3D Gaussian Splatting

Long-tailed label distributions reduce the reliability of deep learning for electrocardiogram (ECG) arrhythmia diagnosis, particularly for clinically important but rare abnormalities. Existing rebalancing and logit adjustment methods mainly address class frequency while overlooking direction-dependent morphological variability across ECG classes. This study proposes Angular Gaussian Supervised Contrastive Learning (AG-SCL) for long-tailed multi-label ECG diagnosis. AG-SCL integrates three components into a unified framework: an Angular Gaussian contrastive branch that models full-covariance class uncertainty on unit-normalized embeddings, Adaptive Logit Adjustment that learns bounded label-state-specific prior corrections instead of fixed frequency-based margins, and tail-aware augmentation that generates morphology-preserving views while protecting the 7-25 Hz QRS-dominant band. The method was evaluated on the public PTB-XL benchmark and a nocturnal ECG dataset comprising 1317 hours of recordings from 141 subjects. AG-SCL achieved the best macro-level performance on both datasets. On PTB-XL, it obtained a balanced accuracy of 0.838, sensitivity of 0.709, specificity of 0.968, mean average precision of 0.495, and TPR at 5% FPR of 0.778. On Noc-ECG, the corresponding values were 0.918, 0.889, 0.947, 0.488, and 0.900. The largest gains occurred in rare or morphologically unstable rhythm classes, while ablation studies confirmed the contributions of full-covariance modelling, Adaptive Logit Adjustment, and tail-aware augmentation. AG-SCL improves long-tailed ECG diagnosis by combining prior calibration with anisotropic representation learning, enhancing sensitivity to rare arrhythmias while maintaining clinically relevant specificity. Our code is available at: https://github.com/Open-EXG/AG-SCL-for-Long-Tailed-ECG.

Techniques for modeling 3D scenes from image collections, such as 3D Gaussian Splatting (3DGS), are capable of generating high-quality novel views by leveraging graphics primitives with view-dependent appearance. In 3DGS, spherical harmonic (SH) are employed to model view-dependent color, resulting in a large number of SH coefficients per primitive and large memory requirements. While compression approaches have been proposed to mitigate this problem, they do not exploit the capabilities of modern Graphics Processing Units (GPUs) for parallel decoding and rendering. In this paper, we propose a method for compressing SH color coefficients using texture compression schemes specifically designed for efficient parallel GPU decoding and supported by dedicated hardware acceleration. It is shown that those methods can compress color coefficients more effectively than 2D textures by exploiting the fact that primitives can be locally grouped and reordered according to color. Furthermore, we introduce a bit-rate control strategy that preserves random access, enabling large-scale parallelization without compromising rendering performance. Experimental results using BC1 and BC7 texture compression formats show that GPU-based decompression can be achieved with negligible or imperceptible degradation in the visual quality of rendered 3DGS scenes.

3D simulation platforms are critical for autonomous driving because they enable end-to-end policy evaluation, thereby reducing development costs and improving safety. In recent years, neural simulation has become predominant, with methods such as NuRec playing a central role; however, these methods remain relatively slow and typically require per-scene tuning. In this work, we present Instant NuRec, a feed-forward neural reconstruction model that turns a short multi-view driving log into a fully simulatable 3D Gaussian Splatting (3DGS) world in a single forward pass. The model accepts multi-view input from a calibrated camera rig and emits a layered output consisting of static and dynamic 3DGS layers, a sky cubemap, and per-camera ISP corrections, while providing native support for non-pinhole camera models via 3DGUT. It reconstructs a 10-20-second multi-camera scene in roughly 1.5 seconds and achieves a PSNR on the Waymo Open Dataset that is 2.01 dB above the strongest evaluated baseline. Instant NuRec is deeply integrated into NuRec and is compatible with AlpaSim for closed-loop simulation.

Radiative Gaussian splatting reconstructs sparse-view CT fast and accurately, and recent work attaches per-Gaussian posteriors to yield per-voxel uncertainty maps. We ask what such a map actually measures: posterior variance is a data-constraint map, not an error map -- its alarms are trustworthy, its all-clears are not. Exploiting the strict linearity of X-ray rendering in the per-Gaussian densities, we derive a clamp-aware closed form that the unchanged rasterizer evaluates exactly in one forward pass, in volume and projection space: the infinite-sample limit of the sampling estimator of concurrent work, at ~8x lower cost. On the official 15-scene benchmark this uncertainty ranks true error on 14 of 15 scenes. Restricted to the object interior -- the tissue a clinician reads -- the ranking collapses (median Spearman 0.11, 0/15 pass), identically for a deep ensemble and for a strictly positive log-normal posterior: three constructions, two estimator families, no survivors. The mechanism is structural: about 90% of in-object error is bias that reproduces across retrainings, invisible to model disagreement; 73-81% of the full-volume correlation is carried by object/surround contrast; and an exactly solvable control puts the observed in-object ranking 4-5x below what a perfectly calibrated posterior with the same sigma-spread would score. The error scale, by contrast, is an engineering problem, and we solve it: reparameterizing the posterior contracts the cross-scene temperature spread from 19.3x to 2.6x, one scene-agnostic temperature transfers to unseen scenes (10/15 leave-one-scene-out), and the repaired scale tracks photon count at the Poisson-predicted -1/2 power. We distill evaluation practice that would have caught the illusion -- masked calibration, seed-wise bias decomposition, an exact-posterior reference -- and release all protocols, seeds and per-run evidence.

While 3D Gaussian Editing (3DGE) has seen substantial progress, text-driven 3D human garment editing remains largely underexplored. Existing 3DGE works typically follow a paradigm that applies 2D editing techniques to multi-view rendered images and updates 3D Gaussians based on the modified images. Extending such methods to 3D human garment editing suffers from low-fidelity outcomes, caused by introduced distortions and garment inconsistencies. A promising breakthrough opportunity arises from the SMPL eXpressive (SMPL-X) model that embodies rich prior information for virtual humans. Motivated by this insight, we propose a text-driven 3D human garment editor termed T3HG-Editor, which delivers high-fidelity and garment consistent results by leveraging geometry and joint priors embedded in SMPL-X. Specifically, T3HG-Editor contains three stages, namely obtainment of editable Gaussians, garment consistent editing, and Gaussian updating with overflow pruning. The obtainment of editable Gaussians begins with seeding Gaussians along SMPL-X normals to generate sufficient near surface Gaussians, followed by a 2D mask constraint that precisely localizes the target Gaussians to be edited. The garment consistent editing aggregates tokens corresponding to the same SMPL-X vertex across multiple views and propagates them to their original views, enforcing garment consistency without requiring additional training. Gaussian updating with overflow pruning employs a Signed Distance Function (SDF) defined on SMPL-X to construct a human distance field, which is then integrated with a 2D semantic mask to prune overflowing Gaussians, thus preventing contamination of non-target regions. Experiments on multiple subjects and diverse garment types demonstrate that T3HG-Editor outperforms state-of-the-art methods in both editing quality and garment consistency.

Reinforcement learning is increasingly being considered for controlling real-world systems, from fusion plasma and autonomous vehicles to drug discovery and drinking water treatment, where reliability is essential and tuning budgets are limited. Actor-critic algorithms share a set of design decisions, such as how the policy is updated, how it represents the distribution over actions, how its gradient is estimated, and how often it is updated relative to the value estimator. Using a control task derived from a real water treatment plant, we analyze over 33,000 experiments to determine how these components affect variability across runs and sensitivity to hyperparameters. Common defaults, such as Gaussian action distributions with pathwise gradient estimators, are among the least reliable configurations, whereas bounded distributions with adaptive update schedules remain robust across a wide range of settings. These findings offer empirical guidance to practitioners across scientific and engineering domains for understanding and making component-level decisions when adapting actor-critic methods to new real-world control settings.

