3D Gaussian Splatting

Referring scene understanding for embodied robots requires grounding object- and relation-centric language queries from a designated viewpoint. While a local semantic Gaussian map can support such grounding within one agent's observations, cooperative settings require this ability to remain effective after independently reconstructed maps are aligned and fused. In this setting, the referred target or its contextual landmark may come from another agent's observations, while spatial relations must still be interpreted from the querying robot's viewpoint. We formulate this problem as cooperative referring Gaussian grounding over fused maps, which requires geometric alignability, instance-level semantic comparability, and view-conditioned relation reasoning. Existing language-aware Gaussian methods mainly focus on single-map querying, whereas Gaussian registration methods optimize geometric or photometric alignment without preserving language-grounding-oriented semantic compatibility. We propose CoRef-GS, a cooperative referring Gaussian splatting framework. CoRef-GS constructs local open-vocabulary instance-aware Gaussian maps, then aligns partially overlapping maps with a cross-agent alignment module by geometric and semantic consistency, and grounds queries using a view-conditioned mask relation graph. We further introduce CoQuad-Ref, a dual-quadruped benchmark spanning both real-world and simulated indoor scenes. Experiments show that, on simulated scenes, CoRef-GS reduces the rotation error from 2.58° after coarse initialization to 0.15° after refinement, and improves real-world referring mIoU over ReferSplat from 52.6% to 68.8%. The established benchmark and source code will be publicly released at https://github.com/ruojiruoli17/CoRef-GS.git.

Conventional 3D Gaussian Splatting assumes a closed set of observations and long optimization schedules. Continual RGB-D mapping in contrast poses the problem that new observations arrive online, while previously reconstructed regions must be preserved. We present EliGSiR (Evidence-guided Load-adaptive Incremental Gaussian Splatting with Image Replay), a continual Gaussian mapper that controls how the available optimization budget is used as the reconstruction evolves. Map-Guided View Scheduling filters redundant incoming views and reconsiders retained views according to the current state of the map. Load-Adaptive Fidelity adjusts supervision resolution to the current mapping load instead of following a fixed resolution schedule. Targeted Geometry Growth separates depth supervision from Gaussian creation and adds geometric capacity only where repeated RGB-D observations indicate missing or misplaced structure. Together, these mechanisms adapt which views are optimized, how much image detail is used, and where the representation grows while mapping remains active. We evaluate EliGSiR on Replica, TUM RGB-D, ScanNet++, and real RGB-D sensor sequences, considering both the final reconstruction and the map available throughout acquisition. On TUM RGB-D fr3/long_office_household, EliGSiR reaches 21.52 dB with the same ground-truth mapping poses used by the controlled baselines, compared with 19.42 dB for SplaTAM. In the tracked-pose comparison, EliGSiR with live ORB-SLAM3 poses reaches 23.02 dB in 155.5 s, compared with 20.10 dB in 230.9 s for CaRtGS using its native tracker. We further evaluate reconstruction throughout acquisition and show how EliGSiR adaptive view scheduling, supervision fidelity, and geometry growth improve the use of the available mapping budget.

We present VGGT-GS SLAM, a monocular 3D Gaussian Splatting SLAM system designed for uncalibrated videos. Starting from feed-forward VGGT pose and depth priors, our system performs submap differentiable bundle adjustment that jointly refines camera poses and a 3D Gaussian map, while optimizing submap-shared intrinsics and radial--tangential distortion through analytic calibration Jacobians. To improve global consistency, we introduce Gaussian-native alignment (GNA) for camera-anchored scale refinement between sequential submaps and verification of loop-closure candidates. Extensive experiments on standard indoor benchmarks show consistent improvements in localization accuracy and strong rendering quality under uncalibrated settings, establishing a strong baseline for uncalibrated Gaussian SLAM.

Autonomous robots operating in partially observed environments must navigate safely while acquiring observations that improve future planning. Existing safety formulations generally reason primarily about geometry. Consequently, geometrically similar scene elements may induce comparable control responses despite having different semantic consequences. We present a semantic risk aware safe-active perception framework for navigation in attributed 3D Gaussian maps. Semantic attributes modulate an Average Value-at-Risk collision clearance model through class dependent risk weights, allowing safety-critical Gaussian primitives to receive greater influence in the composite barrier. The resulting weighted clearances are aggregated into a control barrier function, while a trajectory-relevant active perception barrier promotes observations that reduce geometric map uncertainty along the robot's anticipated motion. Both objectives are integrated in a unified CBF-QP that enforces semantic risk-aware collision avoidance as a hard constraint while relaxing information acquisition when it conflicts with safety or task progress. Experiments demonstrate efficient safety constraint, improved navigation through active perception, semantic dependent trajectory adaptation, and real-robot execution under Ackermann dynamics.

Robot teams that learn a common environment model exchange belief summaries and plan by the expected information gain of their actions. Under conjugate exponential-family beliefs the shared belief is counted once per robot at two points: at fusion, the product of local posteriors counts the common prior $n$ times, and at planning, every robot scores its plan under the same belief and the team converges on the same unknown. Both errors are removed by adding evidence increments to the shared natural parameter, realized increments at fusion and expected increments at planning. The expected increment of a committed teammate gives the next robot its conditional gain; corrected gains sum to the joint gain, the redundancy removed equals the total correlation of the planned observation streams, and sequential commitment keeps the $1/2$ greedy guarantee. The expected increment is exact for Gaussian beliefs with fixed sampling paths and for Dirichlet beliefs under the novelty approximation of discrete active inference, whose team objective has a closed concave form within an explicit bound of the exact mutual information, and fails for finite hypothesis classes, where a short exact enumeration replaces it. Experiments on cooperative RockSample, foraging, and field monitoring show that fusion correction leaves exploration redundancy unchanged, anticipated evidence removes it, and sequential commitment recovers most of the value of centralized joint planning at cost linear in the team size.

Record-level differential privacy exposes a structural misalignment in personalized federated learning when client-specific variation is low-dimensional while training repeatedly releases high-dimensional updates. In this paper, we address this misalignment by releasing a private client context once and confining repeated adaptation to a fixed coefficient space. Beyond dimensionality reduction, the factorized generator induces an adaptive optimization geometry that reshapes noisy updates, and controlled ablations show that most of its private-training gain is retained by radial evolution. To further reduce the communication cost, we realize the Gaussian mechanism for coefficient updates directly through variable-length quantization with finite expected code length, so that the quantization error itself serves as the required privacy perturbation rather than extra distortion. Across MNIST and CIFAR-10, our design matches or outperforms full-model private adaptation across privacy budgets and client heterogeneity, while reducing protected uplink by a factor of 2.67 at $\varepsilon=16$ on CIFAR-10 with comparable future-client accuracy.

