3D Gaussian Splatting

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.

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/.

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) 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.

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

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.

Producing 3D human representations from input views on the fly is essential for immersive live streaming systems, where representation compactness is as critical as high fidelity given limited computational power and transmission bandwidth. Although recent feed-forward reconstruction methods achieve impressive quality through the view-centric prediction of 3D representations, they repeatedly encode the same subject content across multiple views, leading to significant inter-view redundancy. Our key insight is to perform predictions directly in 3D space, enabling the network to learn and produce a highly compact representation. To this end, we propose PointSplat, a novel human-centric approach that directly infers Gaussian primitives from an input point set. The proposed method first estimates a coarse geometric proxy and performs ray casting to prune redundant points and establish explicit 2D--3D correspondences. Subsequently, it employs a Point-Image Transformer to fuse appearance and geometry features, predicting Gaussian attributes in a single forward pass. This design restricts predictions to foreground regions of interest, substantially reducing the total number of Gaussians while improving novel-view rendering quality. Extensive experiments demonstrate that PointSplat achieves higher efficiency and quality while exhibiting strong robustness to variations in view count and image resolution across multiple datasets.

Intrinsic decomposition which expresses image colors as the product of diffuse albedo and shading, possibly augmented with view-dependent residuals has a long history in image editing as it enables the modification of object colors and textures without altering lighting. We extend intrinsic decomposition to radiance fields represented with Gaussian splatting by proposing solutions to three key aspects of such decomposition. First, we describe how to model the intrinsic decomposition as independent sets of Gaussian primitives, which allows each set to adapt to the characteristics of the layer it represents. Second, we present an optimization procedure guided by data-driven predictions to disentangle multi-view photographs of a scene into the aforementioned intrinsic sets. Finally, we provide an editing workflow where users modify the texture of planar surfaces simply by modifying the albedo of that surface in one image. Capturing this edit within the intrinsic radiance field allows re-rendering of the edited scene with plausible lighting under arbitrary viewpoints.

Generating high-quality novel views at real-time frame rates remains a central challenge in 3D vision, particularly in sparse-view scenarios. Neural radiance fields have demonstrated robust reconstruction from limited observations, but their reliance on volumetric rendering leads to high computational cost and slow inference. In contrast, Gaussian Splatting methods achieve real-time rendering through rasterization, but their optimization is highly sensitive to the quality of the initial geometry. This sensitivity becomes especially problematic in sparse-view settings, where limited observations often lead to incomplete or noisy point-cloud reconstructions. In this work, we present AugSplat, a simple framework for improving Gaussian Splatting in sparse-view regimes using radiance-field-based view augmentation. We first train a radiance field on the sparse input views and use it to synthesize additional images from nearby novel viewpoints, increasing the effective view-space coverage available for supervision. These synthetic views are then used as auxiliary supervision during Gaussian Splatting optimization. We study two variants: Staged AugSplat, which uses synthetic views for an initial optimization phase before switching to real images, and Dual AugSplat, which jointly trains on real and synthetic views with a decaying synthetic loss weight. Experiments on sparse-view mip-NeRF 360 scenes show that AugSplat improves reconstruction quality over standard Gaussian Splatting. Staged AugSplat achieves the strongest average performance, while Dual AugSplat provides a closely performing formulation that keeps real-image supervision active throughout training, and both variants preserve real-time rendering at inference.

Echo Planar Imaging (EPI) is the standard acquisition technique for diffusion and functional neuroimaging, enabling rapid imaging but suffering from geometric distortions caused by B0 field inhomogeneities. Existing correction methods first reconstruct distorted images using parallel imaging, then estimate the B0 field and correct the distortion in the image domain. In this sequential process, reconstruction artifacts at high acceleration factors and low SNR at high diffusion b-values degrade B0 estimation and limit the overall correction quality. We propose a physics-informed framework that jointly estimates the B0 field and distortion-free image directly from k-space data, without depending on an intermediate parallel-imaging reconstruction for the correction. The image and the B0 field are each represented as a superposition of Gaussian primitives embedded within an MRI physics forward model. The explicit, continuous parameterization captures both smooth regions and tissue boundaries and supports rotated-view EPI acquisitions without interpolation. The diffusion-weighted image is modeled as real and non-negative, with the image phase absorbed into a per-shot phase factor. Rotated views distribute distortions across multiple phase-encoding orientations, improving point spread function isotropy and providing stronger constraints for B0 estimation. On in vivo brain diffusion EPI, the proposed method attains the closest brain-boundary agreement with a distortion-free structural reference, with the largest improvement over sequential methods at high b-value and high acceleration. Extensive visual comparisons further show improved detail fidelity and noise suppression.

Autonomous driving systems benefit from high-definition (HD) maps that provide critical information about road infrastructure. The online construction of HD maps offers a scalable approach to generate local vectorized maps from onboard sensor observations. Existing methods commonly adopt bird's-eye-view (BEV) features as the intermediate scene representation, encoding the surrounding space with fixed-resolution dense grids. However, map elements are spatially sparse yet require fine-grained geometric localization, making uniformly allocated BEV representations redundant and less effective for vectorized map prediction. In this work, we propose GaussianMap, an online HD map construction framework that learns an adaptive Gaussian representation of the surrounding scene. This representation consists of a set of Gaussian primitives on the BEV plane, each encoding a flexible local region with geometric properties and a feature vector, allowing the model to allocate representational capacity to map-relevant regions. To generate such a representation from sensor observations, we introduce a feed-forward Gaussian encoder that progressively refines these primitives through Gaussian interaction modeling and multi-sensor feature aggregation. The refined Gaussian representation is then splatted into a BEV feature map and decoded into vectorized map predictions. Extensive experiments on nuScenes and Argoverse 2 datasets demonstrate that GaussianMap achieves state-of-the-art performance in both camera-only and camera-LiDAR fusion settings. Our code will be made publicly available.

Gaussian process inference is often limited by cubic computational costs, a challenge that becomes more pronounced in spatio-temporal settings where posterior inference is required over dense grids. While state-space SPDE formulations enable linear complexity in time, exact inference remains cubic in space and deteriorates further when observation locations are disjoint from the prediction locations, which inflates the number of considered spatial points. To address this, we propose the Vanilla-SPDE Exchange, which exploits an equivalence between the standard and SPDE formulations of GP inference to construct a hybrid scheme with improved computational cost. We demonstrate these gains through complexity analysis and numerical experiments.

Multimodal MRI is essential for accurate brain tumor segmentation. However, acquiring all modalities at inference is often challenging in practice, which causes intrinsic uncertainty due to unavoidable information loss. Without modeling this uncertainty, existing methods encode incomplete evidence into deterministic representations that appear plausible but lack reliability. In this regime, we propose a probabilistic representation framework that models representations as Gaussian distributions, where their mean captures task information and their variance measures uncertainty from missing evidence. To make variance reflect information deficiency, we regularize the mean from each partial configuration toward its full-modality counterpart, while scaling the variance with the discrepancy between their aligned means. We further introduce a set-inclusive strategy that exploits the hierarchical structure of modality subsets and enforces an ordering constraint to maintain their consistent uncertainty relationships. Extensive experiments on BraTS 2018 and 2020 demonstrate that our approach offers superior performance over baselines across diverse missing-modality scenarios. Code and model checkpoint are available at https://github.com/atlas-sky/SIUM.

