3D Gaussian Splatting

By far the most common way to estimate an expected loss in machine learning is to draw samples, compute the loss on each one, and take the empirical average. However, sampling is not necessarily optimal. Given an MLP at initialization, we show how to estimate its expected output over Gaussian inputs without running samples through the network at all. Instead, we produce approximate representations of the distributions of activations at each layer, leveraging tools such as cumulants and Hermite expansions. We show both theoretically and empirically that for sufficiently wide networks, our estimator achieves a target mean squared error using substantially fewer FLOPs than Monte Carlo sampling. We find moreover that our methods perform particularly well at estimating the probabilities of rare events, and additionally demonstrate how they can be used for model training. Together, these findings suggest a path to producing models with a greatly reduced probability of catastrophic tail risks.

As 3D Gaussian Splatting (3DGS) gains attention in immersive media and digital content creation, assessing the aesthetics of 3D scenes becomes important in helping creators build more visually compelling 3D content. However, existing evaluation methods for 3D scenes primarily emphasize reconstruction fidelity and perceptual realism, largely overlooking higher-level aesthetic attributes such as composition, harmony, and visual appeal. This limitation comes from two key challenges: (1) the absence of general 3DGS datasets with aesthetic annotations, and (2) the intrinsic nature of 3DGS as a low-level primitive representation, which makes it difficult to capture high-level aesthetic features. To address these challenges, we propose Aes3D, the first systematic framework for assessing the aesthetics of 3D neural rendering scenes. Aes3D includes Aesthetic3D, the first dataset dedicated to 3D scene aesthetic assessment, built on our proposed annotation strategy for 3D scene aesthetics. In addition, we present Aes3DGSNet, a lightweight model that directly predicts scene-level aesthetic scores from 3DGS representations. Notably, our model operates solely on 3D Gaussian primitives, eliminating the need for rendering multi-view images and thus reducing computational cost and hardware requirements. Through aesthetics-supervised learning on multi-view 3DGS scene representations, Aes3DGSNet effectively captures high-level aesthetic cues and accurately regresses aesthetic scores. Experimental results demonstrate that our approach achieves strong performance while maintaining a lightweight design, establishing a new benchmark for 3D scene aesthetic assessment. Code and datasets will be made available in a future version.

Multi-Output Gaussian Processes (MOGPs) provide a principled probabilistic framework for modelling correlated outputs but face scalability bottlenecks when applied to datasets with high-dimensional output spaces. To maintain tractability, existing methods typically resort to restrictive assumptions, such as employing low-rank or sum-of-separable kernels, which can limit expressiveness. We propose the Transformed Latent Variable MOGP (T-LVMOGP), a novel framework that scales MOGPs to a massive number of outputs while preserving the capacity to capture meaningful inter-output dependencies. T-LVMOGP constructs a flexible multi-output deep kernel by mapping inputs and output-specific latent variables into an embedding space using a Lipschitz-regularised neural network. Combined with stochastic variational inference, our model effectively scales to high-dimensional output settings. Across diverse benchmarks, including climate modelling with over 10,000 outputs and zero-inflated spatial transcriptomics data, T-LVMOGP outperforms baselines in both predictive accuracy and computational efficiency.

Strichartz inequalities are a cornerstone of the modern theory of dispersive PDEs, but their extremizers are known explicitly only in a handful of sharp cases. The non-convexity of the underlying functional makes the problem hard, and to our knowledge no systematic numerical attack has been attempted. We propose a simple neural-network-based pipeline that searches for extremizers as critical points of the Strichartz ratio, and apply it in three settings. First, on the Schrödinger group we recover the Gaussian extremizers of Foschi and Hundertmark--Zharnitsky in dimensions $d=1,2$ to within $10^{-3}$ relative error, with no analytical prior. Second, on $59$ further admissible pairs in $d=1$ where the answer is conjectural, the method consistently finds Gaussians, supporting the conjecture that Gaussians are the universal extremizers in the admissible range. Third, on the critical Airy--Strichartz inequality at $γ=1/q$, where existence is open, the optimization does not converge to any $L^2$ profile: instead, the iterates organize themselves as mKdV breathers $B(0,\cdot;α,1,0,0)$ with growing internal frequency $α$, and the discovered ratio approaches the Frank--Sabin universal lower bound $\widetilde A_{q,r}$ from below with a power-law gap $\simα^{-0.9}$. We confirm the same picture with an independent Hermite-basis ansatz. We propose a precise conjecture: the supremum equals $\widetilde A_{q,r}$ and is approached, but not attained, along the breather family. The pipeline thus serves both as a validator on known cases and as a discovery tool when no extremizer exists.

In this article, we study unbalanced optimal transport (UOT) and establish a control-theoretic dynamical extension, which we call the unbalanced density control (UDC), for a class of Gaussian reference measures. In the static setting, we consider UOT with quadratic transport cost and Kullback--Leibler penalties on the marginals relative to prescribed Gaussian measures. We show that the infinite-dimensional variational problem admits an exact Gaussian reduction, yielding a finite-dimensional optimization over masses, means, and covariances, together with a closed-form expression for the optimal transported mass. We then formulate UDC for discrete-time linear systems, where the initial and terminal state measures are imposed softly through KL penalties and the intermediate evolution is governed by controlled linear dynamics with quadratic control cost. For this problem, we prove that any feasible solution can be replaced, without loss of optimality, by a Gaussian initial measure and an affine-Gaussian control policy. This leads to an exact finite-dimensional reformulation and, after a standard covariance-steering lifting, to an SDP-based optimization for fixed mass, again coupled with a closed-form mass update. We further establish existence of optimal solutions and identify a sufficient condition under which the affine-Gaussian UDC policy is deterministic. These results provide globally optimal solution methods for both Gaussian UOT and Gaussian UDC. Finally, we illustrate our results with several numerical examples.

Recent progress in 4D Gaussian Splatting (4DGS) has achieved impressive dynamic scene reconstruction results. While these methods demonstrate remarkable performance, the specific factors behind their gains remain underexplored, making a systematic understanding of the underlying principles challenging. In this paper, we perform a comprehensive analysis of these hidden factors to provide a clearer perspective on the 4DGS framework. We first establish a controlled baseline, FreeTimeGS_ours, by formalizing and reproducing the heuristics of the state-of-the-art FreeTimeGS. Using this framework, we examine 4DGS along its fundamental axes and identify practical secrets, including the emergent temporal partitioning driven by Gaussian durations and the decoupling between photometric fidelity and motion behavior. Based on these insights, we propose FreeTimeGS++, a principled method that employs gated marginalization, UFM-guided initialization, and color correction to improve stability and reproducibility. Our approach yields reproducible results with reduced run-to-run variance.

Accurately recovering human pose and appearance from video is an essential component of scene reconstruction, with applications to motion capture, motion prediction, virtual reality, and digital twinning. Despite significant interest in building realistic human avatars from video, this paper demonstrates that existing methods do not accurately recover the 3D geometry of humans. ViT-based approaches are not consistently reliable and can overfit to 2D views, while NeRF- and Gaussian Splatting-based avatars treat pose and appearance separately, limiting rendering generalization to new poses. To resolve these shortcomings, this paper proposes HumanSplatHMR, a joint optimization framework that refines 3D human poses while simultaneously learning a high-fidelity avatar for novel-view and novel-pose synthesis. Our key insight is to close the loop between geometric pose estimation and differentiable rendering. Unlike prior human avatar methods that rely on accurate human pose obtained through motion capture systems or offline refinement, which are impractical in in-the-wild scenarios, our approach uses only human mesh estimates from a state-of-the-art human pose estimator to better reflect real-world conditions. Therefore, instead of using the human pose only as a deformation prior, HumanSplatHMR backpropagates photometric, segmentation, and depth losses through a differentiable renderer to the pose parameters and global position. This coupling refines the global 3D pose over time, improving accuracy and alignment while producing better renderings from novel views. Experiments show consistent improvements over pose recovery baselines that omit image-level refinement and avatar baselines that decouple pose estimation from avatar reconstruction.

