3D Gaussian Splatting

We present a simple Gaussian approximation to the finite-sample distribution of the classical ridge regression estimator. Our approximation captures the fact that, in finite samples, the ridge regression estimator trades off bias and variance to reduce estimation and prediction error. Our approximation is based on nonstandard asymptotics where $i)$ we let the estimator's regularization parameter grow proportionally to the sample size; and $ii)$ we treat the population regression coefficients as \emph{local} to the reference vector that defines the estimator's direction of shrinkage. In contrast to other asymptotic approximations in the literature, we allow for general forms of heteroskedasticity and autocorrelation in the data generating process (at the cost of considering a low-dimensional model where the number of covariates is not allowed to grow with the sample size). We use our simple Gaussian approximation to propose two new strategies to select the regularization parameter for the ridge regression estimator. The suggested strategies select the regularization parameter to minimize either average or worst-case excess prediction risk, where risk is computed using our suggested Gaussian approximation.

We characterize the finite sample behavior of the log-likelihood ratio statistic in binary logistic regression, uniformly over both the design and the target parameter. For $n\geq d\geq 3$, we determine, up to universal constants, its worst case $(1-δ)$ quantile over all fixed collections of design vectors and all target parameters: $$d\log\left(\frac{e n}{d}\right)+\log\left(\frac{1}δ\right).$$ This is a nonasymptotic analogue of the Wilks $χ^2_d$ phenomenon and requires no regularity assumptions on the design. The low dimensional cases exhibit unusual behavior. The worst case quantile in dimension $d=2$ is sharply of order $$\log\log\log n+\log\left(\frac{1}δ\right).$$ The worst case quantile in dimension $d=1$ is of order $\log(1/δ)$, with no dependence on $n$. Finally, i.i.d. Gaussian design vectors recover the classical Wilks scale. In the regime $n\gtrsim d+\log(1/δ)$, we prove the sharp bound $$d+\log\left(\frac{1}δ\right).$$ Unlike existing asymptotic results, our bounds are uniform over the target parameter, which may depend on $n$, $d$, and $δ$.

Single-image feed-forward 3D Gaussian Splatting (3DGS) aims to directly generate a renderable 3D scene representation from one input image, avoiding the cost of multi-view capture and per-scene optimization. However, existing methods are often constrained by a pixel-aligned representation, where Gaussians are predicted from fixed image-grid locations. Such pixel-aligned primitives can produce promising nearby-view renderings, but they remain weakly coupled to underlying scene surfaces and struggle to preserve coherent structures under large viewpoint shifts. We present InfiniSplat, a feed-forward single-image 3DGS framework that moves from a pixel-aligned representation toward a surface-aligned representation. InfiniSplat constructs this representation by first using geometry-guided sampling to place 2D supports according to depth-induced local surface structure, and then applying a query-conditioned implicit decoder to predict Gaussian attributes from the image features queried at these supports. By grounding support locations in geometry while decoupling Gaussian prediction from fixed pixel centers, InfiniSplat produces Gaussian layouts that better follow scene surfaces and reduce scattered primitives caused by grid discretization. Across multiple cross-dataset NVS evaluations, InfiniSplat achieves state-of-the-art performance compared with single-image feed-forward baselines, and demonstrates zero-shot generalization from Hypersim indoor synthetic training to complex open-world scenes. Project page: https://zju3dv.github.io/InfiniSplat.

In this paper, we propose UniqueSplat, a view-conditioned feed-forward 3D Gaussian Splatting model to reconstruct customized 3D radiance fields for each view query. Existing feed-forward methods such as pixelSplat and MVSplat aim to generate fixed Gaussians across all views of each scene by minimizing the error between rendered views and ground-truth images. However, such fixed Gaussians generally render images from all views and lack the ability to adapt to specific viewpoints, as they do not incorporate target view information when predicting Gaussians. To address this, our UniqueSplat learns the view-conditioned information as a prior and incorporates this knowledge into network parameters, so that Gaussians are dynamically adjusted in accordance with different views. Specifically, we propose a two-branch view-conditioned hyperNetwork to simultaneously learn view-agnostic embeddings and view-specific knowledge, which not only explores the shareable knowledge from various views, but also adapts the model to specific views at test time. Extensive experiments on widely-used datasets including RealEstate10K, ACID and DTU demonstrate the superiority of UniqueSplat over the state-of-the-art methods. Moreover, UniqueSplat encouragingly outperforms existing methods in cross-dataset evaluation, showing its notable generalization ability.

Feed-forward 3D Gaussian Splatting enables efficient novel-view synthesis without per-scene optimization, but most existing methods assume a fixed set of context views and process them jointly. This limits their applicability to online scenarios where calibrated views arrive sequentially and the scene must be updated causally. We present \emph{StreamSplat}, a streaming feed-forward 3DGS framework that incrementally maintains a persistent geometry-grounded scene state and decodes it into renderable 3D Gaussians after each input chunk. StreamSplat centers on a \textbf{Voxel-Aligned Causal Cache (VACC)}, which stores historical 3D tokens in a memory-bounded voxel structure so that memory grows with explored scene geometry rather than stream length. To better reuse history during causal prediction, we introduce \textbf{History-Projected Depth Anchoring (HPDA)} to project cached geometry as depth guidance for current cost-volume estimation, and \textbf{Cache-Guided Feature Injection (CGFI)} to inject cached latent evidence into Gaussian-token regression. Experiments on DL3DV, RealEstate10K, and ScanNet show that StreamSplat remains competitive with state-of-the-art feed-forward 3DGS methods under sparse causal inputs, despite not using future views or full-scene context. More importantly, it scales to long input streams with 256, 512, and 1024 views where fixed-view baselines run out of memory, yielding sustained improvements in novel-view synthesis quality as more observations arrive. The code will be made publicly available upon acceptance.