Robot-assisted minimally invasive surgery (MIS) critically depends on reliable endoscopic perception for navigation and safety. However, conventional endoscopes provide only a limited field of view, leaving large portions of the surrounding anatomy unobserved. Recent neural rendering approaches, such as Neural Radiance Fields and 3D Gaussian Splatting, enable novel view synthesis from endoscopic videos, but their reliance on sparse observations often leads to severe artifacts when extrapolating beyond the training trajectory. In this work, we propose ExtraGS, a framework for enhancing endoscopic view extrapolation through diffusion-guided 3D Gaussian Splatting. Starting from an initial reconstruction, we introduce an uncertainty-guided virtual camera sampling strategy to actively explore blind spots and maximize information gain. The rendered views from these sampled locations are refined using a diffusion model to recover plausible anatomical structures, producing pseudo-observations that guide further optimization. To prevent the generated content from degrading reliable regions, we adopt a confidence-weighted fine-tuning strategy when incorporating these pseudo-observations. Extensive experiments on multiple public endoscopic datasets demonstrate that ExtraGS significantly reduces extrapolation artifacts and achieves state-of-the-art performance in endoscopic novel view synthesis.

Recent 4D Gaussian Splatting (4DGS) methods often fail under fast motion with large inter-frame displacements, where Gaussian attributes are poorly learned during training, and fast-moving objects are often lost from the reconstruction. In this work, we introduce Spatiotemporal Position Implicit Network for 4DGS, coined SPIN-4DGS, which learns Gaussian attributes from explicitly collected spatiotemporal positions rather than modeling temporal displacements, thereby enabling more faithful splatting under fast motions with large inter-frame displacements. To avoid the heavy memory overhead of explicitly optimizing attributes across all spatiotemporal positions, we instead predict them with a lightweight feed-forward network trained under a rasterization-based reconstruction loss. Consequently, SPIN-4DGS learns shared representations across Gaussians, effectively capturing spatiotemporal consistency and enabling stable high-quality Gaussian splatting even under challenging motions. Across extensive experiments, SPIN-4DGS consistently achieves higher fidelity under large displacements, with clear improvements in PSNR and SSIM on challenging sports scenes from the CMU Panoptic dataset. For example, SPIN-4DGS notably outperforms the strongest baseline, D3DGS, by achieving +1.83 higher PSNR on the Basketball scene.

Radar sensing is increasingly used in mobile systems because it operates reliably under poor lighting, adverse weather, and privacy-sensitive settings where cameras and LiDAR often fail. However, most existing radar SLAM systems estimate motion through scan matching on discretized radar heatmaps, which breaks geometric continuity and fails to capture key radar sensing properties, often leading to unstable pose estimation and degraded mapping in regenerate or dynamically changing environments. We present DiffRadar, a real-time radar SLAM system that models radar observations as a differentiable, physics-aware Gaussian field rather than discrete scans. DiffRadar represents the scene as anisotropic Gaussian primitives and renders radar measurements in range-azimuth and Doppler-azimuth spaces through a differentiable radar forward model, enabling joint optimization of robot pose and scene structure directly from radar measurements. We implement DiffRadar on commodity FMCW radar hardware and evaluate it on both the public Radarize benchmark and a controlled stress-test suite that targets common radar SLAM failure modes, including corridor degeneracy, motion regime transitions, dynamic clutter, and long-horizon loop closures. DiffRadar achieves substantial reductions in trajectory error on the benchmark, with especially large gains under feature-poor corridor motion, while more than doubling map consistency and maintaining real-time performance at 70 FPS. These results show that modeling radar observations directly in the signal domain enables substantially more robust and consistent radar-only SLAM for mobile platforms.

We show that the Benjamini--Hochberg procedure can fail to control the false discovery rate (FDR) at its nominal level for correlated two-sided Gaussian $p$-values. We construct a factor model for which, at level $α=0.01$, a rigorous interval-arithmetic certificate proves $FDR>0.0104$ for all sufficiently large numbers of hypotheses. This disproves a conjecture widely believed to be true for twenty years. Monte Carlo experiments are consistent with the theoretical result. The proof was obtained by GPT-5.6 Pro and carefully checked by the author.

This paper proposes a Gaussian-Based Shift-Variant filtered backprojection (FBP) neural network, which is designed for the efficient reconstruction of non-circular trajectory cone beam computed tomography. The traditional differentiable shift-variant FBP model consists of a filtering component and a backprojection process. The filtering component includes operations such as weightings, differentiations, a 2D Radon transform, and a 2D backprojection. The proposed methods build on this framework by introducing a trainable 2D Gaussian model to represent the trajectory-related part in the filtering process, achieving a substantial reduction in the number of trainable parameters. Experimental results demonstrate that the proposed model reduces the parameter count by 99%, while only sacrificing a slight amount of reconstruction quality. Furthermore, the training time for each trajectory is reduced to one-fourth of the original, significantly accelerating convergence. These enhancements demonstrate a considerable augmentation in the model's practicality and effectiveness, making it a valuable asset for real-world applications.

Gaussian Splatting has emerged as an effective representation for video, but existing methods rely on per-video optimization. This leads to slow encoding and limits generalization across videos. To amortize this optimization, we propose HyperGS, a feedforward, optimization-free approach that directly predicts Gaussian representations from any video in a single forward pass, speeding up encoding and decoding by orders of magnitude while generalizing to out-of-distribution videos at higher resolutions. In HyperGS, we design a factorized spatiotemporal Transformer to extract tokens from video, and a learnable query-based Transformer to obtain 8-parameter Gaussian representations for each video frame. We find that naively predicting Gaussians across diverse videos induces a needle-like degeneration that collapses training, and address this with a rank-based geometric regularizer whose strength adapts dynamically to stabilize optimization. HyperGS achieves encoding at $10^4$--$10^5\times$ the speed of per-video Gaussian optimization at matched reconstruction quality while generalizing zero-shot to $720p$ video, enabling higher-resolution rendering without re-encoding. HyperGS improves PSNR by +2.9--3.1 dB over the prior video encoders on K400, SSv2, and UCF101 at a smaller video representation size. By predicting explicit 2D Gaussians in a single forward pass, HyperGS combines the fast, flexible rendering of Gaussian Splatting with the speed and generalization of feedforward prediction, advancing Gaussians as a practical direction for fast and generalizable video representation.

Reconstructing 3D scenes from unordered images remains bottlenecked by expensive Structure-from-Motion (SfM) preprocessing and frozen pose interfaces. We present SalientGS, a unified SfM-to-3D Gaussian Splatting (3DGS) pipeline. Its central contribution is importance-guided Markov Chain Monte Carlo (MCMC) Gaussian allocation, which aggregates multi-view residuals into per-Gaussian underfit and redundancy signals. These signals define a smooth importance-weighted sampling distribution that biases both birth and relocation toward underfit regions. This reallocates capacity from well-fit areas without altering the underlying stochastic gradient Langevin dynamics (SGLD). SalientGS achieves end-to-end reconstruction in 15 minutes with state-of-the-art perceptual quality. The supplementary material provides dedicated sections for Per-Scene Qualitative Comparisons and Per-Image Learned Perceptual Image Patch Similarity (LPIPS) Analysis, including failure cases. Code and evaluation scripts are available at https://github.com/Six-Bit-TX/SalientGS.

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

Recent generalizable 3D Gaussian Splatting models have advanced long-sequence novel view synthesis (NVS), but at the cost of substantial redundant computation. We identify that the redundancy can be mitigated based on two observations: (i) high-precision geometry is not strictly required for high-quality NVS; (ii) appearance learning is generally easier than geometry recovery. Motivated by these insights, we propose an asymmetric architecture that decouples geometry and appearance modeling. The geometry branch processes coarse-grained tokens with most of the parameters for multi-view reconstruction, while the appearance branch operates on fine-grained tokens to capture details using significantly fewer parameters. The two branches interact through bilateral connections, enabling mutual guidance for their respective tasks. This task-aware asymmetry reduces the computational redundancy and allocates the computation more judiciously, thereby increasing parameter efficiency and enabling smaller models to achieve strong performance. On 32-view 960P inputs, our model matches optimization-based methods while delivering nearly 800x speedup, and surpasses the zero-shot performance of state-of-the-art generalizable models with markedly fewer parameters and reduced training/inference overhead, achieving an overall efficiency improvement.