The Gaussian kernel is a widely used similarity measure underlying kernel methods such as kernel PCA and spectral clustering, but computing Gaussian kernel distances for many pairs of points can be expensive. Using Random Fourier Features (RFF), Chen and Phillips [ALT 2017] showed that for points in a $d$-dimensional Euclidean ball in ${\mathbb R}^N$, $t=Ω((d/\varepsilon^2)\log(dR/\varepsilon))$ features suffice to preserve all pairwise Gaussian kernel distances within a $(1\pm\varepsilon)$ factor with high probability. We establish a uniform relative-error embedding theorem for the more general setting of an arbitrary positive-reach submanifold $\mathcal M\subset{\mathbb R}^N$ of intrinsic dimension $d$. We show that $t=O((d/\varepsilon^2)\log(\operatorname{vol}(\mathcal M)^2N^{2d}/(\operatorname{vol}(B_1^d(0))^2\operatorname{rch}(\mathcal M)^{2d}\varepsilon^{2d+1}δ)))$, or approximately $O((d^2/\varepsilon^2)(\log N+\log(1/(\varepsilonδ))))$, RFFs suffice, with probability $1-δ$, to preserve the Gaussian kernel distance between every pair of manifold points up to relative error $\varepsilon$. Thus the bound depends only logarithmically on the ambient dimension and on manifold parameters such as volume and reach, while retaining the $1/\varepsilon^2$ Euclidean rate. We also prove a topological consequence: under the same RFF embedding, persistent homology is preserved in the sense that weighted Cech and Rips filtrations built from Gaussian kernel power distance are $(1\pm\varepsilon_\star)$-interleaved, where $\varepsilon_\star$ accounts for both distance distortion and kernel-weight approximation.

3D Gaussian language fields provide an explicit, spatially grounded representation for 3D visual question answering (VQA), but their dense semantic features can require tens of thousands of embeddings per scene, resulting in substantial storage, memory, and inference costs. We investigate how much of this representation is actually necessary for downstream reasoning. Starting from a full embedding representation, we systematically sparsify its semantic embeddings, including the previously underexplored regime below a single image-equivalent block down to 8 visual tokens. We compare random, geometric, semantic, and joint spatial-semantic selection strategies and introduce an object-based sparsification method that distributes the token budget across detected object instances while retaining background context. Experiments on ScanQA and MV-ScanQA reveal substantial redundancy in dense Gaussian language fields. Strong VQA performance is retained with only a few hundred semantic embeddings, corresponding to less than 1% of the original representation. Object-based selection performs well relative to others, with only modest observed changes down to 256 tokens. At this budget, SparseTalk retains 0.80% of SplatTalk's 32,076-token inference input and 0.332% of the mean 77,207-Gaussian dense field, increasing inference throughput while reducing decoded-feature memory 125-fold.

Let $Y_s=\sqrt{s}X+Z$, where $Z$ is standard Gaussian and independent of the real random variable $X$. We prove that, under the square-exponential moment condition $\mathbb{E}e^{βX^2}<\infty$ for some $β>0$, the scalar minimum mean-square error $\operatorname{mmse}_X(s)$ is analytic at zero signal-to-noise ratio if and only if $X$ is Gaussian, with constant random variables included as degenerate Gaussians. The proof converts estimation in the Gaussian channel into a backward heat flow acting on the moment-generating function $M(z)=\mathbb{E}e^{zX}$. Under the stated tail condition, every non-Gaussian input forces $M$ to have a nonzero complex zero. We show that each zero cluster produces a finite singularity in its localized Borel transform at the action $ξ=z_0^2/2$. After removing the action scale, the Borel coefficients have a nonzero $n^{-1/2}$ prefactor for a simple zero. A zero of multiplicity $m\geq 2$ splits according to the roots of a Hermite polynomial and instead contributes a prefactor $n^{-m/2}e^{r_m\sqrt{2n}}$. A finite-disc localization and relative-cycle continuation argument then show that at least one such singularity survives in the full Borel transform. Thus, for every non-Gaussian input in the stated class, the formal zero-SNR expansion is Gevrey-1 but divergent. Rational-MMSE rigidity and the analogous analyticity criterion for mutual information follow as corollaries.

Xu, Vardi and Safran (ICML 2026) prove that over-parameterized ridge regression over an unstructured random Gaussian feature map groks, with the delay between memorization and generalization growing as $1/λ$ in the weight decay. We show that on a structured feature map the same delay does not appear. For a band-limited Fourier feature map over $\mathbb{Z}_p^2$ carrying a single-character target that lies inside the expressible class, enlarging the band at fixed positive weight decay drives peak held-out accuracy monotonically from $1.00$ to $0.07$, with no memorize-then-generalize regime anywhere along the sweep. The degradation is not an interpolation effect. It sets in at capacity ratio $q/n = 0.638$, far below the interpolation threshold, on separate grounds from the exact null space that appears above it. What does have a sharp boundary is the active support. Holding the nominal dimension fixed and masking the band back to $1089$ active modes restores held-out accuracy of $1.000$ with zero variance across seeds, while the full $4225$-mode band collapses to $0.185$. The number of active modes acts through the teacher-weighted spectrum of the empirical Gram matrix and not through the capacity ratio, which makes this a statement about feature geometry and not a restatement of double descent.

Feed-forward Gaussian splatting models have demonstrated remarkable effectiveness in reconstructing three-dimensional (3D) objects from a few two-dimensional (2D) images, even if they are unseen. As existing methods typically predict Gaussian primitives uniformly across the 3D space, most primitives are placed in non-object regions. This may hinder the representation of fine object details. This paper proposes a Voxel-Selective Gaussian Splatting model (VS-Splat), a new end-to-endfeed-forward Gaussian splatting framework that predicts many primitives only within selected voxels that are likely to belong to an object, without 3D structural supervision. To achieve this, we propose a new learnable voxel selection approach that identifies object-centric voxels only with 2D rendering supervision.Our sparse-view rendering experiments with three benchmark datasets show that proposed VS-Splat outperforms several state-of-the-art methods. We further demonstrate its effectiveness as a backbone for an existing densification method and show that anoptional extension improves its robustness to inaccurate camera pose estimates.

Reconstructing 3D scenes under real-world low-light conditions remains challenging due to severe sensor noise, low signal-to-noise ratios, and degraded photometric consistency, which destabilize geometry estimation and novel view synthesis. Existing approaches often rely on well-lit reference data for reliable Structure-from-Motion (SfM) initialization under degraded inputs or apply per-view enhancement methods that introduce cross-view inconsistencies. To address these limitations, we propose \textbf{NOVA-GS}, a unified noise-aware framework for low-light 3D Gaussian Splatting that subsumes enhancement, denoising, and geometry optimization within a single process. Our method leverages VGGT-based feed-forward estimation to obtain robust camera poses and geometry directly from degraded inputs, eliminating the need for SfM. Building on this initialization, NOVA-GS integrates three coupled components: a structure-aware enhancement module for exposure correction, a self-supervised denoising module with blind-spot masking for pseudo-supervision, and a consistency-driven Gaussian Splatting optimization enforcing cross-view geometric coherence. We further introduce a noise-guided spherical harmonic regularization to suppress view-dependent artifacts in noisy regions. Extensive experiments on diverse real-world low-light datasets demonstrate improved geometric fidelity, color consistency, and robustness without requiring paired supervision or well-lit references. https://shaurya2524.github.io/nova-gs/

Three-dimensional Gaussian Splatting (3DGS) combines explicit primitives with efficient rasterization, yet recent systems increasingly use neural networks to generate or share Gaussian parameters. We characterize this trend along five axes: attribute decoding, spatial sharing, view-conditioned decoding, topology generation, and amortized inference. An analysis of 19 representative methods shows that these choices address different limitations and cannot be reduced to a binary neural label. We also isolate three forms of neural parameterization in a controlled mip-NeRF 360 study. Sharing appearance and opacity improves reconstruction quality, while decoding geometric structure offers no further gain. The evidence favors selective neuralization: shared functions help when they capture reusable correlations without sacrificing the local geometric freedom of explicit splats.