Dynamic 4D Gaussian Splatting has emerged as an efficient representation for dynamic novel view synthesis through explicit scene modeling and real-time rendering. However, existing methods typically require dense multi-view videos for sufficient geometric constraints, making capture expensive and limiting sparse-camera deployment. Reducing input views lowers acquisition cost but weakens geometry supervision, often causing missing structures and floating Gaussians. Depth priors provide geometric cues, yet no single source offers both dense coverage and reliable geometry. Monocular depth provides dense structure but is scale-ambiguous and locally biased, whereas multi-view geometric depth provides incomplete anchors consistent with the reconstruction coordinate system. To exploit their complementarity, we propose D$^2$-4DGS, a sparse-camera dynamic 4D Gaussian Splatting framework guided by dual-source depth priors. We align monocular estimates with valid multi-view geometric depths and verify their consistency to identify reliable geometric anchors. These verified anchors support consistency-aware pruning and depth supervision, while verified geometric depths and aligned mono-only estimates provide candidate geometry for densification in under-reconstructed regions. Finally, RGB-D joint optimization improves appearance fidelity and geometric consistency under sparse-view supervision. Across all nine dataset--view settings, D$^2$-4DGS achieves the highest PSNR, improving by 1.33 dB on average over the best competing method in each setting.

Selecting a complete 3D object from a reconstructed scene with minimal user effort is essential for practical scene editing and embodied interaction. Existing 3DGS-based methods either retrain the Gaussian representation to embed per-object labels, or build dense multi-view SAM observations, both requiring heavy computation and dense viewpoint coverage that is rarely available in practice. We present GaussianSelector, a training-free framework for interactive 3D object selection from sparse views and sparse scribble guidance. Operating directly on native Gaussian primitives, we coarsen dense Gaussians into geometrically coherent superpoints and construct a continuity-weighted graph using appearance and spatial cues. Sparse user scribbles are lifted into 3D via visibility-aware transmittance coverage, and selection is solved as a global graph-cut energy minimization that propagates sparse evidence to a complete 3D object. This design naturally supports multi-round refinement, where users iteratively correct the selection from additional viewpoints to progressively improve the result. Experiments demonstrate that GaussianSelector achieves competitive selection quality against state-of-the-art multi-view SAM-based methods, while requiring significantly fewer interaction views and substantially lower computational overhead. These properties make it well suited for human-in-the-loop 3D scene editing and 3D asset extraction in real-world deployment scenarios.

We present DynActiveGS, a dynamic-aware active reconstruction framework based on 3D Gaussian Splatting (3DGS) for autonomous exploration in dynamic environments. The framework incrementally reconstructs a 3D Gaussian scene representation while suppressing motion-corrupted observations through online uncertainty prediction and uncertainty-weighted Gaussian optimization. A key component of DynActiveGS is the explicit decomposition of uncertainty into structural uncertainty and motion-induced uncertainty, which enables the system to distinguish under-reconstructed static regions from dynamically unreliable areas. Based on these uncertainty fields, DynActiveGS performs dynamic-aware viewpoint selection and dynamic-constrained path planning to favor informative yet stable observations during exploration. The resulting system forms a unified closed-loop pipeline for robust active reconstruction in dynamic scenes. Extensive experiments on challenging dynamic benchmarks demonstrate consistent improvements over existing active reconstruction baselines in reconstruction accuracy, completeness, rendering quality, and exploration efficiency.

Most FDR-controlled feature selection methods are designed for coordinate-wise hypotheses, where each feature has a single weight or importance score. This abstraction fails in sequential and grouped models, where one original feature is represented by a block of sub-features, such as lags, recurrent states, or attention-based interactions. We propose a grouped-feature FDR control framework for such settings. For grouped linear models, we construct null-symmetric block-level mirror statistics with matrix-valued perturbations. For neural sequential models, we combine Permutation SHAP derivatives as model-agnostic block-level importance scores with kernel-based dependence measure. The framework is model-agnostic across network architectures, does not require specifying the covariate distribution, and reduces to Gaussian Mirror or Neural Gaussian Mirror when the block size is one. We prove FDR control for low- and high-dimensional grouped linear models and asymptotic symmetry of smoothed Permutation SHAP derivatives under fixed fitted nonlinear models. Experiments on simulated and real-world datasets show reliable FDR control and improved power under correlated grouped-feature signals.

3D Gaussian Splatting (3DGS) provides efficient rendering of photo-realistic scenes, but its heavy preprocessing and training steps make it a poor fit for applications that require real-time reconstruction in robotics or XR. This capability is important since it allows immediate feedback and interaction with new environments. Visual-inertial odometry (VIO) and simultaneous localization and mapping (VI-SLAM) systems, on the other hand, specifically target these real-time applications, which makes them a good choice for integration with 3DGS. We propose a new method that tracks and reconstructs simultaneously in real-time by leveraging an efficient visual-inertial tracking system based on Basalt together with a novel incremental method built on top of Brush, an efficient Rust-based GPU-vendor-agnostic implementation of 3D Gaussian Splatting. We show that many of the heavy preprocessing and training steps of 3DGS can be replaced with a more efficient incremental training strategy that has direct access to the information generated by the visual-inertial tracking system. Furthermore, we propose and combine multiple practical improvements to increase the efficiency of the training pipeline and adapt it to run in real-time, parallel to the tracking thread. This work highlights the value of exploiting the complementary nature of SLAM and 3DGS, and how that can lead to promising results for real-time 3D reconstruction.