Open-set supervised anomaly detection (OSAD) aims to identify unseen anomalies using limited anomalous supervision. However, existing prototype-based methods typically model normal data via a unimodal Gaussian prior, failing to capture inherent multi-modality and resulting in blurred decision boundaries. To address this, we propose Mixture Prototype Flow Matching (MPFM), a framework that learns a continuous transformation from normal feature distributions to a structured Gaussian mixture prototype space. Departing from traditional flow-based approaches that rely on a single velocity vector, MPFM explicitly models the velocity field as a Gaussian mixture prior where each component corresponds to a distinct normal class. This design facilitates mode-aware and semantically coherent distribution transport. Furthermore, we introduce a Mutual Information Maximization Regularizer (MIMR) to prevent prototype collapse and maximize normal-anomaly separability. Extensive experiments demonstrate that MPFM achieves state-of-the-art performance across diverse benchmarks under both single- and multi-anomaly settings.

We study the problem of denoising observations $Y_i=X_i+Z_i$, where the latent variables $X_i$ are sampled from a low-dimensional manifold in $\mathbb{R}^n$ and the noise variables $Z_i$ are isotropic Gaussian. We propose a convex-relaxation estimator that first reduces dimension by principal component analysis and then projects the observations onto the convex hull of the projected latent manifold. We construct a statistical oracle that estimates its supporting hyperplanes from empirical Gaussian tail probabilities of the noisy sample. Under a lower-mass condition on the latent distribution, we prove finite-sample guarantees for the oracle and derive error bounds for the resulting denoiser. The analysis combines risk bounds for least-squares projection under convex constraints with entropy bounds for convex hulls. We also verify the assumptions of the framework for a Cryo-Electron Microscopy observation model by establishing suitable covering number and Lipschitz estimates for the associated group action and imaging operators.

Large-scale 3D point clouds can consist of hundreds of millions of points. Even after downsampling, these point clouds are too large for modern 3D neural networks. In order to develop a semantic understanding of the scene, the point clouds are divided into smaller subclouds that can be processed. Typically, this division is done using spherical crops, resulting in a loss of surrounding geometric context. To address this issue, we propose alternative methods that produce subclouds with larger crop sizes while maintaining a similar number of points. Specifically, we compare exponential, Gaussian, and linear cropping methods with the spherical method. We evaluated three 3D deep learning model architectures using multiple indoor and outdoor environment datasets. Our results demonstrate that altering the cropping strategy can enhance model performance, especially for large-scale outdoor scenes, yielding new state-of-the-art results. Code is available at https://github.com/mvg-inatech/point_cloud_cropping

We propose a method to reconstruct high-fidelity human avatars from multi-view video that can run on mobile devices. Many works can model high-quality Gaussian-based full-body avatars from multi-view video. However, these methods require heavy computation to obtain pose-dependent appearance, making deployment on mobile devices very difficult. Recent methods distill from pretrained models and model pose-dependent nonlinear Gaussian attributes by linearly combining global pose features with blendshapes. Although they can run on mobile devices, they suffer some loss of detail. We observe that nearby Gaussians are often highly correlated within a local region of the body, and can be linearly modeled with less error. Therefore, we use local linear blendshapes in small body parts to capture global nonlinear changes of Gaussian attributes. To further reduce computation and model size, we propose to remove blendshapes for Gaussians whose attributes change little, yielding a minimal blendshape representation. Our method is an end-to-end training method without a pretrained model. To make it run on multiple devices, we implement our method using WebGPU. Experiments show that our method can render high-quality human avatars with better details, and can reach 120 FPS at 2K resolution on mobile devices.

We characterize the fundamental limits of high-dimensional mean testing under arbitrary truncation, where samples are drawn from the conditional distribution $P(\cdot \mid S)$ for an unknown truncation set $S$ that may hide up to an $\varepsilon$-fraction of the probability mass. For distributions with $p$-th directional moments of magnitude at most $ν_{P,p}$, truncation induces a bias of order $O(ν_{P,p}\varepsilon^{1-1/p})$. This bias creates a sharp information-theoretic detectability floor: when the signal $α$ falls below this threshold, the null and alternative hypotheses are indistinguishable even with infinite data. Above this floor, we prove that a simple second-order test achieving near-optimal sample complexity $n = O\!\left(\frac{\|Σ_P\|}{(α-4ν_{P,p}\varepsilon^{1-1/p})^2}\sqrt{d}\right)$. We further identify a structural escape from this finite-moment bias barrier. Under a directional median regularity assumption, truncation bias improves to linear order $O(\varepsilon)$. This reveals an intermediate regime in which estimation requires $Θ(d)$ samples for uniform recovery, while testing recovers the classical $Θ(\sqrt d)$ rate once truncation bias is eliminated. Together, our results provide a unified framework for mean testing under truncation, connecting finite-moment, sub-Gaussian, and median-regular structural regimes.

3D Gaussian Splatting (3DGS) has emerged as a powerful technique for generating photorealistic renderings of a scene in real-time. However, the volumetric nature of 3DGS limits its ability to accurately capture surface geometry. To address this, 2D Gaussian Splatting (2DGS) was proposed to enable view-consistent and geometrically accurate surface reconstruction from multi-view images. However, 2DGS can be sensitive to the initialization of the Gaussian primitives. Reliance on Structure-from-Motion (SfM) initializations, which can produce poor estimates on challenging image sets, may lead to subpar results. In this work, we enhance 2DGS by incorporating monocular depth and normal priors to improve both geometric accuracy and robustness. We propose a depth-guided initialization strategy for Gaussians and introduce a clustering-based technique for pruning degenerate Gaussians. We evaluate our method on the DTU dataset, where it achieves state-of-the-art results in mesh reconstruction while preserving high-quality novel view synthesis.

Recent advances in Neural Radiance Fields (NeRF) and 3D Gaussian Splatting (3DGS) have made it standard practice to reconstruct 3D scenes from multi-view images. Removing objects from such 3D representations is a fundamental editing task that requires complete and seamless inpainting of occluded regions, ensuring consistency in geometry and appearance. Although existing methods have made notable progress in improving inpainting consistency, they often neglect global lighting effects, leading to physically implausible results. Moreover, these methods struggle with view-dependent non-Lambertian surfaces, where appearance varies across viewpoints, leading to unreliable inpainting. In this paper, we present 3D Gaussian Object Removal in the Intrinsic Space (GOR-IS), a novel framework for physically consistent and visually coherent 3D object removal. Our approach decomposes the scene into intrinsic components and explicitly models light transport to maintain global lighting effects consistency. Furthermore, we introduce an intrinsic-space inpainting module that operates directly in the material and lighting domains, effectively addressing the challenges posed by non-Lambertian surfaces. Extensive experiments on both synthetic and real-world datasets demonstrate that our framework substantially improves the physical consistency and visual coherence of object removal, outperforming existing methods by 13% in perceptual similarity (LPIPS) and 2dB in peak signal-to-noise ratio (PSNR). Code is publicly available at https://applezyh.github.io/GOR-IS-project-page/

3D Gaussian Splatting has emerged as a powerful scene representation for real-time novel-view synthesis. However, its standard adaptive density control relies on screen-space positional gradients, which do not distinguish between geometric misplacement and frequency aliasing, often leading to either over-blurred high-frequency textures or inefficient over-densification. We present a structure-aware densification framework. Our key insight is that the decision to subdivide a Gaussian should be driven by an explicit comparison between its projected screen-space extent and the local structure of the texture it seeks to represent. We introduce a multi-scale frequency analysis combining structure tensors with Laplacian scale space analysis to estimate the dominant frequency at each pixel, enabling robust supervision across varying texture scales. Based on this analysis, we define $η$, a per-Gaussian, per-axis frequency violation metric that indicates when a primitive may be under-resolving local texture details. Unlike methods that perform isotropic splitting (e.g., splitting each Gaussian into two smaller ones with uniform shape), our approach performs anisotropic splitting. For each axis with high $η$, we compute a split factor to better resolve the local frequency content. We further introduce a multiview consistency criterion that aggregates $η$ observations across multiple views. By performing densification early and faster, we skip the lengthy iterative densification phases required by baseline methods and achieve significantly faster convergence. Experiments on standard benchmarks demonstrate that our method also achieves superior reconstruction quality, particularly in high-frequency regions.