Lung cancer causes more deaths than any other malignancy, and low-dose CT screening is the main pathway to early diagnosis. That pathway hinges on the smallest lesions, yet nodules below six millimeters remain hard to detect, because most methods treat a nodule as a generic object and ignore the imaging physics behind its appearance. We show that this appearance is highly regular. Intensity peaks at the geometric center of a nodule and decays radially in a Gaussian pattern, and a fit to 18,218 annotated lesions from three public benchmarks yields a mean radial coefficient of determination above 0.86 in every dataset and size stratum. A square convolution samples both axes uniformly and is mismatched to this radial signal, most severely for small nodules. Guided by this evidence, we propose GRIPNet (Gaussian Radial Intensity Prior Network), a detector in which every module maps to a measurable property of the intensity distribution. Pinwheel convolutions decompose radial gradients, a dual-frequency module separates boundary detail from structural context, dilated masked attention matches the decay extent, and an adaptive loss reweights samples by conspicuity. GRIPNet raises mAP@0.5 to 95.3, 91.6 and 97.9 percent on KanserSet, LUNA16 and Lung-PET-CT-Dx while sharpening high-IoU localization at real-time speed.

Accurate head modeling requires a stable yet expressive geometric representation. Existing Gaussian-based head avatars commonly rely on parametric templates (e.g., FLAME) for Gaussian initialization and deformation, but these templates lack personalized priors and struggle to represent structures such as hair and clothing. To address this issue, we propose MGAvatar, a Gaussian-mesh hybrid representation that jointly models geometry and appearance through two Gaussian-mesh binding modes. Specifically, we introduce vertex-bound Gaussians and constrain their learnable parameters, enabling progressive mesh deformation to represent complex head geometry, while a pose-dependent offset module accounts for non-rigid deformations. Once geometry is stabilized, MGAvatar switches to face-bound Gaussians for appearance modeling. To improve appearance consistency across novel poses and viewpoints, we introduce a view-conditioned neural color field that alleviates artifacts caused by independently optimized Gaussian colors. In addition, we design a Gaussian offset network to predict Gaussian offset maps in the observation space, providing greater flexibility for face-bound Gaussians to capture dynamic facial textures. Extensive experiments on multi-view and monocular videos show that MGAvatar outperforms existing methods in rendering quality, producing high-fidelity head avatars with rich texture details.

Render--match--PnP relocalization establishes correspondences between query image pixels and 3D map points for camera pose recovery, but their potential to support dense depth estimation is often overlooked. To exploit this geometric information, we present RIDE, which estimates dense metric depth from a robot's RGB stream. Given a metrically scaled 3D Gaussian Splatting (3DGS) model, RIDE combines sparse metric depth observations derived from PnP-RANSAC inlier correspondences with the geometric prior of a pretrained video-depth model. To handle uneven and intermittent observations, it integrates global and local depth correction with temporal memory, supporting depth estimation through short observation gaps after metric scale initialization. Trained on public RGB-D videos, RIDE is evaluated on robot sequences without fine tuning. Experiments show improved depth accuracy and temporal consistency over scale-only calibration, demonstrating how localization geometry can support both pose recovery and dense robot perception.

Recovering clean 3D scenes from hazy multi-view images is challenging because haze attenuates scene radiance and introduces atmospheric scattering. Recent scattering-aware Gaussian Splatting methods introduce physical haze models into reconstruction, but they often apply degradation in image space or bind medium-related variables to Gaussian primitives, which can entangle clean scene radiance with atmospheric effects. Moreover, low-transmittance regions provide weakened supervision for Gaussian optimization, causing distant or dense-haze areas to be under-reconstructed. We argue that clean reconstruction under haze requires both scene--medium disentanglement and transmittance-aware optimization rebalancing. To this end, we propose Tri-DehazeGS, a scene--medium decoupled Gaussian Splatting framework. It represents the clean scene with Gaussian primitives, models the participating medium using an independent view-shared tri-plane field, and composes hazy observations through a physical scattering model. We further introduce Medium-Decoupled Transmittance Gradient Compensation (MD-TGC), which compensates haze-suppressed gradients after medium freezing without altering forward rendering. Experiments on real and synthetic haze benchmarks show that Tri-DehazeGS improves clean novel-view reconstruction. Code is available at https://github.com/aptx46/Tri-DehazeGS.

Language Gaussian fields implicitly assume that the primitive carrying semantics remains identifiable across views. This assumption breaks in scalable anchor-decoded representations, where persistent anchors generate view-conditioned child Gaussians whose geometry and appearance vary with the camera. We introduce Ours, a persistent language field for such structured Gaussian scenes. Our key idea is semantic ownership: transient children route observations, while persistent decoder slots and their parent anchors own the language field. We use alpha-compositing responsibilities to accumulate additive directional evidence at slots; these statistics marginalize exactly to anchors. We then complete weakly supported slots with anchor-aligned evidence while preserving the anchor direction, and represent slot detail through low-rank residuals in anchor-relative semantic coordinates. Our primary model, Ours (base), stores anchor features together with compact slot residuals. Ours (light) retains only anchor features, whereas Ours (max) stores the full-dimensional completed slot features explicitly. Without scene-specific semantic optimization, Ours (base) nearly matches Ours (max) across KITTI, Virtual KITTI, and Waymo. On KITTI, it achieves 34.19 2D mIoU with a 2.72 GiB effective feature footprint, compared with 34.20 mIoU and 12.90 GiB for Ours (max). The same accuracy-storage trend holds on Virtual KITTI and Waymo. These results show that language fields on view-conditioned splats require persistent semantic ownership, conserved evidence, and a hierarchy that balances stability, detail, and representation cost. Our code, checkpoints, and benchmark suite will be publicly available.

Neural radiance fields (NeRFs) and 3D Gaussian Splatting (3DGS) encode a scene with complementary inductive biases, but existing cross-representation distillation typically fixes one representation as teacher for the entire scene. A globally fixed teacher can propagate local reconstruction errors. We present RouteBridge, a bidirectional framework that selects the teaching direction for each ray. Its reliability estimator combines photometric residuals with representation-specific geometric evidence and routes supervision from NeRF to 3DGS, from 3DGS to NeRF, or abstains. A renderer-independent interface transfers color, opacity, and normalized depth without shared features or point correspondence. On mip-NeRF 360, the NeRF and 3DGS exports reach 28.56 and 28.77 dB, respectively. The 3DGS export improves over 3DGS by 1.56 dB and over NeRF-GS by 0.45 dB while reducing LPIPS to 0.207. On static three-view DTU, RouteBridge obtains 21.12 dB. Ablations show that both adaptive routing and geometric ray targets contribute to the improvement.