Federated Learning (FL) enables collaborative training of machine learning models across multiple institutions without sharing sensitive data, making it particularly suitable for medical imaging applications. However, heterogeneous data distributions across institutions and potential information leakage through model updates remain important challenges. In this work, we propose DP-SimAgg, a privacy-preserving federated learning framework that integrates similarity-weighted aggregation with a server-side differential privacy mechanism. The proposed method applies L2 clipping to bound collaborator updates, computes similarity-based aggregation weights to mitigate the effects of non-IID data distributions, and injects calibrated Gaussian noise at the central server, providing per-round privacy guarantees under the assumed sensitivity bound. The framework is implemented using Intel's OpenFL platform and evaluated on the FeTS 2022 dataset consisting of 1251 multi-modal MRI scans for brain tumor segmentation. Experimental results demonstrate that DP-SimAgg maintains competitive segmentation performance while providing privacy protection. Under a strict per-round privacy budget (epsilon = 1, cumulative epsilon_total = 20 over 20 rounds), the method achieves Dice scores of 0.6357, 0.5305, and 0.5274 for the enhancing tumor (ET), tumor core (TC), and whole tumor (WT) regions, respectively. With a more relaxed per-round budget (epsilon = 10, cumulative epsilon_total = 200), performance approaches that of the non-private baseline while incorporating a central Gaussian mechanism with per-round (epsilon, delta)-DP accounting under the assumed sensitivity bound. These results highlight the potential of DP-SimAgg for enabling privacy-preserving collaborative learning in medical imaging applications.

We propose Temporally and Spatially Ordered Gaussians (TSOG), a format for efficient representation of 4D Gaussian Splatting (4DGS) content. TSOG extends the Spatially Ordered Gaussians (SOG) framework to the temporal domain by introducing a timeline attribute and temporal parameterization of geometry and appearance attributes. Similar to SOG, TSOG is a lossy format that assigns each Gaussian a unique index and encodes attribute values as index-aligned image data. TSOG is model-agnostic, extensible, and compatible with both discrete and continuous 4DGS representations. Evaluation using a PLYs sequence and FreeTimeGS as baselines, serving as simplistic and state-of-the-art 4DGS representations respectively, shows file size reductions exceeding 90%, with PSNR differences ranging between -0.42 and +0.85 dB. These results demonstrate substantial file size savings with minimal quality degradation, enabling efficient representation, storage, and delivery of dynamic scenes for next-generation 4D content.

Creating photorealistic animatable head avatars from a single image remains a fundamental challenge in digital human synthesis. While recent 3D Gaussian Splatting methods have achieved promising results, they rely on external tracking pipelines whose latency is excluded from inference measurements. Furthermore, they adopt unified representations that entangle geometrically distinct facial regions, limiting both expressiveness and rendering fidelity. We propose SpiD (Split and Drive), a single-image Gaussian head avatar framework built on two disentanglement axes. The compute axis internalizes per-frame driving, eliminating external tracking dependency at inference. The feature axis decomposes the avatar into three specialized Gaussian branches, each modeling a geometrically distinct facial domain. Extensive experiments demonstrate consistently strong performance against state-of-the-art methods while achieving the fastest inference speed among all compared methods on a single GPU with the complete driving pipeline included.

Robust Optimization Over Time (ROOT) is a recent branch of evolutionary dynamic optimization that seeks solutions capable of remaining effective across multiple consecutive environments. Unlike the traditional track-the-moving-optimum (TMO) paradigm, which reoptimizes after every environmental change, ROOT explicitly values persistence. Although the field has grown considerably, most contributions remain algorithmic and empirical, leaving several fundamental properties poorly understood from a theoretical perspective. One such property is survival time, defined as the number of future environments in which a deployed solution continues to satisfy a prescribed quality threshold. While survival time is widely used as a measure of temporal robustness, little is known about how its expected value depends on environmental dynamics, deployment quality, or problem characteristics. This paper studies expected survival time for a fixed deployed solution under isotropic Gaussian environmental dynamics. Modeling survival as a discrete first-exit problem, we derive a rigorous lower bound and a computable multi-step upper bound. The analysis shows that expected survival scales as $Θ(σ^-{2})$ in slowly varying environments and approaches its minimum value of one future change in high dimensions. A comprehensive Monte Carlo study validates the theoretical predictions, examines sensitivity to modeling assumptions and parameter uncertainty, and illustrates how the bounds can support deployment decisions after optimization. The resulting framework provides an analytical characterization of deployment lifetime and identifies when a required deployment horizon can be guaranteed, ruled out, or remains analytically unresolved.

3D Gaussian Splatting (3DGS) has emerged as an effective representation for novel view synthesis and 3D scene reconstruction, creating an increasing demand for reliable quality assessment. Unlike conventional image quality assessment (IQA), the quality of a 3DGS scene depends not only on the perceptual fidelity of rendered views, but also on scene-level factors such as spatial structure and cross-view consistency. Existing IQA methods are limited by their reliance on 2D perceptual cues, whereas general multimodal large language models (MLLMs) are not designed for stable quality regression and may produce unreliable judgments. To address these limitations, a multimodal quality assessment framework is developed for 3DGS scene understanding. First, a 3D-aware quality representation learning framework is introduced by augmenting a VGGT-based encoder with a dedicated quality head. Multi-view images are encoded into view-specific features and aggregated to capture cross-view consistency, while geometric cues are incorporated through joint modeling of depth and point-cloud-related structural information, enabling the learning of structure-aware quality representations beyond appearance-driven features. Second, a grounded multimodal reasoning mechanism is constructed by jointly feeding original images, depth maps, point cloud renderings, and camera parameters into a Qwen-based MLLM.