3D Gaussian Splatting represents scenes as finite mixtures of anisotropic Gaussians whose number of components $K$ is set by heuristic density control or user caps. Variational Bayes Gaussian Splatting (VBGS) recast splat fitting as conjugate variational inference, but $K$ remains fixed. We replace the finite symmetric Dirichlet over mixture weights with a truncated stick-breaking Dirichlet-process prior -- and, as a theory-backed alternative, a sparse overfitted finite Dirichlet -- so that the number of occupied components adapts to the data while every update remains a closed-form coordinate-ascent step; a natural-gradient stochastic variant makes the per-step cost independent of the number of points. We give an exact monotonicity guarantee, a rigorous truncation-error bound correcting an anti-conservative large-$α$ approximation in common use, and an honest account of what the fitted number of components estimates. Empirically: (i) the effective complexity $\hat{K}$ adapts to scene complexity and recovers the true $K$ within $\pm 1$ on well-separated synthetic data with regime-appropriate concentration; (ii) a deconfounded comparison shows the DP prior's contribution is complexity selection, not per-component efficiency -- converged DP fits exceed single-pass fixed-$K$ VBGS by +2.7 dB at matched budgets yet tie an equally converged fixed-$K$ baseline, and on 3D scenes DP-Splat matches or exceeds VBGS's held-out color prediction with 5.9-7.6x fewer components; (iii) the posterior-predictive color variance is well calibrated on model-matched synthetic data; and (iv) the ordering suggested by exact-posterior asymptotics reverses under mean-field coordinate ascent: the DP prior resists over-splitting while the sparse finite mixture saturates its truncation, a gap between variational practice and posterior asymptotics documented across three orders of magnitude in $N$.

Reconstructing high-fidelity 3D scenes from sparse-views remains a central problem in generalizable neural rendering. Existing generalizable 3D Gaussian Splatting (3DGS) methods often exhibit geometric artifacts in sparse-view settings, since supervision based solely on 2D photometric losses cannot resolve depth and correspondence ambiguities. To address this issue, we propose MAC-Splat, a training framework built around direct 3D consistency supervision. MAC-Splat builds on the MASt3R geometric backbone and a frozen DINOv3 encoder to obtain semantically informed 2D correspondences, which serve as geometric anchors for 3D supervision. Using these anchors, we define the Multi-Attribute Consistency (MAC) loss. This objective jointly regularizes the 3D attributes of matched Gaussians, including their position, shape, and appearance, by enforcing agreement in a common world coordinate frame. The formulation is robust to outliers and respects the geometry of covariance matrices, which leads to stable training under sparse-view conditions. Experiments on ScanNet++ show that MAC-Splat outperforms strong baselines, with particularly large gains under different overlap regimes. In particular, it improves average PSNR over Splatt3R by more than 4.5 dB, reduces LPIPS, and maintains performance as the camera pose gap increases. These results indicate that a direct, multi-attribute 3D consistency objective, when combined with high-quality correspondences, is effective for addressing the ill-posed sparse-view reconstruction problem.

Incremental scene reconstruction is essential for real-world applications. Although 3D Gaussian Splatting shows strong potential, most existing approaches require offline conversion of the optimized Gaussians into an intermediate implicit field for explicit mesh extraction, which hinders seamless integration with downstream tasks. To address this limitation, we propose a novel online framework that incrementally reconstructs and updates high-fidelity explicit meshes by directly triangulating a dense geometric Gaussian representation, which supports both high-quality rendering and incremental surface reconstruction. Moreover, we present a direct meshing algorithm that efficiently extracts and updates the mesh from the Gaussian set. To ensure mesh accuracy, we enforce a plane-based pulling constraint that dynamically aligns 3D Gaussian primitives to the approximated local surface. Furthermore, our framework significantly reduces memory and computational overhead during long-sequence processing by dynamically freezing fully optimized historical regions. Experiments on public datasets demonstrate that our method outperforms conventional Gaussian-based methods on both rendering quality and reconstruction accuracy.

We introduce Grassmannian splatting, a dynamic scene representation whose primitives are Gaussians supported on 3-planes in spacetime $\R^4$: generically, spatial 2-planes in uniform translation along their normals. Each primitive carries a unit normal $n \in \mathbb S^3/\{\pm 1\} \cong \mathrm{Gr}(3,4)$ and an unconstrained factor $L \in \mathbb R^{4 \times 3}$, with covariance $$Σ_{4\mathrm{D}} = (P_n L)(P_n L)^T, \qquad P_n = I - n n^T.$$ For generic $L$ and $n \neq \pm e_0$, conditioning on time returns a rank-2 surfel at every frame. The normal of the disk and its velocity along that normal are read off from $n$; the disk shape and the tangential drift of its center are set by $L$. Existing native 4D Gaussian splatting methods [\it{Yang et. al. 2023,Duan et. al. 2024}] slice full-rank spacetime covariances, so their per-frame primitive is a volumetric ellipsoid; since conditioning lowers rank by exactly one, a rank-2 surfel in the slice requires a rank-3 spacetime covariance, and the parameterization above realizes exactly these. The motion model is closed form, i.e. no deformation field is learned, and no custom CUDA is required: the conditioned disk feeds a standard 3DGS rasterizer through its precomputed-covariance interface. A soft clamp in the Schur denominator regularizes the static orientation and continuously bridges rank-3 static and rank-2 dynamic behavior, so static and moving primitives form a single continuous family. On the 17 HyperNeRF scenes of MonoDyGauBench, training is fastest among all compared methods (4.9 to 5.6 times faster than the strongest quality baselines), while ranking second in PSNR, MS-SSIM, and LPIPS. Code: https://github.com/PaulCelanCoding/grassmannian-splatting

Open-vocabulary 3D scene understanding is commonly achieved by embedding 2D vision-language features such as CLIP into a 3D Gaussian Splatting scene, turning it into a text-queryable semantic field. However, attaching a high-dimensional feature to each of millions of Gaussians inflates a single scene to gigabytes, which makes storage and deployment the real bottleneck of these fields. Existing compact methods each learn and ship a per-scene codec, an autoencoder, a quantized codebook, or a distilled feature field, entangling field construction with field storage and never compressing the per-Gaussian assignment that holds the bulk of the cost. We argue that construction and storage should be decoupled, and that storage is a rate-distortion problem over the per-Gaussian binding to a small anchor table, a structure no prior open-vocabulary method compresses. We present CoSAG, which constructs the field without any per-scene training through a closed-form transmittance-weighted lift, spatially grounded semantic anchors, and multi-view denoising, and stores it with a spatially predictive entropy coder that ships no decoder. Because the anchors are spatially grounded, the binding is predictable and therefore highly compressible. The transmittance-weighted lift and multi-view denoising yield a clean, view-consistent assignment, so the entropy coder spends almost no rate on correcting noise and instead codes only the residual against its spatial prediction. CoSAG reaches sub-megabyte storage while matching or exceeding the state of the art across the 2D-rendered, 3D-selection, and dense-LSeg protocols, reducing field size by 37 to 76x relative to LangSplatV2 at higher accuracy.

This book is about the mathematical foundations of data science. 1. Introduction 2. Curses, Blessings, and Surprises in High Dimensions 3. Singular Value Decomposition and Principal Component Analysis 4. Linear Regression and Regularization 5. Graphs, Networks, and Clustering 6. Nonlinear Dimension Reduction and Diffusion Maps 7. Linear Dimension Reduction via Random Projections 8. Optimization for Data Science 9. Classification 10. A Mathematical Introduction to Deep Learning 11. Large Sample Limit of Graph Laplacians 12. Community 13. Concentration of Measure and Gaussian Analysis 14. Matrix Concentration Inequalities 15. Compressive Sensing and Sparsity 16. Low-Rank Matrix Recovery

We present a novel integrated architecture for robust online 3D Gaussian splatting, real-time VR exploration, and speech-driven Vision-Language-Model interaction. Unlike methods assuming clean depth or external poses, our system combines ORB-SLAM3-based pose estimation with online Gaussian reconstruction for noisy real-world data. A VR pipeline enables immersive exploration of incremental reconstructions; a semantic module transcribes voice commands, generates scene descriptions, and records points of interest. Against state-of-the-art online Gaussian splatting methods, we improve image quality on our dataset (+14.5% PSNR, +8.6% SSIM, -14.3% LPIPS) and TUM-RGBD (+11.7% PSNR, +7.8% SSIM, -21.6% LPIPS), with comparable or superior frame rates via quality-speed configurations. We achieve an 88% VLM object-recognition rate.

