiments are conducted on the DFC2019 and IARPA2016 datasets. Compared with six state-of-the-art DSM reconstruction methods, HLC-GS achieves better overall accuracy. Compared with the latest and precision-enhanced EOGS, HLC-GS reduces the average MAE from 1.46 m to 1.18 m and the average RMSE from 2.78 m to 2.58 m over the evaluated scenes, while improving PAG$_{2.5}$ from 86.09% to 88.61%. Overall, these results demonstrate that explicitly modeling per-pixel height-layer consistency alleviates height-layer mixing and improves the geometric quality of 3DGS-based DSM reconstruction from optical satellite imagery.

Record-level differential privacy exposes a structural misalignment in personalized federated learning when client-specific variation is low-dimensional while training repeatedly releases high-dimensional updates. In this paper, we address this misalignment by releasing a private client context once and confining repeated adaptation to a fixed coefficient space. Beyond dimensionality reduction, the factorized generator induces an adaptive optimization geometry that reshapes noisy updates, and controlled ablations show that most of its private-training gain is retained by radial evolution. To further reduce the communication cost, we realize the Gaussian mechanism for coefficient updates directly through variable-length quantization with finite expected code length, so that the quantization error itself serves as the required privacy perturbation rather than extra distortion. Across MNIST and CIFAR-10, our design matches or outperforms full-model private adaptation across privacy budgets and client heterogeneity, while reducing protected uplink by a factor of 2.67 at $\varepsilon=16$ on CIFAR-10 with comparable future-client accuracy.

The Gaussian kernel is a widely used similarity measure underlying kernel methods such as kernel PCA and spectral clustering, but computing Gaussian kernel distances for many pairs of points can be expensive. Using Random Fourier Features (RFF), Chen and Phillips [ALT 2017] showed that for points in a $d$-dimensional Euclidean ball in ${\mathbb R}^N$, $t=Ω((d/\varepsilon^2)\log(dR/\varepsilon))$ features suffice to preserve all pairwise Gaussian kernel distances within a $(1\pm\varepsilon)$ factor with high probability. We establish a uniform relative-error embedding theorem for the more general setting of an arbitrary positive-reach submanifold $\mathcal M\subset{\mathbb R}^N$ of intrinsic dimension $d$. We show that $t=O((d/\varepsilon^2)\log(\operatorname{vol}(\mathcal M)^2N^{2d}/(\operatorname{vol}(B_1^d(0))^2\operatorname{rch}(\mathcal M)^{2d}\varepsilon^{2d+1}δ)))$, or approximately $O((d^2/\varepsilon^2)(\log N+\log(1/(\varepsilonδ))))$, RFFs suffice, with probability $1-δ$, to preserve the Gaussian kernel distance between every pair of manifold points up to relative error $\varepsilon$. Thus the bound depends only logarithmically on the ambient dimension and on manifold parameters such as volume and reach, while retaining the $1/\varepsilon^2$ Euclidean rate. We also prove a topological consequence: under the same RFF embedding, persistent homology is preserved in the sense that weighted Cech and Rips filtrations built from Gaussian kernel power distance are $(1\pm\varepsilon_\star)$-interleaved, where $\varepsilon_\star$ accounts for both distance distortion and kernel-weight approximation.

3D Gaussian language fields provide an explicit, spatially grounded representation for 3D visual question answering (VQA), but their dense semantic features can require tens of thousands of embeddings per scene, resulting in substantial storage, memory, and inference costs. We investigate how much of this representation is actually necessary for downstream reasoning. Starting from a full embedding representation, we systematically sparsify its semantic embeddings, including the previously underexplored regime below a single image-equivalent block down to 8 visual tokens. We compare random, geometric, semantic, and joint spatial-semantic selection strategies and introduce an object-based sparsification method that distributes the token budget across detected object instances while retaining background context. Experiments on ScanQA and MV-ScanQA reveal substantial redundancy in dense Gaussian language fields. Strong VQA performance is retained with only a few hundred semantic embeddings, corresponding to less than 1% of the original representation. Object-based selection performs well relative to others, with only modest observed changes down to 256 tokens. At this budget, SparseTalk retains 0.80% of SplatTalk's 32,076-token inference input and 0.332% of the mean 77,207-Gaussian dense field, increasing inference throughput while reducing decoded-feature memory 125-fold.

Let $Y_s=\sqrt{s}X+Z$, where $Z$ is standard Gaussian and independent of the real random variable $X$. We prove that, under the square-exponential moment condition $\mathbb{E}e^{βX^2}<\infty$ for some $β>0$, the scalar minimum mean-square error $\operatorname{mmse}_X(s)$ is analytic at zero signal-to-noise ratio if and only if $X$ is Gaussian, with constant random variables included as degenerate Gaussians. The proof converts estimation in the Gaussian channel into a backward heat flow acting on the moment-generating function $M(z)=\mathbb{E}e^{zX}$. Under the stated tail condition, every non-Gaussian input forces $M$ to have a nonzero complex zero. We show that each zero cluster produces a finite singularity in its localized Borel transform at the action $ξ=z_0^2/2$. After removing the action scale, the Borel coefficients have a nonzero $n^{-1/2}$ prefactor for a simple zero. A zero of multiplicity $m\geq 2$ splits according to the roots of a Hermite polynomial and instead contributes a prefactor $n^{-m/2}e^{r_m\sqrt{2n}}$. A finite-disc localization and relative-cycle continuation argument then show that at least one such singularity survives in the full Borel transform. Thus, for every non-Gaussian input in the stated class, the formal zero-SNR expansion is Gevrey-1 but divergent. Rational-MMSE rigidity and the analogous analyticity criterion for mutual information follow as corollaries.

Xu, Vardi and Safran (ICML 2026) prove that over-parameterized ridge regression over an unstructured random Gaussian feature map groks, with the delay between memorization and generalization growing as $1/λ$ in the weight decay. We show that on a structured feature map the same delay does not appear. For a band-limited Fourier feature map over $\mathbb{Z}_p^2$ carrying a single-character target that lies inside the expressible class, enlarging the band at fixed positive weight decay drives peak held-out accuracy monotonically from $1.00$ to $0.07$, with no memorize-then-generalize regime anywhere along the sweep. The degradation is not an interpolation effect. It sets in at capacity ratio $q/n = 0.638$, far below the interpolation threshold, on separate grounds from the exact null space that appears above it. What does have a sharp boundary is the active support. Holding the nominal dimension fixed and masking the band back to $1089$ active modes restores held-out accuracy of $1.000$ with zero variance across seeds, while the full $4225$-mode band collapses to $0.185$. The number of active modes acts through the teacher-weighted spectrum of the empirical Gram matrix and not through the capacity ratio, which makes this a statement about feature geometry and not a restatement of double descent.