Three-dimensional Gaussian Splatting (3DGS) enables high-quality real-time novel-view synthesis through explicit Gaussian primitives and differentiable rasterization. 3DGS and Granular Ball Computing (GBC), proposed in 2019, share a natural compatibility in adaptive representation. The efficiency of 3DGS partly stems from a coarse-to-fine and on-demand refinement process that draws on the generation principle of GBC. This connection motivates us to further introduce adaptive granular ball organization into anchor-based 3DGS. Existing anchor-based methods typically construct anchors from sparse SfM point clouds through fixed voxelization, which cannot adequately adapt to spatially non-uniform point distributions and leads to a trade-off among anchor count, model compactness, and rendering quality. To address this issue, we propose 3DGBGS (3D Granular Ball Gaussian Splatting), a compact anchor-based framework for novel-view synthesis. 3DGBGS adaptively partitions SfM point clouds into 3D granular balls, using larger balls to compactly represent smooth and redundant regions and smaller balls to preserve complex geometry and local details. Based on this representation, Granular Ball Anchor Initialization (GBAI) uses granular ball centers to initialize compact anchor positions, while the Granular Ball Scale Prior (GBSP) exploits granular ball radii to provide local scale priors for Gaussian generation. Experiments on four benchmarks show that 3DGBGS reduces initial and final anchors by 37.1% and 10.0%, respectively, and model storage by 9.8% on average, while maintaining comparable rendering quality.

Recent advances in 3D Gaussian Splatting (3DGS)-based wireless radiance field (WRF) reconstruction provide an efficient solution for wireless channel modeling. However, existing WRF reconstruction methods rely on pre-collected observations and offline optimization, and thus struggle to provide real-time channel knowledge. To bridge this gap, we propose CORF-GS, a real-time WRF reconstruction framework that processes sequential optical and radio frequency (RF) keyframes. Specifically, CORF-GS constructs a unified Gaussian representation for optical and RF with shared geometry and modality-specific appearance, allowing high-resolution optical images to provide structural priors for WRF reconstruction. When a new keyframe arrives, CORF-GS first employs optical-guided Gaussian sampling to densify the WRF in under-represented regions. Since light and radio waves may respond differently to the same object surfaces due to wavelength mismatch, relying solely on optical guidance may neglect RF-informative areas. Therefore, CORF-GS performs coupled optical-RF optimization to jointly refine the shared Gaussians. Compared with the existing two-stage training pipelines, this prevents WRF from passively adapting to a frozen optical geometry and encourages the shared Gaussians to adapt to both optical structures and RF power distributions. Simulations show that CORF-GS achieves state-of-the-art RF spectrum synthesis quality and reduces the reconstruction time by $6.4\times$ compared with existing WRF methods.

Large scale Bayesian nonparametrics (BNP) learner such as Stochastic Variational Inference (SVI) can handle datasets with large class number and large training size at fractional cost. Like its predecessor, SVI rely on the assumption of conjugate variational posterior to approximate the true posterior. A more challenging problem is to consider large scale learning on non-conjugate posterior. Recent works in this direction are mostly associated with using Monte Carlo methods for approximating the learner. However, these works are usually demonstrated on non-BNP related task and less complex models such as logistic regression, due to higher computational complexity. In order to overcome the issue faced by SVI, we develop a novel approach based on the recently proposed constant stepsize stochastic gradient ascent to allow large scale learning on non-conjugate posterior. Unlike SVI, our new learner does not require closed- form expression for the variational posterior expectatations. Our only requirement is that the variational posterior is differentiable. In order to ensure convergence in stochastic settings, SVI rely on decaying step-sizes to slow its learning. Inspired by SVI and Adam, we propose the novel use of adaptive stepsizes in our method to significantly improve its learning. We show that our proposed methods is compatible with ResNet features when applied to large class number datasets such as MIT67 and SUN397. Finally, we compare our proposed learner with several recent works such as deep clustering algorithms and showed we were able to produce on-par or outperform the state-of-the-art methods in terms of clustering measures.

We study the generative capabilities of Boltzmann machines to recover systems governed by the majority rule under critical conditions. To this end, we train deep belief networks (DBNs) with different configurations, where the first layer can use Gaussian visible units with more than two states (i.e., non-binary units). We then allow the DBN to "dream" samples conditioned on visible units that we keep fixed, and we measure the deviation of this dreamed system from the real one. We also corroborate, using a discrete thermometer based on a convolutional network, that the reconstructions remain in a critical state. Across several training sessions with different architectures, we show that, despite the complexity of the problem, the DBN can recover samples that remain critical even under input noise, with a gradual degradation of physical observables relative to the original sample.