Recent advances in 3D Gaussian Splatting (3DGS) have enabled high-quality, render-ready scene representations for novel-view synthesis. However, most existing 3DGS pipelines rely on multi-view observations (or non-causal access to future frames) to achieve sufficient coverage, which is often unavailable in on-device robotics and AR settings where sensing is restricted to a single stereo rig. Recovering a high-quality 3DGS scene from one stereo observation, therefore, remains challenging due to occlusions, limited field of view, and missing geometry. We present StereoSplat+, a diffusion-enhanced feed-forward framework that enables causal reconstruction from a single stereo pair. Our method builds on two key components. First, we propose StereoSplat, an input-invariant feed-forward 3D Gaussian estimator that takes a variable number of posed stereo pairs as input and predicts high-quality 3D Gaussians. StereoSplat fuses complementary geometry cues via a cost-volume branch and a triplane-based 3D volume branch and leverages continuous pose encoding to generalize across view counts and camera configurations. Second, since multiple posed stereo pairs are typically unavailable at inference time, we introduce a diffusion-enhanced one-shot progressive inference scheme called StereoSplat+: starting from one stereo pair, we render novel stereo views from the predicted 3DGS, refine them with a one-step diffusion enhancer, and feed them back as additional inputs to update the 3DGS. Experiments on the KITTI-360 dataset show that StereoSplat+ improves novel-view rendering quality and geometry accuracy, especially in occluded regions and under strong view extrapolation, outperforming recent feed-forward 3DGS baselines.

Suppose we observe two sets of $n$ Gaussian vectors in $\mathbb{R}^d$, with the promise that, after applying a permutation of $[n]$ and a rotation of $\mathbb{R}^d$, the two sets are $ρ$-correlated. The Procrustes matching problem asks us to recover the unknown permutation of $[n]$ that aligns the two sets. The problem is well-studied in the low-dimensional regime $d=O(\log n)$, but the high-dimensional regime $d\gg \log n$ has remained largely uncharted: prior matching guarantees require nearly perfect correlation $ρ=1-o(1)$, even for information-theoretic recovery. Our main result is a polynomial-time algorithm for exact recovery at constant correlation. The algorithm works by computing and comparing weighted counts of a specially chosen family of ``wide'' trees. So long as $d\ge \mathrm{polylog}(n)$, the algorithm succeeds with high probability for any $ρ^2>\sqrtα$, where $α\approx 0.338$ is Otter's tree-counting constant. We complement this algorithmic result with an improved information-theoretic guarantee, showing that exact recovery is possible when $ρ^2 \gtrsim \max\{\log n/d,\sqrt{\log n/n}\}$. We also carry out a low-degree advantage calculation, which suggests that the condition $ρ^2 > \sqrtα$ is necessary for any tree-counting algorithm.

Dynamic scene reconstruction remains challenging due to the heterogeneous and spatially varying nature of real-world motion. Although recent 3D Gaussian Splatting methods have introduced diverse deformation formulations for dynamic novel view synthesis, each method typically relies on a single deformation model within its representation, which limits robustness across diverse dynamic scenarios. In this work, we study a fundamental problem-multi-deformation modeling for dynamic 3D Gaussian representations-under two distinct integration constraints that differ in when and how multiple deformation experts interact during training. From a Mixture-of-Experts (MoE) perspective, we view multi-deformation modeling as the problem of combining multiple specialized deformation models within a unified 3D representation. We first introduce Mixture of Deformation Experts (MoDE), which integrates multiple deformation experts directly into the deformable Gaussian Splatting pipeline through joint optimization. In MoDE, experts operate on a shared canonical Gaussian representation, enabling multi-deformation modeling without introducing additional training stages or modifying the original optimization schedule. In contrast, we further present Mixture of Experts for Dynamic Gaussian Splatting (MoE-GS) under a different integration constraint, where deformation experts are optimized independently and combined through a separate routing stage. As a result, expert interaction occurs over non-canonical Gaussian representations after individual optimization. Together, these two approaches provide alternative strategies for multi-deformation modeling, clarifying how integration constraints shape the design and behavior of deformation experts in dynamic 3D Gaussian representations. Our code is available at: https://github.com/cvsp-lab/MoE-GS-studio.

Designing functional and aesthetically coherent floor plans requires exploring a vast space of possible room arrangements, a task that quickly becomes overwhelming for human designers. In this paper, we propose GRE-Diff, a controllable and interactive diffusion-based framework that automates the creation and editing of apartment floor plans under user-specified constraints. By combining AI-generated suggestions with real-time, human-in-the-loop editing, the system enables users to specify room types, room counts, boundary shapes, and editing operations through LLM-parsed instructions or GUI-based interaction. It then generates a diverse set of plausible and well-structured designs for refinement. At the core of our approach is Gaussian Room Embedding (GRE), a continuous latent representation that models each room as a spatial Gaussian distribution capturing its location and extent. Extensive experiments on the RPLAN dataset show that GRE-Diff produces high-quality, constraint-aware, and editable polygonal layouts, offering a practical step toward bridging AI-driven automation and human creativity in spatial design.

Dense visual SLAM is a fundamental problem in robotics. Recent advances in 3DGS have demonstrated its potential for dense SLAM. Existing 3DGS frameworks focus on both appearance and geometry modeling. However, scene geometry is typically more critical for SLAM than novel view synthesis because downstream robotic tasks, such as navigation and obstacle avoidance, rely primarily on accurate spatial geometry rather than photorealistic rendering. This observation raises a natural question: Is it feasible for 3DGS to perform 3D reconstruction without scene appearance modeling? Motivated by this, we propose Geometry-only Gaussian Splatting (GeoGS), which directly reconstructs scene geometry, and further present GeoGS-SLAM, a dense visual SLAM system built upon this representation. Specifically, GeoGS retains only spatial parameters to reduce the number of per-primitive parameters by over 80%. In contrast to existing 3DGS methods, GeoGS focuses solely on geometric reconstruction, which significantly reduces the number of Gaussian primitives, accelerates geometric convergence, and enhances robustness to illumination variations. In addition, we present an effective training framework that optimizes the Gaussian primitives via single-view and multi-view geometric and photometric supervision, and speeds up geometry convergence with a local-plane driven initialization that better aligns primitives with local structures. Furthermore, we introduce a map update strategy for loop closure that globally transforms the Gaussian map to align it with the corrected pose estimates, thereby preventing map tearing caused by inconsistent per-viewpoint pose corrections in existing methods. Extensive experiments on synthetic and real-world benchmarks demonstrate that our method outperforms SOTA methods in terms of online mapping efficiency and geometric reconstruction quality.

Online 3D scene graph generation builds a persistent, structured representation of a scene by incrementally fusing 2D observations into a global 3D graph. Existing online methods treat this fusion as a fully deterministic pipeline, where we identify three sources of uncertainty that are overlooked: observation, 2D model, and 3D representation. We propose PUF: a Plug-and-play, Uncertainty-aware, and training-free Fusion framework. Scene graph node association is reformulated as a probabilistic likelihood over semantic and spatial factors, replacing binary accept/reject gates. Dirichlet evidence accumulation distributes class and relationship evidence across plausible candidates proportional to association likelihood. An optional class-conditional prior completes edges for sparsely or never co-observed object pairs. We instantiate PUF with both a 3D Gaussian and a 3D voxel backend and observe consistent improvements, demonstrating its ability to generalize across different representations. Experiments on the 3DSSG and ReplicaSSG benchmarks show that our method substantially outperforms existing approaches while maintaining real-time latency. These results establish uncertainty-aware fusion as a principled and effective paradigm for online 3D scene understanding. The source code is publicly available at https://github.com/yyyyangyi/PUF.

