3D Gaussian Splatting

This paper focuses on a challenging setting of simultaneously modeling geometry and appearance of hand-object interaction scenes without any object priors. We follow the trend of dynamic 3D Gaussian Splatting based methods, and address several significant challenges. To model complex hand-object interaction with mutual occlusion and edge blur, we present interaction-aware hand-object Gaussians with newly introduced optimizable parameters aiming to adopt piecewise linear hypothesis for clearer structural representation. Moreover, considering the complementarity and tightness of hand shape and object shape during interaction dynamics, we incorporate hand information into object deformation field, constructing interaction-aware dynamic fields to model flexible motions. To further address difficulties in the optimization process, we propose a progressive strategy that handles dynamic regions and static background step by step. Correspondingly, explicit regularizations are designed to stabilize the hand-object representations for smooth motion transition, physical interaction reality, and coherent lighting. Experiments show that our approach surpasses existing dynamic 3D-GS-based methods and achieves state-of-the-art performance in reconstructing dynamic hand-object interaction.

We consider the problems of \emph{learning} and \emph{testing} real-valued convex functions over Gaussian space. Despite the extensive study of function convexity across mathematics, statistics, and computer science, its learnability and testability have largely been examined only in discrete or restricted settings -- typically with respect to the Hamming distance, which is ill-suited for real-valued functions. In contrast, we study these problems in high dimensions under the standard Gaussian measure, assuming sample access to the function and a mild smoothness condition, namely Lipschitzness. A smoothness assumption is natural and, in fact, necessary even in one dimension: without it, convexity cannot be inferred from finitely many samples. As our main results, we give: - Learning Convex Functions: An agnostic proper learning algorithm for Lipschitz convex functions that achieves error $\varepsilon$ using $n^{O(1/\varepsilon^2)}$ samples, together with a complementary lower bound of $n^{\mathrm{poly}(1/\varepsilon)}$ samples in the \emph{correlational statistical query (CSQ)} model. - Testing Convex Functions: A tolerant (two-sided) tester for convexity of Lipschitz functions with the same sample complexity (as a corollary of our learning result), and a one-sided tester (which never rejects convex functions) using $O(\sqrt{n}/\varepsilon)^n$ samples.

Urban scene reconstruction is critical for autonomous driving, enabling structured 3D representations for data synthesis and closed-loop testing. Supervised approaches rely on costly human annotations and lack scalability, while current self-supervised methods often confuse static and dynamic elements and fail to distinguish individual dynamic objects, limiting fine-grained editing. We propose DIAL-GS, a novel dynamic instance-aware reconstruction method for label-free street scenes with 4D Gaussian Splatting. We first accurately identify dynamic instances by exploiting appearance-position inconsistency between warped rendering and actual observation. Guided by instance-level dynamic perception, we employ instance-aware 4D Gaussians as the unified volumetric representation, realizing dynamic-adaptive and instance-aware reconstruction. Furthermore, we introduce a reciprocal mechanism through which identity and dynamics reinforce each other, enhancing both integrity and consistency. Experiments on urban driving scenarios show that DIAL-GS surpasses existing self-supervised baselines in reconstruction quality and instance-level editing, offering a concise yet powerful solution for urban scene modeling.

Recovery from linear measurements under sparse adversarial corruption is typically formulated as an exact-recovery problem: one seeks structural conditions on $\mathbf{A}$ (e.g., restricted isometry property) guaranteeing unique recovery of $\mathbf{x}^\star$ from $\mathbf{y} = \mathbf{A}\mathbf{x}^\star + \mathbf{e}$ with $\|\mathbf{e}\|_0 \leq q$. However, these guarantees provide no guidance once exact recovery fails. This limitation obscures simple robustness phenomena -- for instance, repeated rows in $\mathbf{A}$ can preserve nontrivial information about $\mathbf{x}^\star$ under sparse corruption. In this paper, we study what information about $\mathbf{x}^\star$ can be \emph{uniformly} recovered from $\mathbf{y} = \mathbf{A}\mathbf{x}^\star + \mathbf{e}$ for arbitrary $\mathbf{A}\in\mathbb{R}^{m\times n}$ and \emph{any} $q$-sparse $\mathbf{e}$. We show that the robust information is precisely $\mathbf{x}^\star + \ker(\mathbf{U})$, where $\mathbf{U}$ is the orthogonal projection onto the intersection of rowspaces of all submatrices of $\mathbf{A}$ obtained by deleting $2q$ rows. This clarifies how the row structure of $\mathbf{A}$ governs whether a $q$-sparse corruption allows exact, partial, or only trivial recovery. We further prove every $\mathbf{x}$ minimizing $\|\mathbf{y} - \mathbf{A} \mathbf{x}\|_0$ belongs to $\mathbf{x}^\star + \ker(\mathbf{U})$, yielding a constructive approach to recover this set. For i.i.d. Gaussian matrices, we establish a sharp phase transition between exact and trivial recovery. We sketch two applications: robust network tomography and signal reconstruction from oversampled DCT.

