3D Gaussian Splatting

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.

3D Gaussian Splatting (3DGS) is widely used to capture and render real scenes. Compositing objects from one capture into another has applications in many domains, such as VFX, architecture and interior design, or marketing. However, extracting an object from a source scene and naively pasting it into a target scene will fail to produce realistic results due to the different lighting conditions between the two scenes. To address this problem, we introduce a diffusion model that harmonizes naively composited images with inconsistent lighting. The model is trained with a heterogeneous dataset of image pairs (inconsistent composite input, consistent output), combining synthetic, generated, and real data. Our complete 3D solution allows a user to extract an object from the source scene and composite it into the target scene. From this, the (inconsistent) views of the target scene with the composite object are rendered. Our diffusion model harmonizes each one of these views, which are finally consolidated in a 3DGS representation with a post-optimization step. Our method provides visually compelling results, making object transfer between 3DGS easy to use and significantly improving quality compared to previous methods.

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/

Per-scene 3D Gaussian Splatting (3DGS) enables high-fidelity rendering, but practical robotic and AR scene capture pipelines often depend on external geometric initialization (e.g., SfM point clouds or depth estimates), which can be slow and brittle in on-site deployment. We present ACEsplat, a fast per-scene optimization framework that reconstructs 3D Gaussian representations from RGB images and camera poses only, without requiring external 3D priors (e.g., precomputed SfM models or supervised depth maps). ACEsplat uses a two-stage pipeline: (1) a self-supervised scene coordinate regression (SCR) module builds an internal geometry prior within 4--5 minutes; (2) SCR features and coordinate priors are fused by a lightweight Gaussian initialization head, followed by per-scene 3DGS optimization. On static-view rendering, ACEsplat achieves 29.11 dB PSNR on Wayspots with real-time SLAM poses and 33.20 dB on Cambridge Landmarks with SfM-refined poses. On RealEstate10K sparse-view novel view synthesis, it achieves competitive image fidelity under a challenging 2-view setting. ACEsplat completes scene-specific SCR mapping and 3DGS reconstruction within 15--25 minutes on a single GPU, making it a practical RGB+pose-only solution for rapid scene setup in robotics and mixed-reality applications.

3D Gaussian Splatting (3DGS) has emerged as a promising method for high-quality, real-time 3D reconstruction. To associate 3DGS with mesh representations, existing methods primarily focus on 3DGS-to-mesh reconstruction from multi-view images. In contrast, the problem of converting a mesh into 3DGS has received comparatively less attention. Instead of relying on heuristic strategies that bind 3D Gaussians to the mesh, we propose a novel white-box 3DGS construction framework, termed Mesh2GS, which generates 3DGS directly from mesh geometry based on plenoptic sampling theory, achieving Nyquist-level performance for high-quality global illumination rendering. Firstly, we propose a plenoptic sampling guided 3DGS construction strategy that theoretically derives the minimum sampling rate of the sampled views and the distribution of 3D Gaussians. Second, we propose a novel 3DGS update procedure with albedo--shading decomposition for efficient global-illumination capture. Finally, we introduce a neural illumination enhancement module to handle non-Lambertian effects. Experimental results demonstrate that our method surpasses state-of-the-art baselines and is practically effective for both real-time shared rendering and non-Lambertian effects capturing specular highlights. The project code will be released upon acceptance.

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.

Imaging objects hidden outside the direct line of sight expands the effective field of view and is critical for applications such as autonomous driving and robotic perception. Despite impressive progress in time-of-flight (ToF)-based non-line-of-sight (NLOS) imaging, real-world deployment remains challenging because practical measurements are often collected over spatially limited, arbitrarily shaped relay regions-conditions that violate the planar-wall and dense-sampling assumptions made by most existing methods. To address these limitations, we propose a LOS-guided NLOS imaging pipeline that imposes no geometric assumptions on the relay surface and naturally supports both confocal and non-confocal configurations. Our method represents the hidden scene using 3D Gaussian primitives and couples them with an efficient, differentiable transient rendering model, enabling end-to-end optimization directly from measured transients. We validate our approach on real-world measurements from both a public dataset and a custom-built capture system. Across settings, our method achieves state-of-the-art reconstruction fidelity under spatially limited, sparsely sampled conditions, and significantly outperforms existing methods on complex, arbitrary relay surface geometries.