Pose-Free Feed-forward 3D Gaussian Splatting (3DGS) has recently emerged as a powerful paradigm for fast scene reconstruction. However, its performance degrades significantly in long image sequences due to cumulative camera pose estimation drift, which propagates errors into geometric modeling and severely limits rendering fidelity. In this work, we revisit the long-sequence bottleneck and identify pose drift as the primary factor restricting reconstruction quality. Furthermore, while SfM-based pseudo ground-truth poses introduce sensor noise, purely rendering-based supervision often leads to optimization instability and local minima due to the entangled optimization of geometry and pose. To address the challenges, we propose a synergistic pose-free framework that explicitly couples geometry and appearance via a Raymap-Guided Coupling Module (RGC). Concretely, we anchor Gaussian centers to raymap-induced geometry and jointly optimize RGB reconstruction, raymap consistency, and camera regularization under a unified objective, yielding a bidirectional feedback loop: stronger geometry improves rendering, and appearance supervision in turn refines geometry and pose. To further stabilize learning across wide temporal ranges, we introduce a Dual-Frequency Viewpoint Scheduling strategy that combines easy-to-hard interval expansion with replay of short-interval pairs. Extensive experiments across in-domain and cross-domain datasets show consistent gains in both rendering and pose estimation, with notably improved robustness on long sequences. Ablation studies validate our central insight: explicitly designed geometry-appearance synergy is the key to scalable and drift-robust pose-free feed-forward 3D reconstruction.

We present the dithered Gaussian mechanism, a novel alternative to the discrete Gaussian mechanism for differential privacy that discretizes the private output rather than the noise distribution itself. By interpreting this discretization as post-processing of the Gaussian mechanism, our construction directly inherits the privacy guarantees of the standard Gaussian mechanism while avoiding vulnerabilities caused by finite-precision floating-point outputs. We show that the mechanism is provably randomness-efficient: by sampling the discretized output values directly, the number of high-quality random bits required for privacy can be reduced significantly and made independent of the noise level. This is achieved by separating the randomness into two sources: a high-quality source used for the privacy-critical sampling step, and a high-performance public source, possibly known to the adversary, that supplies the additional randomness needed for randomized discretization. This separation enables the use of cryptographically secure randomness without substantial performance loss. As an application, we study model training with DP-SGD and show that cryptographically secure noise generation with reduced exposure to floating-point vulnerabilities can be achieved with modest practical overhead.

3D Gaussian Splatting provides an explicit representation that jointly models geometry and appearance, serving as a scalable foundation for 3D representation learning. Existing pre-training methods for Gaussian representations, such as masked Gaussian reconstruction, primarily capture local structures but offer limited semantic supervision. In this paper, we propose GaussFusion, a multimodal pre-training framework for 3D Gaussian representations. GaussFusion integrates image and text supervision into masked Gaussian modeling through cross-modal semantic alignment, enabling the Gaussian encoder to learn both visual and language-level semantic information during pre-training. To better adapt masked modeling to the non-uniform distribution of Gaussian primitives, we further propose Gaussian Salience-guided Multi-scale Hole Masking (GSHM). GSHM constructs spatially continuous masked regions based on Gaussian salience. By applying hole masks at multiple scales, GSHM encourages the encoder to capture both fine-grained local patterns and broader structural dependencies. Extensive experiments on downstream tasks demonstrate that GaussFusion improves the transferability of Gaussian representations. Notably, GaussFusion outperforms Gaussian-MAE on ModelNet40 and ScanObjectNN (PB-T50-RS) by 0.61% and 3.85%, respectively.

3D Gaussian splatting (3DGS) is a strong representation for real-time novel-view synthesis, but its standard training pipeline relies on point estimates and hand-tuned heuristics, providing no native uncertainty or principled complexity control. This is most limiting under sparse views or fixed acquisition budgets, where a model must identify weakly supported geometry and select informative views. We introduce a rendering-aware Bayesian 3DGS framework that tracks Gaussian geometry with a Normal-Inverse-Wishart posterior over means and covariances using renderer-derived surrogate summaries. An optional Dirichlet-process extension adds a probabilistic component-usage signal, and the training schedule makes the closed-form versus approximate inference boundary explicit. Re-rendering posterior geometry samples yields native predictive uncertainty for interval calibration and active view selection. In a fixed-budget 16-to-32 active-view task, native NIW acquisition improves PSNR by +0.453 dB and LPIPS by -0.0146 over a scoring-only 3-member standard-ensemble baseline, winning 29/39 scene-seed pairs and 10/13 scene means; it also improves over PPU-style (+0.355 dB) and NIW-proxy (+0.401 dB) acquisition. NIW native intervals reduce 95% coverage error by about 17x relative to a shared proxy (0.046 vs. 0.796) and are about 10x closer to nominal coverage than a 3-member deep ensemble (0.047 vs. 0.454) at roughly one-third the training cost. As a reconstruction compatibility check, paired NIW-vs-standard analysis over 39 scene-seed runs yields +0.030 dB PSNR with 1.6% additional training time. These results position Bayesian 3DGS as a practical probabilistic scene representation for decision-facing tasks such as active view selection.

While feedforward 3D reconstruction excels at efficient novel view synthesis, it typically falters when faced with scenes under varying illumination. To this end, we introduce WildSplat, the first feedforward 3D Gaussian Splatting framework capable of appearance-conditioned novel-view synthesis for unposed in-the-wild images. To handle inconsistent photometric conditions, we propose a dual-branch architecture that explicitly decouples geometry from appearance. The geometry branch extracts an appearance-invariant 3D structure and jointly predicts camera poses. To govern the rendering appearance, the appearance branch injects target appearance cues into the content features via a globally pre-modulated cross-attention mechanism. To further prevent feature entanglement, we introduce a joint multi-reference training strategy that stabilizes the training process. Extensive experiments show that WildSplat surpasses existing optimization-based and feedforward methods, achieving state-of-the-art performance in in-the-wild novel view synthesis and appearance editing from sparse inputs in a single forward pass.

Reconstructing dynamic human-scene environments from monocular videos is a challenging problem that requires jointly modeling scene geometry, camera motion, and non-rigid human dynamics while enabling photorealistic rendering. Recent feed-forward methods can efficiently predict geometry, but they are often limited to non-photorealistic representations such as point clouds and meshes, or they fail to handle non-rigid objects, particularly dynamic humans. To fill this gap, we present GUSH3R (Gaussian-Unified Scene Human 3D Reconstruction), a feed-forward framework for online dynamic human-scene reconstruction. From a monocular human-scene video, our method reconstructs dynamic humans (everyone) and static scenes (everywhere) in a single forward pass (all at once) as 3D Gaussian Splatting (3DGS) primitives (as gaussians), which are geometrically consistent and capable of novel view synthesis. Experiments on monocular human-scene datasets demonstrate that our approach achieves competitive novel view synthesis quality while significantly improving inference efficiency compared to optimization-based methods.

The diagnosis of spinal diseases is often assisted by 3D imaging techniques in clinical practice. However, precise 3D spinal assessment is limited by the high costs of 3D imaging hardware and the challenges posed by the physical differences between imaging modalities, which hinder the generalizability of models. To address these issues, we propose UniSpine-GS, an efficient, physics-aware Gaussian framework designed for novel-view projection rendering in multi-view spine imaging via a 3D-aware representation. Instead of performing explicit 3D reconstruction, our approach learns a geometry-aware Gaussian representation that ensures anatomical consistency across different views. We introduce SPWM, a structure-guided loss reweighting strategy to improve boundary fidelity and local details. We evaluate our method on the CTSpine3D dataset and a newly constructed 3D fetal ultrasound dataset, FeSpine3D. Our results demonstrate that UniSpine-GS significantly outperforms existing methods across all metrics, offering a practical and cost-effective solution for unified multi-view medical imaging. Our code is publicly available at https://github.com/orangeisland66/UniSpine-GS.

Real-time, text-promptable 4D reconstruction is indispensable for autonomous surgical interaction. Severe misalignment between semantic meaning and physical anatomy still persists, largely because existing solutions integrate Vision-Language Models into deformable fields via a rigid coupling scheme that tightly binds semantic features to geometric warping. In this paper, we propose DeGenseGS, Geometrically and Semantically Decoupled Surgical Scene Understanding in 4D Gaussian Splatting, a novel framework that independently models semantic evolution and geometric deformation. Specifically, we propose a HexPlane-based spatiotemporal entanglement module that uses shared kinematic latents to synchronize semantic mutations with scene dynamics, while explicitly disentangling semantic updates from geometric deformation. To further ensure robustness against reconstruction artifacts, we devise a Rasterization-Native Semantic Extraction mechanism that infers semantics from topologically continuous feature maps. Additionally, we incorporate an angular-aligned optimization strategy that conforms to the native hyperspherical latent space, thereby preventing semantic distortion. Extensive evaluations on the CholecSeg8k and EndoVis18 datasets demonstrate that DeGenseGS achieves state-of-the-art performance. Our framework yields enhanced geometric completeness and robust semantic-anatomic alignment, enabling spatially continuous segmentation despite drastic tissue deformation and topological transitions.