This paper proposes an effective Gaussian management framework for high-fidelity scene reconstruction of both appearance and geometry. Unlike recent Gaussian Splatting (GS) pipelines that treat all primitives uniformly during optimization, our framework explicitly manages the attribute activation, representation and pruning of Gaussian. Specifically, our framework first introduces GauSep, a novel densification strategy that selectively activates Gaussian color or normal attributes to alleviate destructive gradient conflicts arising from dual supervision. We further propose GauRep, an adaptive Gaussian representation that dynamically adjusts spherical harmonics (SHs) orders and performs task-decoupled pruning to reduce redundancy at both the individual and global levels. To provide reliable geometric supervision for above mangement process, we additionally introduce CoRe, an regularized surface reconstruction module that distills robust normal fields from an SDF branch to the Gaussian representation through a confidence mechanism. Notably, the proposed Gaussian management is compatible with various reconstruction architectures and can be seamlessly integrated to improve performance while reducing size of the model. Extensive experiments demonstrate that our approach achieves superior or comparable performance in appearance and geometry reconstruction compared with state-of-the-art methods, while using significantly fewer parameters.

Machin-like arctangent relations are classical tools for computing $π$, with efficiency quantified by the Lehmer measure ($λ$). We present a framework for discovering low-measure relations by coupling the PSLQ integer-relation algorithm with number-theoretic filters derived from the algebraic structure of Gaussian integers, making large scale search tractable. Our search yields new 5 and 6 term relations with record-low Lehmer measures ($λ=1.4572, λ=1.3291$). We also demonstrate how discovered relations can serve as a basis for generating new, longer formulae through algorithmic extensions. This combined approach of a constrained PSLQ search and algorithmic extension provides a robust method for future explorations.

While 3D Gaussian Splatting (3DGS) has established new standards for high-fidelity 3D scene modeling, interpreting massive, unstructured Gaussian primitives into meaningful geospatial entities remains a critical challenge for remote sensing and urban applications. Existing 2D-to-3D distillation methods suffer from projection ambiguities, geometric inconsistencies, and computational bottlenecks when applied to complex, large-scale topographies. Furthermore, current benchmarks lack natively aligned 2D-3D ground truth tailored for splatting-based representations. To address these limitations, we propose \textit{PointGauss}, a unified 3D-native framework for robust semantic parsing and instance segmentation. By treating Gaussian primitives as unstructured point sets, PointGauss leverages Point Transformer V3 (PTv3) to extract scale-invariant geometric features directly from Gaussian attributes, effectively resolving projection ambiguities. To ensure scalability in building-scale scenes, we introduce an adaptive region-of-interest cropping strategy and an instance-aware distance-constrained rasterization pipeline for pixel-level, view-consistent projection. Additionally, we present \textbf{SplatSeg-360}, the first rigorous cross-scale benchmark tailored for 3DGS, comprising 32 complex scenes with full 360$^\circ$ coverage and over 6,300 natively aligned 2D-3D masks. Extensive experiments demonstrate that PointGauss operates in real-time and achieves state-of-the-art performance. Notably, it attains approximately 90% 3D-mIoU in large-scale building scenarios and roughly 80% 2D-mIoU in view-consistent 2D instance segmentation, outperforming baseline methods by 16%. (\href{https://github.com/hbycswt/pointgauss#}{Code})