3D Gaussian Splatting achieves exceptional real-time rendering, but its substantial computational and storage demands hinder widespread deployment. Existing accelerated paradigms often aggressively prune primitives for rapid convergence, causing severe loss of high-frequency details. To address this, we tackle the fundamental problem of achieving both exceptional rendering quality and ultra-fast reconstruction speed. In this paper, we propose ACE-GS, a progressive optimization framework tailored for accurate, compressed, and efficient scene representation. We realize that precise primitive management is the key to breaking this trade-off. Therefore, we first design a momentum consistency-guided densification strategy, strictly constraining primitive growth onto authentic geometric manifolds to avoid computational waste while significantly accelerating convergence. Building upon this efficient initialization, we deploy a statistical sensitivity-driven sparsification mechanism to precisely prune redundant primitives, yielding a further compressed footprint. Finally, to thoroughly compensate for the risk of micro-structure loss caused by the aforementioned strict primitive control, we introduce a cross-dimensional residual frequency compensation scheme that explicitly back-injects high-frequency error energy into primitive attributes, perfectly restoring sharp geometric details. Extensive experiments validate our superiority. While maintaining a highly compact scene representation, our system achieves up to 3.7 times training acceleration against the rapid framework Speedy-Splat. Requiring only 3 to 5 minutes to converge, ACE-GS secures the highest structural similarity and achieves a peak PSNR improvement of up to 0.89 dB over the original 3DGS, establishing a new benchmark for ultra-fast and high-fidelity novel view synthesis.

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.

3D Gaussian Splatting (3DGS) has emerged as a promising technique for novel view synthesis. However, 3DGS requires dense input views to achieve high-quality rendering. In sparse-view scenarios, 3DGS often prones to overfitting, resulting in noticeable artifacts and degraded rendering quality. Previous methods explore to address this issue by introducing additional priors (e.g. depth priors) or integrating regularization techniques (e.g. Dropout). However, these methods are often applied without principled guidance. In particular, prior-based augmentation typically samples novel viewpoints randomly, while Dropout-based regularization randomly removes Gaussians. The compounded randomness introduces uncertainty and instability, limiting the fidelity of novel view synthesis. In this paper, we propose a novel method for sparse-view 3DGS that incorporates Fisher Information to quantitatively guide the utilization of geometric priors and regularization. Specifically, our method comprises two key components: (1) Stereo augmentation with Fisher Information. By leveraging Fisher Information, we actively select most informative supporting views and use depth priors to curate reliable pseudo ground truths, which reduces randomness in augmentation and improves stability and rendering fidelity; (2) Uncertainty-aware regularization. We reduce the instability of Dropout-based regularization by using Fisher Information to quantitatively measure the uncertainty of each 3D Gaussian, and adaptively adjust the removal probability, leading to more stable and effective regularization. With these two components, our method effectively mitigates overfitting and improves the stability of optimization in sparse-view 3DGS, resulting in superior rendering fidelity. Extensive experiments show that our method achieves state-of-the-art performance in sparse-view novel view synthesis benchmarks.

Gaussian Splatting has enabled real-time neural rendering, yet existing LiDAR-inertial-visual (LIV) Gaussian mapping pipelines remain fragile under illumination changes and texture-deficient scenes due to their reliance on RGB photometric cues. We present LIT-GS, a LiDAR-inertial-thermal Gaussian Splatting framework that injects LiDAR-derived plane geometry as an explicit constraint in both pose/structure refinement and Gaussian optimization. Specifically, we exploit LIV visual map points as confidence-aware cross-modal anchors to establish reliable thermal-LiDAR associations, and incorporate weighted LiDAR point-to-plane residuals into bundle adjustment to jointly refine camera poses and 3D points under weak thermal supervision. Building on the refined structure, we further introduce a LiDAR-plane-regularized differentiable splatting objective that constrains rendered 3D points to align with locally observed planes, mitigating surface thickening and structural drift in low-contrast thermal imagery. Experiments on proprietary sequences and public datasets demonstrate that LIT-GS consistently improves geometric accuracy and rendering quality over state-of-the-art LIV-based Gaussian Splatting baselines, particularly in challenging lighting conditions.