With Large Language Model (LLM) pre-training and fine-tuning shifting its focus from data volume to data quality, quality data selection has emerged as a critical research topic. Existing online data selection methods for LLM training are typically "batch-constrained", limiting optimization to local utility within random batches. To overcome this, we propose GAIA (Global Adaptive Instruction tuning via GAussian processes), a framework that formulates data valuation as a global estimation process. GAIA employs Gaussian Process regression to model continuous utility manifolds across the semantic space, utilizing an adaptive strategy fusion mechanism to dynamically prioritize high-utility samples. By casting the strategy-posterior update as an instance of the classical fixed-share Hedge framework for tracking the best expert, we inherit a dynamic-regret guarantee that characterizes GAIA's robustness under non-stationary quality scores during training. Empirical evaluations on three datasets demonstrate that GAIA significantly outperforms state-of-the-art baselines like \greats, establishing our method as a scalable and robust solution for efficient instruction tuning.

Real-to-sim reconstruction for embodied AI requires geometry that is useful for collision reasoning, navigation, and agent-environment interaction, not only photorealistic novel-view synthesis. However, close-range urban facades are difficult for video-to-3D reconstruction: glass, reflections, repeated windows, and weak texture can produce visually plausible renderings with unstable surface geometry. We introduce shell-supervised Gaussian Splatting, a reconstruction-stage framework that uses an external facade structural shell as lightweight geometric supervision for video-driven Gaussian reconstruction. The method aligns an exterior shell to the video reconstruction frame, renders per-view depth, camera-space normal, and valid-mask maps, and applies these cues through mask-gated losses during Gaussian optimization. This design preserves RGB-driven appearance while regularizing only visible shell-supported facade regions. Experiments on anonymized close-range urban facade scenes show improved facade orientation and visible-surface point-cloud consistency over photo-only, monocular-cue, and surface-oriented Gaussian baselines, while maintaining comparable held-out rendering quality.

Reconstructing dynamic 3D scenes from monocular videos is challenging due to scene complexity and temporal dynamics. With the advancement of 3D Gaussian Splatting in novel view synthesis, existing methods extend 3D Gaussians to 4D domain with deformation fields, trajectories or spatiotemporal 4D volumes to model scene element deformation. However, these methods suffer from long training time, low rendering speed or high memory consumption for per-frame reconstruction of 4D volumes, without fully exploiting dense dynamic information. To address this issue, we propose Flow Splatting, which constructs the velocity field and enables the conventional splatting technique to render optical flow from the velocity field to supervise dynamics learning process from monocular videos. Specifically, we extend 4D volumes with time varying means and covariance to represent complex dynamics. Then, we construct and approximate the velocity field naturally based on this representations. While conventional volume rendering techniques support to render color fields, we extend the volume rendering strategy to splat the velocity field by considering the influence of camera motions. We conduct experiments on various benchmarks to demonstrate the efficiency and effectiveness of our method. Compared to the state-of-the-art methods, our model achieves better image quality with less time consumption and higher rendering speed.

Merging multiple 3D Gaussian Splatting (3DGS) scenes into a single unified Gaussian representation is essential for large-scale 3D mapping and long-term map management. Despite its importance, this area remains underexplored, and existing solutions exhibit several limitations. Learning-based methods attempt direct correspondence between Gaussian primitives and require training on large 3DGS datasets. Image-based optimization methods depend heavily on coarse initialization from generic foundation models and often incur expensive refinement. We present \ourmodel. Our method constructs a 3D scene graph from a 3DGS and its rendered images, \textit{reformulating 3DGS registration as a graph registration problem}. The proposed 3D scene graph represents each 3DGS at a higher-level representation, enabling a globally consistent understanding of semantic information and structural context for accurate registration. To further construct a seamless unified scene, we introduce a Self-Supervised Test-Time Optimization. Naively merging two 3D Gaussian scenes often suffers from occlusion artifacts such as hollows and floaters. To alleviate this issue, we refine the merged Gaussians to preserve visual consistency between the original scenes and the merged scene. We evaluate our method on real and synthetic benchmarks, demonstrating competitive registration accuracy and merged scene rendering quality.

Visual SLAM performance often deteriorates in complex real-world applications. Semantic 3D Gaussian SLAM commonly fuses 2D semantic priors into a persistent 3D map using uniform optimization weights. However, such priors are not equally reliable in online mapping: occlusions, unsupported semantic boundaries, and ambiguous ray geometry can introduce persistent semantic artifacts into the global Gaussian map. We propose VCS-SLAM, a geometry-validated semantic evidence fusion framework for RGB-D 3D Gaussian SLAM. Instead of treating all semantic observations as uniformly valid supervision, VCS-SLAM evaluates their geometric reliability through visibility consistency, surface-supported boundary evidence, and ray-level conflict uncertainty. The resulting reliability-aware objective suppresses occluded semantic updates, reduces unsupported semantic bleeding, and delays premature label assignment in ambiguous regions. Experiments on Replica demonstrate improved semantic consistency, boundary preservation, and reconstruction quality. Results on ScanNet further show that VCS-SLAM maintains competitive tracking performance under real RGB-D inputs

Arbitrary-Scale Super-Resolution (ASR) reconstructs images at continuous magnification factors. Recent methods accelerate inference by replacing computationally heavy implicit neural decoders with explicit 2D Gaussian Splatting (GS). However, since standard Gaussians are smooth low-pass primitives, modeling edges and fine textures requires multiple overlapping, well-aligned splats, which creates severe bottlenecks during rasterization. To address this, we introduce Resonant Brane Splatting (RBS), a feed-forward ASR framework. RBS replaces flat Gaussians with Branes: expressive primitives that emit spatially varying colors to natively model local contrast and complex textures within a single footprint. We achieve this by augmenting the standard Gaussian envelope with internal Gaussian-Hermite modes, assigning a distinct color coefficient to each. The zero-order mode recovers standard GS, while higher-order modes capture high frequencies. We predict Brane parameters directly from low-resolution features. Because Branes provide a mathematically richer formulation than simple Gaussians, far fewer primitives need to overlap to reconstruct a given target pixel. To exploit this, we introduce an efficient fully differentiable rasterizer with a precise culling strategy based on the classical quantum turning point. This allows us to safely skip negligible regions, drastically reducing the rendering overhead. Experiments on standard ASR benchmarks show that RBS improves reconstruction quality over implicit and GS baselines, while achieving superior speed-quality trade-off than prior GS methods.

Arbitrary-Scale Super-Resolution (ASR) aims to reconstruct high-resolution images at any continuous magnification. While 2D Gaussian Splatting (GS) has recently shown great promise for ASR, current methods struggle to balance visual quality and computational cost. Approaches targeting high fidelity rely on powerful backbones and uniform, highly dense Gaussian grids, leading to prohibitive memory and inference costs. Conversely, methods prioritizing efficiency aggressively simplify their architectures, severely compromising visual quality. To bridge this gap, we observe that a core capability of GS remains largely underexplored in ASR: the potential for dynamic densification, i.e., the spatially adaptive allocation of Gaussians based on image content. Unlike standard scene fitting, where densification is guided by a known ground truth, applying this to ASR is highly non-trivial because the high-resolution target is exactly what the model must predict. To address this challenge, we propose QuADA-GS, an approach that retains a powerful representational backbone but autonomously predicts where to allocate Gaussians relying strictly on the low-resolution input. By adopting a sparse approach, QuADA-GS refines features and increases Gaussian density strictly where structural complexity demands it. Because this adaptive allocation produces a non-uniform hierarchical topology, we introduce a novel, highly efficient communication mechanism to process these sparse features, bypassing standard dense bottlenecks. Extensive experiments indicate that our approach successfully balances visual quality and computational requirements, providing an improved and competitive trade-off for ASR.