3D Gaussian Splatting (3D GS) is widely adopted for novel view synthesis due to its high training and rendering efficiency. However, its efficiency relies on the key assumption that Gaussians do not overlap in the 3D space, which leads to noticeable artifacts and view inconsistencies. In addition, the inherently diffuse boundaries of Gaussians hinder accurate reconstruction of sharp object edges. We propose Softmax-GS, a unified solution that addresses both the view-inconsistency and the diffuse-boundary problem by enforcing a softmax-based competition in overlapping regions between two Gaussians. With learnable parameters controlling the strength of the competition, it enables a continuous spectrum from smooth color blending to crisp, well-defined boundaries. Our formulation explicitly preserves order invariance for any two overlapping Gaussians and ensures that the output transmittance remains unchanged irrespective of the extent of overlapping, preventing undesirable discontinuities in the rendered output. Ablation experiments on simple geometries demonstrate the effectiveness of each component of Softmax-GS, and evaluations on real-world benchmarks show that it achieves state-of-the-art performance, improving both reconstruction quality and parameter efficiency.

Recently, generalizable human Gaussian splatting from sparse-view inputs has been actively studied for the photorealistic human rendering. Most existing methods rely on explicit geometric constraints or predefined structural representations to accurately position 3D Gaussians. Although these approaches have shown the remarkable progress in this field, they still suffer from inconsistent feature representations across multi-view inputs due to complex articulations of the human body and limited overlaps between different views. To address this problem, we propose a novel method to accurately localize 3D Gaussians and ultimately improve the quality of human rendering. The key idea is to unproject latent embeddings encoded from each viewpoint into a shared 3D space through predicted depth maps and recalibrate them belonging to the same body part based on cross-view attention. This helps the model resolve the spatial ambiguity occurring in highly textured regions as well as occluded body parts, thus leading to the accurate localization of 3D Gaussians. Experimental results on benchmark datasets show that the proposed method efficiently improves the performance of generalizable human Gaussian splatting from sparse-view inputs.

Wide Field-of-View (WFoV) reconstruction enhances 3D ultrasound imaging by providing valuable anatomical context for segmentation models and visualization. Clinical ultrasound volumes are predominantly acquired using convex probes, which generate expanding, diverging acoustic beams to maximize anatomical coverage. Stitching these sweeps together traditionally introduces significant compounding artifacts and aliasing due to depth-dependent resolution changes. Here, we introduce Ultra-Wide-NeRF, a Multivariate 3D Gaussian (MVG) NeRF-based method for WFoV ultrasound reconstruction. By explicitly modeling the complex beam geometry using distance-dependent convex volumetric sampling and anisotropic 3D Gaussians, our method inherently mitigates these compounding artifacts and provides anti-aliasing. Beyond simply reconstructing a static 3D grid, our NeRF-based approach yields a continuous neural representation of the tissue, enabling the synthesis of high-fidelity novel views from arbitrary virtual trajectories. We validate Ultra-Wide-NeRF for intracardiac echocardiography on phantom and porcine datasets, demonstrating that our method expands the spatial context important in intraoperative navigation. Code will be open-sourced upon publication.

Mixture-of-Experts (MoE) has become a prevalent backbone for large vision-language models (VLMs), yet how modality-specific signals should guide expert routing remains under-explored. Existing routing strategies are either hand-crafted or modality-agnostic, relying on idealized priors that ignore the layer-dependent modality fusion patterns in MoE-VLMs and provide little guidance for expert specialization. We propose Soft Modality-guided Expert Specialization (SMoES), which consists of dynamic soft modality scores that capture layer-dependent fusion patterns, an expert binning mechanism aligned with expert-parallel deployment, and an inter-bin mutual information regularization that encourages coherent modality specialization. Our method leverages attention-based or Gaussian-statistics modality scores to optimize mutual information regularization. Experiments across four MoE-based VLMs and 16 benchmarks demonstrate improvement on both effectiveness and efficiency: 0.9% and 4.2% average gain on multimodal and language-only tasks, 56.1% reduction in EP communication overhead, and 12.3% throughput improvement under realistic deployment. These results validate that aligning routing with modality-aware expert specialization unlocks MoE-VLM capacity and efficiency.

Egocentric video provides a unique view into human perception and interaction, with growing relevance for augmented reality, robotics, and assistive technologies. However, rapid camera motion and complex scene dynamics pose major challenges for 3D reconstruction from this perspective. While 3D Gaussian Splatting (3DGS) has become a state-of-the-art method for efficient, high-quality novel view synthesis, variants, that focus on reconstructing dynamic scenes from monocular video are rarely evaluated on egocentric video. It remains unclear whether existing models generalize to this setting or if egocentric-specific solutions are needed. In this work, we evaluate dynamic monocular 3DGS models on egocentric and exocentric video using paired ego-exo recordings from the EgoExo4D dataset. We find that reconstruction quality is consistently lower in egocentric views. Analysis reveals that the difference in reconstruction quality, measured in peak signal-to-noise ratio, stems from the reconstruction of static, not dynamic, content. Our findings underscore current limitations and motivate the development of egocentric-specific approaches, while also highlighting the value of separately evaluating static and dynamic regions of a video.

This work presents GS-DOT, a novel image reconstruction framework based on Gaussian Splatting (GS) for diffuse optical tomography (DOT). Inspired by GS for rendering applications, absorption coefficients are represented as a sparse sum of anisotropic Gaussian primitives optimized to fit measured time-resolved point-spread functions through analytic gradients and Adam optimization. This is the first adaptation of GS algorithms in the photon diffusion regime, where the ray transport function is replaced by the diffusion functions to enable accurate modeling of light transport in highly scattering media. Validation on synthetic tissue models demonstrate high accuracy in localization and quantification of reconstructed absorption maps for both clean and noisy signals. GS-DOT has demonstrated high robustness to noise and showed a huge reduction in memory demand.

Gaussian Splatting (GS) has emerged as an efficient approach for high-quality novel view synthesis. While early GS variants struggled to accurately model the scene's geometry, recent advancements constraining the Gaussians' spread and shapes, such as 2D Gaussian Splatting, have significantly improved geometric fidelity. In this paper, we present Pixel-Aligned 1DoF Gaussian Splatting (PAGaS) that adapts the GS representation from novel view synthesis to the multi-view stereo depth task. Our key contribution is modeling a pixel's depth using one-degree-of-freedom (1DoF) Gaussians that remain tightly constrained during optimization. Unlike existing approaches, our Gaussians' positions and sizes are restricted by the back-projected pixel volumes, leaving depth as the sole degree of freedom to optimize. PAGaS produces highly detailed depths, as illustrated in Figure 1. We quantitatively validate these improvements on top of reference geometric and learning-based multi-view stereo baselines on challenging 3D reconstruction benchmarks. Code: davidrecasens.github.io/pagas

Local Optima Networks (LONs) represent the global structure of search spaces as graphs, but their construction requires iterative execution of a search algorithm to find local optima and approximate transitions between Basins of Attraction (BoAs). In continuous optimization, this high computational cost prevents systematic investigation of the relationship between LON features and evolutionary algorithm performance. To address this issue, we propose an alternative definition of BoAs for Max-Set of Gaussians (MSG) landscapes with explicitly tunable multimodality. This bypasses search-based BoA identification, enabling low-cost LON construction. Moreover, we leverage Novelty Search (NS) to explore the parameter space of the MSG landscape generator, producing instances with diverse graph topologies. Our experiments show that the proposed BoAs closely align with gradient-based BoAs, and that NS successfully generates instances with varied search difficulty and connectivity patterns among optima. Finally, over the instances generated by NS, we predict the success rate of two well-established evolutionary algorithms from LON features. While our LON construction is specific to MSG landscapes, the proposed framework provides a dataset that serves as a foundation for landscape-aware optimization.

3D Gaussian Splatting (3DGS) has revolutionized neural rendering, yet existing methods remain predominantly research prototypes ill-suited for production-level deployment. We identify a critical "Industry-Academia Gap" hindering real-world application: unpredictable resource consumption from heuristic Gaussian growth, the "sparsity shield" of current benchmarks that rewards hallucination over physical fidelity, and severe multi-sensor data pollution. To bridge this gap, we propose YOGO (You Only Gaussian Once), a system-level framework that reformulates the stochastic growth process into a deterministic, budget-aware equilibrium. YOGO integrates a novel budget controller for hardware-constrained resource allocation and an availability-registration protocol for robust multi-sensor fusion. To push the boundaries of reconstruction fidelity, we introduce Immersion v1.0, the first ultra-dense indoor dataset specifically designed to break the "sparsity shield." By providing saturated viewpoint coverage, Immersion v1.0 forces algorithms to focus on extreme physical fidelity rather than viewpoint interpolation, and enables the community to focus on the upper limits of high-fidelity reconstruction. Extensive experiments demonstrate that YOGO achieves state-of-the-art visual quality while maintaining a strictly deterministic profile, establishing a new standard for production-grade 3DGS. To facilitate reproducibility, part scenes of Immersion v1.0 dataset and source code of YOGO has been publicly released. The project link is https://jjrcn.github.io/yogo-project-home/.