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.

Dynamic 3D hand reconstruction from egocentric videos is essential for next-generation computing platforms such as AR/VR and AI glasses. Despite its importance, most prior works focus either on multi-view 3D hand reconstruction or on 4D human body reconstruction. Egocentric 4D hand reconstruction remains challenging due to fast head motion, rapid hand dynamics, severe occlusions, and inherent ambiguity from single-view observations. To address these challenges, we introduce Hand-4DGS, the first feed-forward framework for reconstructing dynamic 4D hands directly from egocentric videos, enabling both fast (~60 FPS) inference and strong generalization. Our approach incorporates a mesh-guided representation for structural priors and temporal convolutions to model dynamic motion. We evaluate our framework on two challenging egocentric datasets, H2O and ARCTIC, and demonstrate significant improvements over baselines. Our method benefits from the generalization capability of feed-forward networks and effective 2D image supervision through Gaussian splatting, without requiring expensive 3D hand pose ground-truth annotations.

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.

3D Gaussian Splatting (3DGS) enables high-fidelity and real-time 3D scene reconstruction, but scaling training to large-scale scenes requires optimizing hundreds of millions of Gaussians across multiple GPUs. Existing distributed approaches either partition scenes into isolated regions, causing global inconsistency, or rely on global Gaussian-level exchanges, which lead to substantial growth in inter-GPU communication and quickly dominate iteration time. We propose Splaxel, a communication-efficient distributed 3DGS training framework based on pixel-level local rendering and global composition. Instead of synchronizing Gaussians, each GPU renders its local subset and exchanges only partial pixel values, maintaining mathematical consistency while keeping communication cost stable as the scene size increases. Splaxel further reduces pixel-level redundancy through geometric and transmittance visibility prediction and improves GPU utilization via conflict-free camera-view consolidation. Evaluated on large-scale datasets with up to 120M Gaussians, Splaxel achieves up to 7.6$\times$ speedup over the state-of-the-art distributed 3DGS framework while preserving high reconstruction quality.

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.

Existing low-light image enhancement methods often face a bottleneck between the representation capacity of illumination-field modeling and computational complexity. To address this issue, this paper proposes an Adaptive Illumination Gaussian Splatting Network (AIGS-Net), an ultra-lightweight architecture for fast low-light enhancement. Unlike conventional static priors, AIGS-Net constructs an input-adaptive 2D Gaussian Splatting illumination field. The opacity of Gaussian basis functions is dynamically modulated by relative luminance statistics of the input image, and spatially varying illumination compensation is rendered through ordered alpha compositing. To guide adaptive illumination compensation efficiently, a zero-parameter nonlinear multiscale contextual encoding module is introduced to extract low-frequency structures and local contrast cues without additional convolutional weights. To suppress noise amplification and sensor-induced color bias, AIGS-Net integrates noise-mask estimation, locked single-channel Gamma mapping, cross-channel consistency regularization, and target color-alignment constraints. Experiments on LOL and LSRW benchmarks show that AIGS-Net improves detail recovery and color fidelity while requiring only approximately 40 learnable parameters, achieving an effective trade-off between enhancement quality and extreme inference efficiency.

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

3D Gaussian Splatting (3DGS) has significantly advanced real-time novel view synthesis by representing scenes as dense collections of anisotropic 3D Gaussian primitives. However, the irregular spatial distribution of Gaussians often leads to poor GPU utilization, as warp divergence and redundant computation degrade rendering performance. To address this, we present Local-GS, a warp-coherent rendering paradigm that, organizes Gaussian primitives with respect to SIMT (Single Instruction, Multiple Threads) execution boundaries rather than scene geometry. Specifically, we propose three warp-coherent stages: a hoisting stage that precomputes shared parameters at tile level, a culling stage that discards warps with no contribution, and a blending stage that replaces per-pixel branching with a uniform instruction stream. Across extensive benchmarks on multiple datasets, Local-GS improves efficiency without compromising quality. As a plug-and-play optimization, it provides additional performance gains to all tested baselines, culminating in a $7.76\times$ speedup on Deep Blending scenes.