We develop sampling methods, which consist of Gaussian invariant versions of random walk Metropolis (RWM), Metropolis adjusted Langevin algorithm (MALA) and second order Hessian or Manifold MALA. Unlike standard RWM and MALA, we show that Gaussian invariant sampling can lead to ergodic estimators with improved statistical efficiency. This is due to a remarkable property of Gaussian invariance that allows us to obtain exact analytical solutions to the Poisson equation for Gaussian targets. These solutions can be used to construct efficient and easy to use control variates for variance reduction of estimators under any intractable target. We demonstrate the new samplers and estimators in several examples, including high dimensional targets in latent Gaussian models where we compare against several advanced methods and obtain state-of-the-art results. We also provide theoretical results regarding geometric ergodicity, and an optimal scaling analysis that shows the dependence of the optimal acceptance rate on the Gaussianity of the target.

This paper studies the $\ell^p$-Lipschitz constants of ReLU neural networks $Φ: \mathbb{R}^d \to \mathbb{R}$ with random parameters for $p \in [1,\infty]$. The distribution of the weights follows a variant of the He initialization. In the case of zero-bias networks, we derive high probability upper and lower bounds for wide networks that differ at most by a factor that is logarithmic in the network's depth. Remarkably, the behavior of the $\ell^p$-Lipschitz constant varies significantly between the regimes $p \in [1,2)$ and $p \in [2,\infty]$. For $p \in [2,\infty]$, the $\ell^p$-Lipschitz constant behaves similarly to $\Vert g\Vert_{p'}$, where $g \in \mathbb{R}^d$ is a $d$-dimensional standard Gaussian vector and $1/p + 1/p' = 1$. In contrast, for $p \in [1,2)$, the $\ell^p$-Lipschitz constant aligns more closely to $\Vert g \Vert_{2}$. We extend our analysis to networks with possibly non-zero biases drawn from arbitrary symmetric distributions. In this case, we obtain high probability upper and lower bounds that differ at most by a factor that is logarithmic in the network's width and linear in its depth.

3D Gaussian Splatting (3DGS) has emerged as a powerful technique for novel view synthesis, combining high-quality reconstruction with efficient rendering. It has been widely adopted in domains such as AR/VR, robotics, and autonomous driving. However, achieving real-time performance on resource-constrained platforms remains challenging due to strict power and area budgets. Prior accelerators improve hardware performance but still overlook key inefficiencies, including insufficient rasterization efficiency, poor sorting scalability, and pipeline imbalance. This paper presents an architecture-algorithm co-design to address these challenges. First, we propose axis-shared rasterization, which precomputes and reuses common terms along the X- and Y-axes, reducing multiply-and-accumulate (MAC) operations by up to 38% while preserving high parallelism. Second, we develop a novel order-independent transmittance method that removes the need for explicit sorting by leveraging a lightweight multilayer perceptron (MLP) to directly approximate the transmittance of each Gaussian, enabling efficient alpha blending with negligible quality loss. Third, we design a unified reconfigurable PE array that supports both rasterization and MLP inference, sustaining high utilization without costly sorting hardware. Our experiments demonstrate that our design preserves rendering quality while achieving a 1.33 to 1.88x speedup over state-of-the-art 3DGS accelerators. Our code is open source at https://github.com/WangZhican/ISCA26_3DGS_Acc.

Prevailing activation functions such as Swish and GELU tend toward domain-specific optima, Swish was discovered via neural architecture search on vision benchmarks, while GELU dominates transformer-based language models, and neither offers any mechanism to adapt its gating shape to individual layers. This rigidity is especially consequential in transformer FFN blocks, where LayerNorm, unlike BatchNorm, does not suppress the gradient pathologies that activation choice induces across depth. We propose SG-Blend, a per layer adaptive activation that combines SSwish, a bias-corrected, parametric Swish variant we also introduce, with learnable sharpness \b{eta} and zero-centering bias γ, with GELU through a per-layer blend coefficient α, letting each layer locate its own optimum along the SSwishGELU continuum at a cost of only three additional scalars per FFN block, with \b{eta} initialized to 1.0 and learned freely via backpropagation. On BERT-style IMDB classification (5 seeds), it matches peak accuracy (81.31%) while reducing seed-to-seed variance by 42% relative to GELU. Furthermore, it generalizes to autoregressive pretraining, achieving the lowest validation perplexity (49.10) on WikiText103 among all baselines. Crucially, ablations confirm the interpolation structure itself drives these gains, delivering reliable, top-tier performance. Beyond natural language processing, we demonstrate that SG-Blend generalizes robustly to a wider variety of tasks, extending its efficacy to computer vision and other diverse domains.