Reconstructing 3D scenes under real-world low-light conditions remains challenging due to severe sensor noise, low signal-to-noise ratios, and degraded photometric consistency, which destabilize geometry estimation and novel view synthesis. Existing approaches often rely on well-lit reference data for reliable Structure-from-Motion (SfM) initialization under degraded inputs or apply per-view enhancement methods that introduce cross-view inconsistencies. To address these limitations, we propose \textbf{NOVA-GS}, a unified noise-aware framework for low-light 3D Gaussian Splatting that subsumes enhancement, denoising, and geometry optimization within a single process. Our method leverages VGGT-based feed-forward estimation to obtain robust camera poses and geometry directly from degraded inputs, eliminating the need for SfM. Building on this initialization, NOVA-GS integrates three coupled components: a structure-aware enhancement module for exposure correction, a self-supervised denoising module with blind-spot masking for pseudo-supervision, and a consistency-driven Gaussian Splatting optimization enforcing cross-view geometric coherence. We further introduce a noise-guided spherical harmonic regularization to suppress view-dependent artifacts in noisy regions. Extensive experiments on diverse real-world low-light datasets demonstrate improved geometric fidelity, color consistency, and robustness without requiring paired supervision or well-lit references. https://shaurya2524.github.io/nova-gs/

Three-dimensional Gaussian Splatting (3DGS) combines explicit primitives with efficient rasterization, yet recent systems increasingly use neural networks to generate or share Gaussian parameters. We characterize this trend along five axes: attribute decoding, spatial sharing, view-conditioned decoding, topology generation, and amortized inference. An analysis of 19 representative methods shows that these choices address different limitations and cannot be reduced to a binary neural label. We also isolate three forms of neural parameterization in a controlled mip-NeRF 360 study. Sharing appearance and opacity improves reconstruction quality, while decoding geometric structure offers no further gain. The evidence favors selective neuralization: shared functions help when they capture reusable correlations without sacrificing the local geometric freedom of explicit splats.

Feed-forward Gaussian splatting models have demonstrated remarkable effectiveness in reconstructing three-dimensional (3D) objects from a few two-dimensional (2D) images, even if they are unseen. As existing methods typically predict Gaussian primitives uniformly across the 3D space, most primitives are placed in non-object regions. This may hinder the representation of fine object details. This paper proposes a Voxel-Selective Gaussian Splatting model (VS-Splat), a new end-to-endfeed-forward Gaussian splatting framework that predicts many primitives only within selected voxels that are likely to belong to an object, without 3D structural supervision. To achieve this, we propose a new learnable voxel selection approach that identifies object-centric voxels only with 2D rendering supervision.Our sparse-view rendering experiments with three benchmark datasets show that proposed VS-Splat outperforms several state-of-the-art methods. We further demonstrate its effectiveness as a backbone for an existing densification method and show that anoptional extension improves its robustness to inaccurate camera pose estimates.

Lung cancer causes more deaths than any other malignancy, and low-dose CT screening is the main pathway to early diagnosis. That pathway hinges on the smallest lesions, yet nodules below six millimeters remain hard to detect, because most methods treat a nodule as a generic object and ignore the imaging physics behind its appearance. We show that this appearance is highly regular. Intensity peaks at the geometric center of a nodule and decays radially in a Gaussian pattern, and a fit to 18,218 annotated lesions from three public benchmarks yields a mean radial coefficient of determination above 0.86 in every dataset and size stratum. A square convolution samples both axes uniformly and is mismatched to this radial signal, most severely for small nodules. Guided by this evidence, we propose GRIPNet (Gaussian Radial Intensity Prior Network), a detector in which every module maps to a measurable property of the intensity distribution. Pinwheel convolutions decompose radial gradients, a dual-frequency module separates boundary detail from structural context, dilated masked attention matches the decay extent, and an adaptive loss reweights samples by conspicuity. GRIPNet raises mAP@0.5 to 95.3, 91.6 and 97.9 percent on KanserSet, LUNA16 and Lung-PET-CT-Dx while sharpening high-IoU localization at real-time speed.

Accurate head modeling requires a stable yet expressive geometric representation. Existing Gaussian-based head avatars commonly rely on parametric templates (e.g., FLAME) for Gaussian initialization and deformation, but these templates lack personalized priors and struggle to represent structures such as hair and clothing. To address this issue, we propose MGAvatar, a Gaussian-mesh hybrid representation that jointly models geometry and appearance through two Gaussian-mesh binding modes. Specifically, we introduce vertex-bound Gaussians and constrain their learnable parameters, enabling progressive mesh deformation to represent complex head geometry, while a pose-dependent offset module accounts for non-rigid deformations. Once geometry is stabilized, MGAvatar switches to face-bound Gaussians for appearance modeling. To improve appearance consistency across novel poses and viewpoints, we introduce a view-conditioned neural color field that alleviates artifacts caused by independently optimized Gaussian colors. In addition, we design a Gaussian offset network to predict Gaussian offset maps in the observation space, providing greater flexibility for face-bound Gaussians to capture dynamic facial textures. Extensive experiments on multi-view and monocular videos show that MGAvatar outperforms existing methods in rendering quality, producing high-fidelity head avatars with rich texture details.

Language Gaussian fields implicitly assume that the primitive carrying semantics remains identifiable across views. This assumption breaks in scalable anchor-decoded representations, where persistent anchors generate view-conditioned child Gaussians whose geometry and appearance vary with the camera. We introduce Ours, a persistent language field for such structured Gaussian scenes. Our key idea is semantic ownership: transient children route observations, while persistent decoder slots and their parent anchors own the language field. We use alpha-compositing responsibilities to accumulate additive directional evidence at slots; these statistics marginalize exactly to anchors. We then complete weakly supported slots with anchor-aligned evidence while preserving the anchor direction, and represent slot detail through low-rank residuals in anchor-relative semantic coordinates. Our primary model, Ours (base), stores anchor features together with compact slot residuals. Ours (light) retains only anchor features, whereas Ours (max) stores the full-dimensional completed slot features explicitly. Without scene-specific semantic optimization, Ours (base) nearly matches Ours (max) across KITTI, Virtual KITTI, and Waymo. On KITTI, it achieves 34.19 2D mIoU with a 2.72 GiB effective feature footprint, compared with 34.20 mIoU and 12.90 GiB for Ours (max). The same accuracy-storage trend holds on Virtual KITTI and Waymo. These results show that language fields on view-conditioned splats require persistent semantic ownership, conserved evidence, and a hierarchy that balances stability, detail, and representation cost. Our code, checkpoints, and benchmark suite will be publicly available.