We prove the gap-entropy conjecture for fixed-confidence best-arm identification with independent unit-variance Gaussian arms, means in $[0,1]$, and a unique optimal arm. For each suboptimal arm $i$, let $Δ_i=μ_*-μ_i$ be its gap from the optimal mean, and write $H=\sum_{i\ne *}Δ_i^{-2}$. Let $p_r$ be the fraction of $H$ contributed by arms with $2^{-(r+1)}<Δ_i\le2^{-r}$, and let $\mathrm{Ent}(I)=\sum_{r:p_r>0} p_r\log(1/p_r)$. Among all algorithms that identify the optimal arm with probability at least $1-δ$ on every Gaussian instance, the optimal expected number of samples on a given instance, averaged over all permutations of the arm labels, is within absolute constant factors of $H(\log(1/δ)+\mathrm{Ent}(I))$. Moreover, there is an algorithm, independent of the instance, whose expected number of samples is bounded by a constant multiple of this quantity plus $g^{-2}\log\log(e^e/g)$, where $g=\min_{i\ne *}Δ_i$ is the gap to the closest competitor.

3D Gaussian Splatting (3DGS) renders novel views in real time, but an uncertainty heatmap does not certify that a rendered view meets a certain prediction coverage. We treat novel-view synthesis as structured regression and ask that, with probability at least $1-α$, RGB prediction boxes cover at least a $1-β$ fraction of pixels in a new view. We propose View-Structured Conformal Prediction (VSCP). It splits the pre-calibration scale into a spatial shape from the renderer and a transferable view-difficulty factor, which predicts the smallest view-wise multiplier that shape needs. A held-out quantile over views (View-CP) then gives finite-sample validity even when transferring to new scenes. The same factorization makes the analysis exact: a conformity score is the ratio of oracle to predicted view difficulty, and excess width separates into a test-side and a calibration-side term. Across 13 real scenes, pixel-pooled calibration reaches 89.9% marginal pixel coverage but only 61.4% view-event coverage at a 90% target, while View-CP reaches 91.7--92.0%. At matched coverage VSCP cuts width by 22.1% against a constant scale, and matches a ten-model ensemble's 21.0% reduction using only one model per scene and four rather than ten rasterization passes per query. VSCP also improves on the closest single-model baseline, the 3DGS-U field, by 4.7 points ($p=0.0225$). The view predictor transfers from bounded source families to all nine unbounded Mip-NeRF360 scenes. There the full scale beats the constant scale with 20.7% width saving on all nine scenes. It also keeps an 18.3% saving under a different densification backbone and runs at 216--280 FPS on an RTX4090.

We develop Gaussian approximation bounds in higher-order Wasserstein distance $W_p$, $p\geq2$, for sums of multivariate martingale differences generated by a uniformly ergodic Markov chain. Under an $L^{(2+η)p}$-moment condition with $η>0$, we establish the explicit bound $O\left( p^3 \|A\|_4^2 + pd^{1/4}\|A\|_2^{1/2}\|A\|_4^2 \right)$ where $A\in\mathbb{R}^n$ collects the $L^{(2+η)p}$-sizes of the $n$ individual martingale increments. In the balanced-increment regime where the individual increments have comparable sizes of order $n^{-1/2}$, it yields the first optimal $O(n^{-1/2})$ Gaussian approximation rate for fixed $p$ and $d$. Consequently, we also obtain the first optimal $O(n^{-1/2})$ $W_p$ Gaussian approximation rate for multivariate additive functionals of uniformly ergodic Markov chains. Our analysis develops two techniques for addressing the interplay between higher-order Wasserstein distance and temporal dependence. First, building on the Ornstein--Uhlenbeck relative-score approach of Fang and Koike (2023), we formulate the bound in terms of antisymmetric Stein couplings while retaining the conditional tensor structure. Second, we develop a refresh-then-maximal coupling that combines an independent first-step resampling, which preserves the desired Stein identity, with a subsequent maximal coupling that provides effective control of the coupling increment. These tools may be useful more broadly for Gaussian approximation under temporal dependence.

Quantization schemes based on randomized rotations have recently received renewed attention, including the roles of MMSE and unbiased reconstruction scalings. In this note, we point out the connection to classical results in statistical signal processing and communication theory. Specifically, the two reconstruction scales used in the EDEN line of work admit a natural interpretation as finite-dimensional, realization-dependent counterparts of the Wiener and unbiased coefficients in the classical CDEF formulation. At finite blocklength, the CDEF +1 relation holds pointwise for each rotation realization as an exact geometric (Pythagorean) identity, but does not hold after averaging the distortions over the rotation. The classical SNR relation $\sf{SNR}_{\rm MMSE}=\sf{SNR}_{\rm MMSE,U}+1$ is recovered as $d\to\infty$: once the overall scale is handled separately, the empirical coordinate statistics of a randomly rotated vector approach their i.i.d. Gaussian counterparts, and the rotation-dependent quantities concentrate. Importantly, EDEN goes beyond this classical correspondence: for every finite $d$, its Haar-rotation formulation guarantees exact conditional unbiasedness, a stronger property than the second-order notion of unbiasedness in CDEF. We further comment on two distinct roles random rotations play in quantization: one is approximate Gaussianization of the coordinates; the other is decorrelation of reconstruction errors across quantization branches.

Autonomous navigation in unstructured environments requires robust scene understanding, yet Vision-Language Models (VLMs) often suffer from semantic ambiguity, where conflicting predictions can lead to dangerous failures. To address this, we present a novel pipeline for vision-based traversability estimation that explicitly models contextual uncertainty. Our approach utilizes Conceptual Anchoring to ground open-vocabulary VLM predictions onto a continuous physical traversability scale. By formulating the model's responses as a Gaussian Context Distribution (GCD), we derive both a dense traversability map and a dense uncertainty map based on the statistical properties of the distribution. Experimental validation on the real-world GOOSE dataset demonstrates that our proposed uncertainty metric effectively correlates with sources of ambiguity, such as visual artifacts and mixed terrain overlap. The method exhibits competitive performance while offering the distinct advantage of providing statistical uncertainty estimates to address semantic ambiguity, enabling safer and more reliable autonomous behavior in complex outdoor settings.

3D Gaussian Splatting has recently revolutionised novel view synthesis as well as many other 3D vision methods and applications. Drawing inspiration from this representation, we now rethink textures to overcome the main issues of UV mapping while considerably lowering their memory footprint. Heat Kernel Textures (HKTex) eliminate UV unwrapping as well as their persistent issues of wasted UV space, seams, distortions, vertex-duplication, and varying resolution. Grounded in discrete Riemannian geometry and intrinsically defined on any manifold surface discretised as a triangular mesh, HKTex uses anisotropic heat kernels as geodesic equivalents to Gaussians. Like our kernels, also the optimisation of their position and the adaptive densification strategies were redefined to operate on the surface of the object to be textureised. Our novel representation is also fully integrated with a physically based renderer and can be optimised either from existing textures or multi-view images. Our project page and code are available at circle-group.github.io/research/HeatKernelTextures.