The rapid proliferation of Internet of things (IoT) devices has significantly expanded the cyber-attack surface, necessitating robust and privacy-preserving intrusion detection systems (IDS). However, centralized learning approaches often suffer from severe performance degradation due to high-dimensional traffic data, extreme class imbalance, and highly non-independent and identically distributed (non-IID) data across heterogeneous edge devices. To address these challenges, this paper proposes F-ACVAE, a federated adaptive conditional variational autoencoder framework that enables collaborative model training across distributed IoT devices without sharing raw data. F-ACVAE incorporates selective parameter aggregation, where local encoders remain private while globally shared components are synchronized to preserve discriminative latent structures. To further enhance stability under extreme non-IID settings and feature distribution shifts, we introduce a novel constrained momentum Gaussian aggregation (CMGA) strategy that combines update clamping with momentum-based smoothing to mitigate client drift. Extensive experiments on the N-BaIoT dataset demonstrate that F-ACVAE achieves an average accuracy and macro F1-score of 99%, outperforming state-of-the-art baselines. Moreover, the selective aggregation mechanism reduces communication overhead by approximately 62%, making the framework particularly suitable for resource-constrained IoT environments. These results highlight the effectiveness of F-ACVAE in achieving high detection performance while ensuring privacy preservation and communication efficiency.

Current feed-forward 3D reconstruction methods predict pixel aligned Gaussian primitives, resulting in highly redundant representations. A natural solution is to prune the redundant Gaussians, but naive pruning introduces severe artifacts and often requires inference time fine-tuning, breaking the feed-forward paradigm. Based on previous works, high frequency regions require more Gaussian primitives, while low frequency regions can be represented with significantly fewer primitives. Motivated by this, we propose a novel approach to explicitly control the number of Gaussians by leveraging local texture information. Our approach achieves this through three key components: (1) texture estimation to capture spatial variation in scene detail, (2) texture-aware pruning that removes redundant Gaussians from low frequency regions, and (3) an adaptive Gaussian head that predicts the modified attributes of the retained primitives without breaking the feed-forward paradigm. Experiments on RE10K, ACID, DL3DV, Tanks and Temples, and DTU demonstrate the effectiveness of our approach, while ablation studies validate the contributions of its key components.

Removing unwanted objects from reconstructed 3D scenes is an important task in computer vision, supporting applications in AR/VR, robotics, and digital content creation. Existing methods typically complete the entire masked region in a single step and without effectively utilizing semantic information from other views, leading to difficulties in handling complex geometric details and textures. In this work, we propose a novel framework that integrates Semantic-guided Block Matching (SBM) and Region-Wise Progressive Refinement (RPR) for high-quality 3D object removal. First, we leverage DINOv2 to encode semantic guidance from multi-view observations, and the best match tokens are decoded to complete missing regions in the target view while maintaining cross-view consistency. Second, we introduce a RPR strategy that segments the target mask into multiple subregions and selectively refines those with poor visual quality. Our method is built upon Gaussian Splatting, ensuring high-fidelity scene reconstruction with efficient computation. Experimental results demonstrate that our approach outperforms existing Gaussian-based methods in terms of perceptual quality and coherence in 3D object removal.

We present a real-time LiDAR-based framework for Gaussian Splatting SLAM that tightly couples fast G-ICP registration with spherical rasterization-based dense mapping for large-scale sequences. Leveraging LiDAR geometry rather than appearance, we reuse tracking-estimated local covariances to initialize Gaussians with range-aware scales and to derive surface normals for geometry-aware map optimization. We further introduce a covariance-derived geometry score that measures local complexity and drives pruning in planar regions and selective densification in structurally rich areas, while optimized Gaussians and LiDAR-specific confidence cues are fed back to improve tracking robustness. On the Newer College dataset, our method achieves an F-score of 86.78% using purely online trajectories at real-time speed ($>$20 FPS), and additional experiments on other datasets confirm its stability and scalability.

Reconstructing high-fidelity 3D building models from UAV imagery is essential for large-scale digital twin development. However, existing 3D Gaussian Splatting (3DGS) techniques often struggle with building facades, failing to capture sharp geometric transitions. To address this, we propose a semantic edge regularization framework that supervises 3DGS to produce crisp architectural boundaries. Our method leverages SAM 3 to generate precise building masks, from which we extract architecturally significant edges. During training, we align rendered image gradients with these extracted edges, forcing the Gaussians to converge into sharp structural geometries. Evaluations across campus environments, dense urban centers, and custom residential datasets demonstrate significant improvements in edge fidelity without requiring architectural modifications to the 3DGS pipeline. Our approach proves robust across diverse building types, roof geometries, and urban densities.

Challenges remain in ego-centric 3D scene generation due to limited view overlap and the dominant influence of individual perspectives on scene interpretation. These factors hinder the creation of viewpoint-consistent and semantically aligned visual content, as well as the construction of accurate geometric structures. In this paper, we propose CGGS, a text-to-3D framework aiming to enhance 3D-content-awareness and address geometric distortions in ego-centric scene generation. Firstly, the Ego-centric Generator is proposed by fine-tuning a Multi-View Latent Diffusion Model with consistency-augmented loss to generate consistent, high-fidelity 2D content aligned with textual descriptions. Then, Layout Decorator leverages optical flow and point-track correspondence to estimate depth, therefore producing dense point clouds as coarse layouts from the ego-centric 2D priors. Building on this initialization, Geometric Refiner is proposed to enhance 3D Gaussian reconstruction via an entropy-based Mutual Information Depth Loss (MID) combined with a hierarchical optimization scheme for improving visual quality and geometric structure. Comprehensive experiments demonstrate that CGGS outperforms previous methods in generating coherent and accurate text-driven 3D scenes. Project page: https://cggs-26.github.io/cggs26/.

Multi-view 3D surface reconstruction is a longstanding challenge in computer vision. Although recent large-scale reconstruction methods based on 3D Gaussian Splatting (3DGS) achieve impressive novel-view synthesis, producing high-quality surfaces over large scenes remains difficult, due to complex geometry, long optimization, and limited memory. In this paper, we propose a novel yet simple partitioning method to efficiently and faithfully reconstruct large-scale scene surfaces. Our key insight lies in a scene partitioning method based on viewpoint orientation. This partitioning approach ensures that views with similar orientations are jointly involved for more accurate depth estimations, leading to precise surface reconstructions and balanced computation on multiple GPUs in parallel. In addition, we propose a strategy to detect and repair missing regions in the initial point cloud caused by sparse viewpoints or insufficient textures, thereby further improving the geometric quality. Extensive experiments on the GauU-Scene, MatrixCity, and UrbanScene3D datasets demonstrate that our method outperforms the state-of-the-art approaches in surface reconstruction for large-scale scenes. Project page: https://hanl2010.github.io/VOP-GS.

3D reconstruction from sparse views is a challenging task in 3D computer vision. Recent studies on 3D Gaussian Splatting (3DGS) have achieved remarkable results with sparse views in novel view synthesis, yet reconstructing high-quality geometric surfaces from sparse views remains a challenge, due to the limited geometry clues and the discreteness of Gaussians. In this paper, we propose a novel 3DGS-based method for high-fidelity surface reconstruction from sparse views. Our key insight is to introduce a normal-guided depth propagation approach, which can extend depth information from high-confidence regions to constrain the depth in low-confidence areas. Additionally, we propose an abnormal depth edge-aware regularization to address depth discontinuities caused by the discreteness of Gaussians. Extensive experiments on DTU and Tanks-and-Temples datasets demonstrate that our method outperforms the state-of-the-art methods in sparse view surface reconstruction. Project page: https://hanl2010.github.io/DP-GS.