Recovering clean 3D scenes from hazy multi-view images is challenging because haze attenuates scene radiance and introduces atmospheric scattering. Recent scattering-aware Gaussian Splatting methods introduce physical haze models into reconstruction, but they often apply degradation in image space or bind medium-related variables to Gaussian primitives, which can entangle clean scene radiance with atmospheric effects. Moreover, low-transmittance regions provide weakened supervision for Gaussian optimization, causing distant or dense-haze areas to be under-reconstructed. We argue that clean reconstruction under haze requires both scene--medium disentanglement and transmittance-aware optimization rebalancing. To this end, we propose Tri-DehazeGS, a scene--medium decoupled Gaussian Splatting framework. It represents the clean scene with Gaussian primitives, models the participating medium using an independent view-shared tri-plane field, and composes hazy observations through a physical scattering model. We further introduce Medium-Decoupled Transmittance Gradient Compensation (MD-TGC), which compensates haze-suppressed gradients after medium freezing without altering forward rendering. Experiments on real and synthetic haze benchmarks show that Tri-DehazeGS improves clean novel-view reconstruction. Code is available at https://github.com/aptx46/Tri-DehazeGS.

Render--match--PnP relocalization establishes correspondences between query image pixels and 3D map points for camera pose recovery, but their potential to support dense depth estimation is often overlooked. To exploit this geometric information, we present RIDE, which estimates dense metric depth from a robot's RGB stream. Given a metrically scaled 3D Gaussian Splatting (3DGS) model, RIDE combines sparse metric depth observations derived from PnP-RANSAC inlier correspondences with the geometric prior of a pretrained video-depth model. To handle uneven and intermittent observations, it integrates global and local depth correction with temporal memory, supporting depth estimation through short observation gaps after metric scale initialization. Trained on public RGB-D videos, RIDE is evaluated on robot sequences without fine tuning. Experiments show improved depth accuracy and temporal consistency over scale-only calibration, demonstrating how localization geometry can support both pose recovery and dense robot perception.

We introduce Complex-Valued Quadratic Phase Gaussian (CVQPG), a novel hologram representation method that replaces standard 2D Gaussian representations used in 2D Gaussian Splatting with 2D quadratic phase functions. CVQPG incorporates additional learnable parameters to control the curvature of these bases. We evaluate our approach against state-of-the-art methods, exceeding the visual quality by +0.19 dB (RGB) and +0.33 dB (grayscale) on average in holographic reconstructions. Specifically, our equal parameter count evaluations show that modulating the primitive's wavefront is an effective and lightweight enhancement for hologram representations. In addition, our frequency domain analysis illustrates that CVQPG has successfully preserved the mid-to-high frequency band of natural images.

Neural radiance fields (NeRFs) and 3D Gaussian Splatting (3DGS) encode a scene with complementary inductive biases, but existing cross-representation distillation typically fixes one representation as teacher for the entire scene. A globally fixed teacher can propagate local reconstruction errors. We present RouteBridge, a bidirectional framework that selects the teaching direction for each ray. Its reliability estimator combines photometric residuals with representation-specific geometric evidence and routes supervision from NeRF to 3DGS, from 3DGS to NeRF, or abstains. A renderer-independent interface transfers color, opacity, and normalized depth without shared features or point correspondence. On mip-NeRF 360, the NeRF and 3DGS exports reach 28.56 and 28.77 dB, respectively. The 3DGS export improves over 3DGS by 1.56 dB and over NeRF-GS by 0.45 dB while reducing LPIPS to 0.207. On static three-view DTU, RouteBridge obtains 21.12 dB. Ablations show that both adaptive routing and geometric ray targets contribute to the improvement.

We prove the gap-entropy conjecture for fixed-confidence best-arm identification with independent unit-variance Gaussian arms, means in $[0,1]$, and a unique optimal arm. For each suboptimal arm $i$, let $Δ_i=μ_*-μ_i$ be its gap from the optimal mean, and write $H=\sum_{i\ne *}Δ_i^{-2}$. Let $p_r$ be the fraction of $H$ contributed by arms with $2^{-(r+1)}<Δ_i\le2^{-r}$, and let $\mathrm{Ent}(I)=\sum_{r:p_r>0} p_r\log(1/p_r)$. Among all algorithms that identify the optimal arm with probability at least $1-δ$ on every Gaussian instance, the optimal expected number of samples on a given instance, averaged over all permutations of the arm labels, is within absolute constant factors of $H(\log(1/δ)+\mathrm{Ent}(I))$. Moreover, there is an algorithm, independent of the instance, whose expected number of samples is bounded by a constant multiple of this quantity plus $g^{-2}\log\log(e^e/g)$, where $g=\min_{i\ne *}Δ_i$ is the gap to the closest competitor.

Sparse-view X-ray 3D reconstruction is essential for reducing radiation exposure, but recovering a density field from a handful of X-ray projections is severely ill-posed. Recently, 3D Gaussian Splatting has achieved state-of-the-art performance in sparse-view reconstruction by representing the volume using explicit, optimized primitives, but it requires dozens of projected views. With fewer views, reconstruction quality degrades severely since the explicit primitives are optimized freely without any anatomical information. Anatomical structures, in contrast, share similar geometry and density across a population. Their variations are bounded within a limited range that statistical shape models can capture. This paper proposes a shape-guided Gaussian splatting framework for sparse-view X-ray 3D reconstructions. Our contribution lies in driving Gaussian positions toward anatomically valid configurations, alongside atlas-based density regularization. Our method ensures anatomically consistent reconstruction and improves PSNR by 2.83 dB over a state-of-the-art Gaussian splatting baseline with as few as 5 views. Code Available: https://github.com/polyshape-lab/ShapeGuidedGaussian