Underwater 3D scene reconstruction is crucial for multimedia applications in adverse environments, such as underwater robotic perception and navigation. However, the complexity of interactions between light propagation, water medium, and object surfaces poses significant difficulties for existing methods in accurately simulating their interplay. Additionally, expensive training and rendering costs limit their practical application. Therefore, we propose Tensorized Underwater Gaussian Splatting (TUGS), a compact underwater 3D representation based on physical modeling of complex underwater light fields. TUGS includes a physics-based underwater Adaptive Medium Estimation (AME) module, enabling accurate simulation of both light attenuation and backscatter effects in underwater environments, and introduces Tensorized Densification Strategies (TDS) to efficiently refine the tensorized representation during optimization. TUGS is able to render high-quality underwater images with faster rendering speeds and less memory usage. Extensive experiments on real-world underwater datasets have demonstrated that TUGS can efficiently achieve superior reconstruction quality using a limited number of parameters. The code is available at https://liamlian0727.github.io/TUGS

Sorting and permutation learning are key concepts in optimization and machine learning, especially when organizing high-dimensional data into meaningful spatial layouts. The Gumbel-Sinkhorn method, while effective, requires N*N parameters to determine a full permutation matrix, making it computationally expensive for large datasets. Low-rank matrix factorization approximations reduce memory requirements to 2NM (with M << N), but they still struggle with very large problems. SoftSort, by providing a continuous relaxation of the argsort operator, allows differentiable 1D sorting, but it faces challenges with multidimensional data and complex permutations. In this paper, we present a novel method for learning permutations using only N parameters, which dramatically reduces storage costs. Our method extends SoftSort by iteratively shuffling the N indices of the elements and applying a few SoftSort optimization steps per iteration. This modification significantly improves sorting quality, especially for multidimensional data and complex optimization criteria, and outperforms pure SoftSort. Our method offers improved memory efficiency and scalability compared to existing approaches, while maintaining high-quality permutation learning. Its dramatically reduced memory requirements make it particularly well-suited for large-scale optimization tasks, such as "Self-Organizing Gaussians", where efficient and scalable permutation learning is critical.

We study the fundamental problem of calibrating a linear binary classifier of the form $σ(\hat{w}^\top x)$, where the feature vector $x$ is Gaussian, $σ$ is a link function, and $\hat{w}$ is an estimator of the true linear weight $w^\star$. By interpolating with a noninformative $\textit{chance classifier}$, we construct a well-calibrated predictor whose interpolation weight depends on the angle $\angle(\hat{w}, w_\star)$ between the estimator $\hat{w}$ and the true linear weight $w_\star$. We establish that this angular calibration approach is provably well-calibrated in a high-dimensional regime where the number of samples and features both diverge, at a comparable rate. The angle $\angle(\hat{w}, w_\star)$ can be consistently estimated. Furthermore, the resulting predictor is uniquely $\textit{Bregman-optimal}$, minimizing the Bregman divergence to the true label distribution within a suitable class of calibrated predictors. Our work is the first to provide a calibration strategy that satisfies both calibration and optimality properties provably in high dimensions. Additionally, we identify conditions under which a classical Platt-scaling predictor converges to our Bregman-optimal calibrated solution. Thus, Platt-scaling also inherits these desirable properties provably in high dimensions.

