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

Polynomial Stein discrepancies (PSD) provide a scalable alternative to kernel Stein methods for measuring sample quality and goodness-of-fit testing, but their statistical properties remain poorly understood. We show that increasing polynomial degree primarily amplifies signal without adequately controlling variance, rather than directly optimising the signal-to-noise ratio (SNR). Under suitable assumptions, this might lead to a failure mode in which the $\text{SNR}^2$ can provably decay exponentially with polynomial degree. Motivated by this observation, we reformulate Stein discrepancy construction as an explicit $\text{SNR}^2$ maximisation problem, yielding a Rayleigh quotient over Stein features. This perspective motivates $λ$-PSD, an approximate scalable covariance-aware reweighting scheme defined in a low-dimensional subspace. Under Gaussian settings, we show that $λ$-PSD avoids the exponential $\text{SNR}^2$ collapse and achieves a stable $\text{SNR}^2$. Empirically, $λ$-PSD substantially improves test power while retaining linear-time complexity in the number of samples, highlighting the importance of SNR-aware design for scalable Stein discrepancies.

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Out-of-distribution (OOD) 3D relighting requires novel view synthesis under unseen lighting conditions that differ significantly from the observed images. Existing relighting methods, which assume consistent light source distributions between training and testing, often degrade in OOD scenarios. We introduce MetaGS to tackle this challenge from two perspectives. First, we propose a meta-learning approach to train 3DGaussian splatting, which explicitly promotes learning generalizable Gaussian geometries and appearance attributes across diverse lighting conditions, even with biased training data. Second, we embed fundamental physical priors from the Blinn-Phong reflection model into Gaussian splatting, which enhances the decoupling of shading components and leads to more accurate 3D scene reconstruction. Results on both synthetic and real-world datasets demonstrate the effectiveness of MetaGS in challenging OOD relighting tasks, supporting efficient point-light relighting and generalizing well to unseen environment lighting maps.

However, its capability for accurate surface reconstruction remains underexplored. Due to the discrete and unstructured nature of Gaussians, supervision based solely on image rendering loss often leads to inaccurate geometry and inconsistent multi-view alignment. In this work, we propose a novel method that enhances the geometric representation of 3DGaussians through view alignment (VA). Specifically, we incorporate edge-aware image cues into the rendering loss to improve surface boundary delineation. To enforce geometric consistency across views, we introduce a visibility-aware photometric alignment loss that models occlusions and encourages accurate spatial relationships among Gaussians. To further mitigate ambiguities caused by lighting variations, we incorporate normal-based constraints to refine the spatial orientation of Gaussians and improve local surface estimation. Additionally, we leverage deep image feature embeddings to enforce cross-view consistency, enhancing the robustness of the learned geometry under varying viewpoints and illumination. Extensive experiments on standard benchmarks demonstrate that our method achieves stateof-the-art performance in both surface reconstruction and novel view synthesis. The source code is available at https://github.com/LeoQLi/VA-GS.

Opaque objects reconstructed by 3DGaussian Splatting (3DGS) often exhibit a falsely transparent surface, leading to inconsistent background and internal patterns under camera motion in interactive viewing. This issue stems from the ill-posed optimization in 3DGS. During training, background and foreground Gaussians are blended via α-compositing and optimized solely against the input RGB images using a photometric loss. As this process lacks an explicit constraint on surface opacity, the optimization may incorrectly assign transparency to opaque regions, resulting in view-inconsistent and falsely transparent output. This issue is difficult to detect in standard evaluation settings (i.e., rendering static images), but becomes particularly evident in object-centric reconstructions under interactive viewing.

Novel view synthesis from monocular videos of dynamic scenes with unknown While camera recent poses remains advances a in fundamental 3D representations challenge such in computer as Neural vision Radiance and graphics. Fields (NeRF) scenes, and they 3D struggle Gaussian with Splatting dynamic (3DGS) content ha and ve sho typically wn promising rely on results pre-computed for static camera poses. We present 4D3R, a pose-free dynamic neural rendering framework that Our method decouples first static leverages and dynamic 3D foundational components models through for initial a tw pose o-stage and approach.

Open-vocabulary querying in 3D space is crucial for enabling more intelligent perception in applications such as robotics, autonomous systems, and augmented reality. However, most existing methods rely on 2D pixel-level parsing, leading to multi-view inconsistencies and poor 3D object retrieval. Moreover, they are limited to static scenes and struggle with dynamic scenes due to the complexities of motion modeling. In this paper, we propose Segment then Splat, a 3D-aware open vocabulary segmentation approach for both static and dynamic scenes based on Gaussian Splatting. Segment then Splat reverses the long-established approach of "segmentation after reconstruction" by dividing Gaussians into distinct object sets before reconstruction.

In this work, we present a novel level-of-detail (LOD) method for 3DGaussian Splatting that enables real-time rendering of large-scale scenes on memoryconstrained devices. Our approach introduces a hierarchical LOD representation that iteratively selects optimal subsets of Gaussians based on camera distance, thus largely reducing both rendering time and GPU memory usage. We construct each LOD level by applying a depth-aware 3D smoothing filter, followed by importancebased pruning and fine-tuning to maintain visual fidelity. To further reduce memory overhead, we partition the scene into spatial chunks and dynamically load only relevant Gaussians during rendering, employing an opacity-blending mechanism to avoid visual artifacts at chunk boundaries. Our method achieves state-of-the-art performance on both outdoor (Hierarchical 3DGS) and indoor (Zip-NeRF) datasets, delivering high-quality renderings with reduced latency and memory requirements.

Visual autoregressive modeling has recently demonstrated potential in image tasks by enabling coarse-to-fine, next-level prediction. Most indoor 3D occupancy prediction methods, however, continue to rely on dense voxel grids and convolution-heavy backbones, which incur high computational costs when applying such coarse-tofine frameworks. In contrast, cost-efficient alternatives based on Gaussian representations--particularly in the context of multi-scale autoregression--remain underexplored. To bridge this gap, we propose DFGauss, a Dynamic Focused masking framework for multi-scale 3DGaussian representation. Unlike conventional approaches that refine voxel volumes or 2D projections, DFGauss directly operates in the 3DGaussian parameter space, progressively refining representations across resolutions under hierarchical supervision. Each finer-scale Gaussian is conditioned on its coarser-level counterpart, forming a scale-wise autoregressive process. To further enhance efficiency, we introduce an importance-guided refinement strategy that selectively propagates informative Gaussians across scales, enabling spatially adaptive detail modeling. Experiments on 3D occupancy benchmarks demonstrate that DFGauss achieves competitive performance, highlighting the promise of autoregressive modeling for scalable 3D occupancy prediction.