The Gaussian Error Linear Unit is usually motivated as the expected output of an input-dependent Bernoulli gate. This work gives an alternative interpretation: GELU is the expected output of a hard linear gate with a Gaussian random threshold. This view provides a generative interpretation for the Bernoulli gate: the gate opens once the input clears a latent Gaussian threshold. This interpretation stems from a decomposition based on well-known results in stochastic inventory theory and leads to a threshold-transmission family that includes ReLU, GELU, SiLU/Swish, and hard swish as special cases. By considering a latent uniform threshold, we recover a hard-swish-like piecewise-polynomial gate whose nonlinear transition is confined to a finite interval, yielding fixed- and learned-width variants. Controlled experiments on compact vision and language models show that calibrated or learned uniform-threshold gates are consistently competitive with GELU, ReLU, and SiLU/Swish, improve over them in most tested settings, and use the finite transition region nontrivially.

3D Gaussian Splatting (3DGS) has revolutionized novel-view synthesis with its fast and high-fidelity rendering. However, rendering at high FPS and low latency across various scenes remains a challenge, especially when large amounts of 3D Gaussian ellipsoids appear in the scene. To address this issue, we introduce TemporalGS, to the best of our knowledge, the first training-free plug-and-play algorithmic approach to accelerate 3DGS rendering without any post-training or post-processing, implemented on top of tile-based software rasterization. The key idea is that, instead of rendering frames independently as 3DGS, we leverage the temporal priors, represented by novel geometry and appearance buffers, etc., to reduce redundancy of Gaussian preprocessing, sorting, and rasterization operations of consecutive frames. Specifically, we propose two acceleration strategies: (1) temporal dynamic culling, which filters out Gaussians that contribute less to current frame rendering; (2) selective rendering, which renders only a small portion of tiles that cannot be approximated by the temporal priors. By adapting and interleaving these two strategies, TemporalGS yields a simple but effective plug-and-play solution for 3DGS rendering speed-up without any training. Extensive experiments show that TemporalGS achieves comparable or even better performance compared to existing state-of-the-art post-training or post-processing-based 3DGS rendering acceleration approaches. TemporalGS can significantly enhance the rendering speed of various 3DGS methods, achieving up to $1.48\times$ acceleration, while maintaining competitive rendering quality. We further extend our TemporalGS to hardware rasterization-based 3DGS to show the portability of our algorithm.

This paper introduces a fast method for high-quality 3D Gaussian Splatting (3DGS) reconstruction without traditional Structure-from-Motion (SfM). The proposed approach leverages 3D Foundation Models (3DFMs) for camera pose and point-cloud initialization, then jointly optimizes both camera poses and Gaussian primitives using a depth-guided loss function. This enables fast convergence even from rough initialization with as few as 50-60 input views. To further improve reconstruction quality in sparse-view scenarios, an MLP-based pose refinement module is introduced alongside depth-guided supervision from the foundation model. Extensive experiments on Mip-NeRF 360, Tanks and Temples, and RobustNeRF demonstrate that the proposed method achieves competitive reconstruction quality (23.61 dB PSNR, 0.19 LPIPS) while reducing training time to approximately three minutes per scene. The proposed method produces ready-to-use 3DGS models at a fraction of the time required by existing pipelines, making it suitable for near real-time applications in robotics, VR, and autonomous navigation.

3D Gaussian Splatting (3DGS) enables high-quality real-time novel-view synthesis, but practical scenes often contain millions of Gaussians, making compression essential for deployment on limited hardware. Existing reduction methods are effective but mostly heuristic: they provide no multiplicative approximation guarantee for the rendered objective, and thus rely heavily on costly post-pruning finetuning to recover quality. We ask a basic question: can a 3DGS scene be provably replaced by a much smaller weighted subset (coreset) while preserving the objective of interest? We first show that, in the unrestricted setting, no non-trivial multiplicative 3DGS coreset exists. We then show that multiplicative guarantees are not impossible, but resolution-dependent. For a prescribed rendering resolution, such as representative views or grids of views/rays, we provide the first weighted coreset construction theorem for 3DGS. The construction samples Gaussians by sensitivity: provable importance scores measuring each Gaussian's role in the full-scene objective. Finally, under explicit validity and log-transmittance stability assumptions, we turn this objective guarantee into a rendering guarantee. Empirically, our method is strongest where deployment needs it most: aggressive compression with no or minimal recovery compute. In prune-only and very short finetuning regimes, it achieves state-of-the-art performance, showing that principled importance estimation can be both theoretically meaningful and practically useful. Open-source code is available at https://github.com/waseem-m/3dgs_provable_coresets.

Inverse rendering aims to recover both 3D geometry and physically meaningful material properties from images, enabling applications such as relighting and novel view synthesis. Optimization-based methods achieve high fidelity but require costly per-scene fitting, while image-space learning-based approaches often suffer from multi-view inconsistencies and lack an explicit 3D representation for stable novel view rendering. We present a feed-forward multi-view reconstruction framework for inverse rendering that directly predicts a structured 3D Gaussian representation with intrinsic material attributes. Each Gaussian primitive is parameterized by mean, normal, opacity, rotation, scale, albedo, metallic, and roughness, enabling a disentangled and physically grounded scene representation. Our model integrates priors from a material estimation network with a multi-view 3D reconstruction backbone, allowing joint prediction of geometry and reflectance parameters in a single forward pass. Experiments on synthetic and real-world datasets demonstrate improved multi-view consistency compared to 2D baselines, accurate material recovery, and stable novel view rendering. Our representation further supports physically-based relighting and more faithful modeling of view-dependent effects compared to existing RGB-based feed-forward reconstruction methods. Our project webpage is: $\href{https://poliik.github.io/invsplat/}{\text{https://poliik.github.io/invsplat/}}$.

Generating a 3D dental volume from a single panoramic radiograph (PXR) could provide a low-radiation alternative to Cone-Beam Computed Tomography (CBCT), but the problem is highly underdetermined: panoramic acquisition integrates 3D attenuation along curved X-ray paths into a 2D image, leaving depth-resolved anatomy unobserved. Existing implicit and generative approaches often produce oversmoothed geometry or anatomically inconsistent hallucinations, lacking geometry-driven supervision and relying on smooth representations unable to precisely localize sharp anatomical boundaries. We propose X-Splat, the first Gaussian Splatting framework for generating CBCT-like 3D dental volumes from a single PXR. X-Splat uses the known panoramic acquisition geometry as a generation scaffold: learnable anisotropic Gaussian primitives are initialized along the X-ray paths that formed the input image and adjusted in a single feed-forward pass, constrained by Beer-Lambert reprojection and multi-view radiographic training supervision. A lightweight residual refiner adds dataset-level anatomical priors without overriding the geometry already resolved by the Gaussians. We train on synthetic PXR-CBCT pairs, enabling direct volumetric supervision without paired real scans. We further introduce segmentation-based geometry-aware metrics, providing the first evaluation of PXR-based generation over maxillofacial anatomy. X-Splat outperforms NeRF- and GAN-based baselines, recovering individual teeth, cortical boundaries, and alveolar structure, including the mandibular canal which prior methods fail to reconstruct. Code will be available at https://github.com/tomek1911/X-Splat

Manipulating fast and dynamically moving targets in unstructured 3D environments remains challenging for embodied AI. Existing visual-language-action models and world models struggle with accurate 3D geometry and physically meaningful forecasting. We propose PhysMani, a framework that couples a physics-principled 3D Gaussian world model with a future-aware action policy model. The world model learns a divergence-free Gaussian velocity field via online optimization for fast and physically grounded future dynamics prediction. The policy model integrates the predicted 3D scene future dynamics through a learnable token based cross-attention module. We introduce PhysMani-Bench, a dynamic manipulation benchmark with 16 tasks, and demonstrate a superior success rate over strong baselines in both simulation and real-world robot experiments.