Long-tail hazardous scenarios are essential for safety-oriented autonomous driving, yet they are difficult to collect and reproduce at scale. Editable 3D Gaussian Splatting (3DGS) simulation offers a promising alternative by reconstructing real driving scenes and supporting controllable scene editing. However, edited 3DGS-rendered videos still suffer from a significant Sim-to-Real gap, including rendering artifacts, degraded foreground assets, inconsistent illumination, and temporal flickering. Existing restoration and video generation methods are insufficient for this task, as they often fail to jointly repair 3DGS-specific artifacts, improve visual realism, and ensure temporal consistency. To fill this gap, we propose RealityBridge, a structure-preserving and asset-aware Sim-to-Real framework for edited 3DGS driving videos. RealityBridge uses multimodal controls, including rendered videos, foreground masks, edge maps, and semantic masks, together with a lightweight GateNet for adaptive condition allocation across backbone layers. We further construct targeted training data and introduce autoregressive long-video training with reward-guided post-training to improve restoration quality, temporal stability, and hallucination suppression. Extensive experiments on internal and public driving datasets show that RealityBridge outperforms existing methods in artifact removal, illumination harmonization, and long-sequence temporal consistency.

Obstacle avoidance is essential for safe navigation and motion planning. Recent radiance field reconstruction methods enable object detection and modeling with high fidelity, but remain too memory- and compute-intensive for on-board perception-based path planning. To address these limitations, we propose PolyMerge to convert a large, photorealistic 3D Gaussian Splatting (3DGS) model of a scene into a lightweight representation of convex polytopes whose union provably over-approximates all obstacles in the original 3DGS model. PolyMerge tunes the polytope count to trade off conservativeness and compute cost, and integrates with control barrier functions (CBFs) to plan collision-free paths. We showcase PolyMerge in simulation and hardware experiments on a Crazyflie drone, which uses PolyMerge to compute and follow safe trajectories in real time under severe onboard compute constraints, outperforming baselines in speed while guaranteeing safety. For our code and videos, visit https://athlon76.github.io/PolyMerge-website/.

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.

Existing single image dehazing methods are often constrained by computational redundancy in pixel-level optimization and the lack of physical interpretability in implicit neural networks. These limitations hinder the balance between representation efficiency and reconstruction fidelity. To address these issues, we propose Dehaze-GaussianImage, the first zero-shot framework that introduces 2D Gaussian Splatting (2DGS) into the image dehazing domain to break the traditional pixel-grid processing paradigm. Distinct from static convolutional neural networks (CNNs) or Transformers, our approach models hazy images as continuous and dynamically evolvable anisotropic Gaussian fields. Specifically, we propose a novel reconstruction-decoupling zero-shot learning strategy that embeds the atmospheric scattering model into the Gaussian parameter space. This strategy drives Gaussian primitives to adaptively split, clone, and prune during optimization, achieving geometric-level decoupling of the transmission medium and clear textures. Furthermore, explicit structure-preserving constraints are introduced to suppress artifacts commonly caused by traditional physical priors. Experimental results demonstrate that the proposed method achieves state-of-the-art (SOTA) performance in a fully unsupervised manner with minimal parameters, highlighting the potential of explicit Gaussian representation for low-level vision tasks.

Low-light image enhancement aims to recover clear images from low-illumination observations and is crucial for high-level downstream vision tasks. However, existing methods frequently encounter color distortion and structural artifacts when balancing global smooth illumination adjustment and local high-frequency detail recovery. To address these issues, we propose CGS-Retinex as the first low-light image enhancement framework based on explicit-implicit joint modeling. Our framework deeply integrates continuous Gaussian splatting with Retinex theory. Specifically, we represent the image grid as a continuous parameter field and propose a continuous Gaussian renderer to estimate the spatially continuous global illumination distribution. This approach fundamentally eliminates grid artifacts caused by discrete Gaussian sampling. Furthermore, we introduce an implicit neural representation to model reflectance independently. We leverage shallow high-frequency features to guide the network in accurately reconstructing degraded texture details. Within the Retinex framework, we incorporate physics-inspired brightness consistency constraints and illumination smoothness regularization to enable explicit illumination and implicit reflectance to maintain proper exposure and achieve high-fidelity recovery of high-frequency structures and colors. Extensive experiments demonstrate that CGS-Retinex significantly suppresses dark-region noise and overexposure while achieving exceptional high-frequency structural fidelity and color restoration by precisely decoupling illumination and texture. This work establishes a novel continuous physical representation paradigm for low-light image enhancement.