Latent domain watermarking for diffusion models embeds watermarks directly into the latent prior, enjoying non-intrusiveness to model parameters and seamless integration with the generation process. However, due to the violation of latent Gaussianity or sensitivity to normal and malicious perturbations during latent inversion, existing methods are prone to watermark detection or removal attacks. A further overlooked problem is the violation of the i.i.d. latent condition after watermarking, which leads to latent correlation degradation and generation fidelity loss. Although this has been externally measured by FID, the internal correlation structure has yet to be rigorously characterized. To address the above issues, and motivated by the rotation-invariant property of isotropic Gaussian, we propose \textit{Latent Angular Watermarking (LAW)}, which encodes watermark bits as antipodal angles ($\pmπ/2$ relative to a reference pair) between disjoint pairs of latent elements while preserving the Gaussianity. The antipodal ($π$-separation) encoding maximizes geometric separation between bit values, and we prove that the decoding angular-error variance is proportional to the norm of the latent pair, i.e., $\operatorname{var}(Δφ) \propto 1/ρ^2$. We further propose a magnitude-driven variant, LAW-M, which anchors watermark bits in the most geometrically stable latent dimensions, yielding additional robustness gains. Theoretically, we provide a rigorous characterization of the induced correlation degradation, deriving in closed form the autocorrelation structure of the watermarked latent and proving that correlations are confined to a sparse, structured set of off-diagonal elements with fixed $\pmπ/4$ values.

We describe and evaluate BF-ConvUNeXt, a compact bias-free ConvNeXt U-Net for blind additive-white-Gaussian-noise color image denoising, combining four existing ingredients so a single property survives end to end: a frozen depthwise Gabor stem (oriented band-pass, zero trainable parameters), a Laplacian-pyramid encoder routing the high-frequency residual into each skip connection, a ConvNeXt-V1 U-Net body, and bias-free construction throughout (no additive bias, linear head, LeakyReLU, variance-only batch norm). Together these make the 0.82M-parameter network exactly degree-1 homogeneous at inference, D(alpha y) = alpha D(y), licensing a Miyasawa/Tweedie score reading of the residual and blind generalization across noise levels from one model. We train a single blind model on a noise-sigma curriculum (sigma approximately 6.4 to 64, 0-255 scale); it extrapolates past that ceiling without a cliff, degrading smoothly to 22.8 dB at sigma=150 and 20.0 dB at sigma=200. Evaluated unchanged on four standard color sets (CBSD68, Kodak24, McMaster, Urban100) at sigma in {15,25,50}, it matches or beats DnCNN and FFDNet on every set and level, averaging about +0.7 dB over DnCNN. Against heavyweight CNN/transformer state of the art it trails by a small margin (roughly 0.3-1.7 dB depending on set) at 1/15 to 1/39 of their parameters. The homogeneity is inference-only and checkpoint-specific, and the learned residual is a local, not global, score (non-conservative Jacobian), so plug-and-play/RED guarantees do not transfer; it still drives stochastic sampling and linear inverse problems (inpainting, super-resolution, deblurring, compressive sensing).

Faithful inverse rendering requires visibility and indirect radiance to explain secondary illumination and inter-reflection, yet rasterization-oriented Gaussian representations do not naturally support the secondary-ray queries needed to recover them. We present IRGS++ (Inter-Reflective Gaussian Splatting), a unified robust and efficient Gaussian inverse rendering framework. During transport-aware optimization, IRGS++ employs differentiable 2D Gaussian ray tracing on surface-oriented Gaussian primitives to query visibility and indirect radiance on the fly and evaluate the full rendering equation for inter-reflective transport. This physical core makes Gaussian inverse rendering physically grounded beyond rasterized appearance modeling. To make this backbone useful beyond low-gloss dielectric scenes, the framework incorporates metallic-aware material modeling and robust reflective initialization for glossy, specular, and metallic materials. To make it practical, multiple importance sampling and denoising stabilize finite-sample rendering, while mesh-based secondary-attribute queries reduce the cost of relighting under novel illumination. Quantitative evaluations on low-gloss and glossy benchmarks show improved decomposition and relighting quality together with favorable quality--speed trade-offs under the reported configurations, while real-world studies illustrate plausible relighting under novel illumination.

Dynamic scene reconstruction with 3D Gaussian Splatting requires a balance between fine-grained motion modeling, structural stability, and compact representation. Existing per-primitive methods provide flexible local deformation but often suffer from redundant primitive growth, while anchor-based methods improve spatial regularity at the cost of suppressing locally varying motion. To address these issues, we present GrainGS, a dynamic Gaussian framework that combines a hierarchical anchor scaffold with per-Gaussian deformation. A static warm-up stage first establishes a time-invariant canonical representation from observations across all timestamps. During joint training, a stop-gradient operation blocks the deformation-mediated gradient pathway to the canonical positions while preserving their direct refinement through the reconstruction objective. Each Gaussian then predicts independent temporal offsets for position, rotation, and scale, enabling detailed local motion within a structurally constrained scaffold. A canonical-residual appearance decomposition further models frame-dependent photometric changes without forcing them into geometric deformation. Experiments on synthetic monocular and real-world multiview benchmarks show that GrainGS achieves high reconstruction quality, real-time novel view synthesis, and compact storage. Under the synthetic benchmark setting, it reaches an average peak signal-to-noise ratio of 36.98 decibels, renders at 435.6 frames per second, and requires 4.67 megabytes of storage.

We propose FA-LAM, a Focus-Aware Large Avatar Model for one-shot animatable Gaussian head creation, while simultaneously enabling static 3D and dynamic 4D full-head recovery. The core of our method lies in a thorough analysis of the attention mechanisms and the entangled reconstruction and animation training pipeline adopted by prior state-of-the-art approaches. Our analysis identifies two main factors that compromise the quality of 3D full-head generation: (1) incorrect and noisy attention activations, and (2) conflicts between the tasks of reconstruction and animation. To address the first issue, we introduce a symmetric and semantic attention regularization strategy that leverages the inherent semantics and structural symmetry of human heads. To disentangle the objectives of reconstruction and animation, we develop a novel dual-phase training pipeline that separates the model's capabilities for large-view hallucination and animation into distinct modules. Moreover, we enhance our model to support multi-view and streaming 4D reconstruction in an efficient and memory-friendly manner through a core autoregressive modification with tailored visibility-aware token fusion. Collectively, these innovations enable FA-LAM to reconstruct animatable Gaussian full heads with superior quality, particularly in fine facial regions and large viewing angles.