Recent advances in 3D Gaussian Splatting (3DGS) have enabled significant progress in dense dynamic Simultaneous Localization And Mapping (SLAM). Prevailing methods typically discard predefined dynamic objects, ignoring that transiently static objects offer valuable geometric constraints for pose estimation. A recent work attempts to leverage this potential by employing per-pixel uncertainty maps to quantify the magnitude of motion. While this approach enables transiently static objects to enhance pose estimation, it erroneously integrates these objects into the static map, resulting in persistent artifacts. Moreover, its reliance on purely geometric information leads to ambiguous object boundaries in the uncertainty maps. To overcome these limitations, we present DL-SLAM, a monocular Gaussian Splatting SLAM system built upon a novel dual-level probabilistic framework. Our method computes dynamic probability maps by combining semantic and geometric information. These pixel-level probabilities are lifted to 3D and aggregated to derive an object-level dynamic probability for each instance. Object-level probability enables the categorical pruning of dynamic Gaussians, resulting in an artifact-free static map. The static map, in turn, provides a geometrically consistent guidance to refine the pixel-wise probabilities, enhancing their reliability. Experimental results demonstrate that DL-SLAM outperforms existing approaches, improving tracking accuracy by up to 13% while generating high-fidelity semantic maps.

Recent advances in 3D content generation from text or images have achieved impressive results, yet view inconsistency from 2D generators and the scarcity of high-quality 3D data remain significant bottlenecks. Existing solutions typically adapt large-scale pre-trained text-to-image latent diffusion models to generate 3D Gaussian Splats (3DGS). However, these approaches often rely on training complex cascade pipelines that are computationally expensive and scalability-limited. Most critically, the quality of generated 3D assets is inherently constrained by each component capacity and compressed latent space, leading to decoding artifacts and accumulated errors. To address these limitations, we propose PixGS, a single-stage pipeline for direct high-quality 3DGS generation, which leverages recent advances in pixel-space diffusion to bypass lossy latent compression while still benefiting from the vast 2D generative priors. By directly denoising 3D Gaussian attributes at each timestep, our method enables precise, splat-level regularization of both appearance and geometry. Furthermore, we introduce a comprehensive supervision strategy that incorporates surface normals, depth, and high-frequency structural information, which is often overlooked in prior works. Experiments demonstrate that PixGS outperforms current state-of-the-art methods while maintaining a fast inference speed (1s on a single A100 GPU), offering a robust and efficient alternative to multi-stage generation pipelines.

3D Gaussian Splatting has demonstrated remarkable potential in novel view synthesis. In contrast to small-scale scenes, large-scale scenes inevitably contain sparsely observed regions with excessively sparse initial points. In this case, supervising Gaussians initialized from low-frequency sparse points with high-frequency images often induces uncontrolled densification and redundant primitives, degrading both efficiency and quality. Intuitively, this issue can be mitigated with scheduling strategies, which can be categorized into two paradigms: modulating target signal frequency via densification and modulating sampling frequency via image resolution. However, previous scheduling strategies are primarily hardcoded, failing to perceive the convergence behavior of scene frequency. To address this, we reframe the scene reconstruction problem from the perspective of signal structure recovery and propose SIG, a novel scheduler that synchronizes image supervision with Gaussian frequencies. Specifically, we derive the average sampling frequency and bandwidth of 3D representations, and then regulate the training image resolution and the Gaussian densification process based on scene frequency convergence. Furthermore, we introduce Sphere-Constrained Gaussians, which leverage the spatial prior of initialized point clouds to control Gaussian optimization. Our framework enables frequency-consistent, geometry-aware, and floater-free training, achieving state-of-the-art performance by a substantial margin in both efficiency and rendering quality in large-scale scenes. The code is available at: https://github.com/weiyixue999/Signal_Structure_Aware_Gaussian

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.

Interactive segmentation of 3D Gaussians offers a compelling opportunity for real-time manipulation of 3D scenes, thanks to the real-time rendering capability of 3D Gaussian Splatting (3DGS). However, existing methods require a time-consuming per-scene setup - typically tens of seconds or even minutes - before interactive segmentation can begin on a raw 3DGS scene. This setup involves multi-view mask preparation, mask lifting, and feature distillation, creating a major bottleneck for online applications. To address this limitation, we aim to completely eliminate the setup stage for interactive 3DGS segmentation while keeping the segmentation time practical (under 1 second). In this work, we present SAGO (Segment Any Gaussians Online), a novel setup-free framework for interactive 3DGS segmentation. By introducing virtual drones, our method reframes the 3D segmentation problem as an online Next-Best-View (NBV) planning task formulated within a Markov process. Extensive experiments demonstrate that SAGO can extract clean 3D assets directly from 3D Gaussians with sub-second latency, thereby enabling a broad range of downstream applications such as object manipulation and scene editing. Moreover, our method achieves over a 50x speedup compared to the previous setup-free 3DGS segmentation frameworks.

3D Gaussian Splatting (3DGS) enables real-time novel view synthesis for static scenes. Extending it to dynamic scenes via deformation fields has recently attracted significant attention, particularly for dynamic scene reconstructionband distractor-free. However, existing deformation networks lack explicit motion awareness: they neither capture long-term motion intensity nor exploit short-term temporal coherence, leading to inaccurate foreground deformation and pseudo-static residuals in the background. We present MVFusion-GS, a method that enhances deformation networks with two complementary motion-aware mechanisms. The Motion-Variance Guided Refinement aggregates per-Gaussian deformation statistics across time to estimate motion variance and uses it to guide dynamic-static separation during deformation prediction. The MotionFormer Temporal Attention module applies Transformer self-attention over neighboring timesteps to model local motion dependencies and improve temporal consistency. Extensive experiments on both dynamic scene reconstruction and distractor-free reconstruction benchmarks demonstrate state-of-the-art performance, showing that explicit motion awareness improves both foreground motion modeling and static background reconstruction.

Standard MipNeRF360-style 3D Gaussian Splatting (3DGS) evaluation holds out every N-th frame -- but these frames have trained neighbors on both sides, so the metric measures near-trajectory interpolation rather than spatial generalization. We introduce a fair matched-count protocol that isolates this effect: both arms train on the same number of images and differ only in whether the holdout is spread evenly (interpolation) or forms a contiguous spatial sector (extrapolation). Our primary finding is a large, consistent interpolation-extrapolation gap of 3~12dB -- several times the differences typically reported between competing methods. The gap is robust to training noise, is in two cases large enough to flip a method ranking under multi-seed confirmation, and -- crucially -- persists across three representation families, including a non-Gaussian volumetric neural radiance field (NeRF), so it reflects spatial coverage rather than any one representation. Diagnostically, it is dominated by a diffuse/geometry-proxy component and tracks each view's angular distance to its nearest training view, a zero-cost signal that also guides capture planning; loss-side regularization yields only marginal gains. Standard holdouts remain useful for near-trajectory rendering but should not, alone, be read as evidence of spatial generalization. Prior work notes protocol sensitivity; ours is, to our knowledge, the first to combine matched-count paired holdout, cross-representation quantification, and a diagnostic analysis Table 1. We describe a spatial-holdout benchmark toolkit with standardized splits and baselines for 16 scenes, which we are preparing for public release.

We present World from Motion, a method for generating freely renderable dynamic 3D Gaussian representations from monocular videos. Our approach conditions a video model on dense, pixel-aligned renderings that encode appearance, geometry, and 3D scene motion along both input and target camera trajectories to correct rendering artifacts and fill in missing regions from an initial reconstruction. To train this model, we construct a dataset of aligned multiview video pairs and dynamic 3DGS representations, with simulated artifacts characteristic of monocular reconstruction. At test time, we distill the model's generations, including newly observed regions and motions, back into a single consistent, high-quality dynamic 3DGS, improving both novel-view synthesis and the underlying 3D motion. Our method sets a new state of the art in 4D reconstruction and seamlessly generalizes to in-the-wild videos with large viewpoint changes and dynamic motions.

Fast quadrotor flight requires safe obstacle avoidance under tight onboard compute limits. While 3D Gaussian Splatting (3DGS) provides a continuous, geometry-aware scene representation for perception-driven navigation, existing 3DGS safety filters use reduced-order models such as single- and double-integrators that ignore actuator limits and assume commanded accelerations are realized instantaneously. Building on an analytic collision cone barrier for 3DGS, we introduce a nonlinear, actuator-aware safety filter enforced through the full quadrotor dynamics. We derive a high-relative-degree collision cone exponential CBF and a backup CBF that preserves QP feasibility under input constraints using a forward-simulated backup policy. Compared with a state-of-the-art 3DGS safety filter, our approach reduces trajectory jerk by 47% and runs 2.25 times faster. We validate the method in simulation and on hardware for real-time navigation in cluttered, perception-derived environments.