3D Gaussian Splatting (3DGS) has been widely used in 3D reconstruction and 3D generation. However, the rapid adoption of 3D Gaussian Splatting raises growing concerns about information leakage and unauthorized use, urging the exploration of effective watermarking techniques. However, existing methods are limited by low capacity, fragility under geometric perturbations, and the infeasible requirement for costly fine-tuning or pipeline modifications, motivating the need for a generalizable, feed-forward framework capable of robust multi-modal embedding with minimal intrusion. In this paper, we propose a new framework X-SG$^2$S which can simultaneously inject 1D to 3D watermarks for copyright protection, while keeping the high fidelity of original 3DGS scenes. Specifically, we first split the watermarks into message patches. A self-adaptive gate is developed to select the injection positions of the watermark messages. Then, we use an XD (multi-dimensional) injection head to inject multi-modal messages into sorted 3DGS points. To restore watermarking messages, a learnable gate is developed to recognize the watermarked locations, from which our XD-extraction heads are used to restore hidden messages. X-SG$^2$S is the first framework to unify 1D-to-3D watermarking and enable simultaneous multi-modal watermark embedding in 3DGS, achieving this with minimal rendering interference and zero modifications to parameters or pipelines. Extensive experiments demonstrate that X-SG$^2$S effectively preserves consistency between the watermark and the original 3DGS, exhibits robustness against model degradation, and maintains accurate judgment capabilities.

Implicit Neural Representations (INRs) approximate discrete data through continuous functions and are commonly used for encoding 2D images. Traditional image-based INRs employ neural networks to map pixel coordinates to RGB values, capturing shapes, colors, and textures within the network's weights. Recently, GaussianImage has been proposed as an alternative, using Gaussian functions instead of neural networks to achieve comparable quality and compression. Such a solution obtains a quality and compression ratio similar to classical INR models but does not allow image modification. In contrast, our work introduces a novel method, MiraGe, which uses mirror reflections to perceive 2D images in 3D space and employs flat-controlled Gaussians for precise 2D image editing. Our approach improves the rendering quality and allows realistic image modifications, including human-inspired perception of photos in the 3D world. Thanks to modeling images in 3D space, we obtain the illusion of 3D-based modification in 2D images. We also show that our Gaussian representation can be easily combined with a physics engine to produce physics-based modification of 2D images. Consequently, MiraGe allows for better quality than the standard approach and natural modification of 2D images

Despite their empirical success across a wide range of generative tasks, the fundamental principles underlying the ability of diffusion models to learn data distributions are poorly understood. In this work, we develop a new mathematical framework that explains how diffusion models can effectively learn low-dimensional distributions from a finite number of training samples without suffering from the curse of dimensionality. Specifically, motivated by the intrinsic low-dimensional structure of image data, we theoretically analyze a setting in which the data distribution is modeled as a mixture of low-rank Gaussians. Under suitable network parameterization, we show that optimizing the training objective of diffusion models is equivalent to solving the canonical subspace clustering problem over the training samples, where each subspace basis corresponds to the low-rank covariance of a Gaussian component. This equivalence allows us to show that the sample complexity for learning the underlying distribution scales linearly with the intrinsic dimension of the data, rather than exponentially with the ambient dimension. Our theoretical findings are further supported by empirical evidence that demonstrates phase transition phenomena in generalization on both synthetic and real-world image datasets. Moreover, we establish a correspondence between the learned subspace bases and semantic attributes of image data, providing a principled foundation for controllable image generation.

In this paper, we propose MoDGS, a new pipeline to render novel views of dy namic scenes from a casually captured monocular video. Previous monocular dynamic NeRF or Gaussian Splatting methods strongly rely on the rapid move ment of input cameras to construct multiview consistency but struggle to recon struct dynamic scenes on casually captured input videos whose cameras are either static or move slowly. To address this challenging task, MoDGS adopts recent single-view depth estimation methods to guide the learning of the dynamic scene. Then, a novel 3D-aware initialization method is proposed to learn a reasonable deformation field and a new robust depth loss is proposed to guide the learning of dynamic scene geometry. Comprehensive experiments demonstrate that MoDGS is able to render high-quality novel view images of dynamic scenes from just a casually captured monocular video, which outperforms state-of-the-art meth ods by a significant margin. The code is publicly available now.