Pixel-aligned Gaussian splatting enables efficient and generalizable novel-view synthesis. However, high-resolution rendering faces a critical trade-off where increasing input resolution improves detail at the expense of quadratically rising network computational cost. Conversely, maintaining low-resolution inputs stabilizes this cost but results in insufficient Gaussian density and artifacts. To address this, we propose SubSplat, which introduces Sub-pixel Gaussian Reparameterizer(SPGR) to subdivide primary Gaussians into fine-grained primitives, restoring structural density directly from low-resolution features. We further enhance the reparameterization quality through feature aggregation, which effectively captures high-frequency details across multiple views. Experiments on RealEstate10K and ACID demonstrate that SubSplat achieves high-fidelity rendering with superior efficiency. Our results validate that the proposed framework successfully resolves the trade-off between reparameterization fidelity and network computational cost inherent in pixel-aligned Gaussian Splatting.

Recent advances in 3D scene editing have leveraged iterative diffusion models to update input views. However, this process is computationally expensive and struggles to produce sharp details. Meanwhile, ``hallucination drift'' frequently introduces multi-view inconsistencies, leading to structural artifacts when rendering novel viewpoints. To address this problem, we present 3D-GIMP (3D Gaussian Inpainting Meets Patch Matching), a novel hybrid paradigm designed for high-fidelity object removal in 3D Gaussian Splatting. Instead of diffusing every view, 3D-GIMP performs a single generative inpainting on a key reference view, which serves as an appearance prior. We then introduce a 3D-aware PatchMatch algorithm to propagate these reference textures across all remaining views via correspondence matching, effectively bypassing the stochastic nature of frame-by-frame diffusion. By prioritizing reconstructive consistency over iterative generation, 3D-GIMP maintains high-frequency details across arbitrary resolutions while ensuring a mathematically consistent 3D reconstruction. Our experiments demonstrate that 3D-GIMP not only achieves competitive inpainting quality as previous methods using diffusion in multiple views, but also outperforms these methods in rendering speed and view consistency.

We study Gaussian averaging as a smooth surrogate for quantized neural models. Under bounded local oscillation, we derive a local dimension-dependent bound on |f-g|, linking Gaussian smoothing to the stability analysis of discontinuous networks. We compute closed-form Gaussian averages of the rectified linear unit (ReLU) and sign activation functions, and illustrate the mechanism on a high-dimensional binary perceptron, where layer-preactivation aggregation under an explicit quantization-noise surrogate yields the Gaussian envelope used in inference-side smoothing and training-side smooth surrogate gradients.

Vision-centric 3D occupancy prediction provides dense scene representations essential for autonomous driving and robotic navigation, yet existing methods struggle to scale to high voxel resolutions due to prohibitive computational costs. To address this, we introduce GaussianSeed, a progressive multi-scale Gaussian occupancy prediction framework that organizes primitives into a coarse-to-fine hierarchy. Benefiting from this hierarchical design, GaussianSeed effectively circumvents the memory bottlenecks inherent in dense representations, successfully scaling to a $0.1\text{m}$ spatial resolution while maintaining real-time inference capabilities. To comprehensively evaluate high-resolution geometric perception, we further construct TJScenes, a panoramic six-camera occupancy dataset with highly detailed $0.1\text{m}$ annotations. Extensive experiments on Occ3D-nuScenes and TJScenes demonstrate that GaussianSeed delivers the lowest latency among all evaluated methods while maintaining highly competitive accuracy, advancing the efficiency-quality frontier of high-resolution 3D occupancy prediction. Codes are available at https://github.com/Athameral/GUSD

We study Gaussian-width complexity on statistical manifolds through a pair of functionals: the primal Fisher width $w_G(T) = w(G^{1/2}T)$, induced by the Fisher metric, and the inverse-Fisher width $w_{G^{-1}}(T) = w(G^{-1/2}T)$, induced by the inverse Fisher metric. The two widths play complementary statistical roles. On the learning side, the Fisher width measures the size of local parameter fluctuations in the geometry induced by the Fisher information. For Fisher-regular losses, we prove that the scale $w_G(H_r)/\sqrt n$ is attained on sufficiently small Fisher balls. On the recovery side, the inverse-Fisher width captures the effect of anisotropic Gaussian measurements whose covariance is determined by the inverse Fisher information. For sparse recovery, the resulting geometry depends not only on sparsity but also on the position of the active coordinates in the Fisher spectrum. We obtain a two-sided estimate for the corresponding statistical dimension, together with support-sensitive recovery estimates and a natural ordering of supports with different curvature profiles. Finally, we establish a sharp relation between the primal and inverse-Fisher widths. On any common compact coordinate set $T$, they satisfy $$w_G(T)w_{G^{-1}}(T)\geq w(T)^2.$$ Thus, Fisher anisotropy may transfer complexity from one geometry to the other, but cannot reduce both widths relative to the Euclidean scale.

We consider the problem of constructing a $K$-class classifier from the combination of $O(\log K)$ simple binary classifiers -- this is a natural paradigm to construct a sophisticated classifier in a distributed manner with each agent performing a relatively straightforward task. We study the fundamental performance limits of such a classifier when the corresponding binary classifiers are hyperplanes. For a stylized Gaussian setting where the $K$ class centers are independent Gaussian points in $\mathbb R^d$ and the observations are corrupted by Gaussian noise, we derive explicit performance bounds across several decoding and dimensional regimes. Extensive simulation experiments provide strong empirical validation of the presented theoretical results.