Consumer-level applications require fast optimization of 3D Gaussian Splatting (3DGS) with high-fidelity novel view rendering. However, existing 3DGS acceleration approaches still incur substantial computation on redundant pixels while sacrificing fine details. In this paper, we present TurboGS, an error-guided training framework that accelerates 3DGS by concentrating optimization on perceptually informative pixels. TurboGS is built upon four core components: (1) a tile-wise sparse pixel sampling, which, driven by multi-view reconstruction errors during training, prioritizes challenging regions and skips well-reconstructed ones to avoid redundant gradient computation; (2) a tile-wise structure-aware loss with sparse Normalized Cross-Correlation, which provides sparse yet effective supervision to preserve fine details and stabilize training; (3) an error-driven Gaussian density control strategy, which dynamically allocates model capacity and removes redundant primitives; and (4) a tailored hybrid optimizer that couples Hessian-informed updates with Adam moment damping to stabilize and improve convergence under sparse supervision. Experiments on standard benchmarks demonstrate that TurboGS can deliver on par or superior rendering quality within 100 seconds on a single RTX 5090 GPU card (up to 10x training speedup over vanilla 3DGS).

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/.

3D Gaussian Splatting (3DGS) has shown strong potential for high-fidelity talking head synthesis. However, enabling fine-grained, interpretable, and editable facial expression control remains fundamentally challenging due to intrinsic conflicts between speech-driven facial dynamics and explicit expression signals. Existing methods rely on implicit multimodal fusion, leading to spatial entanglement and temporal instability. We present EmoZone-Talker, a novel framework that reformulates audio-driven facial animation as a structured spatial-temporal coordination problem under cross-modal conflicts. Our approach introduces an explicit spatial disentanglement and temporal dynamics modeling of facial motion. Specifically, we propose Synergy Zones with Prioritized Attention Bias (SZ-PAB) to explicitly decouple modality contributions via region-wise constraints guided by anatomical priors, and a Channel-Independent Temporal AU Encoder (CIT-AE) to model temporally coherent AU dynamics. By integrating these representations into 3D Gaussian deformation, EmoZone-Talker enables precise and interpretable control over facial expressions. Extensive experiments demonstrate that our method improves expression controllability and realism, with notable gains in upper-face accuracy and temporal coherence, while preserving high rendering quality and accurate lip synchronization. Code will be publicly released to facilitate reproducibility and further research.

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 present MoVerse, a real-time video world model that creates an interactively navigable scene from a single narrow-field-of-view image. This setting is challenging because the input observes only a small fraction of the environment, while interactive roaming requires a complete surrounding world, persistent geometry, controllable camera motion, and temporally coherent high-fidelity observations. MoVerse addresses this problem by separating world construction from observation rendering. It first expands the input into a gravity-aligned 360$^\circ$ panorama with topology-aware diffusion, closing the missing field of view before 3D reasoning. It then lifts the panorama into a persistent 3D Gaussian scaffold using panoramic geometry-aware residual prediction, yielding a dense and directly renderable spatial memory. Finally, a Gaussian-conditioned video renderer translates scaffold renderings along user-specified camera trajectories into photorealistic video. To make this renderer practical for interaction, we train a bidirectional diffusion teacher for high-quality conditional rendering and distill it into a causal autoregressive student for bounded-latency streaming. This design combines the controllability and long-range consistency of explicit 3D representations with the perceptual quality of generative video models. MoVerse supports real-time scene roaming at 8FPS on a single NVIDIA RTX4090 GPU, demonstrating a practical path toward single-image world creation with interactive video output.

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 $\mathcal{R}_μ = \frac{\log^{1 + o(1)} μ}μ \mathcal{R}_1$.

This paper proposes a novel loss concept for supervised classification tasks. Rather than enforcing a direct mapping from each input sample to a single assigned label, we define an optimization objective over all classifier outputs as a bimodal Gaussian distribution. This softer target formulation implicitly captures class ambiguity, mitigates overfitting, and encourages the learning of more robust decision boundaries, all without requiring additional label information. Experimental results demonstrate consistent improvements in robustness, with particularly pronounced gains in low-data regimes, while requiring only minimal modifications to standard training pipelines.