Kolmogorov--Arnold Networks (KANs) have recently attracted attention as edge-based neural architectures in which learnable univariate functions replace conventional fixed activation functions. A key source of flexibility in KANs is the choice of basis functions used to parameterize the learnable edge functions. In this context, Gaussian basis functions provide a simple and efficient alternative to splines. However, their performance depends strongly on the scale (shape) parameter $ε$, whose role has not been studied systematically. In this paper, we investigate how $ε$ affects Gaussian KANs through first-layer feature geometry, conditioning, and approximation behavior. Our central observation is that scale selection is governed primarily by the first layer, since it is the only layer constructed directly on the input domain and any loss of distinguishability introduced there cannot be recovered by later layers. From this viewpoint, we analyze the first-layer feature matrix and identify a practical operating interval, $$ε\in \left[\frac{1}{G-1},\frac{2}{G-1}\right],$$ where $G$ denotes the number of Gaussian centers. We interpret this interval not as a universal optimality result, but as a stable and effective design rule, and validate it through brute-force sweeps over $ε$ across function-approximation problems with different collocation densities, grid resolutions, network architectures, and input dimensions, as well as physics-informed problems. We further show that this range is useful for fixed-scale selection, variable-scale constructions, constrained training of $ε$, and efficient scale search using early training MSE. In this way, the paper positions scale selection as a practical design principle for Gaussian KANs rather than as an ad hoc hyperparameter choice.

3D Gaussian Splatting (3DGS) has revolutionized novel view synthesis with high-quality rendering through continuous aggregations of millions of 3D Gaussian primitives. However, it suffers from a substantial memory footprint, particularly during training due to uncontrolled densification, posing a critical bottleneck for deployment on memory-constrained edge devices. While existing methods prune redundant Gaussians post-training, they fail to address the peak memory spikes caused by the abrupt growth of Gaussians early in the training process. To solve the training memory consumption problem, we propose a systematic memory-bounded training framework that dynamically optimizes Gaussians through iterative growth and pruning. In other words, the proposed framework alternates between incremental pruning of low-impact Gaussians and strategic growing of new primitives with an adaptive Gaussian compensation, maintaining a near-constant low memory usage while progressively refining rendering fidelity. We comprehensively evaluate the proposed training framework on various real-world datasets under strict memory constraints, showing significant improvements over existing state-of-the-art methods. Particularly, our proposed method practically enables memory-efficient 3DGS training on NVIDIA Jetson AGX Xavier, achieving similar visual quality with up to 80% lower peak training memory consumption than the original 3DGS.

We establish central and non-central limit theorems for sequences of functionals of the Gaussian output of an infinitely-wide random neural network on the d-dimensional sphere . We show that the asymptotic behaviour of these functionals as the depth of the network increases depends crucially on the fixed points of the covariance function, resulting in three distinct limiting regimes: convergence to the same functional of a limiting Gaussian field, convergence to a Gaussian distribution, convergence to a distribution in the Qth Wiener chaos. Our proofs exploit tools that are now classical (Hermite expansions, Diagram Formula, Stein-Malliavin techniques), but also ideas which have never been used in similar contexts: in particular, the asymptotic behaviour is determined by the fixed-point structure of the iterative operator associated with the covariance, whose nature and stability governs the different limiting regimes.

Reducing the number of Gaussian-tile pairs is one of the most promising approaches to improve 3D Gaussian Splatting (3D-GS) rendering speed on GPUs. However, the importance difference existing among Gaussian-tile pairs has never been considered in the previous works. In this paper, we propose AdaGScale, a novel viewpoint-adaptive Gaussian scaling technique for reducing the number of Gaussian-tile pairs. AdaGScale is based on the observation that the peripheral tiles located far from Gaussian center contribute negligibly to pixel color accumulation. This suggests an opportunity for reducing the number of Gaussian-tile pairs based on color contribution. AdaGScale efficiently estimates the color contribution in the peripheral region of each Gaussian during a preprocessing stage and adaptively scales its size based on the peripheral score. As a result, Gaussians with lower importance intersect with fewer tiles during the intersection test, which improves rendering speed while maintaining image quality. The adjusted size is used only for tile intersection test, and the original size is retained during color accumulation to preserve visual fidelity. Experimental results show that AdaGScale achieves a geometric mean speedup of 13.8x over original 3D-GS on a GPU, with only about 0.5 dB degradation in PSNR on city-scale scenes.

Gaussian Splatting has recently become one of the most popular frameworks for photorealistic 3D scene reconstruction and rendering. While current rasterizers allow for efficient mappings of 3D Gaussian splats onto 2D camera views, this work focuses on mapping 2D image information (e.g. color, neural features or segmentation masks) efficiently back onto an existing scene of Gaussian splats. This 'opposite' direction enables applications ranging from scene relighting and stylization to 3D semantic segmentation, but also introduces challenges, such as view-dependent colorization and occlusion handling. Our approach tackles these challenges using the normal equation to solve a visibility-weighted least squares problem for every Gaussian and can be implemented efficiently with existing differentiable rasterizers. We demonstrate the effectiveness of our approach on scene relighting, feature enrichment and 3D semantic segmentation tasks, achieving up to an order of magnitude speedup compared to gradient descent-based baselines.

The paper considers the computation of L1 regularization paths in a state space setting, which includes L1 regularized Kalman smoothing, linear SVM, LASSO, and more. The paper proposes two new algorithms, which are duals of each other; the first algorithm applies to L1 regularization of independent variables while the second applies to L1 regularization of dependent variables. The heart of the proposed algorithms is parametric Gaussian message passing (i.e., Kalman-type forward-backward recursions) in the pertinent factor graphs. The proposed methods are broadly applicable, they (usually) require only matrix multiplications, and their complexity can be competitive with prior methods in some cases.

Low-altitude Gaussian splatting (LAGS) facilitates 3D scene reconstruction by aggregating aerial images from distributed drones. However, as LAGS prioritizes maximizing reconstruction quality over communication throughput, existing low-altitude resource allocation schemes become inefficient. This inefficiency stems from their failure to account for image diversity introduced by varying viewpoints. To fill this gap, we propose a groupwise heterogeneous graph neural network (GW-HGNN) for LAGS resource allocation. GW-HGNN explicitly models the non-uniform contribution of different image groups to the reconstruction process, thus automatically balancing data fidelity and transmission cost. The key insight of GW-HGNN is to transform LAGS losses and communication constraints into graph learning costs for dual-level message passing. Experiments on real-world LAGS datasets demonstrate that GW-HGNN significantly outperforms state-of-the-art benchmarks across key rendering metrics, including PSNR, SSIM, and LPIPS. Furthermore, GW-HGNN reduces computational latency by approximately 100x compared to the widely-used MOSEK solver, achieving millisecond-level inference suitable for real-time deployment.