Gaussian graphical model selection is usually studied under independent sampling, but in many applications the data arise as a single trajectory of a dependent stochastic process. We study exact recovery of the graph from one trajectory of random-scan Gaussian Glauber dynamics. Existing techniques for this problem either inherit the mixing time of the chain, which can be super-polynomial in the dimension $p$ without strong assumptions, or are suboptimal in the minimum normalized edge strength $κ$. We propose two algorithms that are mixing-free and attain the $κ^{-2}$ dependence of the information-theoretic lower bounds. Both instantiate a shared dueling-neighborhood search meta-algorithm with a local statistic built directly from the update sequence. For every fixed precision matrix and deterministic initialization, the first algorithm fits a least-squares regression at the updates of each node and has pointwise recovery horizon $\widetilde O(pd^{2}/κ^{2})$, where $d$ is the maximum degree. Its horizon depends logarithmically on a local conditioning quantity and on the initialization potential. The second algorithm is based on counting occurences of a specific update pattern and requires $\widetilde O(pd^{4}/κ^{2})$ updates, with no dependence on any condition number. The central technical challenge is that both statistics are built from dependent, non-stationary observations. Our analysis tackles this by demonstrating how to extract fresh Gaussian innovations from the update sequence, which yields mixing-free control of appropriate quantities. Neither the algorithms nor their analyses invoke stationarity, a spectral gap, or mixing conditions.

Recent advances in differentiable Gaussian splatting have highlighted the potential of primitive-based approaches as alternative scene representations for interactive, high-quality, volume visualization (VolVis) of large datasets. However, the explicit nature of current primitive-based methods, combined with isolated optimization for each VolVis scene, results in redundant, non-compact representations. We present ECoNGS, an efficient compressive neural Gaussian splatting framework for VolVis scene representation. ECoNGS employs lightweight neural networks to dynamically predict implicit, editable Gaussian splats from explicit anchor points, effectively combining model compactness and parameter efficiency of implicit representations with high-performance rendering of explicit primitives. We explore a joint learning strategy that clusters geometrically similar scenes and shares parameters across them, significantly reducing overall training time and model size while maintaining reconstruction fidelity. To achieve a more compact scene representation, we further compress the explicit anchor attributes using a neural entropy model that estimates their probability distributions, enabling compact storage via entropy coding. We systematically investigate Gaussian initialization strategies and propose a simple yet effective scheme tailored for VolVis scenes, improving reconstruction accuracy and accelerating convergence. We evaluate ECoNGS qualitatively and quantitatively across various univariate and multivariate VolVis scenes, highlighting its superior performance over prior methods in training time, reconstruction quality, and model size. In particular, compared with the prior method iVR-GS, ECoNGS improves reconstruction quality by up to 2.2 dB in PSNR while reducing the model size by up to 6.1x and the training time by up to 5.9x. The code is available at https://github.com/TouKaienn/ECoNGS.

Vision-only occupancy prediction requires recovering a semantic 3D occupancy field from calibrated surround-view images, where each view provides observations with ambiguous depth along camera rays. Existing methods have progressed from dense structured representations to sparse Gaussian primitives, improving the efficiency of 3D scene representation. However, Gaussian learning still relies primarily on image domain features, which provide limited explicit geometric information for volumetric reasoning. Our key observation is that effective Gaussian occupancy modeling requires not only sparse primitives, but also richer geometric and semantic learning cues. In this paper, we propose VGOcc, which learns visual and geometric cues from foundation models for Gaussian modeling. VGOcc incorporates these cues into primitive initialization and refinement, yielding a representation termed Visual-Geometric Gaussians tailored to semantic occupancy prediction. Specifically, we propose Visual-Geometric Gaussian Birth to form spatially balanced Gaussian centers from ray depth hypotheses, while visual semantic features initialize primitive attributes. Next, we design Pose-Aware Feature Learning to combine foundation tokens with camera embeddings and calibrated ray information. Features from neighboring views are then aggregated at projected 3D locations for each Gaussian refinement stage. Finally, Gaussian decoder refines birth Gaussians with pose-aware features and renders them into semantic occupancy. Experiments on nuScenes demonstrate that VGOcc achieves state-of-the-art performance in vision-only 3D occupancy prediction. Codes will be available at https://github.com/JHLin42in/VGOcc.

3D Gaussian Splatting (3DGS) achieves high-quality real-time rendering by representing a scene with a large collection of anisotropic Gaussian primitives. However, complex scenes often require millions of Gaussians, resulting in substantial storage and rendering costs. Existing compression methods mainly reduce redundancy through primitive-wise pruning, attribute quantization, clustering, or neural coding, while redundancy caused by strongly overlapping and non-orthogonal Gaussian basis functions remains largely unexplored. We present QIRF, a quantum-inspired non-orthogonal function-space compression method for 3D Gaussian Splatting. QIRF models neighboring Gaussian primitives as a local non-orthogonal basis and formulates primitive reduction as a subspace-aware selection problem. Specifically, an analytic Gaussian overlap matrix and a radiance-response density matrix are constructed to characterize functional redundancy and rendering relevance. Generalized eigendecomposition is then used to identify the dominant local subspace and select representative Gaussian primitives. An RRDM-based response model and detail-aware safeguarding further preserve visually important high-frequency structures under aggressive pruning. Experiments on 13 scenes from Mip-NeRF 360, Tanks and Temples, and Deep Blending show that QIRF reduces the Gaussian count and raw PLY storage by 71.7 percent on average, corresponding to approximately 3.54 times compression, while maintaining reconstruction quality comparable to 3DGS and achieving a marginal average PSNR improvement of 0.10 dB. QIRF also improves the average rendering speed over 3DGS by 34.3 percent. These results suggest that non-orthogonal function-space redundancy is an important yet underexplored source of representational redundancy in explicit Gaussian radiance fields.