We give a simple, unified, and nearly tight bound for sampling arbitrary logconcave distributions from a warm start using the In-and-Out algorithm along with exponential lifting. The main new ingredient in the analysis is an improved bound on the Poincaré constant of a lifted distribution. As a consequence, the resulting convergence rate is nearly tight for both constrained settings (e.g., Gaussian restricted to a convex body) and well-conditioned settings (e.g., strongly logconcave and smooth densities).

Feed-forward 3D Gaussian Splatting (3DGS) removes the need for time-consuming per-scene optimization required by traditional 3DGS. However, existing feed-forward approaches struggle with real-world photo collections that include diverse lighting conditions and transient objects. In this paper, we present Wild3R, a feed-forward approach for unconstrained sparse photo collections. The main bottleneck is the lack of training data that provides multiple viewpoints, a variety of illuminations, and transient variations necessary for learning robust scene representations. To address this, we introduce the WildCity dataset, which comprises 200 scenes, 170 lighting conditions, and transient objects, resulting in 337,500 images in total. By leveraging the dataset, our model learns appearance consistency across viewpoints conditioned on reference views, while removing transient content. Extensive experiments demonstrate that our method outperforms existing feed-forward approaches and achieves results competitive with prior per-scene optimization-based methods.

Low-light novel view synthesis is challenging because dark multi-view images contain noise, weak structural detail, and compressed dynamic range. Recent 3D Gaussian Splatting (3DGS) methods address these challenges by generating pseudo ground-truth (pseudo-GT) images as supervision targets when paired normal-light references are unavailable. Existing pseudo-GT methods apply a uniform linear gain to all pixels, which clips bright regions while providing insufficient enhancement in dark regions, limiting reconstruction quality. We observe that nonlinear tone mappings, long established in 2D low-light enhancement, have not been explored for pseudo-GT generation in 3D reconstruction. Accordingly, we propose a scene-adaptive nonlinear tone-curve framework that replaces linear pseudo-GT with nonlinear alternatives. The framework introduces percentile-based normalisation for scene-agnostic curve application, a scene-adaptive offset for automatic black-level adjustment, and two complementary curves: Adaptive SoftExp (ASE), a bounded exponential curve, and Adaptive Poly3 (AP3), a data-driven cubic polynomial. The module changes only the pseudo-GT computation and leaves the 3DGS backbone unchanged. Experiments on three benchmarks covering 21 scenes show that both curves consistently outperform the linear baseline with PSNR improvements up to +4.34 dB on LOM and +3.25 dB on RealX3D. Both curves achieve similar performance despite their different mathematical forms, suggesting the improvement is curve-agnostic. Code is available at https://github.com/lvmingzhe/adaptiveToneCurve

While 3D Gaussian Splatting (3DGS) achieves impressive real-time rendering, it frequently struggles to synthesize high-frequency textures, a limitation heavily exacerbated in memory-constrained and rate-distortion-optimized (RDO) pipelines. To address this, we propose a versatile 2D perceptual wrapper that enhances the rendered outputs of existing 3DGS representations in a content- and view-dependent manner. Our method leverages a lightweight synthesis network conditioned on pseudo-random Gaussian noise to synthesize perceptually plausible textures. Supervised by Wasserstein Distortion, the network learns to match local feature statistics rather than strictly enforcing pixel-wise reconstruction fidelity, effectively mitigating the blurriness inherent in standard frameworks. We demonstrate the broad applicability of our plug-and-play approach across vanilla, memory-constrained, and RDO 3DGS methods. Comprehensive subjective and objective experiments confirm that our method significantly improves over existing baselines, yielding superior perceptual quality at sharply reduced file or model sizes.