SLAM systems based on 3D Gaussian Splatting (3DGS) have recently demonstrated promising reconstruction accuracy for dense 3D scene representations. However, current 3DGS systems struggle to meet the strict demands of real-world deployments due to severe limitations in operational performance and map adaptability. To this end, we propose LightSplat, a hybrid-representation RGB-D SLAM framework. It synergizes local sparse features for robust and fast tracking with a dual-thread backend that progressively constructs dense Gaussian submaps. Crucially, we enable online loop closure through feature-accelerated 3DGS registration, refining overall map consistency through pose graph optimization. Ultimately, LightSplat achieves the online reconstruction of high-fidelity Gaussian map. Extensive experiments on multiple datasets and real-world robotic platform demonstrate that our method achieves near state-of-the-art reconstruction quality and the capability to accommodate practical camera motions, maintaining an average framerate of 8 FPS. Overall, LightSplat provides an efficient and robust foundation for deploying high-fidelity 3DGS in real-world environments.

Estimating the 6D pose of textureless objects without prior CAD models remains a critical challenge due to the lack of appearance features. While recent generalizable approaches alleviate the dependence on object-specific models, their performance on low-texture objects is often limited by insufficient geometric constraints in the underlying representations. In this work, we propose PG-Pose, a geometry-aware framework combining Planar-based Gaussian Splatting (PGS) reconstruction and Geometry-driven pose optimization. In the offline representation extraction stage, three distinct representations of the object are extracted from multi-view reference RGB images with known poses. PG-Pose reconstructs a 3D Gaussian representation and renders high-fidelity depth maps to generate 3D point clouds through back projection. In the online pose inference stage, the initial pose of the input image is estimated by 2D-3D correspondence matching between the input image and the reconstructed 3D point clouds, followed by a PGS-Refiner for iterative pose optimization. Evaluations on the OnePose-LowTexture datasets, PG-Pose achieves an average accuracy of 94.2% ADD(S)@0.1d, with a 2.1% improvement average accuracy compared with the state-of-the-art (SOTA) GS-based approach. To further demonstrate the effectiveness of PG-Pose for industrial robots in grasping tasks, we deploy it on a dual-arm industrial robot and successfully realize the grasping task on an unseen object.

Efficient, fully automatic, and physically plausible 4D Gaussian synthesis is an important goal for dynamic scene generation. Recent physics-based methods couple 3D Gaussians with the Material Point Method (MPM) to generate physically driven motion, but extending this paradigm to heterogeneous multi-part objects and interacting multi-object scenes remains challenging. Object-level physical assignment collapses distinct parts into a single material state, while one-shot predictions from large language models, vision-language models, or agents neither reliably bind different materials to identified parts nor verify that the resulting MPM configuration is executable. Score Distillation Sampling (SDS)-based parameter optimization, meanwhile, requires repeated per-scene score evaluations and gradient backpropagation, incurring lengthy optimization and potentially yielding suboptimal or unstable solutions. We therefore present PhysMAS, a physics-grounded multi-agent framework. From a motion prompt and four scene views, an Object-Part Scene Agent establishes persistent identities and calls a Material Reasoning Agent for part-wise profiles. It invokes solver-aware skills to bind these identities and profiles to per-particle MPM fields and execute all objects in a shared domain; the framework then screens candidate forward-simulation results. This supports heterogeneous multi-part and interacting multi-object scenes without per-scene diffusion-score backpropagation. Extensive experiments demonstrate that, compared with recent physics-based 4D Gaussian baselines that rely on SDS, PhysMAS achieves better semantic alignment and perceived physical plausibility while requiring less runtime.

While machine-learning interatomic potentials (MLIPs) have successfully learned potential energy surfaces (PES) and atomic forces, many practical applications, such as vibrational analysis and transition state search, rely heavily on the PES Hessian. Yet standard MLIPs are trained on energy and forces alone, and existing methods that incorporate the Hessian into training objectives require architectural modifications and incur significant computational and memory overheads from higher-order backpropagation. To address these limitations, we propose two Hessian-derived data augmentation schemes: isotropic Gaussian displacement (\textbf{UniAug}) and normal mode-weighted displacement (\textbf{ModeAug}). Both methods utilize simple Taylor expansions, achieving effective augmentation without altering training objectives or extending the autograd graph. This allows seamless, plug-and-play integration with existing architectures and training pipelines. Comprehensive evaluations across non-equilibrium and equilibrium datasets demonstrate that our approach enhances model accuracy where reference forces are large while providing practical, task-specific guidelines.

Restricted eigenvalue (RE) bounds govern stable recovery by norm-regularized estimators. For isotropic sub-Gaussian measurements, the benchmark sample size is $1+w(A)^2$, where $w(A)$ is the Gaussian width of the normalized descent cone. The COLT 2015 open-problem note (Banerjee et al., 2015) asked whether the same law follows for heavy-tailed designs from a uniform small-ball condition alone. We give an explicit and systematic negative answer to the general question as formulated there: the proposed law fails in its full dimension-free, arbitrary-set form, and the missing obstruction is simultaneous threshold occupancy. A constant-width polyhedral descent cone with fixed small-ball constants has zero empirical RE on every sample path up to half the ambient dimension. More generally, every finite range space admits exact threshold encoding in an arbitrarily narrow spherical cap and a lift to a full polyhedral descent-cone section. For every fixed threshold VC dimension $d$, as $β\downarrow0$, the sharp worst-case sample complexity is $Θ(β^{-1}[d\log(1/β)+\log(1/δ)])$. The separation persists under exact isotropy and all finite moments: on the same constant-width cone, Gaussian measurements succeed with $O(1+\log(1/δ))$ samples, whereas an isotropic heavy-tailed design fails pathwise for $n\lesssim\sqrt{p/\log p}$. Gaussian smoothing yields an everywhere-positive $C^\infty$ density while retaining arbitrarily poor RE. Under isotropy, a distribution-free fallback governed by affine dimension times squared enclosing radius is sharp on this family.

A key bottleneck in 3D Gaussian Splatting training is the continual growth of Gaussian primitives, which increases optimization cost and slows convergence, especially at high resolutions. We propose Laplacian Frequency Hierarchies, a simple yet efficient 3DGS scheme that combines Laplacian image decomposition with coarse-to-fine, frequency-staged training. After fitting lower-frequency structure, we archive the corresponding Gaussian field so that subsequent fields can optimize higher-frequency residuals without carrying the full primitive burden, and we compose the rendered components in the image domain via a Laplacian-style reconstruction at inference time. This design reduces the number of active Gaussians during training, thereby lowering optimization overhead and accelerating training. The proposed scheme is plug-and-play and orthogonal to prior 3DGS accelerations: it can be directly combined with strong backbones such as Taming-3DGS and FastGS to improve training speed with competitive reconstruction quality. It achieves average speedups of 1.73x and 1.21x at 1K setting, and 1.74x and 1.33x at 4K setting on Taming-3DGS and FastGS, with larger gains on more challenging scenes and increasingly pronounced benefits at higher resolutions.