Motivated by confidence-guided parallel unmasking in masked discrete diffusion, we study a single selection step in a stylized Gaussian random-field model. A locally dependent nonnegative score field represents position wise uncertainty, and the scheduler selects the K positions with the smallest scores. Dependence among the selected positions is measured through a distance-dependent Gaussian correlation model. This separation provides a tractable framework for quantifying how the geometry of low-score locations affects the dependence cost of factorized parallel decoding. We establish two complementary results. In a conservative sub-square-root regime, the conditional Gaussian total correlation of the selected block vanishes in probability. At the square-root scale, it remains non-negligible with positive asymptotic probability and admits a strictly positive expectation lower bound. Synthetic experiments support the predicted finite-size behavior. These results provide a rigorous stochastic-geometry baseline for understanding how budget size, score dependence, and spatial correlation jointly shape one-step confidence-based selection in masked discrete diffusion.

We study distributionally robust linear chance-constrained problems in which uncertainty is modeled by a Gaussian mixture model (GMM). Finite-support distributionally robust (FDR) formulations, widely used in data-driven robust optimization, robustify over empirical mixture support points and therefore primarily stress-test the fitted nominal mixture. This can be insufficient when service reliability depends on structural misspecification of the nominal mixture-support parameters. To address this limitation, we describe the ambiguity set of distributions by developing a novel formulation of a Wasserstein-2 metric that uses the Bures-Wasserstein (BW) metric over probability measures with finite second moments. Unlike FDR, which generally sets finitely many empirical support points a priori, the proposed ambiguity set allows the worst-case distribution to endogenously determine both how many mixture components receive mass and where their means and covariances lie within a continuous support. For the resulting ambiguity set, under mild regularity conditions, we prove strong duality for the inner worst-case chance-constraint problem and derive its semi-infinite reformulation. We then develop an adaptive cutting-surface algorithm, which endogenously determines the locations of mixture components receiving mass, and the mean and covariances of the Gaussian distributions at these locations. The algorithm attains any prescribed optimality gap in finitely many iterations, while a block-alternating local search identifies new components. A case study using the electric-vehicle charging-station energy-allocation problem demonstrates the framework's practical value in achieving any reliability targets. CDR also induces structural changes in energy allocations, unlike FDR, whose allocations remain close to the nominal solution.

We consider defining risk probability in stochastic control problems under distribution ambiguity. Current approaches for chance-constrained control typically assume that the true state distribution is known and Gaussian distributed. These assumptions are not amenable to many real-world engineering applications where system dynamics are nonlinear and only approximately modeled. In this work, we define a distribution ambiguity set and, with a variational expression for exponential integrals, bound the expected risk value under an unknown distribution that resides within a relative entropy distance of a nominal Gaussian reference distribution. Our bound recovers the reference risk value in the zero-divergence limit. A method is presented to determine the relative entropy distance defining the ambiguity set that is a function of the reference covariance evolution and second-order dynamical truncation errors. The resulting contributions provide a framework for handling distributional ambiguity in nonlinear covariance steering problems. A stochastic spacecraft guidance example is presented to demonstrate our contributions.

3D Gaussian Splatting (3DGS) achieves high-fidelity novel view synthesis in real-time; however its training efficiency and representation compactness are hindered by excessive primitive proliferation. To address this challenge, we formulate the structural evolution of 3DGS as a global budget-constrained optimization problem and derive an optimality condition, which requires the marginal utility of structural resources to be balanced across spatial regions under a finite primitive budget. Based on this formulation, we propose SPARE-GS, a general plug-and-play framework that dynamically aligns the distribution of 3D Gaussian primitives with regional representational demand. SPARE-GS estimates capacity-normalized regional demand, assigns adaptive target quotas, and uses regional budget deviations to coordinate densification, pruning and adaptive termination toward a more balanced structural allocation. Extensive experiments across standard, accelerated, and structure-enhanced 3DGS pipelines demonstrate that SPARE-GS reduces the Gaussian count and training time by an average of 30.38% and 23.81%, respectively, while improving the average PSNR. Moreover, the resulting compact representations reduce downstream processing time and improve the rate-distortion performance of diverse compression and pruning methods, demonstrating the broad applicability of global structural budget regulation.

On-the-fly reconstruction is a key requirement for many applications in robotics and autonomous navigation. Variational Bayes Gaussian Splatting (VBGS) enables continual learning without replay buffers using Coordinate Ascent Variational Inference (CAVI), but its per-frame iterations over all observed points make it too slow for real-time use with strict memory and latency requirements. We present ImprovedVBGS, an accelerated framework for on-the-fly continual reconstruction. This is achieved primarily through (i) spatially truncated variational inference, and (ii) improved reassignment that uses forwarding, truncation and eliminates wasteful dynamic recompilation. On the NeRF synthetic dataset, we reduce mean per-frame latency from ~84.0 s to ~0.050 s on an RTX 3070 Ti, a 1680x speed-up while maintaining reconstruction quality. We also improve novel-view synthesis quality using an exact renderer with no added training costs.

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.

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.

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.

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.

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.

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.

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.

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.