Klindt, LeCun, and Balestriero (arXiv:2605.26379) proved that Joint-Embedding Predictive Architectures (JEPAs) achieve linear identifiability, the linear recovery of the world's true latent variables, if and only if the world's latent dynamics follow a Gaussian, stationary process. This Gaussian boundary implies a fundamental limit on temporal consistency: for any non-Gaussian physical system, the representation error of a statistical World Model grows monotonically with time. We prove that this limit is an artifact of the statistical alignment mechanism, not a property of World Models in general. We introduce the Physics-Grounded Symbolic Architecture (PGSA) and prove three results: (1) a PGSA achieves exact linear identifiability for all physical regimes, regardless of the latent distribution; (2) the per-step error of a PGSA is bounded by numerical precision alone; and (3) as a direct consequence, a PGSA maintains temporal consistency for an unbounded number of transitions, a property we term near-infinite temporal consistency. We further prove that statistical World Models cannot achieve this property for any non-Gaussian system, regardless of model capacity or the volume of training data. The algebraic cores of four of the theorems are formalized in Lean 4 with Mathlib4 v4.31.0 (zero sorry placeholders); the Klindt et al. converse is taken as an external premise. The contrast establishes that symbolic grounding in the causal generator of the world's dynamics is the sufficient condition and, in non-Gaussian regimes, the only condition for near-infinite temporal consistency.

We study the task of density estimation, where we hope to accurately estimate a probability density from $n$ samples. A textbook method for density estimation in total variation distance is the minimum-distance estimator approach, where we conclude both the algorithm and the analysis merely from bounding the VC dimension of a particular concept class (the so-called Yatracos class). While this technique has originally yielded sharp guarantees primarily for total variation distance, in this work we extend the minimum-distance estimator approach for learning within Hellinger distance. Our main observation is that we may produce an analogous recipe for Hellinger (where we only require bounding the VC dimension of a related concept class) by drawing connections to recent results yielding reverse data processing inequalities. This recipe is flexible enough to accommodate fast algorithms originally designed for total variation distance; by modifying the approach of Acharya et al. (2017) we conclude the first near-linear time algorithm for learning classes including univariate mixtures of log-concave densities and mixtures of Gaussians (with arbitrary variances), with near-optimal sample complexity.

Gaussian splatting methods have become increasingly popular for neural reconstruction of the real world. However, they are often limited in scale and resolution due to compute and memory constraints. We present a multi-GPU Gaussian splatting approach that scales reconstruction to higher resolutions and larger scenes while abstracting away the code complexity typically associated with distributing a model. To accomplish this, we propose a PyTorch backend that distributes the Gaussian parameters and splatting operators across GPUs via CUDA unified memory and NVLink. Because distribution occurs at the operator level, the model code requires no explicit cross-device communication. More broadly, the backend exposes multiple GPUs as an aggregate PyTorch device and supports other PyTorch operators. We demonstrate city-scale reconstructions with street-level detail consisting of over 1 billion Gaussian splats, more than 25 times as many as the current state of the art.

We introduce TRON, a rendering framework that combines 3D Gaussian ray tracing with neural rendering to enable realistic and controllable rendering of real-world 3D scenes under novel lighting, dynamic object motion, object insertion, and material editing. Prior approaches that rely solely on physically based rendering (PBR) of Gaussian representations struggle to achieve realistic relighting due to imperfections in reconstructed geometry, material estimates, and light transport estimation. At the same time, neural rendering methods often lack an explicit scene representation, limiting their ability to support interactive editing with fine-grained manipulation. TRON bridges these two paradigms. We use intrinsic decomposition priors from a learned inverse rendering model to regularize the material properties of a Gaussian field, and repurpose a ray tracer to provide radiometric guidance rather than final pixels. By treating this output as a structured 3D scaffold, we empower a lightweight neural renderer to bridge the domain gap between shading-model constrained estimates and photorealistic output. Our key insight is that the combination of explicit 3D knowledge with robust material priors provides speed and controllability, while neural rendering enables the synthesis of photorealistic images. To support real-world scenarios, we train our neural renderer with a multi-stage strategy consisting of large-scale pretraining and targeted fine-tuning on a newly constructed dataset of 2.1M rendered synthetic and real-world frames from 3D reconstructions. TRON outperforms Gaussian-based relighting methods in realism, and prior neural renderers in editability and speed. To the best of our knowledge, TRON is the first method to enable practical interactive applications in captured 3D environments, offering realistic appearance under dynamic geometric, lighting and material conditions.