3D Gaussian Splatting (3DGS) renders novel views in real time, but an uncertainty heatmap does not certify that a rendered view meets a certain prediction coverage. We treat novel-view synthesis as structured regression and ask that, with probability at least $1-α$, RGB prediction boxes cover at least a $1-β$ fraction of pixels in a new view. We propose View-Structured Conformal Prediction (VSCP). It splits the pre-calibration scale into a spatial shape from the renderer and a transferable view-difficulty factor, which predicts the smallest view-wise multiplier that shape needs. A held-out quantile over views (View-CP) then gives finite-sample validity even when transferring to new scenes. The same factorization makes the analysis exact: a conformity score is the ratio of oracle to predicted view difficulty, and excess width separates into a test-side and a calibration-side term. Across 13 real scenes, pixel-pooled calibration reaches 89.9% marginal pixel coverage but only 61.4% view-event coverage at a 90% target, while View-CP reaches 91.7--92.0%. At matched coverage VSCP cuts width by 22.1% against a constant scale, and matches a ten-model ensemble's 21.0% reduction using only one model per scene and four rather than ten rasterization passes per query. VSCP also improves on the closest single-model baseline, the 3DGS-U field, by 4.7 points ($p=0.0225$). The view predictor transfers from bounded source families to all nine unbounded Mip-NeRF360 scenes. There the full scale beats the constant scale with 20.7% width saving on all nine scenes. It also keeps an 18.3% saving under a different densification backbone and runs at 216--280 FPS on an RTX4090.

3D Gaussian Splatting (3DGS) enables real-time novel view synthesis but produces millions of primitives through adaptive densification, leading to significant storage overhead. Learned-mask pruning methods such as LP-3DGS address this by assigning each Gaussian a learnable mask to identify and prune redundant primitives. However, we identify a limitation of this paradigm: the steep slope of the Gumbel-Sigmoid activation drives mask values to the extremes within the short mask-training window, before the importance ranking has stabilized, producing a sharply bimodal distribution from which that ranking can no longer be reliably recovered. We propose LinearMask-GS, which replaces Gumbel-Sigmoid with a linear increment activation that keeps mask values in a mid-confidence regime throughout mask training, producing a stable, unimodal mask distribution whose ranking tracks importance. On Mip-NeRF 360, our method achieves 3.6x and 1.6x Gaussian reductions over 3DGS and LP-3DGS, respectively, while maintaining or improving rendering quality. For outdoor scenes, it yields a 1.6x reduction (from 2.18M to 1.36M) with notable gains in PSNR (+0.38 dB), SSIM (+0.025), and LPIPS (-0.029).

We develop Gaussian approximation bounds in higher-order Wasserstein distance $W_p$, $p\geq2$, for sums of multivariate martingale differences generated by a uniformly ergodic Markov chain. Under an $L^{(2+η)p}$-moment condition with $η>0$, we establish the explicit bound $O\left( p^3 \|A\|_4^2 + pd^{1/4}\|A\|_2^{1/2}\|A\|_4^2 \right)$ where $A\in\mathbb{R}^n$ collects the $L^{(2+η)p}$-sizes of the $n$ individual martingale increments. In the balanced-increment regime where the individual increments have comparable sizes of order $n^{-1/2}$, it yields the first optimal $O(n^{-1/2})$ Gaussian approximation rate for fixed $p$ and $d$. Consequently, we also obtain the first optimal $O(n^{-1/2})$ $W_p$ Gaussian approximation rate for multivariate additive functionals of uniformly ergodic Markov chains. Our analysis develops two techniques for addressing the interplay between higher-order Wasserstein distance and temporal dependence. First, building on the Ornstein--Uhlenbeck relative-score approach of Fang and Koike (2023), we formulate the bound in terms of antisymmetric Stein couplings while retaining the conditional tensor structure. Second, we develop a refresh-then-maximal coupling that combines an independent first-step resampling, which preserves the desired Stein identity, with a subsequent maximal coupling that provides effective control of the coupling increment. These tools may be useful more broadly for Gaussian approximation under temporal dependence.

Sparsity is a powerful structural resource in optimization and statistics. We develop frameworks for leveraging sparsity in sampling problems over the Hamming slice $\mathcal{X}_k^d:=\{\mathbf{x}\in\{\pm 1\}^d:|\{i:\mathbf{x}_i=1\}|=k\}$, in high-dimensional regimes where $k\ll d$ (i.e., where $\mathcal{X}_k^d$ is \emph{highly magnetized}). We use our frameworks to design improved samplers for canonical problems in the study of \emph{Ising models} and \emph{Bayesian sparse linear regression}. Our first main result considers the \emph{Sherrington--Kirkpatrick} (SK) model restricted to fixed-magnetization slices $\mathcal{X}_k^d$. We give a polynomial-time sampler for fixed-magnetization SK models at any inverse temperature $β>0$, under arbitrary external fields, provided that $k\le c_βd$ for an appropriate constant $c_β$. By combining this result with an annealing strategy for estimating normalizing constants, we obtain polynomial-time samplers for the SK model at arbitrarily low temperatures under a sufficiently strong external field of strength $h$. In the large-$β$ limit, our framework permits sampling at field strengths within constant factors of the \emph{Almeida--Thouless line} delineating the replica-symmetric and replica-symmetry-breaking regions ([dAT78]), improving polynomially over the field strength $h(β)$ required by the recent work of [BAR26]. Our second main result concerns the measurement complexity of polynomial-time Bayesian sparse linear regression. Recent work by [KSTZ25] shows how to sample from the canonical \emph{Gaussian spike-and-slab posterior} with expected sparsity $k$, at any signal-to-noise ratio, given $n\gtrsim k^3\log^3 d$ Gaussian measurements. We improve this requirement to $n\gtrsim k^{3/2}\log^2 d+k\log^3 d$, using a common sparsity-aware framework underlying both our results.

High-fidelity vehicle assets are essential for controllable traffic scene generation, particularly for synthesizing rare and safety-critical long-tail scenarios. However, reconstructing a reusable vehicle representation from in-the-wild onboard images remains challenging for two reasons. First, image-to-3D generation methods generally produce models without reliable metric scale. Second, onboard cameras usually observe only one side of a target vehicle, making conventional multi-view reconstruction incomplete on unobserved regions. To solve these problems, we propose a feed-forward vehicle asset reconstruction method, which leverages two complementary priors to reconstruct 3D Gaussian representations for vehicles using sparse one-sided observations. To achieve metric-scale reconstruction, a visual foundation model is first utilized to serve as a visual prior for Gaussian initialization. The Gaussian attributes are then estimated by a learnable encoder-decoder module. A symmetry-aware cloning strategy is presented to complete the unobserved side directly in Gaussian space, which exploits the bilateral structure of vehicles as a geometric prior. Experiments on the public dataset demonstrate that the proposed method significantly outperforms existing approaches in both vehicle asset completeness and geometric accuracy.