Gaussian splatting (GS) has garnered significant attention in VR/AR and digital content creation due to its explicit parameterization and efficient rendering capabilities. However, existing GS-based methods for deformable objects face two key limitations: (i) illumination is erroneously baked into textures, causing physically inconsistent responses under dynamic deformations and lighting changes; (ii) snapshot-based reconstruction restricts post-reconstruction material editing. To address these challenges, we propose Deformable and Relightable GS (DR-GS), a unified Gaussian framework that integrates physically-based inverse rendering, relighting, and deformation-aware manipulation. Through explicitly disentangling geometry, illumination, and material representations, DR-GS overcomes the limitations of static snapshots, resolving unrealistic appearance under varying conditions while enabling post-reconstruction parameter editing. Extensive experiments show that DR-GS achieves leading visual quality across static reconstruction, dynamic deformation, and relighting, reliably preserving reflections and specular highlights on glossy surfaces. It further establishes a fully decoupled geometry-illumination-material pipeline, enabling high-quality 3D asset creation and comprehensive post-editing.

Predicting the aerodynamic performance (e.g. lift, drag, and moment coefficients) of an aircraft is challenging -- computational models are biased and direct simulations are prohibitive. A pragmatic way to overcome this limitation is by calibrating low-fidelity computational predictions with experimental measurements. This, however, requires calibrating against \emph{sparse} measurements contaminated with \emph{uncertainty} in both the control inputs and the measured aerodynamic response. We develop a methodology to address this problem based on Gaussian process surrogates and the classical Kennedy-O'Hagan calibration. A surrogate model learned on abundant-but-cheap low-fidelity data is calibrated with a sparse set of measurement data. Crucialy, we develop a Bayesian latent Gaussian process based approach that marginalizes the calibrated surrogate model over the input uncertainty, while also matching the marginal mean and variance of the measured output uncertainty. Once calibrated, our surrogate model predicts the uncertainty in aerodynamic coefficients with very high accuracy, including at extrapolative input settings. We validate our calibrated surrogate model predictions against measurement data with \emph{true} uncertainty intervals to demonstrate that the model places $94.2-95.8\%$ of its predictive samples inside the released $95\%$ truth intervals, with endpoint cumulative probabilities very close to the nominal 0.025 and 0.975 levels.

3D Gaussian Splatting~(3DGS) has emerged as a promising paradigm for reconstructing streamable free-viewpoint video~(FVV) from multi-view videos. However, 3DGS-based FVVs typically lack user interaction and editing capabilities, which diminishes the immersive experience. Recent research has integrated language features from CLIP into 3DGS via distillation, enabling open-vocabulary queries and supporting many downstream applications. Nevertheless, the stringent requirements of FVV, low frame size and high FPS, make current language Gaussian representations unsuitable for language-embedded FVV. In this paper, we propose DLGStream, a novel language-embedded FVV representation that streams time-varying language features alongside Gaussian attributes to support 4D environment interaction, scene editing, and spatial intelligence. Specifically, we propose a dual-opacity dynamic language Gaussian representation, which maintains two opacity attributes for color and language features to deal with performance degradation that occurs when colors and features are jointly optimized. Furthermore, we introduce an interpolation-based deformation field to reduce temporal redundancy. This deformation field can also be used for 4D frame interpolation, boosting FVV sequences from low to high FPS. Experimental results demonstrate that DLGStream achieves superior performance in both on open-vocabulary segmentation and reconstruction quality with an average frame size of merely 43 KB. The code is available on \href{https://github.com/kkkzh/DLGStream}{https://github.com/kkkzh/DLGStream}.

Reconstructing dynamic human--object interaction scenes from monocular video is difficult because the human, manipulated object, and background obey different motion models while sharing the same pixels. Existing dynamic radiance-field and Gaussian-splatting methods often entangle these components, causing object motion to leak into the human or static scene, and monocular human reconstruction remains underconstrained in regions that are rarely observed. We present CoGS, a compositional Gaussian-splatting framework for monocular human--object scene reconstruction. CoGS decomposes the video into three coordinated branches: an articulated human initialized from a complete canonical prior, a rigid object field driven by an estimated object trajectory, and a static scene field regularized by weak scene-only planar primitives when available. A six-stage optimization schedule first stabilizes the human and object independently, then fuses them with the scene under full-image supervision, visibility-aware human anchoring, object silhouette and motion constraints, and delayed scene regularization. This design keeps each component responsible for its own geometry and motion while allowing photometric evidence to correct the final composite. Experiments on HOSNeRF and NeuMan show that CoGS improves both human--object interaction reconstruction and in-the-wild human--scene rendering, achieving stronger fidelity and perceptual quality across full-frame and human-focused evaluations. Code will be released upon publication.

Inverse rendering requires separating illumination from surface materials, which is highly ambiguous due to their tight coupling in observed images. While Gaussian Splatting is efficient for novel view synthesis, existing relightable methods approximate scene lighting using discrete point lights, global environment maps, or implicit representations. By ignoring the physical spatial extent of real-world emitters, these approaches produce incorrect light attenuation and unrealistic shadows. We present AEGIR (Area Emitters for Gaussian Inverse Rendering), a framework that explicitly models local area emitters within a relightable Gaussian Splatting representation. Joint optimization of emitters, materials, and geometry is challenging due to flexible emitter parameterization, which increases both the number of parameters and the ambiguity between illumination and materials. We address this by introducing a differentiable deferred rendering pipeline that integrates multiple importance sampling with targeted regularization. As a result, AEGIR accurately simulates local light transport and achieves more consistent decomposition. Experiments show that explicit area emitters improve illumination reconstruction and enhance downstream tasks, including novel view synthesis, controlled relighting, and virtual object insertion, particularly in scenes with complex local lighting.

We study the fundamental problem of learning a high-dimensional Gaussian truncated to an unknown halfspace. Lee, Mehrotra and Zampetakis (FOCS'24) recently obtained the first polynomial time algorithm for this problem, but their resulting sample and time complexity bounds are not optimal. Under non-trivial truncation, for any target accuracy $\varepsilon > 0$ and dimension $d$ we give an efficient algorithm that uses $n = \tilde{O}(d^2/\varepsilon^2)$ samples and learns the underlying Gaussian to error $\varepsilon$ in total variation distance. Our algorithm is also fast: its runtime is dominated by the cost of computing the empirical covariance matrix. Both our sample and time complexity are optimal in terms of $d$ and $\varepsilon$ even without truncation: in this regard, we can learn a Gaussian under halfspace truncation for free. The key ingredient behind our result is a novel reinterpretation of the low-degree moments of the truncated Gaussian in terms of a relative truncation parameter. This relative truncation parameter uniquely determines the parameters of the untruncated Gaussian and enables direct parameter recovery. This reinterpretation allows us to circumvent the time intensive projected stochastic gradient descent procedure that is widely used in learning under truncation.

The objective of this paper is to improve radiological gradings measured on MRIs of spines, by resampling scans so that the new view planes are better aligned with the target anatomy than the original sparse images. To this end, we adapt 3D Gaussian Splatting to form a volumetric reconstruction starting from sparse anisotropic MRIs, and imaging planes aligned with the anatomy relevant for clinical evaluation are then sampled and rendered. The novel view plane is optimal for diagnostic radiological grading of the target anatomy, whereas the original MRI is not. The resampled scans are then used to predict ordinal severity grades of localised stenosis conditions in spinal MRIs. We compare our method against Voxel Interpolation resampling, which takes the average of inverse-distance weighted nearest neighbour intensities for each target coordinate. Experiments show that across all stenosis conditions, resampled scans using Gaussian Splatting produce more accurate stenosis gradings compared to the raw scans which do not include the complete anatomy in-plane, as well as images resampled using Voxel Interpolation.