3D Gaussian Splatting (3DGS) has emerged as a powerful explicit representation enabling real-time, high-fidelity 3D reconstruction and novel view synthesis. However, its practical use is hindered by the massive memory and computational demands required to store and render millions of Gaussians. These challenges become even more severe in 4D dynamic scenes. To address these issues, the field of Efficient Gaussian Splatting has rapidly evolved, proposing methods that reduce redundancy while preserving reconstruction quality. This survey provides the first unified overview of efficient 3D and 4D Gaussian Splatting techniques. For both 3D and 4D settings, we systematically categorize existing methods into two major directions, Parameter Compression and Restructuring Compression, and comprehensively summarize the core ideas and methodological trends within each category. We further cover widely used datasets, evaluation metrics, and representative benchmark comparisons. Finally, we discuss current limitations and outline promising research directions toward scalable, compact, and real-time Gaussian Splatting for both static and dynamic 3D scene representation.

High dynamic range (HDR) novel view synthesis (NVS) aims to reconstruct HDR scenes from multi-exposure low dynamic range (LDR) images. Existing HDR pipelines heavily rely on known camera poses, well-initialized dense point clouds, and time-consuming per-scene optimization. Current feed-forward alternatives overlook the HDR problem by assuming exposure-invariant appearance. To bridge this gap, we propose InstantHDR, a feed-forward network that initializes 3D HDR scenes from uncalibrated multi-exposure LDR collections in a fast single forward pass. Specifically, we design a geometry-guided appearance modeling for multi-exposure fusion, and a meta-network for generalizable scene-specific tone mapping. Due to the lack of HDR scene data, we build a pre-training dataset, called HDR-Pretrain, for generalizable feed-forward HDR models, featuring 168 Blender-rendered scenes, diverse lighting types, and multiple camera response functions. Comprehensive experiments show that our InstantHDR delivers a single-forward HDR initialization at approximately 700 times the speed of SoTA optimization-based methods, and reaches comparable quality in real settings after lightweight post-optimization while remaining approximately 20 times faster. All code, models, and datasets: https://github.com/Bugjudger/InstantHDR.

Depth completion aims to predict a dense depth map from a color image with sparse depth measurements. Although deep learning methods have achieved state-of-the-art (SOTA), effectively handling the sparse and irregular nature of input depth data in deep networks remains a significant challenge, often limiting performance, especially under high sparsity. To overcome this limitation, we introduce the Gaussian Belief Propagation Network (GBPN), a novel hybrid framework synergistically integrating deep learning with probabilistic graphical models for end-to-end depth completion. Specifically, a scene-specific Markov Random Field (MRF) is dynamically constructed by the Graphical Model Construction Network (GMCN), and then inferred via Gaussian Belief Propagation (GBP) to yield the dense depth distribution. Crucially, the GMCN learns to construct not only the data-dependent potentials of MRF but also its structure by predicting adaptive non-local edges, enabling the capture of complex, long-range spatial dependencies. Furthermore, we enhance GBP with a serial & parallel message passing scheme, designed for effective information propagation, particularly from sparse measurements. Extensive experiments demonstrate that GBPN achieves SOTA performance on the NYUv2 and KITTI benchmarks. Evaluations across varying sparsity levels, sparsity patterns, and datasets highlight GBPN's superior performance, notable robustness, and generalizable capability.

The appearance of a smoky scene is shaped by two processes that a camera records together: the participating medium alters scene radiance in a view-dependent way, and the image signal processor (ISP) then remaps the result through a nonlinear tone and color transformation. Recovering a clean 3D scene requires separating both. Per-view sRGB dehazing acts only after the ISP has entangled them; standard 3D reconstruction ignores the medium and absorbs it into scene geometry and radiance. FujinSplat addresses the problem in the RAW domain, where the two processes remain separable. A per-scene Base ISP is fitted from the scene's hazy RAW captures to its own camera renderings and then frozen, providing a fixed photometric anchor that performs no dehazing. Analyzing expert corrections reveals a compact, low-dimensional correction space identifiable from RAW alone. FujinSplat therefore fits per-view action answers at the training poses and trains a single scene-agnostic controller to regress them from RAW; the corrected views supervise one static 3D Gaussian representation, jointly with a bounded per-view residual that reconciles cross-view photometric inconsistencies. On the RealX3D real-world smoke benchmark FujinSplat clearly outperforms the strongest comparable baseline, ahead of both physics-based reconstruction and restoration-then-3DGS pipelines. Code is available at https://github.com/I2WM/FujinSplat .