Quantization schemes based on randomized rotations have recently received renewed attention, including the roles of MMSE and unbiased reconstruction scalings. In this note, we point out the connection to classical results in statistical signal processing and communication theory. Specifically, the two reconstruction scales used in the EDEN line of work admit a natural interpretation as finite-dimensional, realization-dependent counterparts of the Wiener and unbiased coefficients in the classical CDEF formulation. At finite blocklength, the CDEF +1 relation holds pointwise for each rotation realization as an exact geometric (Pythagorean) identity, but does not hold after averaging the distortions over the rotation. The classical SNR relation $\sf{SNR}_{\rm MMSE}=\sf{SNR}_{\rm MMSE,U}+1$ is recovered as $d\to\infty$: once the overall scale is handled separately, the empirical coordinate statistics of a randomly rotated vector approach their i.i.d. Gaussian counterparts, and the rotation-dependent quantities concentrate. Importantly, EDEN goes beyond this classical correspondence: for every finite $d$, its Haar-rotation formulation guarantees exact conditional unbiasedness, a stronger property than the second-order notion of unbiasedness in CDEF. We further comment on two distinct roles random rotations play in quantization: one is approximate Gaussianization of the coordinates; the other is decorrelation of reconstruction errors across quantization branches.

While 3D Gaussian Splatting (3DGS) has emerged as a powerful representation for real-time novel view synthesis, rendering high-fidelity scenes often relies on a massive number of Gaussian primitives, incurring substantial storage and computational overhead. Existing simplification techniques are largely intrusive, requiring training-time pruning, architectural modifications, or computationally expensive per-scene fine-tuning. These drawbacks limit their deployment on off-the-shelf pretrained models. In this paper, we propose CVT-GS, a novel optimization-free post-hoc simplification framework that directly compresses trained 3DGS scenes without sacrificing visual fidelity. Our approach first constructs spatially coherent cells over Gaussian centers via a geometry-aware Centroidal Voronoi Tessellation (CVT). Subsequently, a lightweight neural cell merger predicts the geometry and appearance of a single, highly representative Gaussian primitive for each cell under differentiable rendering supervision. By formulating simplification as a rendering-aware many-to-one merging process rather than naive primitive pruning, CVT-GS outputs a standard 3DGS scene that is seamlessly compatible with existing renderers. Experiments on various datasets demonstrate the superiority of our method. Notably, when achieving a 100-fold reduction in Gaussian points, our method operates 12 times faster than state-of-the-art methods while improving the PSNR by 1.3 dB.

Autonomous navigation in unstructured environments requires robust scene understanding, yet Vision-Language Models (VLMs) often suffer from semantic ambiguity, where conflicting predictions can lead to dangerous failures. To address this, we present a novel pipeline for vision-based traversability estimation that explicitly models contextual uncertainty. Our approach utilizes Conceptual Anchoring to ground open-vocabulary VLM predictions onto a continuous physical traversability scale. By formulating the model's responses as a Gaussian Context Distribution (GCD), we derive both a dense traversability map and a dense uncertainty map based on the statistical properties of the distribution. Experimental validation on the real-world GOOSE dataset demonstrates that our proposed uncertainty metric effectively correlates with sources of ambiguity, such as visual artifacts and mixed terrain overlap. The method exhibits competitive performance while offering the distinct advantage of providing statistical uncertainty estimates to address semantic ambiguity, enabling safer and more reliable autonomous behavior in complex outdoor settings.

Gaussian splats provide a fast, high-fidelity representation for 3D objects but are often constructed from incomplete input data in practice, leaving missing regions. Existing completion methods either do not preserve the original splats or require scarcely available 3D training data. We propose GSComplete, which combines 3D generation based on Score Distillation Sampling with a novel preservation loss that encourages the original splats to be preserved where they should be visible. This effectively completes the Gaussian splat object using only 2D diffusion priors while fully preserving existing splats and generating new splats only in missing regions, without occluding the input. To evaluate our approach, we introduce a new dataset of partial Gaussian splat objects and show that GSComplete achieves significantly more accurate preservation of the input than existing methods with comparable plausibility of the completed result. Our code and dataset will be made available upon acceptance.

We present EdMCGS (Event-driven Markov chain Gaussian Splatting), an end-to-end method for reconstructing dynamic 3D scenes from extreme-low-frame-rate RGB together with an event stream, which can then be rendered at any intermediate timestamp. Methods relying solely on RGB images generate numerous artifacts due to the lack of evidence from between consecutive frames. To supply this missing evidence, we model the scene motion as an event-driven Markov chain, in which the sparse RGB frames anchor the state at their own timestamps while the events recorded within an interval drive the transition across it. Since the transition reads the events of the current interval, it remains active at inference and produces the in-between motion of the 3D Gaussians directly from the events rather than by interpolation, which sets our method apart from prior work that uses events only as training-time supervision. The state is carried by a compact set of control points, each driven by the events sampled in the neighborhood of its own image projection, and a temporal local isometry term keeps the propagated motion locally rigid. Experiments on synthetic and real-world scenes show that EdMCGS outperforms both RGB-based and event-based baselines, while rendering in real time with far fewer Gaussians than the strongest event-based baseline. We release our source code and a new dataset at https://github.com/joseclipse/EdMCGS.

Gaussian Splatting has been effective in inferring scene representations that excel in novel view synthesis. Multiple splats cooperate seamlessly to synthesize the pixels of novel views and are jointly optimized even though they only affect each other indirectly, via pixels they project to in common. We present an approach that enables direct communication among splats to enhance the geometric structures they form in 3D. This is accomplished by Tensor Voting, which was originally designed to infer structures from noisy inputs and has been adapted here to provide supervision during test-time optimization, leading to more accurate scene geometry. We introduce a new class of 3D losses that do not rely on rendering and can be combined with essentially all losses previously reported in the literature. Our 3D losses are especially effective when the input views are sparse and geometric regularization is essential due to limited supervision from the images. Our method is easy to integrate with a diverse set of backbones, and our experiments on the DTU and Tanks-and-Temples datasets demonstrate that TV-SGS improves the geometry of the outputs compared to the backbone, while maintaining or improving rendering quality.