In this paper, we present a novel geometry-aware style transfer framework for 3D Gaussian splatting (3DGS) that simultaneously transfers appearance attributes and geometric structures. Unlike prior works that primarily focus on color-based stylization and often overlook structural adaptation, our method explicitly incorporates geometry adaptation through a decoupled optimization scheme that alternately updates color and geometry parameters. This strategy alleviates potential interference between color and geometry updates, leading to stable and consistent scene-level geometry transformation. The decoupled optimization is enabled by the proposed geometry-aware contrastive feature matching (GCFM). GCFM integrates RGB, depth, and edge cues into a contrastive objective and is employed in both optimization phases to effectively transfer structural characteristics from style images to Gaussian primitives. Extensive experiments show that our approach achieves superior performance in both qualitative fidelity and quantitative metrics, significantly outperforming existing 3DGS-based stylization methods. Our code is available at \href{https://github.com/oweixx/gast}{https://github.com/oweixx/gast}.

Despite modeling temporal motion, dynamic 3D Gaussian Splatting (3DGS) methods still inherit a static densification strategy that is ill-suited for dynamic scenes. This neglect of temporal behavior leads to under-reconstructed and blurry dynamic regions, as short-lived Gaussians receive sparse supervision and fail to densify effectively. We propose a Visibility-Aware Densification (VAD) framework that integrates temporal visibility into the densification process, ensuring that Gaussians are refined based on their actual temporal presence. A Temporally-Adaptive Thresholding (TAT) mechanism further adjusts each Gaussian's densification threshold according to its temporal lifespan, promoting balanced refinement of both static and dynamic regions. Finally, a Temporal Offset Warping (TOW) design enhances deformation capacity around temporal centers, extending the lifespan of highly dynamic Gaussians and facilitating more effective densification. Our approach achieves substantial improvements in the visual quality of dynamic regions, outperforming existing methods across three dynamic multi-view benchmark datasets. Moreover, the proposed VAD module generalizes across diverse dynamic 3DGS methods, consistently improving dynamic reconstruction as a plug-and-play component.

The quantum nature of light determines the inherent Poisson stochasticity of photon detection, which is ubiquitous in photography, microscopy, and astronomy. However, our controlled numerical studies reveal that the signal-dependency, heteroscedasticity, and statistical asymmetry of Poisson-mixed noise make it challenging for existing denoisers to learn. In contrast, i.i.d. Gaussian noise, with its statistical independence and symmetric distribution, is easier to model for networks. To address this gap, we propose Poisson2Gaussian (P2G), a noise Gaussianization method that explicitly converts complex real-world noise to i.i.d. Gaussian noise via probability density matching beyond low-order moments. We also design an unbiased denoising framework that synergizes P2G with downstream denoisers, ensuring convergence to the underlying signal without requiring paired clean data or explicit noise parameters. Extensive experiments demonstrate that P2G consistently achieves state-of-the-art performance across diverse datasets. In challenging scenarios where noise strongly deviates from Gaussian statistics, our method improves the PSNR by up to 0.75 dB. Notably, P2G is architecture-agnostic and can provide universal improvements for various denoisers. The source code will be publicly available.

Gaussian Processes (GPs) are a powerful tool for Bayesian time-series modeling, yet their cubic computational cost remains a severe barrier for application to long, high-cadence datasets in astronomy. While specialized scalable solvers like Celerite elegantly reduce this scaling to linear time, repeatedly evaluating the exact likelihood during iterative Bayesian sampling is a bottleneck for developing more complex models, like hierarchical or additive models in which Celerite is only one component. To make this inference computationally tractable, we introduce a generative surrogate framework. By utilizing a Variational Autoencoder (VAE) to learn a compressed representation of the Celerite prior, we map highly correlated stochastic dependencies into a low-dimensional, isotropic manifold. This transition completely bypasses exact covariance operations, shifting the computational burden to a rapid neural network forward pass. Through an extensive simulation study, we show that the generative surrogate accurately reproduces the structural fidelity of exact physical kernels like Celerite. Finally, we demonstrate embedding our VAE approximation into an additive model that combines Celerite and a hidden Markov model (HMM) for stellar flare detection in time series data of stars. We evaluate the joint VAE+HMM architecture against the exact Celerite+HMM framework on empirical astrophysical time series and demonstrate that the proposed methodology achieves significant reductions in computational time, enabling the rigorous, large-scale characterization of stellar flares across massive data archives.

Sparse-view computed tomography is a severely ill-posed inverse problem, where recent 3D Gaussian Splatting methods offer an efficient explicit representation for tomographic reconstruction. However, we find that projection-domain optimization can be misleading in this setting: the rendered projections may continue to improve while the reconstructed volume deteriorates. We identify this failure mode as Projection-Volume Fidelity Divergence (PVFD), a representation-level optimization drift caused by anisotropic Gaussian deformation and view-specific primitive co-adaptation under sparse Radon constraints. To characterize this behavior, we introduce geometry- and volume-level diagnostics that measure needle-like Gaussian degeneration and the stability of the voxelized density field. Based on these observations, we propose LADES, a ground-truth-free optimization controller for sparse-view Gaussian tomography. LADES combines Linearly Annealed Dropout, which applies strong stochastic masking in early training to disrupt premature primitive co-adaptation and gradually restores full capacity for structural consolidation, with Structure-Aware Early Stopping, which terminates densification according to the saturation of Gaussian population growth rather than validation PSNR. Experiments on sparse-view CT reconstruction show that LADES improves volumetric fidelity, suppresses structural degeneration, and substantially reduces training time while maintaining competitive projection accuracy. These results suggest that robust Gaussian-based tomography requires monitoring and controlling volumetric structure, rather than optimizing projection fit alone.

Jamming and spoofing pose significant threats to wireless and satellite navigation by disrupting radio-frequency (RF) signals and compromising availability and integrity. Robust RF interference direction finding through angle-of-arrival (AoA) estimation is therefore essential for detecting and localizing anomalous signals. Although data-driven methods perform well under line-of-sight (LoS) conditions, their performance degrades in practical environments due to non-line-of-sight (NLoS) multipath propagation. In this work, we propose a hybrid learning framework that incorporates physics-informed constraints into deep neural networks to improve the robustness of AoA estimation. A neural network is trained to estimate the azimuth and elevation of incoming signals received by a four-element antenna array, while a physics-informed loss enforces consistency between the predicted angles and inter-antenna phase differences under a plane-wave model. We further introduce a latent-space classifier to distinguish LoS from NLoS samples. Since inter-antenna phase differences under LoS propagation exhibit domain-invariant structure across environments, the physics-based loss is applied only to LoS samples, promoting physically consistent and domain-invariant representations without over-constraining the model in NLoS scenarios. In addition, domain-incremental learning (DIL) across NLoS environments with varying scatterer distributions improves cross-domain generalization. Evaluations on real-world datasets show that the proposed method reduces AoA estimation error by up to 6° in low-exemplar settings compared with DIL baselines.