While 3D Gaussian Splatting (3DGS) has revolutionized 3D reconstruction and novel-view synthesis, scenarios with limited input views often lead to poor reconstruction quality and artifacts in rendered novel views. Recent efforts attempt to utilize powerful diffusion priors, yet they typically process rendered and reference views concatenated along an additional dimension in a single network. These methods overlook an inherent nature that different views should maintain appearance similarity but differ in structure due to view shifts, leading to blur caused by conflicts between the two properties. In this paper, we propose DualDiff, a novel pipeline that leverages dual diffusion priors with a Structure-Appearance Attention (SAA) module to introduce reference guidance for refining low-quality novel views rendered from flawed 3D representations. Specifically, we retain one diffusion branch to focus on extracting structural information from the low-quality novel views, while introducing another branch to ensure appearance consistency with reference views. Furthermore, we present a 3D reconstruction framework named DualDiff3D, which integrates a reliability-enhanced Render-Refine-Optimize (RRO) loop to progressively and robustly incorporate the refined novel views, yielding more accurate 3DGS. Extensive experiments demonstrate that our approach outperforms state-of-the-art methods even in the inference-only setting, with further performance gains achievable through training. Our code and pre-trained weights are available at https://github.com/Akaneqwq/DualDiff3D.

Recent extensions of 3D Gaussian Splatting (3DGS) enable real-time novel view synthesis in dynamic scenes by learning time-conditioned Gaussian deformations. However, existing MLP-based methods typically estimate deformations independently at each timestamp, making them less robust to large or abrupt motions. To address this issue, we propose \textbf{EvoGS}, a 3DGS-based dynamic reconstruction framework that models Gaussian deformation as a temporal evolution process. EvoGS maintains persistent deformation states for each Gaussian, extrapolates future states from historical deformation states, and corrects the predictions with MLP-derived observations. The correction is adaptively weighted using a temporal residual memory and evolution statistics such as deformation velocity and trajectory deviation. To further improve reconstruction quality, EvoGS introduces deformation-aware densification. Clone and split operations are performed along corrected deformation directions, while an uncertainty-aware strategy suppresses densification for Gaussians with unstable deformation histories. Experiments show that EvoGS improves dynamic novel view synthesis quality and achieves competitive performance across benchmarks.

Semantic segmentation in 3D Gaussian Splatting (3DGS) is crucial for advancing 3D scene understanding. Existing methods predominantly rely on feature distillation, which incurs substantial per-scene training overhead and often yields blurred segmentation boundaries. We identify that these boundary artifacts are driven in part by insufficient viewpoint coverage and boundary overflow of anisotropic Gaussian primitives. To address these challenges, we propose VCAR, a training-free coarse-to-fine segmentation strategy based on View Completeness and Axis-aware Boundary Refinement. In the coarse stage, a visibility-based weighted multi-view voting scheme rapidly localizes the target. In the fine stage, an object-centric sphere derived from the coarse result generates supplementary viewpoints via Spherical Spiral Sampling (SSS), allowing multi-view voting on the augmented views to precisely refine object boundaries and suppress irrelevant 3D Gaussians. Moreover, we introduce Axis-aware Boundary Refinement (ABR) to mitigate artifacts from anisotropic primitives. By decomposing the projected 2D covariance into per-axis contributions, ABR identifies the dominant axis responsible for boundary leakage and applies targeted anisotropic compression exclusively along that axis. Extensive experiments on NVOS and LERF demonstrate that VCAR achieves state-of-the-art segmentation accuracy and efficiency without training. Our code is available at https://github.com/DDKK0526/VCAR.

Volumetric video enables immersive free viewpoint rendering of dynamic real world scenes, yet existing methods struggle with long sequences and complex motions, often leading to temporal instability and visual artifacts. To address these challenges, we propose \ourname, a Gaussian splatting based framework for volumetric video reconstruction. Our key insight is that explicitly tracking long term complex motion with individual Gaussian primitives is inherently unstable. Instead, we organize Gaussians around time conditioned anchors that localize their spatial and temporal support, thereby reducing long range motion complexity. We further introduce a temporal windowing strategy to activate only anchors relevant to the queried time, which improves scalability and temporal coherence. In addition, to ensure spatial and temporal stability, we design a compact set of multi level anchor features that encode global features, local spatial features, and local temporal features, jointly constraining Gaussian generation. Extensive experiments demonstrate that \ourname \ consistently outperforms prior methods on long sequence volumetric videos with complex motions. Project page: https://github.com/WuJH2001/ATGS.

Reference-guided stylization of scenes represented by 3D Gaussian Splatting (3DGS) is important for efficient and controllable 3D content creation. Existing VGG-feature-based 3D stylization methods provide stable rendered-view optimization, but often under-represent expressive reference style cues; diffusion models offer stronger image priors, yet direct per-view or score-based diffusion guidance can lead to view drift, local artifacts, and hard-to-control appearance updates. We present DReSG, a 3D-grounded residual-feedback framework for stylized Gaussian splatting. DReSG represents attention-guided diffusion proposals as residual targets relative to the current render, and progressively absorbs these residuals into a shared Gaussian scene through multi-view Gaussian feedback. To make this feedback stable and controllable, DReSG modulates residual strength during target construction and combines coverage-aware view selection with conflict-filtered color updates during multi-view fitting. Extensive experiments demonstrate that DReSG achieves competitive reference-guided stylization while better preserving scene structure and cross-view stability. Our project page is available at https://vpx-ecnu.github.io/DReSG-website/.

Snapshot Compressive Imaging (SCI) offers an efficient solution for high-speed video acquisition and, under exposure-time camera--scene relative motion, multi-view scene capture by compressing temporal or spatial information into a single 2D measurement. While recent studies have explored SCI for 3D scene reconstruction, existing methods struggle with significant challenges due to information loss, limited viewpoint diversity, and the computational burden of jointly optimizing 3D representations and camera poses. In this work, we propose a novel framework that reconstructs high-quality 3D scenes from a single SCI measurement by leveraging 3D Gaussian Splatting (3DGS) and the powerful priors of large-scale vision foundation models (VFMs). Our primary reconstruction combines measurement-derived 3D VFM initialization with SCI-aware Gaussian optimization. After coarse-stage convergence, an auxiliary 2D VFM provides pseudo-view supervision at synthesized viewpoints for local appearance refinement. To further address the instability caused by ambiguous SCI supervision during 3DGS optimization, we introduce Opacity-Guided Splitting and Growth Regulation (OSGR), an SCI-specific densification strategy that augments split candidates using local opacity statistics, discourages loss-compensating opacity inflation through mean-opacity regulation, and bounds representation growth with explicit candidate-ratio and Gaussian-count constraints. Extensive experiments across multiple benchmarks demonstrate that our method achieves the strongest overall performance, combining leading reconstruction quality and robustness to viewpoint variation with competitive computational efficiency.

Recent query-based feed-forward 3DGS methods represent a scene using learnable queries, each aggregating multi-view evidence and decoding a group of Gaussians. Ideally, different queries should specialize in coherent local regions of the scene. However, we observe that Gaussians decoded from the same query often scatter across distant scene regions, resulting in weak query-level spatial coherence and poor alignment with the scene structure. We attribute this behavior to the purely latent representation of existing Gaussian queries. To address this limitation, we introduce LocusGS, which augments each Gaussian query with a 3D anchor state consisting of a center and a support radius. The anchor state is progressively refined across decoder layers and is used throughout query interaction, multi-view feature aggregation, and Gaussian generation. Specifically, an anchor-to-ray geometric bias guides each query toward spatially relevant image observations, while anchor-centered decoding organizes its Gaussians within a local region. Experiments on novel view synthesis benchmarks show that LocusGS improves rendering quality over query-based Gaussian token baselines under the same Gaussian budget. Further analysis shows that the learned anchors form coherent spatial layouts and lead to more structured Gaussian distributions, demonstrating that explicit anchor states improve the spatial organization. Our project page: https://leo-frank.github.io/LocusGS_viewer.