Dynamic 3D Gaussian Splatting methods achieve strong training-view PSNR on monocular video but generalize poorly: on the D-NeRF benchmark we measure an average train-test PSNR gap of 6.18 dB, rising to 11 dB on individual scenes. We report two findings that together account for most of that gap. Finding 1 (the role of splitting). A systematic ablation of the Adaptive Density Control pipeline (split, clone, prune, frequency, threshold, schedule) shows that splitting is responsible for over 80% of the gap: disabling split collapses the cloud from 44K to 3K Gaussians and the gap from 6.18 dB to 1.15 dB. Across all threshold-varying ablations, gap is log-linear in count (r = 0.995, bootstrap 95% CI [0.99, 1.00]), which suggests a capacity-based explanation. Finding 2 (the role of deformation coherence). We show that the capacity explanation is incomplete. A local-smoothness penalty on the per-Gaussian deformation field -- Elastic Energy Regularization (EER) -- reduces the gap by 40.8% while growing the cloud by 85%. Measuring per-Gaussian strain directly on trained checkpoints, EER reduces mean strain by 99.72% (median 99.80%) across all 8 scenes; on 8/8 scenes the median Gaussian under EER is less strained than the 1st-percentile (best-behaved) Gaussian under baseline. Alongside EER, we evaluate two further regularizers: GAD, a loss-rate-aware densification threshold, and PTDrop, a jitter-weighted Gaussian dropout. GAD+EER reduces the gap by 48%; adding PTDrop and a soft growth cap reaches 57%. We confirm that coherence generalizes to (a) a different deformation architecture (Deformable-3DGS, +40.6% gap reduction at re-tuned lambda), and (b) real monocular video (4 HyperNeRF scenes, reducing the mean PSNR gap by 14.9% at the same lambda as D-NeRF, with near-zero quality cost). The overfitting in dynamic 3DGS is driven by incoherent deformation, not parameter count.

Wireless radiance field (WRF) reconstruction aims to learn a continuous, queryable representation of radio frequency characteristics over 3D space and direction, from which specific quantities, such as the spatial power spectrum (SPS) at a receiver given a transmitter position, can be predicted. While Gaussian splatting (GS)-based method has surpassed Neural Radiance Fields (NeRF)-based method for this task, existing adaptations largely transplant vision pipelines, limiting physical interpretability and accuracy. We introduce BiSplat-WRF, a planar GS framework that retains the expressiveness of 3D GS while removing unnecessary projections and incorporating global EM coupling and mutual scattering among primitives. Each primitive is a 2D planar Gaussian with 3D coordinates, rendered directly on the angular domain of the SPS. A bilinear spatial transformer (BST) aggregates inter-primitive relations on an angular grid and, via attention, captures long-range electromagnetic dependencies, thereby enforcing globally aware EM interactions that reflect the complex physics of the wireless environment. On spatial spectrum synthesis task, BiSplat-WRF surpasses NeRF-based and prior GS-based baselines with respect to the Structural Similarity Index (SSIM); comprehensive ablation studies validate the contribution of BST. We also provide a larger BiSplat-WRF+ variant that further increases SSIM at a higher computation cost, serving as a strong reference for future studies.

Recent years have witnessed the rapid emergence of 3D Gaussian splatting (3DGS) as a powerful approach for 3D reconstruction and novel view synthesis. Its explicit representation with Gaussian primitives enables fast training, real-time rendering, and convenient post-processing such as editing and surface reconstruction. However, 3DGS suffers from a critical drawback: the number of primitives grows drastically for scenes with high-frequency appearance details, since each primitive can represent only a single color, requiring multiple primitives for every sharp color transition. To overcome this limitation, we propose neural Gabor splatting, which augments each Gaussian primitive with a lightweight multi-layer perceptron that models a wide range of color variations within a single primitive. To further control primitive numbers, we introduce a frequency-aware densification strategy that selects mismatch primitives for pruning and cloning based on frequency energy. Our method achieves accurate reconstruction of challenging high-frequency surfaces. We demonstrate its effectiveness through extensive experiments on both standard benchmarks, such as Mip-NeRF360 and High-Frequency datasets (e.g., checkered patterns), supported by comprehensive ablation studies.

We present Cloth-HUGS, a Gaussian Splatting based neural rendering framework for photorealistic clothed human reconstruction that explicitly disentangles body and clothing. Unlike prior methods that absorb clothing into a single body representation and struggle with loose garments and complex deformations, Cloth-HUGS represents the performer using separate Gaussian layers for body and cloth within a shared canonical space. The canonical volume jointly encodes body, cloth, and scene primitives and is deformed through SMPL-driven articulation with learned linear blend skinning weights. To improve cloth realism, we initialize cloth Gaussians from mesh topology and apply physics-inspired constraints, including simulation-consistency, ARAP regularization, and mask supervision. We further introduce a depth-aware multi-pass rendering strategy for robust body-cloth-scene compositing, enabling real-time rendering at over 60 FPS. Experiments on multiple benchmarks show that Cloth-HUGS improves perceptual quality and geometric fidelity over state-of-the-art baselines, reducing LPIPS by up to 28% while producing temporally coherent cloth dynamics.

In this work, we revisit several key design choices of modern Transformer-based approaches for feed-forward 3D Gaussian Splatting (3DGS) prediction. We argue that the common practice of regressing Gaussian means as depths along camera rays is suboptimal, and instead propose to directly regress 3D mean coordinates using only a self-supervised rendering loss. This formulation allows us to move from the standard encoder-only design to an encoder-decoder architecture with learnable Gaussian tokens, thereby unbinding the number of predicted primitives from input image resolution and number of views. Our resulting method, TokenGS, demonstrates improved robustness to pose noise and multiview inconsistencies, while naturally supporting efficient test-time optimization in token space without degrading learned priors. TokenGS achieves state-of-the-art feed-forward reconstruction performance on both static and dynamic scenes, producing more regularized geometry and more balanced 3DGS distribution, while seamlessly recovering emergent scene attributes such as static-dynamic decomposition and scene flow.

We propose a compositional method for constructing a complete 3D head avatar from a single image. Prior one-shot holistic approaches frequently fail to produce realistic hair dynamics during animation, largely due to inadequate decoupling of hair from the facial region, resulting in entangled geometry and unnatural deformations. Our method explicitly decouples hair from the face, modeling these components using distinct deformation paradigms while integrating them into a unified rendering pipeline. Furthermore, by leveraging image-to-3D lifting techniques, we preserve fine-grained textures from the input image to the greatest extent possible, effectively mitigating the common issue of high-frequency information loss in generalized models. Specifically, given a frontal portrait image, we first perform hair removal to obtain a bald image. Both the original image and the bald image are then lifted to dense, detail-rich 3D Gaussian Splatting (3DGS) representations. For the bald 3DGS, we rig it to a FLAME mesh via non-rigid registration with a prior model, enabling natural deformation that follows the mesh triangles during animation. For the hair component, we employ semantic label supervision combined with a boundary-aware reassignment strategy to extract a clean and isolated set of hair Gaussians. To control hair deformation, we introduce a cage structure that supports Position-Based Dynamics (PBD) simulation, allowing realistic and physically plausible transformations of the hair Gaussian primitives under head motion, gravity, and inertial effects. Striking qualitative results, including dynamic animations under diverse head motions, gravity effects, and expressions, showcase substantially more realistic hair behavior alongside faithfully preserved facial details, outperforming state-of-the-art one-shot methods in perceptual realism.

We propose Skelebones, a Scaffold-Skin Rigging System built on three steps: (1) Bones compress temporally consistent Gaussian or mesh sequences into free-form bones with smooth skinning weights, approximating non-rigid deformations via linear blend skinning (LBS); (2) Skeleton extracts the Mean Curvature Skeleton (MCS) from the canonical shape and temporally refines its topology and kinematics into a compact skeletal structure; and (3) Binding connects the skeleton and bones through non-parametric Partwise Motion Matching (PartMM), which synthesizes novel bone motions by matching, retrieving, and blending existing ones. Together, these steps compress the dynamics of 4D shapes into compact skelebones that are simultaneously controllable and expressive. The resulting representation is category-agnostic, meaning template-free; motion-adaptive, with dynamic topology; and topology-correct, with a skeleton consistent with the surface geometry. PartMM requires no learning. We validate our method on both synthetic and real-world datasets, achieving substantial reanimation improvements on unseen poses: a 17.3 dB PSNR gain over LBS on DNA-Rendering and a 45.6 dB gain over Bag-of-Bones on ActorsHQ, while preserving high rendering fidelity for characters with complex non-rigid dynamics. PartMM generalizes robustly to both Gaussian and mesh representations, excelling in low-data regimes of approximately 1,000 frames, with a 48.4 RMSE improvement over LBS and improvements of more than 20 over GRU- and MLP-based methods. Code will be publicly released at https://cookmaker.cn/gaussianimate/.