Dynamic 3D Gaussian splatting faces a fundamental tension between motion consistency and visual fidelity. Deformation-based approaches preserve temporal correspondence but suffer from motion over-factorization, oversmoothing high-frequency dynamics. In contrast, 4D-primitive methods capture fine visual details yet incur temporal overparameterization, breaking object identity and leading to severe storage overhead. To resolve this, we introduce Multi4D, a framework for high-fidelity dynamic Gaussian Splatting based on multi-level competitive allocation. Instead of a monolithic representation, we distribute modeling capacity across three structured levels: static structure, persistent dynamic geometry, and transient appearance primitives. Through shared rasterization and residual-driven optimization, these levels dynamically compete to explain photometric error, enabling adaptive specialization without pre-assigned decomposition. This allocation preserves long-term motion consistency while capturing fine dynamic detail, achieving state-of-the-art rendering quality and real-time performance with significantly fewer dynamic primitives. Furthermore, because our representation explicitly tracks compact persistent Gaussians over time, semantic features can be embedded afterward, enabling Multi4D to achieve state-of-the-art 4D segmentation accuracy with an order-of-magnitude speedup. Project page: https://batfacewayne.github.io/Multi4D.io/

3D Gaussian Splatting (3DGS) has achieved state-of-the-art photorealistic rendering, but the representation gap prevents these assets from being physically interactive. Production-grade physics engines do not understand the 3DGS representation, while prior physics-for-3DGS methods are monolithic silos. These prior works are fundamentally limited, demonstrating only object-centric physics in isolated environments, such as on an ideal plane. They are incapable of interacting with complex static collision geometry or heterogeneous assets. We propose a novel framework that, for the first time, bridges this gap by enabling 3DGS assets to participate in scene-level, heterogeneous, multi-solver physical simulations. Our core contribution is a Representation Abstraction Framework that translates all diverse assets, including 3DGS, virtual meshes, and fluids, into a unified physical particle set. This abstraction is key to enabling complex behaviors, such as the non-rigid deformation of 3DGS assets, within a unified physics pipeline. This particle set, along with the static scene collision boundaries derived from scene capture, is processed within a solver-agnostic physics kernel. The physical results are then mapped back to drive each asset's specific visual reconstruction. This architecture unlocks capabilities impossible with prior art. We demonstrate complex, two-way interactions between deformable 3DGS assets, standard CG assets such as fluids and meshes, and large-scale captured static environments, showcasing realistic coupled phenomena that were previously unattainable.

We consider the parameter estimation problem in logistic regression with Gaussian design: the estimation of a fixed unknown parameter $θ^*\in \mathbb{R}^d$ ($\|θ^*\|_2\ge 1$) from $n$ i.i.d. samples $\{(x_i,y_i)\}_{i=1}^n$, where $x_i\sim N(0,I_d)$ and $y_i|x_i \sim {\rm Bernoulli}(1/(1+\exp(-x_i^\top θ^*)))$. Our main aim is to characterize the finite-sample estimation performance and convergence behavior of gradient descent (GD) on the maximum likelihood objective (i.e., the logistic loss). Under small $O(1)$ stepsize and $0$ initialization, we show that GD linearly converges to a small neighborhood of $θ^*$ achieving an $\ell_2$ error of order $O(\sqrt{\|θ^*\|_2^5d/n})$. This substantially goes beyond existing theoretical results that lack non-asymptotic estimation error rate and exhibit much slower parameter convergence. We also establish a faster local linear convergence to the same statistical error under a large $Θ(\|θ^*\|_2)$ stepsize. The main technical component is to show that the gradient of the logistic loss satisfies a certain approximate invertibility condition (AIC). To that end, we uniformly control the deviation of the gradient from its population counterpart by covering and peeling arguments, and then show that the population GD is a contraction by a delicate analysis based on the eigenvalues of population Hessian matrices. Finally, we build upon the recent work Matsumoto and Mazumdar (2025) and devise a novel efficient estimator that attains a sharper rate in high dimensions. This indicates that the existing non-asymptotic guarantees exhibit sub-optimal dependence on $\|θ^*\|_2$, and that in many regimes $Θ(\sqrt{\|θ^*\|_2d/n})$ is the tight estimation error rate. Numerical examples are provided to corroborate our theoretical results.

Robust obstacle segmentation is essential for the safety of intelligent robots, where LiDAR-based perception systems play a fundamental role in the robot-environment interaction. While extensive LiDAR-based approaches have demonstrated high performance on common obstacles in urban scenarios, their results on tiny obstacles such as curbs, gravel, and potholes remain unsatisfactory due to the significant similarity between tiny obstacles and inherent road undulations. Moreover, their segmentation accuracy even deteriorates sharply when the LiDAR scans suffer from degradation in challenging off-road scenes. To overcome these bottlenecks, we propose LOGOS, a LiDAR-only unified tiny obstacle segmentation system, which models the road surface as a continuous mixture of 2D Gaussian primitives and distinguishes tiny obstacles via high-presicion elevation estimation. Unlike existing Gaussian splatting methods that rely on iterative RGB training, LOGOS is a backpropagation-free LiDAR-only approach. It directly estimates Gaussian parameters via a freespace-aware initialization by incrementally pruning non-road primitives using smoothness constraints. Subsequently, pointwise signed distances are computed via a novel normal-aware elevation splatting function, ensuring robustness to both flat and sloped terrains. We evaluate LOGOS on a highly heterogeneous benchmark of point cloud frames collected from urban mobility scenarios and mining haulage off-road environments. These data are practically acquired using different LiDAR sensors and exhibit large variations in point density, terrain roughness, and obstacle types. Experiments on the road and off-road scenes demonstrate that LOGOS significantly outperforms other state-of-the-art methods, particularly in degraded point cloud regions and challenging off-road scenarios, while maintaining real-time efficiency.

Differential privacy (DP) has become the gold standard for ensuring the privacy protection of machine learning and statistical algorithms in recent decades. A plethora of algorithms and methods have been developed to enhance the utility of DP algorithms while maintaining the same level of DP. However, these are often overly complex or computationally ineffective. We propose a novel approach focusing on denoising the output of the simple additive Gaussian mechanism by adopting the idea of \textit{empirical Bayes estimation}. We highlight that the empirical Bayes approach can reduce the mean-squared error solely by taking the output of the Gaussian mechanism as input. Our numerical studies show that this simple yet powerful approach can be applied to improve upon various statistical problems, including histogram release, principal component analysis, and linear regression, often outperforming existing private algorithms.

Recent multimodal survival prediction models have demonstrated strong predictive performance by leveraging complementary information across modalities. However, such models generally assume data completeness and exhibit limited robustness toward missing modalities, which are frequently encountered in real-world clinical settings. We propose the Evidential Missing Modality Survival Fusion (EMMS) model for multimodal survival prediction under missing modalities. EMMS offers a straightforward, computationally effective approach to survival analysis without requiring a generative phase for missing data. By employing Dempster-Shafer theory and Gaussian Random Fuzzy Numbers for multimodal decision fusion, it considers both aleatoric and epistemic uncertainty alongside modality reliability for fusion. Moreover, the model treats missing modalities as vacuous evidence, preventing interference with available inputs and naturally reflecting increased uncertainty and calibrated predictions. Extensive experiments on four cancer datasets demonstrate state-of-the-art performance while providing calibrated and interpretable uncertainty estimates under incomplete multimodal observations, without introducing additional computational overhead.

Efficiently retrieving specific 3D instances from large-scale scenes via natural language prompts remains a formidable challenge in multimedia analysis. Existing approaches predominantly follow a "scene-level embedding" paradigm, which requires distilling high-dimensional semantic features into every 3D primitive. This strategy suffers from a fundamental architectural bottleneck: memory and computational costs scale linearly with scene complexity, inevitably triggering out-of-memory (OOM) failures in city-scale environments. To address this barrier, we propose QueryGaussian, a training-free framework for expeditious and scalable open-vocabulary 3D instance retrieval. Unlike holistic semantic distillation, QueryGaussian employs an instance-level query mechanism that decouples semantic understanding from geometric representation. Specifically, we leverage pre-trained 2D vision models to interpret user prompts and lift segmentation masks into 3D via a concurrent maximum-weight association strategy, ensuring semantic-visual consistency. To mitigate projection ambiguity, we introduce a temporal fusion module with multi-stage adaptive density clustering. Experimental results demonstrate that QueryGaussian not only matches the accuracy of state-of-the-art methods but also delivers a decisive efficiency leap, reducing GPU memory usage by over 70% and accelerating inference by 180x. Crucially, QueryGaussian enables expeditious instance retrieval on city-scale scenes containing tens of millions of Gaussians using consumer-grade hardware.