3D Gaussian Splatting has recently revolutionised novel view synthesis as well as many other 3D vision methods and applications. Drawing inspiration from this representation, we now rethink textures to overcome the main issues of UV mapping while considerably lowering their memory footprint. Heat Kernel Textures (HKTex) eliminate UV unwrapping as well as their persistent issues of wasted UV space, seams, distortions, vertex-duplication, and varying resolution. Grounded in discrete Riemannian geometry and intrinsically defined on any manifold surface discretised as a triangular mesh, HKTex uses anisotropic heat kernels as geodesic equivalents to Gaussians. Like our kernels, also the optimisation of their position and the adaptive densification strategies were redefined to operate on the surface of the object to be textureised. Our novel representation is also fully integrated with a physically based renderer and can be optimised either from existing textures or multi-view images. Our project page and code are available at circle-group.github.io/research/HeatKernelTextures.

SLAM systems based on 3D Gaussian Splatting (3DGS) have recently demonstrated promising reconstruction accuracy for dense 3D scene representations. However, current 3DGS systems struggle to meet the strict demands of real-world deployments due to severe limitations in operational performance and map adaptability. To this end, we propose LightSplat, a hybrid-representation RGB-D SLAM framework. It synergizes local sparse features for robust and fast tracking with a dual-thread backend that progressively constructs dense Gaussian submaps. Crucially, we enable online loop closure through feature-accelerated 3DGS registration, refining overall map consistency through pose graph optimization. Ultimately, LightSplat achieves the online reconstruction of high-fidelity Gaussian map. Extensive experiments on multiple datasets and real-world robotic platform demonstrate that our method achieves near state-of-the-art reconstruction quality and the capability to accommodate practical camera motions, maintaining an average framerate of 8 FPS. Overall, LightSplat provides an efficient and robust foundation for deploying high-fidelity 3DGS in real-world environments.

Estimating the 6D pose of textureless objects without prior CAD models remains a critical challenge due to the lack of appearance features. While recent generalizable approaches alleviate the dependence on object-specific models, their performance on low-texture objects is often limited by insufficient geometric constraints in the underlying representations. In this work, we propose PG-Pose, a geometry-aware framework combining Planar-based Gaussian Splatting (PGS) reconstruction and Geometry-driven pose optimization. In the offline representation extraction stage, three distinct representations of the object are extracted from multi-view reference RGB images with known poses. PG-Pose reconstructs a 3D Gaussian representation and renders high-fidelity depth maps to generate 3D point clouds through back projection. In the online pose inference stage, the initial pose of the input image is estimated by 2D-3D correspondence matching between the input image and the reconstructed 3D point clouds, followed by a PGS-Refiner for iterative pose optimization. Evaluations on the OnePose-LowTexture datasets, PG-Pose achieves an average accuracy of 94.2% ADD(S)@0.1d, with a 2.1% improvement average accuracy compared with the state-of-the-art (SOTA) GS-based approach. To further demonstrate the effectiveness of PG-Pose for industrial robots in grasping tasks, we deploy it on a dual-arm industrial robot and successfully realize the grasping task on an unseen object.

Efficient, fully automatic, and physically plausible 4D Gaussian synthesis is an important goal for dynamic scene generation. Recent physics-based methods couple 3D Gaussians with the Material Point Method (MPM) to generate physically driven motion, but extending this paradigm to heterogeneous multi-part objects and interacting multi-object scenes remains challenging. Object-level physical assignment collapses distinct parts into a single material state, while one-shot predictions from large language models, vision-language models, or agents neither reliably bind different materials to identified parts nor verify that the resulting MPM configuration is executable. Score Distillation Sampling (SDS)-based parameter optimization, meanwhile, requires repeated per-scene score evaluations and gradient backpropagation, incurring lengthy optimization and potentially yielding suboptimal or unstable solutions. We therefore present PhysMAS, a physics-grounded multi-agent framework. From a motion prompt and four scene views, an Object-Part Scene Agent establishes persistent identities and calls a Material Reasoning Agent for part-wise profiles. It invokes solver-aware skills to bind these identities and profiles to per-particle MPM fields and execute all objects in a shared domain; the framework then screens candidate forward-simulation results. This supports heterogeneous multi-part and interacting multi-object scenes without per-scene diffusion-score backpropagation. Extensive experiments demonstrate that, compared with recent physics-based 4D Gaussian baselines that rely on SDS, PhysMAS achieves better semantic alignment and perceived physical plausibility while requiring less runtime.

While machine-learning interatomic potentials (MLIPs) have successfully learned potential energy surfaces (PES) and atomic forces, many practical applications, such as vibrational analysis and transition state search, rely heavily on the PES Hessian. Yet standard MLIPs are trained on energy and forces alone, and existing methods that incorporate the Hessian into training objectives require architectural modifications and incur significant computational and memory overheads from higher-order backpropagation. To address these limitations, we propose two Hessian-derived data augmentation schemes: isotropic Gaussian displacement (\textbf{UniAug}) and normal mode-weighted displacement (\textbf{ModeAug}). Both methods utilize simple Taylor expansions, achieving effective augmentation without altering training objectives or extending the autograd graph. This allows seamless, plug-and-play integration with existing architectures and training pipelines. Comprehensive evaluations across non-equilibrium and equilibrium datasets demonstrate that our approach enhances model accuracy where reference forces are large while providing practical, task-specific guidelines.

3D scene representations like NeRF and 3D Gaussian Splatting (3DGS) suffer severe artifacts in sparse-view settings. Recent generative 3D artifact fixers attempt to address this, but rely on paired corrupted and clean renders requiring costly, per-scene reconstructions across varying view configurations. While 2D image augmentations act as instant regularizers, no explicit equivalents exist for 3D representations to preserve spatial consistency across views, an essential property for 3D-aware training. We propose 3D Morphological Perturbations as an optimization-free regularizer that preserves spatial consistency. Leveraging explicit 3DGS, we treat each Gaussian as a fundamental building block - analogous to a 2D pixel - and apply perturbations across its morphological parameter space via scale, rotation, and pruning. Our method eliminates per-scene 3DGS optimization loops from dataset curation while enabling models to learn stronger geometric priors than sparse-view baselines in diagnostic ablations conducted on a lightweight video diffusion sandbox. Scaled to a 14B-parameter video model via ControlNet, our approach maintains visual fidelity while reducing mean depth error by 12.5% over state-of-the-art image-to-image 3D artifact refiners, ultimately boosting downstream robotics policy success rates by up to 8.0% across 3 of 4 manipulation tasks.