We present ViewSplat, a view-adaptive 3D Gaussian splatting network for novel view synthesis from unposed images. While recent feed-forward 3D Gaussian splatting has significantly accelerated 3D scene reconstruction by bypassing per-scene optimization, a fundamental fidelity gap remains. We attribute this gap to the limited capacity of single-step feed-forward networks to regress static Gaussian primitives that satisfy all viewpoints. To address this limitation, we shift the paradigm from static primitive regression to view-adaptive splatting. Instead of a rigid Gaussian representation, our pipeline learns a view-adaptive latent representation. Specifically, ViewSplat initially predicts base Gaussian primitives alongside the weights of scene-conditioned View MLPs. During rendering, these MLPs take target-view coordinates as input and predict view-dependent residual updates for each Gaussian attribute (i.e., 3D position, scale, rotation, opacity, and color). This mechanism, which we term view-adaptive splatting, allows each primitive to rectify initial estimation errors, effectively capturing high-fidelity appearances. Extensive experiments demonstrate that ViewSplat achieves state-of-the-art fidelity while maintaining fast inference and real-time rendering; our large backbone variant runs at 15 FPS during inference and 90 FPS during rendering. Our project page is available at https://cvlab-uos.github.io/ViewSplat.

Despite their output being ultimately consumed by human viewers, 3D Gaussian Splatting (3DGS) methods often rely on ad-hoc combinations of pixel-level losses, resulting in blurry renderings. To address this, we systematically explore perceptual optimization strategies for 3DGS by searching over a diverse set of distortion losses. We conduct the first-of-its-kind large-scale human subjective study on 3DGS, involving 39,320 pairwise ratings across several datasets and 3DGS frameworks. A regularized version of Wasserstein Distortion, which we call WD-R, emerges as the clear winner, excelling at recovering fine textures without incurring a higher splat count. WD-R is preferred by raters more than $2.3\times$ over the original 3DGS loss, and $1.5\times$ over the current best method Perceptual-GS. WD-R also consistently achieves state-of-the-art LPIPS, DISTS, and FID scores across various datasets, and generalizes across recent frameworks, such as Mip-Splatting and Scaffold-GS, where replacing the original loss with WD-R consistently enhances perceptual quality within a similar resource budget (number of splats for Mip-Splatting, model size for Scaffold-GS), and leads to reconstructions being preferred by human raters $1.8\times$ and $3.6\times$, respectively. We also find that this carries over to the task of 3DGS scene compression, with $\approx 50\%$ bitrate savings for comparable perceptual metric performance.

Anchor-driven 4D Gaussian streaming methods such as Instant Gaussian Stream (IGS) update a dynamic scene each frame from a compact set of Gaussian anchors, chosen by default with Farthest Point Sampling (FPS) at a fixed budget of $8{,}192$. Because these anchors act as control points that drive the whole scene through linear blend skinning, the rule used to choose them ought to affect reconstruction quality. We test this by holding the IGS pipeline fixed and changing only the sampler, comparing FPS, random, uniform, an opacity-scale heuristic, and a learned policy across budgets and refinement settings on N3DV and MeetingRoom. At deployment budgets the sampler has no measurable effect: a cheap random or uniform sampler at $4{,}096$ anchors matches FPS@8192 within measurement error, the default budget is over-provisioned, and the result holds on a second backbone (3DGStream). The learned policy is mixed rather than consistently better: it can improve the N3DV validation set at tight budgets, but does not give a stable cross-dataset rule, and selection is never the bottleneck because refinement dominates runtime. We will release our full sweep and evaluation protocol as a sampler benchmark.

We study mean estimation for a Gaussian distribution with identity covariance in $\mathbb{R}^d$ under a missing data scheme termed realizable $ε$-contamination model. In this model an adversary can choose a function $r(x)$ between 0 and $ε$ and each sample $x$ goes missing with probability $r(x)$. Recent work Ma et al., 2024 proposed this model as an intermediate-strength setting between Missing Completely At Random (MCAR) -- where missingness is independent of the data -- and Missing Not At Random (MNAR) -- where missingness may depend arbitrarily on the sample values and can lead to non-identifiability issues. That work established information-theoretic upper and lower bounds for mean estimation in the realizable contamination model. Their proposed estimators incur runtime exponential in the dimension, leaving open the possibility of computationally efficient algorithms in high dimensions. In this work, we establish an information-computation gap in the Statistical Query model (and, as a corollary, for Low-Degree Polynomials and PTF tests), showing that algorithms must either use substantially more samples than information-theoretically necessary or incur exponential runtime. We complement our SQ lower bound with an algorithm whose sample-time tradeoff nearly matches our lower bound. Together, these results qualitatively characterize the complexity of Gaussian mean estimation under $ε$-realizable contamination.

Non-conservative uncertainty bounds are essential for making reliable predictions about latent functions from noisy data, and thus, a key enabler for safe learning-based control. In this domain, kernel methods such as Gaussian process regression are established techniques, thanks to their inherent uncertainty quantification mechanism. Still, existing bounds either pose strong assumptions on the underlying noise distribution, are conservative, do not directly apply in the multi-output case, or are difficult to integrate into downstream tasks. This paper addresses these limitations by presenting a tight, deterministic bound for multi-output functions in Reproducing Kernel Hilbert Spaces (RKHSs) subject to bounded noise. It is obtained through an unconstrained, duality-based formulation, which shares the same structure as classic Gaussian process confidence bounds, and can thus be straightforwardly integrated into downstream optimization pipelines. We show that the proposed bound generalizes existing results and illustrate its application using an example inspired by quadrotor dynamics learning.

3D Gaussian Splat (3DGS) enables high-fidelity, real-time novel view synthesis by representing scenes with large sets of anisotropic primitives, but often requires millions of Splats, incurring significant storage and transmission costs. Most existing compression methods rely on GPU-intensive post-training optimization with calibrated images, limiting practical deployment. We introduce \textbf{NanoGS}, a training-free and lightweight framework for Gaussian Splat simplification. Instead of relying on image-based rendering supervision, NanoGS formulates simplification as local pairwise merging over a sparse spatial graph. The method approximates a pair of Gaussians with a single primitive using mass preserved moment matching and evaluates merge quality through a principled merge cost between the original mixture and its approximation. By restricting merge candidates to local neighborhoods and selecting compatible pairs efficiently, NanoGS produces compact Gaussian representations while preserving scene structure and appearance. NanoGS operates directly on existing Gaussian Splat models, runs efficiently on CPU, and preserves the standard 3DGS parameterization, enabling seamless integration with existing rendering pipelines. Experiments demonstrate that NanoGS substantially reduces primitive count while maintaining high rendering fidelity, providing an efficient and practical solution for Gaussian Splat simplification. Our project website is available at \href{https://saliteta.github.io/NanoGS/}{https://saliteta.github.io/NanoGS/}.

Object-level 3D reconstruction play important roles across domains such as cultural heritage digitization, industrial manufacturing, and virtual reality. However, existing Gaussian Splatting-based approaches generally rely on full-scene reconstruction, in which substantial redundant background information is introduced, leading to increased computational and storage overhead. To address this limitation, we propose an efficient single-object 3D reconstruction method based on 2D Gaussian Splatting. By directly integrating foreground-background probability cues into Gaussian primitives and dynamically pruning low-probability Gaussians during training, the proposed method fundamentally focuses on an object of interest and improves the memory and computational efficiency. Our pipeline leverages probability masks generated by YOLO and SAM to supervise probabilistic Gaussian attributes, replacing binary masks with continuous probability values to mitigate boundary ambiguity. Additionally, we propose a dual-stage filtering strategy for training's startup to suppress background Gaussians. And, during training, rendered probability masks are conversely employed to refine supervision and enhance boundary consistency across views. Experiments conducted on the MIP-360, T&T, and NVOS datasets demonstrate that our method exhibits strong self-correction capability in the presence of mask errors and achieves reconstruction quality comparable to standard 3DGS approaches, while requiring only approximately 1/10 of their Gaussian amount. These results validate the efficiency and robustness of our method for single-object reconstruction and highlight its potential for applications requiring both high fidelity and computational efficiency.