We study the task of agnostically learning general (as opposed to homogeneous) ReLUs under the Gaussian distribution with respect to the squared loss. In the passive learning setting, recent work gave a computationally efficient algorithm that uses $poly(d,1/ε)$ labeled examples and outputs a hypothesis with error $O(opt)+ε$, where $opt$ is the squared loss of the best fit ReLU. Here we focus on the interactive setting, where the learner has some form of query access to the labels of unlabeled examples. Our main result is the first computationally efficient learner that uses $d polylog(1/ε)+\tilde{O}(\min\{1/p, 1/ε\})$ black-box label queries, where $p$ is the bias of the target function, and achieves error $O(opt)+ε$. We complement our algorithmic result by showing that its query complexity bound is qualitatively near-optimal, even ignoring computational constraints. Finally, we establish that query access is essentially necessary to improve on the label complexity of passive learning. Specifically, for pool-based active learning, any active learner requires $\tildeΩ(d/ε)$ labels, unless it draws a super-polynomial number of unlabeled examples.

Deep Neural Networks (DNNs) typically require extensive datasets for effective training. In the medical domain, acquiring large-scale data is often challenging due to privacy concerns and the rarity of certain diseases. To address this data scarcity, we investigate the efficacy of training DNN models using synthetic data, generated based on domain-specific medical knowledge. Specifically, we develop a knowledge-driven Gaussian-composition synthesis algorithm for single-lead II ECGs, in which each heartbeat is represented by Gaussian-shaped P, Q, R, S, and T wave components. Using this simulator, we generate synthetic data for four abnormal electrocardiogram (ECG) classes: atrial fibrillation (AF), atrial flutter (AFLT), premature ventricular complex (PVC), and Wolff-Parkinson-White Syndrome (WPW). We evaluate the utility of this synthetic data by conducting abnormal ECG classification using ten different DNN architectures. Our results demonstrate that synthetic-to-real training improves classification performance for three of the four target abnormalities, with the largest architecture-averaged gain of $33.2\%$ observed for AFLT. Further analysis reveals that the performance enhancement from synthetic data is more pronounced with smaller real-world datasets. These findings suggest that domain-knowledge-based synthetic ECGs can serve as a useful pre-training resource, particularly in scenarios where real-world data are limited or difficult to obtain.

Forecasting the future evolution of dynamic scenes is crucial in autonomous driving. However, existing feed-forward paradigms are primarily designed for interpolation. When extended to future extrapolation, they suffer from ghosting artifacts under large displacements and are constrained by simplified motion assumptions or strict future priors. To overcome these challenges, we propose Envision4D, a fully self-supervised feed-forward framework for pose-free future extrapolation. Specifically, we introduce a Future Pose Prediction module that infers future camera parameters via an iterative denoising process. Furthermore, to capture non-linear dynamics, we propose In-layer Temporal Attention and employ Conditioned Motion Lifting, which transforms the highly uncertain extrapolation process into robust relational mappings. Finally, a Progressive Training Strategy is utilized to stabilize unsupervised motion learning against error accumulation. Extensive experiments demonstrate that Envision4D achieves state-of-the-art performance, significantly outperforming existing methods in future view synthesis.

Reconstructing dynamic and interactive 3D scenes from real-world observations remains a fundamental challenge in computer vision and robotics. While recent advances in 3D Gaussian Splatting have enabled high-fidelity static reconstruction, extending it to interactive environments with articulated robots and manipulable objects remains difficult due to complex contact interactions and abrupt pose changes. To address these challenges, we introduce ManiSplat, a unified framework that reconstructs controllable and decoupled Gaussian digital twins directly from monocular ego-view robotic videos. Our method introduces a Graph-Structured Disentangled Representation that separates the robot, objects, and background into independently optimizable Gaussian subfields organized within a scene graph. To ensure stability, we propose a Task-Oriented Spatio-Temporal Alignment module that leverages the inherent logic of manipulation tasks-alternating between Motion and Skill phases-to construct accurate pseudo-ground-truth trajectories. Finally, a joint photometric-geometric optimization ensures the reconstructed scenes are temporally coherent, physically consistent, and simulation-ready. Extensive experiments demonstrate that our approach reconstructs interaction-driven dynamic scenes with high fidelity and controllability, effectively supporting downstream robotic tasks and policy learning.