Accurate, site-specific channel information is crucial for optimizing next-generation wireless networks. Among various approaches, localized statistical channel modeling (LSCM), which models the channel multipath angular power spectrum (APS) from the reference signal received power (RSRP) measurement, has emerged as a state-of-the-art method tailored for efficient network optimization. However, despite its effectiveness, LSCM cannot predict APS at the vast majority of locations where no measurements are available, which significantly restricts its applicability in large-scale, real-world scenarios. To address this challenge, we present \emph{point-cloud-assisted tangent Gaussian splatting} (PC-TGS), the first framework to \emph{extrapolate} APS to unmeasured outdoor grids by integrating sparse radio measurements with dense LiDAR-based geometry. PC-TGS represents environmental scatterers as anisotropic 3D Gaussians, initialized and refined through a relaxed-mean reparameterization of the raw point cloud. A tangent-plane projection accurately maps each Gaussian into the local angular domain, while a depth-aware electromagnetic splatting process aggregates their contributions. To ensure practical deployment, we derive a closed-form Gaussian-weighted average (GWA) for APS bin integration and provide a provable error bound. { Evaluations on a LiDAR-scanned city-scale dataset (5M points, 6,310 RSRP samples) demonstrate that PC-TGS achieves better APS and RSRP prediction performance compared to state-of-the-art baselines and faster inference time for APS extrapolation task. These results highlight the potential of PC-TGS to enable geometry-aware and data-efficient channel prediction in large-scale wireless digital twins.

Barren plateaus are stated as an average-case phenomenon: pick an ansatz, initialize it naively, and concentration follows. This has led to the common view that a potential cure for barren plateaus is simply to initialize the parameters more carefully. Here we show that the situation is subtler. We introduce a first-moment framework that gives a simple operator-level diagnostic for when an initialization may escape the fully concentrated barren-plateau fixed point, and for comparing the biases induced by different initialization strategies. Our framework recovers several known initialization schemes such as identity and Gaussian initialization, but also shows that barren-plateau avoidance is highly non-unique. Indeed, many shifted, biased, and non-symmetric parameter distributions can avoid concentration, and these choices need not be equivalent. In fact, our results show that one can generate exponentially many families of inequivalent initialization strategies. Then, our numerics indicate that different first-moment-distinct initializations can lead to different attained minima, suggesting that avoiding barren plateaus via smart initializations can trade the exponential concentration problem for the challenge of selecting the right trainable pocket amongst many options.

We study the privacy of releasing functional posterior sample paths from a Gaussian process (GP) when the entire training set including covariates and responses is private. Unlike standard differential-privacy (DP) mechanisms that inject external noise, posterior sampling is intrinsically random and we show that this randomness provides useful privacy guarantees. We derive Rényi-DP guarantees separating privacy leakage through the posterior mean from a distinct channel induced by the data-dependent posterior covariance. The analysis identifies effective ridge regularisation and covariance scale as the principal privacy-controlling quantities and yields sharper guarantees in several regimes of practical interest as well as extensions to repeated and adaptive releases. Membership inference attacks confirm the predicted dependence on regularisation, covariance scale and the number of released paths. Utility experiments on downstream posterior sampling tasks identify noisy observation regimes where privacy-compatible regularisation preserves useful samples. Finally we identify large-data asymptotic regime in which the privacy parameter and posterior mean-square risk vanish simultaneously, yielding privacy for free. Together, these results provide a comprehensive characterisation of privacy and utility of GP posterior sampling.

Online 3D reconstruction from monocular image sequences is a challenging and ongoing research topic. 3D Gaussian Splatting (3DGS), leveraging its high-quality real-time rendering capability, empowers online 3D reconstruction to represent dense scenes with enhanced expressiveness, and thus holds great promise for a wide range of applications such as robotics and AR/VR. However, existing online 3DGS methods still suffer from some key challenges: fragile camera pose estimation due to the lack of global optimization, and low optimization efficiency in large-scale or long-sequence scenarios. To address these issues, we propose a robust and efficient online voxelized 3DGS reconstruction framework integrated with global $\text{Sim}(3)$ optimization, which enables reliable camera tracking and efficient global loop closure for both camera poses and voxelized 3DGS. To accelerate the convergence of the voxelized 3DGS, we further introduce a color residual learning strategy, which not only boosts optimization speed but also enhances rendering quality. Extensive experiments on diverse indoor and outdoor datasets demonstrate that our method achieves state-of-the-art performance in both camera pose estimation accuracy and rendering quality, while retaining real-time efficiency. Additionally, we develop and deploy a real-world UAV-based active reconstruction system grounded on our proposed method, validating its robustness and generalizability for practical online 3D reconstruction tasks. Our code and data are available at https://github.com/TrickyGo/MoonSplat.

Pansharpening aims to generate high-resolution multispectral (HRMS) images by fusing low-resolution multispectral (LRMS) and panchromatic (PAN) observations. Most existing deep learning methods treat pansharpening as fixed-grid prediction, which limits scale adaptation. To address this, we propose GSPan, a framework that introduces 2D Gaussian Splatting (GS) into pansharpening. Instead of directly predicting pixels, GSPan represents band-wise residual details as continuous and learnable 2D Gaussian primitives. We design a Dual-Stream Hierarchical Interaction (DSHI) architecture with a Spatial-Spectral Interactive Attention (SSIA) module to estimate these primitives from complementary PAN and MS observations. The predicted primitives are rendered as a residual detail field and injected into the upsampled MS image. This continuous representation allows GSPan to render fused images on arbitrary target sampling grids without scale-specific retraining. It further enables a Scale-Decoupled Asymmetric Inference (SDAI) strategy, which estimates primitives at a reduced resolution and renders the fused image at the target resolution for efficient large-scene pansharpening. Experiments on QuickBird, GaoFen-2, WorldView-3, and WorldView-3-4K datasets show that GSPan delivers state-of-the-art fusion performance. Moreover, SDAI markedly accelerates inference, achieving a favorable trade-off between computational efficiency and fusion quality. Our results demonstrate the potential of continuous Gaussian residual representations as a flexible and scale-decoupled alternative to fixed-grid prediction.

Gaussian width is a central geometric complexity measure in high-dimensional probability, compressed sensing, convex optimization, and learning theory. It quantifies the average extent of a set along random directions, thereby capturing the effective dimension of constraint sets, hypothesis classes, and descent cones. However, this notion is intrinsically Euclidean. Statistical models instead carry a natural Riemannian geometry induced by the Fisher information metric, where directions are scaled according to statistical distinguishability rather than ambient Euclidean length. We introduce Fisher width, a Fisher-geometric analogue of Gaussian width for statistical manifolds. At a parameter point $θ$, Fisher width replaces the Euclidean identity by the local metric tensor $G(θ)^{1/2}$, measuring the Gaussian width of the Fisher-rescaled set. This makes the resulting quantity sensitive to local statistical curvature and invariant under smooth reparameterizations. We develop the basic theory of Fisher width, showing that it retains key structural features of Gaussian width, including concentration, metric perturbation stability, and spectral comparison bounds with the Euclidean baseline, while also capturing anisotropic geometric effects invisible to Euclidean measures. As an application, we prove a generalization bound for Fisher-Lipschitz hypothesis classes and propose computable estimators, which we evaluate empirically on MNIST across three model classes. Fisher width is to statistical manifolds what Gaussian width is to Euclidean convex bodies. This work lays the foundation for studying complexity and learning on curved statistical manifolds.