Accurate trajectory prediction is critical for safe autonomous navigation in crowded environments. While many trajectory predictors output Gaussian distributions to represent the multi-modal distribution over future pedestrian positions, the reliability of their confidence levels often remains unaddressed. This limitation can lead to unsafe or overly conservative motion planning when the predictor is integrated with an uncertainty-aware planner. Existing Gaussian trajectory predictors primarily rely on the Negative Log-Likelihood loss, which is prone to predict over- or under-confident distributions, and may compromise downstream planner safety. This paper introduces a novel loss function for calibrating prediction uncertainty which leverages Kernel Density Estimation to estimate the empirical distribution of confidence levels. The proposed formulation enforces consistency with the properties of a Gaussian assumption by explicitly matching the estimated empirical distribution to the Chi-squared distribution. To ensure accurate mean prediction, a Mean Squared Error term is also incorporated in the final loss formulation. Experimental results on real-world trajectory datasets show that our method significantly improves the reliability of confidence levels predicted by different State-Of-The-Art Gaussian trajectory predictors. We also demonstrate the importance of providing planners with reliable probabilistic insights (i.e. calibrated confidence levels) for collision-free navigation in complex scenarios. For this purpose, we integrate Gaussian trajectory predictors trained with our loss function with an uncertainty-aware Model Predictive Control on scenarios extracted from real-world datasets, achieving improved planning performance through calibrated confidence levels.

Sparse-view computed tomography (CT) is critical for reducing radiation exposure to patients. Recent advances in radiative 3D Gaussian Splatting (3DGS) have enabled fast and accurate sparse-view CT reconstruction. Despite these algorithmic advancements, practical reconstruction fidelity remains fundamentally bounded by the quality of the captured data, raising the crucial yet underexplored problem of X-ray active view selection. Existing active view selection methods are primarily designed for natural-light scenes and fail to capture the unique geometric ambiguities and physical attenuation properties inherent in X-ray imaging. In this paper, we present Perturbed Gaussian Ensemble, an active view selection framework that integrates uncertainty modeling with sequential decision-making, tailored for X-ray Gaussian Splatting. Specifically, we identify low-density Gaussian primitives that are likely to be uncertain and apply stochastic density scaling to construct an ensemble of plausible Gaussian density fields. For each candidate projection, we measure the structural variance of the ensemble predictions and select the one with the highest variance as the next best view. Extensive experimental results on arbitrary-trajectory CT benchmarks demonstrate that our density-guided perturbation strategy effectively eliminates geometric artifacts and consistently outperforms existing baselines in progressive tomographic reconstruction under unified view selection protocols.

Post-training with reinforcement learning (RL) has recently shown strong promise for advancing multimodal agents beyond supervised imitation. However, RL remains limited by poor data efficiency, particularly in settings where interaction data are scarce and quickly become outdated. To address this challenge, GIPO (Gaussian Importance sampling Policy Optimization) is proposed as a policy optimization objective based on truncated importance sampling, replacing hard clipping with a log-ratio-based Gaussian trust weight to softly damp extreme importance ratios while maintaining non-zero gradients. Theoretical analysis shows that GIPO introduces an implicit, tunable constraint on the update magnitude, while concentration bounds guarantee robustness and stability under finite-sample estimation. Experimental results show that GIPO achieves state-of-the-art performance among clipping-based baselines across a wide range of replay buffer sizes, from near on-policy to highly stale data, while exhibiting superior bias--variance trade-off, high training stability and improved sample efficiency. Code is available at https://github.com/distanceLu/GIPO.

Constant-stepsize stochastic approximation (SA) is widely used in learning for computational efficiency, yet the distribution of the iterates is typically intractable. Classical asymptotics results give $X_k^{(α)} \approx X^{(α)} \approx x^\star+\sqrtαY$, where $X^{(α)}$ is the steady state and $Y$ is an appropriate Gaussian limit, by progressively taking the time $k\uparrow\infty$ and stepsize $α\downarrow0$. Such limit results, however, do not quantify finite-time, finite-stepsize errors. We develop an explicit pre-limit characterization for SA with i.i.d.\ and Markovian noise. We establish existence and uniqueness of the stationary law, a geometric Wasserstein convergence to stationarity, and almost-sure and $L^3$ convergence of the steady state to the root $x^\star$, identifying the scale $\sqrtα$ as first-order fluctuation. At this scale, we derive a higher-order quantitative Gaussian approximation with a Wasserstein error, using Stein's method and Poisson equation techniques. We further obtain non-uniform Berry--Esseen-type tail bounds, incorporating both steady-state approximation and finite-time convergence errors. We instantiate the theory for strongly convex smooth SGD, linear SA, and nonlinear contractive SA. Beyond strong convexity, for general convex SGD, we identify a Gibbs limiting law and prove a pre-limit Wasserstein approximation error under stability and Stein-equation hypothesis, which are validated numerically.

Spectral gradient methods, such as the Muon optimizer, modify gradient updates by preserving directional information while discarding scale, and have shown strong empirical performance in deep learning. We investigate the mechanisms underlying these gains through a dynamical analysis of a nonlinear phase retrieval model with anisotropic Gaussian inputs, equivalent to training a two-layer neural network with the quadratic activation and fixed second-layer weights. Focusing on a spiked covariance setting where the dominant variance direction is orthogonal to the signal, we show that gradient descent (GD) suffers from a variance-induced misalignment: during the early escaping stage, the high-variance but uninformative spike direction is multiplicatively amplified, degrading alignment with the true signal under strong anisotropy. In contrast, spectral gradient descent (SpecGD) removes this spike amplification effect, leading to stable alignment and accelerated noise contraction. Numerical experiments confirm the theory and show that these phenomena persist under broader anisotropic covariances.

This paper introduces an analytical approach to quantifying and optimizing the distributional discrepancy in generative diffusion models. For a multivariate Gaussian source, we explicitly derive the closed-form evolution trajectory and the resulting Kullback-Leibler (KL) divergence between the distributions of the source data and the reversely sampled data. Asymptotic analysis via the Euler-Maclaurin expansion characterizes the convergence behavior of this KL divergence, extracting its dominant term as an explicit functional of the noise schedule. Minimizing this dominant term via the calculus of variations yields a noise schedule described by a tangent law, inherently determined by the source covariance spectrum. We further prove that the Gaussian source exhibits an extremal property for the KL divergence among general source distributions with a given covariance. We also utilize the analytical KL divergence as a principled metric to identify efficient time discretization strategies for pretrained diffusion models, and demonstrate via experiments over diverse datasets that the identified strategies consistently outperform established baselines, particularly under constrained function evaluation budgets.

Building one-shot 3D animatable head avatars is an important yet challenging problem. Existing methods generally collapse under large camera pose variations, compromising the realism of 3D avatars. In this work, we propose a new framework to tackle the novel setting of one-shot 3D full-head animatable avatar reconstruction in a single forward pass via inpainted UV-space Gaussian modeling, enabling 360$^\circ$ rendering views and real-time animation. To facilitate efficient animation control, we model 3D head avatars with Gaussian primitives embedded on the surface of a parametric face model within the UV space, and project the input image features to the UV space, resulting in incomplete local UV feature maps. To inpaint the missing regions, we obtain knowledge of full-head geometry and textures from rich 3D full-head priors within a pretrained 3D generative adversarial network (GAN) for global full-head feature extraction and multi-view supervision. Specifically, to enhance the fidelity of 3D reconstruction during inpainting, we take advantage of the symmetric nature of the UV space and human faces to fuse incomplete yet detailed local UV feature maps with the extracted global full-head textures, resulting in inpainted UV Gaussian attribute maps for avatar modeling. Extensive experiments demonstrate that our method is the first to achieve high-quality 3D full-head animatable avatar modeling, significantly improving side and back views while outperforming state-of-the-art animation approaches, thereby improving the realism of 3D animatable avatars.

Gaussian Splatting has emerged as a powerful representation for high-quality, real-time 3D scene rendering. While recent works extend Gaussians with learnable textures to enrich visual appearance, existing approaches allocate a fixed square texture per primitive, leading to inefficient memory usage and limited adaptability to scene variability. In this paper, we introduce adaptive anisotropic textured Gaussians (A$^2$TG), a novel representation that generalizes textured Gaussians by equipping each primitive with an anisotropic texture. Our method employs a gradient-guided adaptive rule to jointly determine texture resolution and aspect ratio, enabling non-uniform, detail-aware allocation that aligns with the anisotropic nature of Gaussian splats. This design significantly improves texture efficiency, reducing memory consumption while enhancing image quality. Experiments on multiple benchmark datasets demonstrate that A TG consistently outperforms fixed-texture Gaussian Splatting methods, achieving comparable rendering fidelity with substantially lower memory requirements. Project page: http://github.com/Rickyeeeeee/A2TG.