3D Gaussian Splatting has become a de facto scene representation for novel view synthesis, yet robustly learning 3D Gaussian primitives from visual input remains challenging. Standard optimization relies on gradient-based updates, but a common issue is the gradient vanishing phenomenon: a pixel far from a Gaussian primitive often has diminishing gradient magnitudes to influence primitive attributes, resulting in suboptimal scene reconstruction. In this paper, we propose a method to address gradient vanishing with a piecewise truncated gradient formulation that improves the optimization stability and robustness to initializations. We show that our method consistently improves 3D Gaussian Splatting with random and COLMAP initializations while being generalizable across static and dynamic Gaussian Splatting. As a by-product, we also examine the limitations of current benchmarks for dynamic scenes, and introduce a novel dataset for benchmarking dynamic Gaussian Splatting using synthetic 3D scenes. We demonstrate the effectiveness of our method in both static and dynamic settings for the public benchmarks and our proposed dataset.

Restricted eigenvalue (RE) bounds govern stable recovery by norm-regularized estimators. For isotropic sub-Gaussian measurements, the benchmark sample size is $1+w(A)^2$, where $w(A)$ is the Gaussian width of the normalized descent cone. The COLT 2015 open-problem note (Banerjee et al., 2015) asked whether the same law follows for heavy-tailed designs from a uniform small-ball condition alone. We give an explicit and systematic negative answer to the general question as formulated there: the proposed law fails in its full dimension-free, arbitrary-set form, and the missing obstruction is simultaneous threshold occupancy. A constant-width polyhedral descent cone with fixed small-ball constants has zero empirical RE on every sample path up to half the ambient dimension. More generally, every finite range space admits exact threshold encoding in an arbitrarily narrow spherical cap and a lift to a full polyhedral descent-cone section. For every fixed threshold VC dimension $d$, as $β\downarrow0$, the sharp worst-case sample complexity is $Θ(β^{-1}[d\log(1/β)+\log(1/δ)])$. The separation persists under exact isotropy and all finite moments: on the same constant-width cone, Gaussian measurements succeed with $O(1+\log(1/δ))$ samples, whereas an isotropic heavy-tailed design fails pathwise for $n\lesssim\sqrt{p/\log p}$. Gaussian smoothing yields an everywhere-positive $C^\infty$ density while retaining arbitrarily poor RE. Under isotropy, a distribution-free fallback governed by affine dimension times squared enclosing radius is sharp on this family.

Large-scale 3D surface reconstruction from aerial imagery is fundamental to geospatial mapping and urban modeling. Recent advances in 3D Gaussian Splatting (3DGS) have demonstrated considerable potential for this task. However, existing methods still face three major challenges in large and complex scenes: scene partitioning may split continuous scene elements across independently optimized sub-regions; geometric constraints mainly focus on the attributes of individual Gaussians while overlooking their local organization; and uniform regularization struggles to accommodate heterogeneous geometric structures. To address these issues, we propose STARS-GS, a structure-aware 3DGS framework for large-scale surface reconstruction. First, we introduce a structure-aware scene partitioning strategy that better preserves continuous scene structures during partitioning and reduces cross-region geometric inconsistencies and stitching artifacts through boundary refinement. Second, we develop neighborhood-aware Gaussian organization that extends geometric constraints from individual primitives to their neighborhood organization, encouraging Gaussians to better conform to local surface geometry. Third, we introduce adaptive surface regularization that adjusts the regularization strength according to local geometric characteristics, promoting geometric consistency in structured regions while preserving plausible variations in unstructured regions. Extensive experiments on large-scale aerial photogrammetry benchmarks demonstrate that STARS-GS consistently outperforms the evaluated Gaussian-based methods in surface reconstruction. It increases the average F1-score from 0.640 for the second-best method to 0.698, corresponding to a relative improvement of approximately 9.1%, demonstrating effective improvements in geometric accuracy and surface completeness.

We present PointGT, a point-based 3D representation that enables simultaneous editing of object geometry and appearance. Existing reconstruction and view synthesis techniques produce volumetric 3D representations that are high-quality and photorealistic, but are difficult to edit. In particular, recent efforts to enable texture editing for 3D Gaussian Splatting representations are not compatible with geometry edits and deformations. Our method combines a point-based representation that is well-suited for geometry deformations with a learned UV mapping technique that enables high-resolution texture editing. We show that PointGT enables fine-grained editing of both geometry and texture in point-based neural representations with high rendering quality.

A key bottleneck in 3D Gaussian Splatting training is the continual growth of Gaussian primitives, which increases optimization cost and slows convergence, especially at high resolutions. We propose Laplacian Frequency Hierarchies, a simple yet efficient 3DGS scheme that combines Laplacian image decomposition with coarse-to-fine, frequency-staged training. After fitting lower-frequency structure, we archive the corresponding Gaussian field so that subsequent fields can optimize higher-frequency residuals without carrying the full primitive burden, and we compose the rendered components in the image domain via a Laplacian-style reconstruction at inference time. This design reduces the number of active Gaussians during training, thereby lowering optimization overhead and accelerating training. The proposed scheme is plug-and-play and orthogonal to prior 3DGS accelerations: it can be directly combined with strong backbones such as Taming-3DGS and FastGS to improve training speed with competitive reconstruction quality. It achieves average speedups of 1.73x and 1.21x at 1K setting, and 1.74x and 1.33x at 4K setting on Taming-3DGS and FastGS, with larger gains on more challenging scenes and increasingly pronounced benefits at higher resolutions.

While 3D Gaussian Splatting (3DGS) has revolutionized 3D reconstruction and novel-view synthesis, scenarios with limited input views often lead to poor reconstruction quality and artifacts in rendered novel views. Recent efforts attempt to utilize powerful diffusion priors, yet they typically process rendered and reference views concatenated along an additional dimension in a single network. These methods overlook an inherent nature that different views should maintain appearance similarity but differ in structure due to view shifts, leading to blur caused by conflicts between the two properties. In this paper, we propose DualDiff, a novel pipeline that leverages dual diffusion priors with a Structure-Appearance Attention (SAA) module to introduce reference guidance for refining low-quality novel views rendered from flawed 3D representations. Specifically, we retain one diffusion branch to focus on extracting structural information from the low-quality novel views, while introducing another branch to ensure appearance consistency with reference views. Furthermore, we present a 3D reconstruction framework named DualDiff3D, which integrates a reliability-enhanced Render-Refine-Optimize (RRO) loop to progressively and robustly incorporate the refined novel views, yielding more accurate 3DGS. Extensive experiments demonstrate that our approach outperforms state-of-the-art methods even in the inference-only setting, with further performance gains achievable through training. Our code and pre-trained weights are available at https://github.com/Akaneqwq/DualDiff3D.