Training embodied agents in the real world requires skilled operators and expensive hardware. Simulation environments offer a compelling alternative by enabling large-scale, cost-effective data augmentation. Consequently, rapidly constructing high-fidelity simulation scenes with a minimal sim-to-real gap has become a critical objective in robot learning. While reconstruction-based methods provide superior visual quality, current workflows are hindered by inefficient data acquisition and subpar foreground object extraction. We thus propose GASE, a highly automated system for simulation scene construction. GASE leverages multi-view video streams from panoramic camera arrays to enable rapid environment scanning. To ensure high-quality asset generation, our pipeline introduces a camera-pose-based strategy that robustly extracts objects across frames in the 2D domain, followed by high-fidelity scene inpainting. Foreground objects and the static background are then reconstructed independently and seamlessly imported into physics simulators for policy training. Extensive experiments demonstrate that GASE outperforms existing 3D Gaussian-based methods in segmentation accuracy by over 10% while achieving state-of-the-art inpainting quality. Furthermore, real-robot deployments across manipulation and navigation tasks maintains a performance gap of less than 10% compared to policies trained purely on real-world data. These results confirm that GASE provides an efficient and highly effective solution for bridging the sim-to-real gap. Code will be released.

Neural operators provide fast surrogates for PDEs but their deterministic predictions limit their use in tasks requiring uncertainty quantification (UQ), especially under geometric variability. Existing approaches primarily model uncertainty in network parameters, largely overlooking the geometry-aware representations learned by the operator itself. We propose REEF-GP (Residual on Embedded Features Gaussian Process), a post-hoc UQ framework that fits a GP to the residuals of a frozen neural operator whose internal embeddings define the kernel feature space. Rather than learning a separate feature map, REEF-GP adapts the operator's intrinsic coordinate-feature representations to construct geometry-aware uncertainties. To ensure stability and scalability on unstructured domains, REEF-GP incorporates spectral-normalized projections, heteroscedastic geometry-aware noise, and efficient subset-based training that avoids restrictive low-rank approximations. Across five PDE benchmarks with varying geometries, REEF-GP preserves predictive accuracy while achieving calibrated uncertainty estimates competitive with deep ensembles but at a fraction of their cost. Our approach remains robust under geometric distribution shift, with uncertainty concentrating in physically meaningful regions (e.g., shock fronts). Our results demonstrate that accurate and scalable post-hoc UQ for neural operators can be achieved directly in their learned feature space, offering a practical alternative to parameter-centric approaches.

Bayesian Neural Networks (BNNs) offer opportunities for greatly enhancing the trustworthiness of conventional neural networks by monitoring the uncertainties in decision-making. A significant drawback for BNN inference at the extreme edge, however, is the imperative need to incorporate Gaussian Random Number Generators (GRNG) within each neuron. State-of-the-art GRNG algorithms heavily depend on multiple arithmetic operations and the use of extensive look-up tables, posing significant implementation challenges for ultra-low power hardware implementations. To overcome this, this paper presents an innovative binary tree random number generator (TreeGRNG) allowing the use of ultra-low-cost constant comparators instead of arithmetic units. We further enhance the TreeGRNG proposal with a set of hardware-aware optimizations exploiting the Gaussian properties. The optimized TreeGRNG surpasses the State-of-the-Art (SoTA) in terms of distribution accuracy while achieving a 3.7$\times$ reduction in energy per sample and boosting the throughput per unit area by 5.8$\times$. Moreover, our TreeGRNG proposal possesses a distinct advantage over the current SoTA in terms of flexibility, as it easily enables designers to adjust the shape of the sampled probability distribution, extending beyond the capabilities of traditional GRNGs, opening the horizon towards future probabilistic AI designs. The TreeGRNG design is available open-source in the link

Single image dehazing continues to be hindered by the loss of high-frequency details and the difficulty of accurate physical scattering modeling. To address these issues, we propose Fi-Gaussian, a frequency-aware implicit Gaussian splatting network for single image dehazing. Unlike explicit rendering methods that rely on 3D point clouds, our method employs implicit Gaussian splatting to adaptively model the underlying distribution of clear images as a continuous representation in 2D feature space. The core of the network is a frequency-aware implicit Gaussian splatting module, which decouples low-frequency structural information and high-frequency texture information in the frequency domain and then performs adaptive Gaussian aggregation with complex-valued weights to recover fine details. In addition, a physics-driven scattering renormalization mechanism is introduced to estimate the transmission map and atmospheric light under the guidance of implicit Gaussian priors. Extensive experiments on multiple benchmark datasets demonstrate that Fi-Gaussian achieves state-of-the-art quantitative performance and produces visually superior dehazed results, validating the effectiveness of implicit Gaussian splatting for low-level vision tasks.

The growing demand for high-fidelity 4D hand-object interaction (HOI) data in embodied AI and spatial computing is currently bottlenecked by the reliance on pre-scanned object templates and physical markers. While recent methods have demonstrated promising results in reconstructing 4D hand-object interaction from videos, they are highly sensitive to initial estimates of hand and object poses. Yet, estimating these poses from images is challenging, in particular under severe occlusion which is inherent in hand-object interaction scenarios. We propose a novel system for the robust and accurate reconstruction of hands and objects from synchronized and calibrated multi-view videos without requiring any templates or markers. Our system consists of two main components with key innovations: (1) a multi-view feed-forward transformer model that aggregates cross-view geometry and temporal cues to provide a reliable, metric-consistent initialization for both poses and dense object geometry, and (2) a hand-object physics-aware Gaussian-based optimization framework to refine the initial estimates, integrating tetrahedral constraints, collision refinement, and appearance decomposition to produce physically plausible and visually accurate reconstruction. Validated on public benchmarks and an extensive internal dataset, our pipeline achieves highly robust, artifact-free reconstruction, providing an efficient foundation for automated 4D asset generation. Our project page are available at https://zyshen021.github.io/HOSTPG/.

Stochastic trace estimation is a standard tool for approximating the trace of a large-scale matrix available only through matrix-vector products. However, in tensor-structured settings, unstructured Gaussian or Rademacher test vectors may be prohibitively expensive to store and compute with, while cheaper rank-one tensor-product vectors can require sample complexities that grow exponentially with the tensor order. This work studies Gaussian random tensor train vectors as a structured alternative for stochastic trace estimation. We show that, with a suitable choice of the tensor train rank, random tensor train vectors recover dimension-independent guarantees for the Girard--Hutchinson estimator. In particular, a median-of-means variant with tensor train rank $r \geq d-1$ achieves the same dependence on the accuracy $\varepsilon$ and failure probability $δ$ as the classical estimator based on unstructured Gaussian vectors. We further prove an oblivious subspace injection result for sketches formed from independent Gaussian random tensor train vectors: tensor train rank $r\geq d-1$ and $\mathcal{O}(\varepsilon^{-2}(k+\log(1/δ)))$ samples suffice for a $k$-dimensional target subspace. Finally, we investigate the use of such sketches within the Nyström++ framework. We show that the resulting estimator can achieve the desired $\mathcal{O}(\varepsilon^{-1})$ sample complexity under an additional spectral-tail condition. These results provide clarififcation on both the potential and the limitations of random tensor train vectors in stochastic trace estimation.