Multi-output Gaussian process regression scales cubically in the number of observations times outputs, and dense kernel-matrix methods need bespoke handling whenever different outputs are observed at different inputs. We express multi-output Gaussian process regression as a Forney-style factor graph in which a nearest-neighbor chain orders a fixed candidate set of $C$ inputs into a one-dimensional sequence. Along this chain, latent Matérn processes evolve through linear-Gaussian transition factors, while the linear model of coregionalization mixes $L$ latent processes into $D$ outputs through a deterministic mixing factor and per-output scalar observation factors. Posterior computation reduces to exact Gaussian message passing on the chain at cost $\mathcal{O}(C(DL^2 + L^3))$ after chain construction, and missing observations omit their local factor without any covariance-matrix restructuring. The formulation therefore scales in the number of data samples and in the rate of missing observations, while remaining best suited to candidate sets in low input dimension.We compare the factor-graph formulation against an exact kernel-matrix baseline, a sparse-variational inducing-point baseline, and a nearest-neighbor baseline on a synthetic input-dimension sweep and on electricity time series forecasting. At low input dimension the factor-graph posterior tracks the exact kernel-matrix posterior closely, and the gap grows gradually as input dimension increases while staying competitive with both approximate baselines. On the electricity time series our factor-graph formulation matches all three baselines in forecast accuracy while scaling linearly in the number of data points, where the exact kernel-matrix method becomes infeasible and the inducing-point baseline remains substantially slower.

Regulating the latent space to an isotropic Gaussian distribution provides a stable and information-maximized landscape for world model planning. However, the latent space property and successful planning remain disconnected. We first study this by comparing SIGReg and VISReg, two regularization loss functions with the same distribution target but different properties. Compared with SIGReg, VISReg has more flexibility in controlling the weights of center, scale, and shape regularization, and a larger batch size brings a finer distribution approximation. We find that the former, despite being beneficial in self-supervised learning (SSL), does not help the planning, whereas the latter improves the planning success on out-of-domain (OOD) datasets. This motivates a deep understanding of the factors that correlate with the success rate. Unlike the previous metrics focusing on the encoded latent only, we propose the Veracity-Influence-Sobriety score (VIScore), a metric that quantifies the reachability and capacity of a predictor given the encoded feature, and the hallucination of the searching-based planner. Compared with straightness, physical-state probing, and empowerment, we show that, with the measurement covering encoder, predictor, and planner, VIScore explains the success rate better than the others, as reflected by a strong Spearman correlation. Specifically, VIScore consistently achieves a Spearman correlation over 0.75 on both seen and unseen models and datasets on the cross-task success rate pool. Moreover, VIScore is the only metric that has a calibration error below the constant fit across all testing scenarios, showcasing the importance of these three aspects in planning success. We hope this metric can help future studies on world model design and diagnosis.

While 3D Gaussian Splatting (3DGS) has advanced open vocabulary scene understanding, existing methods remain confined to explicit queries. They struggle to interpret implicit intents, complex spatial constraints, and commonsense reasoning required for practical embodied interactions. To address this gap, we introduce the task of reasoning 3D Gaussian segmentation and construct two benchmarks, Causal-LERF and Causal-ScanNet. These benchmarks systematically evaluate commonsense, spatial, affordance, and counterfactual reasoning. Evaluations reveal that current state of the art methods perform poorly on these reasoning challenges. Therefore, we propose CausalSplat, a framework that integrates vision-language models with 3D scene graphs to disentangle explicit structural perception from implicit logical inference. Extensive experiments demonstrate that CausalSplat achieves state of the art performance on our reasoning benchmarks while showing strong generalizability on standard referring and open vocabulary 3D segmentation tasks. Project Page: https://jiayuding031020.github.io/CausalSplat

Feed-forward Gaussian reconstruction has recently emerged as an efficient approach for driving scene reconstruction. However, prevailing LiDAR-based methods preserve the initial correspondence between observed points and Gaussian primitives, treating the initialized primitive set as the final representation. Unlike optimization-based 3DGS, these methods cannot accumulate gradients during training to determine how the scenes representation should be densified. Meanwhile, the shared sparse backbone only fuses observations from different timestamps implicitly, without explicitly aggregating cross-time evidence for individual primitives. In this paper, we present Learning Gaussian Structure (LGS), a framework that enhances both Gaussian structure and primitive attributes. Our key observation is that changes in local gradient responses induced by a prune or add intervention reveal whether the corresponding structural adjustment benefits reconstruction. Based on this observation, our Gaussian Densify Policy learns a Densify Map comprising Prune and Addition Scores from controlled interventions, and directly adjusts the Gaussian structure during inference. We further develop a compact Cross-Time Point Query that explicitly retrieves and aggregates neighboring features from Gaussian primitives at other timestamps for reliable attribute prediction. Extensive experiments on the Waymo Open Dataset and PandaSet demonstrate that LGS consistently outperforms existing methods.

3D scene reconstruction, modeling, and rendering are highly relevant for numerous tasks, and 3D Gaussian splatting has become a standard choice in this context. Its feed-forward variants provide fast reconstruction from sparse input views but often produce per-pixel primitives, leading to highly redundant and thus inefficient representations. We present a structure-aware merging pipeline that takes per-pixel primitives from any feed-forward method and consolidates them into a compact, content-adaptive Gaussian set while largely retaining visual quality at just $\frac{1}{20}^\text{th}$ of the Gaussians of a per-pixel method. We group spatially coherent Gaussians of similar appearance into variable-size clusters via adaptive superpixel segmentation guided by a saliency map, which allocates fine segments to textured regions and coarse segments to homogeneous areas. We compress each cluster into a compact latent representation through a learned encoder, then match and consolidate representations across views based on geometric overlap and feature similarity via a learned merger. A level-of-detail decoder then produces the final Gaussians at a controllable resolution, enabling a flexible quality-efficiency trade-off at inference. As a post-processing module, the pipeline is backbone-agnostic, leveraging the strengths of existing feed-forward methods. This leads to better and more robust quality than achieved by previous approaches that target a reduction in primitive count, while providing a highly compact representation, that can be rendered efficiently.