Recent extensions of 3D Gaussian Splatting (3DGS) enable real-time novel view synthesis in dynamic scenes by learning time-conditioned Gaussian deformations. However, existing MLP-based methods typically estimate deformations independently at each timestamp, making them less robust to large or abrupt motions. To address this issue, we propose \textbf{EvoGS}, a 3DGS-based dynamic reconstruction framework that models Gaussian deformation as a temporal evolution process. EvoGS maintains persistent deformation states for each Gaussian, extrapolates future states from historical deformation states, and corrects the predictions with MLP-derived observations. The correction is adaptively weighted using a temporal residual memory and evolution statistics such as deformation velocity and trajectory deviation. To further improve reconstruction quality, EvoGS introduces deformation-aware densification. Clone and split operations are performed along corrected deformation directions, while an uncertainty-aware strategy suppresses densification for Gaussians with unstable deformation histories. Experiments show that EvoGS improves dynamic novel view synthesis quality and achieves competitive performance across benchmarks.

In indoor environments, object positions frequently change due to human activities or embodied-agent interactions, causing previously constructed scene graphs to become inconsistent with the current scene. To address this issue, we propose DSG, a dynamic 3D scene graph construction framework that detects object changes and performs spatial relationship reasoning. First, we construct a semantic-aware 3D Gaussian scene representation and develop a dual-view rendering-based object change detection method to enable reliable scene graph node updates. Second, we propose a spatial relationship reasoning method that incorporates multi-granularity visual context, enabling a large language model to identify a richer set of interobject spatial relationships. Furthermore, we introduce DynTHOR, a dynamic indoor scene graph benchmark built on the AI2-THOR simulation platform for evaluating scene graph construction in dynamic environments. Extensive experiments on Dyn-THOR, 3RScan, and real-world scenes demonstrate that DSG consistently outperforms existing methods in both object node construction and spatial relationship reasoning, significantly improving the accuracy of dynamic scene graph construction.

We study dynamic Gaussian Splatting from monocular videos. While recent advancements in dynamic Gaussian splatting offer a promising foundation for modeling dynamic scenes, they often overfit to the training views and fail under occlusion or complex scene motion due to the lack of reliable regularization signals in under-constrained regions. We propose Semantic Motion Graph (SMG), a novel approach models the Gaussian motion as the low-rank semantic motion. Our key insight is that the real-world scene motion is often structured by semantic coherence: regions that are spatially close and semantically related tend to exhibit consistent dynamics. To leverage this prior, we construct SMG to model structured motion of the scene. The Gaussian motion is driven by the motion of SMG nodes. We further observe that the uncertainty of Gaussian motion arises from both unreliable off-the-shelf priors and weakly constrained regions during optimization. SMG addresses this by using reliable graph nodes to guide the motion of nearby unreliable nodes. To evaluate dynamic Gaussian splatting under challenging real-world scenarios, we introduce a new multiview dataset collected under an ego-exo setup. Extensive experiments demonstrate that SMG achieves state-of-the-art performance on monocular dynamic Gaussian splatting across challenging real-world benchmarks. Project page: https://smg-gaussian.github.io/.

Semantic segmentation in 3D Gaussian Splatting (3DGS) is crucial for advancing 3D scene understanding. Existing methods predominantly rely on feature distillation, which incurs substantial per-scene training overhead and often yields blurred segmentation boundaries. We identify that these boundary artifacts are driven in part by insufficient viewpoint coverage and boundary overflow of anisotropic Gaussian primitives. To address these challenges, we propose VCAR, a training-free coarse-to-fine segmentation strategy based on View Completeness and Axis-aware Boundary Refinement. In the coarse stage, a visibility-based weighted multi-view voting scheme rapidly localizes the target. In the fine stage, an object-centric sphere derived from the coarse result generates supplementary viewpoints via Spherical Spiral Sampling (SSS), allowing multi-view voting on the augmented views to precisely refine object boundaries and suppress irrelevant 3D Gaussians. Moreover, we introduce Axis-aware Boundary Refinement (ABR) to mitigate artifacts from anisotropic primitives. By decomposing the projected 2D covariance into per-axis contributions, ABR identifies the dominant axis responsible for boundary leakage and applies targeted anisotropic compression exclusively along that axis. Extensive experiments on NVOS and LERF demonstrate that VCAR achieves state-of-the-art segmentation accuracy and efficiency without training. Our code is available at https://github.com/DDKK0526/VCAR.

3D Gaussian Splatting (3DGS) enables photorealistic real-time novel view synthesis, yet placing a virtual camera to capture a desired frame remains largely manual. Existing language-guided approaches in 3D scenes mainly focus on object-centric grounding, determining what to observe but rarely controlling how it should appear in a single frame, such as subject orientation or frame layout. To address this limitation, we introduce a new task, Text-Instructed Viewpoint Grounding (TIVG), which aims to identify a 6-DoF camera pose in a 3D Gaussian scene whose rendered frame aligns with a text instruction. To solve this task, we propose CapFrame, a partially differentiable framework that converts language into geometric pseudo labels for camera pose optimization. CapFrame follows a Retrieve-Translate-Refine pipeline: it retrieves relevant views and ranks them through a Question-Evaluation process with MLLMs, translates the instruction into orientation and layout pseudo labels, and refines the camera pose via differentiable optimization with layout and orientation losses in 3DGS. Experiments on 38 real-world scenes with 135 instructions indicate that CapFrame produces viewpoints better aligned with texts than heuristic viewpoint search and adapted trajectory generation baselines, validated by VLM metrics, MLLM judges, and user studies. Code is available at: https://github.com/jirongli/CapFrame

Volumetric video enables immersive free viewpoint rendering of dynamic real world scenes, yet existing methods struggle with long sequences and complex motions, often leading to temporal instability and visual artifacts. To address these challenges, we propose \ourname, a Gaussian splatting based framework for volumetric video reconstruction. Our key insight is that explicitly tracking long term complex motion with individual Gaussian primitives is inherently unstable. Instead, we organize Gaussians around time conditioned anchors that localize their spatial and temporal support, thereby reducing long range motion complexity. We further introduce a temporal windowing strategy to activate only anchors relevant to the queried time, which improves scalability and temporal coherence. In addition, to ensure spatial and temporal stability, we design a compact set of multi level anchor features that encode global features, local spatial features, and local temporal features, jointly constraining Gaussian generation. Extensive experiments demonstrate that \ourname \ consistently outperforms prior methods on long sequence volumetric videos with complex motions. Project page: https://github.com/WuJH2001/ATGS.