We study the graph alignment problem for correlated Gaussian Orthogonal Ensemble (GOE) matrices, where the goal is to recover a hidden vertex permutation given two correlated symmetric Gaussian matrices $(A, B)$ with correlation $1/\sqrt{1+σ^2}$. While the maximum likelihood estimator is information-theoretically optimal, its computation, which reduces to a quadratic assignment problem, is intractable. Motivated by this, we analyze convex relaxations based on minimizing $\|AX - XB\|_F$ over the set of doubly stochastic matrices and the unit hypercube. We show that when the correlation parameter satisfies $σ= o(n^{-1/2}/\log^4 n)$, the solution of either relaxation $(X^\star)$ concentrates around the ground-truth permutation matrix $(Π^\star)$, i.e., $\|X^\star-Π^\star\|_F^2 = o(n)$, implying recovery of all but a vanishing fraction of vertices after simple post-processing. Combined with existing lower bounds, our results precisely characterize that $\|X^\star-Π^\star\|_F^2$ transitions from $o(n)$ for $σ= \tilde{o}(n^{-1/2})$ to $Ω(n)$ for $σ= \tildeΩ(n^{-1/2})$. In doing so, our analysis significantly tightens prior results and extends them beyond doubly stochastic relaxations.

In this work, we tackle the following question: Can neural networks trained with gradient-based methods achieve the optimal computational-statistical tradeoff in learning Gaussian single-index models? Prior research has shown that any polynomial-time algorithm under the statistical query (SQ) framework requires $Ω(d^{s^\star/2}\lor d)$ samples, where $s^\star$ is the generative exponent representing the intrinsic difficulty of learning the underlying model. However, it remains unknown whether neural networks can achieve this sample complexity. Inspired by prior techniques such as label transformation and landscape smoothing for learning single-index models, we propose a unified gradient-based algorithm for training a two-layer neural network in polynomial time. Our method is adaptable to a variety of loss and activation functions, covering a broad class of existing approaches. We show that our algorithm learns a feature representation that strongly aligns with the unknown signal $θ^\star$, with sample complexity $\widetilde{O} (d^{s^\star/2} \lor d)$, matching the SQ lower bound up to a polylogarithmic factor for all generative exponents $s^\star\geq 1$. Furthermore, we extend our approach to the setting where $θ^\star$ is $k$-sparse for $k = o(\sqrt{d})$ by introducing a novel weight perturbation technique that leverages the sparsity structure. We derive a corresponding SQ lower bound of order $\widetildeΩ(k^{s^\star})$, matched by our method up to a polylogarithmic factor. Our framework, especially the weight perturbation technique, is of independent interest, and suggests potential gradient-based solutions to other problems such as sparse tensor PCA.

Recent Gaussian splatting (GS) methods have shown that scenes can be represented efficiently with optimisable Gaussians for high-quality reconstruction and rendering. In this paper, building on this principle, we introduce SplatlessDF, a continuous distance field (DF) mapping framework that uses anisotropic Gaussian elements from a spatial rather than photometric perspective. SplatlessDF directly parameterises the Gaussians and optimises to recover a differentiable DF, enabling distances and gradients to be queried in the spatial domain for downstream robotic tasks such as navigation. Furthermore, SplatlessDF can be coupled with 2D Gaussian splatting (2DGS), providing a unified framework based solely on Gaussian primitives that can learn continuous DF and surface models and supports photometric rendering. We consider two settings: a standalone DF-only formulation and a joint DF-rendering formulation coupled with 2DGS. Experiments show that the standalone formulation provides efficient and accurate distance and gradient queries, while the joint formulation improves rendering geometry and simultaneously models a continuous DF. These results highlight the potential of GS-style representations not only for surface modelling and rendering but also for mapping representations suited to robotic navigation.

Markovian Whittle-Matérn fields have been convergently approximated by discrete Gauss Markov Random Fields (GMRFs) with sparse precision matrices using a Finite Element approximation of the two-parameter family, $$(κ^2 - Δ)^{α/2} u = \mathcal{W}, \;\; κ\in \mathbb{R}, \; α\in \mathbb{N}.$$ of SPDEs. Using recent developements in the analysis of Discrete Exterior Calculus (DEC), we present a different, yet closely related, convergent GMRF approximation to these Matérn fields over complete, boundaryless Riemannian manifolds discretized as well-centered simplicial complexes. This convergent method (i) is agnostic to $α, κ$ and thus allows a universal approximation scheme for the precision and covariance matrices of the entire $(α, κ)$-family of GMRFs, so they may be inferred rather than guessed. (ii) inherently models pointwise and piecewise-smoothed measurements of a random field and approximates both equally well (iii) is computationally independent of the interpolants used - it suffers no overhead if one convergent interpolant were replaced with another suitable interpolant over the same mesh. Furthermore, we show that, on discretizations that are well-connected in a precise sense, and volume-concentrated, the precision matrices are spectral functions of a graph-laplacian. We provide a low rank approximator to the family of such Matérn GMRFs and mention a use case: reducing the number of measurements needed to model the GMRF by compressed-sensing.

Estimation-of-distribution algorithms (EDAs) are a powerful class of evolutionary methods for black-box optimization, especially when little is known about the structure of the objective. Whereas classical evolutionary algorithms rely on hand-designed mutation and crossover operators, hard to devise for unknown problem structures, and a source of bias, EDAs sidestep operator design entirely: they fit a probability distribution to the best individuals and sample the next generation from it. EDAs are well established on continuous parameter spaces, but they have not previously been generalized to sparse ones, in which most coefficients of a good solution are exactly zero. Existing sparse black-box optimizers therefore reintroduce exactly what EDAs were designed to avoid: hand-crafted sparsity operators, bi-level schemes alternating between support set and active values, zeroing thresholds, and other baked-in assumptions. We close this gap by proposing multivariate zero-inflated Gaussian (ZIG) distributions as EDA sampling laws. A latent Gaussian model with separate indicator and value dimensions represents sparsity patterns, correlations among active parameters, and the interactions between the two, so sparsity patterns and active values are optimized jointly, hierarchy-free. We show that the latent parameters of this model are identifiable from observed samples, unlike in the missing-data settings where related constructions originate, and introduce practical amortized inversion-based estimators for them. The estimators accurately recover latent correlation structures, and on the Lunar Lander benchmark the resulting ZIG-EDA converges faster and reaches higher final returns than a dense Gaussian EDA, a hand-crafted sparse evolutionary algorithm, and an ad-hoc sparse EDA, while finding controllers with only a small fraction of parameters active.

We introduce a new simple model to study the fitness progress of Evolution Strategies (ES) in generic problems. In this model, we bypass the underlying fitness landscape and assume that the mutation of any individual produces an offspring whose fitness relative to the parent is given by an invariant distribution $Z$, such as a mean-shifted Gaussian. This serves as a prototypical model for the optimisation landscape when an evolution algorithm operates far from the global optimum. This simple model can be used to approximate the optimisation process for problems where it is intractable to model the exact fitness function, including tasks such as hyperparameter tuning in machine learning models. We rigorously analyse the expected growth rate $\mathcal{R}_μ$ of the continuous steady-state $(μ+1)$-ES in this model. Unlike comma-selection strategies, the steady-state $(μ+1)$-ES maintains overlapping generations, introducing complex mathematical dependencies among surviving parents that make it harder to analyse. We give a general technique to analyse the the $(μ+ 1)$-ES by constructing modified processes whose growth rates provably sandwich that of the original process. These modified processes are then easier to analyse but still close enough to the true process to give a tight bound on the expected growth rate. When $Z = \mathcal{N}(-δ, 1)$ and $μ\le e^δ$, we show that $\mathcal{R}_μ = \frac{\log^{1 + o(1)} μ}μ \mathcal{R}_1$.