Point cloud segmentation is critical for 3D scene understanding. However, sparse and irregular point distributions provide limited appearance evidence, making geometry-only features insufficient to distinguish objects with similar shapes but distinct appearances e.g., color, texture, and material. We propose Gaussian-to-Point (G2P), which transfers Gaussian attributes from 3D Gaussian Splatting to point clouds for more discriminative and appearance-consistent segmentation. Our G2P addresses the misalignment between optimized Gaussians and original point geometry by establishing point-wise correspondences. By distilling opacity-derived visibility cues, we mitigate the geometric ambiguity that limits existing models. Additionally, Gaussian scale attributes enable precise boundary localization in complex 3D scenes. Extensive experiments demonstrate that our approach achieves competitive performance on standard benchmarks and shows notable improvements on geometrically challenging classes, without pretrained 2D features or language supervision in our segmentation pipeline.

3D Gaussians have become a powerful scene representation for real-time splatting and high-quality novel-view synthesis. This has motivated generalizable splatting -- methods that adapt feed-forward geometry prediction networks to produce per-pixel Gaussians from a set of images. However, most generalizable splatting pipelines are supervised primarily through a view-synthesis loss to predict Gaussian orientation, anisotropic scale, opacity, and appearance in addition to their locations. We show that this learning objective is under-constrained. Models trained with view synthesis alone produce splats whose orientations and scales have no geometric connotation. The result is that, while producing decent view-synthesis performance, nearly all generalizable splatting methods produce geometrically inaccurate and misaligned Gaussians. We introduce G3Splat, a geometry-consistent generalizable splatting framework that addresses these degeneracies through differentiable geometric priors on the predicted 3D Gaussians, making the learning problem well-posed. These priors encourage the per-pixel splats to remain on their viewing rays and to orient themselves in accordance with local surfaces. Our priors are architecture-agnostic and can be incorporated into any previously studied geometric backbone for generalizable splatting, as well as different scene representations. We test G3Splat with both DUSt3R-style and VGGT-style backbones to predict pixel-aligned full-rank 3DGS as well as surfel-like 2DGS. Trained on RE10K, G3Splat produces Gaussian splats with significantly higher geometric fidelity than baselines, providing state-of-the-art novel-view depth, mesh reconstruction, and relative pose estimation performance while preserving novel-view synthesis quality, as evaluated on datasets such as ACID and ScanNet. Code and pretrained models are released on our project page.

Portrait animation has witnessed tremendous quality improvements thanks to recent advances in video diffusion models. However, these 2D methods often compromise 3D consistency and speed, limiting their applicability in real-world scenarios, such as digital twins or telepresence. In contrast, 3D-aware feedforward facial animation methods -- built upon 3D representations, such as neural radiance fields or Gaussian splatting -- ensure 3D consistency and achieve faster inference speed, but come with inferior expression details. In this paper, we address this portrait animation trilemma (speed, 3D consistency, and expressiveness) and propose a pipeline that instantly converts an in-the-wild single image into a 3D-consistent, fast yet expressive animatable representation via a feed-forward encoder. Unlike previous computationally intensive global fusion mechanisms (e.g., multiple attention layers) for fusing 3D structural and animation information, our design employs an efficient lightweight local fusion strategy to achieve high animation expressivity. Furthermore, our animation representation is decoupled from the face's 3D representation and learns motion implicitly from data, eliminating the dependency on pre-defined parametric models that often constrain animation capabilities. Our method runs at 107.31 FPS for animation and pose control, representing a 3-4 order of magnitude speedup versus the state of the art while achieving comparable animation quality, thus surpassing alternative designs that trade speed for quality or vice versa.

Large Vision-Language Models (LVLMs) often produce plausible but unreliable outputs, making robust uncertainty estimation essential. Recent work on semantic uncertainty estimates relies on external models to cluster multiple sampled responses and measure their semantic consistency. However, these clustering methods are often fragile, highly sensitive to minor phrasing variations, and can incorrectly group or separate semantically similar answers, leading to unreliable uncertainty estimates. We propose Semantic Gaussian Process Uncertainty (SGPU), a Bayesian framework that quantifies semantic uncertainty by analyzing the geometric structure of answer embeddings, avoiding brittle clustering. SGPU maps generated answers into a dense semantic space, computes the Gram matrix of their embeddings, and summarizes their semantic configuration via the eigenspectrum. This spectral representation is then fed into a Gaussian Process Classifier that learns to map patterns of semantic consistency to predictive uncertainty, and that can be applied in both black-box and white-box settings. Across six LLMs and LVLMs on eight datasets spanning VQA, image classification, and textual QA, SGPU consistently achieves state-of-the-art calibration (ECE) and discriminative (AUROC, AUARC) performance. We further show that SGPU transfers across models and modalities, indicating that its spectral representation captures general patterns of semantic uncertainty.

We propose a method to reconstruct dynamic fire in 3D from a limited set of camera views with a Gaussian-based spatiotemporal representation. Capturing and reconstructing fire and its dynamics is highly challenging due to its volatile nature, transparent quality, and multitude of high-frequency features. Despite these challenges, we aim to reconstruct fire from only three views, which consequently requires solving for under-constrained geometry. We solve this by separating the static background from the dynamic fire region by combining dense multi-view stereo images with monocular depth priors. The fire is initialized as a 3D flow field, obtained by fusing per-view dense optical flow projections. To capture the high frequency features of fire, each 3D Gaussian encodes a lifetime and linear velocity to match the dense optical flow. To ensure sub-frame temporal alignment across cameras we employ a custom hardware synchronization pattern -- allowing us to reconstruct fire with affordable commodity hardware. Our quantitative and qualitative validations across numerous reconstruction experiments demonstrate robust performance for diverse and challenging real fire scenarios.

Recent advances in 3D Gaussian Splatting (3DGS) have enabled Simultaneous Localization and Mapping (SLAM) systems to build photorealistic maps. However, these maps lack the open-vocabulary semantic understanding required for robotic interaction. Integrating language features into SLAM remains a significant challenge, as storing high-dimensional features incurs excessive memory and rendering overhead, while existing methods with static models lack adaptability for novel environments. We propose LEGO-SLAM (Language-Embedded Gaussian Optimization SLAM), a framework that achieves real-time, open-vocabulary mapping within a 3DGS-based SLAM system. At the core of our method is a scene-adaptive autoencoder that distills high-dimensional language embeddings into a compact 16-dimensional feature space, reducing the memory per Gaussian and accelerating rendering. Unlike static approaches, our encoder adapts online to unseen scenes. These compact features also enable a language-guided pruning strategy that identifies semantic redundancy, reducing the map's Gaussian count by up to 58% while maintaining rendering quality. Furthermore, we introduce a language-based loop detection approach that reuses the language features already extracted for mapping, eliminating the need for a separate detection model. Experiments demonstrate that LEGO-SLAM achieves competitive mapping quality and tracking accuracy, all while providing open-vocabulary capabilities at 15 FPS. Our project page is available at https://lab-of-ai-and-robotics.github.io/LEGO-SLAM/

Complex-valued Gaussian primitives have recently been explored for representing holographic radiance fields in 3D novel view synthesis. In this work, we extend this line of research to the hologram optimization domain and propose a structured representation based on complex-valued 2D Gaussian primitives. Inspired by Gabor's theory, we show that our primitive attains the minimum space-frequency uncertainty and reduces the parameter search space by 5:1 compared to per-pixel parameterization. To enable end-to-end training, we develop a differentiable rasterizer for our representation, integrated with a GPU-optimized light propagation kernel in free space. Extensive experiments show that our method reduces VRAM usage by up to 30% and accelerates optimization by 50% over standard autodiff-based implementations, delivers up to 13 dB higher PSNR than prior Gaussian-based methods, and achieves up to 3200x faster rendering while maintaining reconstruction quality on par with existing CGH approaches. For evaluation, we introduce a conversion procedure that adapts our representation to practical hologram formats, including smooth and random phase-only holograms. By reducing the hologram parameter search space, our representation enables a more scalable hologram estimation in the next-generation computer-generated holography systems.