Single-frame surround-view reconstruction faces severe geometric instability and rendering artifacts due to minimal inter-camera overlap. While existing methods rely on complex decoders or auxiliary cues, they remain bottlenecked by the weak geometric capacity of upstream features. We argue that leveraging pretrained visual geometry priors strengthens upstream representations and alleviates the geometric ambiguity in sparse surround views. To this end, we propose VGGD, a visual geometry foundation-aware 3D Gaussian Splatting framework for feed-forward surround-view driving reconstruction, which shifts geometric modeling to the frontend and adapts foundation priors to the driving camera setting. First, VGGD leverages VGGT to provide transferable multi-view geometric prior tokens. Next, we introduce a Dual-Path Neck to decouple geometry-consistent and appearance-aware representations, improving appearance completion in weakly observed regions. We further apply Scale Warmup to stabilize early geometry learning and suppress scale drift under ego-pose changes. Finally, we use a hybrid pixel--volume Gaussian decoder to produce a renderable 3D Gaussian scene for novel-view synthesis. Experiments on the nuScenes single-frame benchmark show that VGGD achieves the best overall rendering quality among the compared methods and improves relative geometric consistency.

We introduce LEGO for advanced open-vocabulary scene understanding. Beyond basic concept recognition, its core innovation lies in capturing the intrinsic semantic hierarchies within the scene, such as the "flowerpot -> bouquet -> bud -> petal" lineage. While foundation models like SAM can identify multi-granular structures in 2D, their partitions are strictly perspective-bound and lack cross-view consensus. LEGO self-adaptively re-grades volatile multi-view SAM granularities into a unified, 3D-consistent hierarchy. This provides precise supervision for the structurally coherent, multi-level segmentation of 3D scenes. By grounding these segments with CLIP embeddings, LEGO recovers open-vocabulary semantic logic across hierarchical levels. Furthermore, by incorporating spatial relationships, we elevate these segments into level-wise language scene graphs, effectively empowering Large Language Models to perform complex, context-aware spatial reasoning and precise visual grounding. Experimental results demonstrate that LEGO establishes new state-of-the-art performance across both promptable and open-vocabulary 3D segmentation benchmarks, exhibiting advanced hierarchical scene decomposition and context-aware spatial reasoning.

How expressive is prompting a transformer? Answering this question is important for separating the roles of prompting, architecture, and pretraining in transformer models, and for determining whether task-specific behavior must be stored in model weights or can instead be induced at inference time through the prompt. We show, in an approximation-theoretic sense, that pretraining is optional: a single-layer softmax attention network with random, untrained weights can approximate any Hölder function on a compact manifold when steered by an appropriate soft prompt. Guided by the connection between softmax attention and kernel methods, we construct explicit soft prompts (a prompt per target function, independent of the query) as solutions to linear systems matching attention logits to Gaussian kernel exponents, under which the frozen transformer emulates the classical Nadaraya-Watson kernel estimator. The construction requires only a mild rank condition on the weights, which we show holds almost surely under Gaussian initialization. The prompted network inherits the theoretical guarantees of kernel regression, leading to universal approximation theorems with minimax-optimal rates that depend on the intrinsic dimension. We further quantify the cost of prompting, exposing a tradeoff between the norm of the constructed soft prompt tokens, prompt length, and hidden dimension. Numerical experiments corroborate the constructions and predicted rates.

Adaptive procedures must work without nuisance information an oracle may use, such as a gradient scale or smoothness index, and robust procedures may have to answer queries whose coordinate and inspection time are chosen only after the data are seen. Such comparisons are meaningful only when the oracle advantage and validity contract are stated explicitly. We formalize nuisance adaptation via a slice-normalized minimax ratio retaining the worst-case instance within each nuisance slice, and separately define the robustness cost of expanding from one preannounced Gaussian query to arbitrary post-hoc inspection. Our main result is a finite-horizon composition law for Gaussian certification: from M independent coordinates, a familywise certifier protecting every coordinate and time up to T pays optimal normalized squared half-width of order log(eM) + log log(e^eT), within the sample-mean-centered rectangular class. Epoch stitching gives the upper bound; independent Gaussian block increments across coordinates and geometric time scales give a matching lower bound, already holding on a geometric checkpoint grid, forcing quantiles of the realized maximum width so selection and stopping taxes add. Two benchmark regimes complete the picture: unknown gradient scale in online convex optimization has constant cost, while pointwise adaptation over nested Holder classes costs order (log n / log log n)^(s1/(2s1+1)). Cast as model monitoring, the law lets an analyst inspect any of M slice metrics at any data-dependent time: the naive fixed-query band's selected coverage degrades sharply, to 0.30 at M=1 and to zero for M>=10, while the epoch-stitched certifier holds familywise coverage at an additive iterated-logarithm width cost. Experiments put both sharp predictions at risk of refutation; both survive.

We introduce conditional cylindrical neural networks for approximating functionals of conditional laws in McKean-Vlasov equations with common noise. Fourier moments of the initial law and truncated signatures of the time augmented common noise are mapped by a mixture density network to a Gaussian mixture approximation of the conditional law. A cylindrical neural network then evaluates the target functional through analytic integrals against this predicted measure. Rough path well posedness and stability provide a conditional law map that is continuous in the initial distribution and the rough driver and agrees almost surely with the classical conditional law at the Itô Brownian lift. Combining this continuity with Fourier separation, signature uniqueness, Wasserstein density of Gaussian mixtures, and neural universal approximation, we prove an $L^2$ universal approximation theorem for continuous square integrable functionals. The numerical study implements the resulting two stage procedure on six examples, including non Gaussian initial laws, nonlinear drift, multiplicative common noise, and a two dimensional state. Independent particle references are used when no closed form law is available. The learned conditional law and functional approximations consistently improve on the empirical particle plug in, and additional experiments examine feature sensitivity, training from one terminal observation per common noise scenario, and Itô--Stratonovich consistency.

We present FlexSplat, a feed-forward framework for novel view synthesis (NVS) from uncalibrated, object-centric multi-view image collections. A recent line of query-based methods reconstructs a compact set of 3D Gaussians by treating them as transformer queries that are refined with multi-view deformable attention; these methods, however, assume that camera poses are given. FlexSplat removes this assumption: a geometry transformer is trained jointly with the Gaussian decoder to predict per-image camera parameters and depth, which in turn ground a depth-guided Gaussian parameterization and a multi-view deformable cross-attention that aggregates evidence across all input views into a single, view-consistent set of primitives. An uncertainty-weighted depth-consistency objective lets the jointly trained geometry adapt to the reconstruction task, while the cross-view consensus formed during decoding absorbs the residual error of the estimated cameras and depth. The representation uses a compact Gaussian budget that is decoupled from the input resolution - unlike pixel-aligned methods, the primitive count does not grow with the image grid - and is not dictated by the number of views. On ShapeNet-SRN and Google Scanned Objects (GSO), FlexSplat matches or approaches posed state-of-the-art reconstructors while requiring neither camera poses nor ground-truth depth, and matches the best perceptual (LPIPS) quality among the compared methods on GSO. Our results indicate that a jointly trained geometry front-end is sufficient to bring calibration-free operation to query-based Gaussian reconstruction while staying within 0.7 dB PSNR of posed methods and matching their perceptual quality.

Traffic data collection is dominated today by deep object detectors followed by tracking-by-detection, a pipeline that presupposes what is often missing in practice: a detector already trained on the class one wants to count. We revisit a purely geometric traffic-sensing pipeline for Single Board Computers in which detection is class-agnostic: moving objects come from background subtraction and thresholding, and counting is decided by a geometric rule on an imaginary line across the road, a software inductive loop detector. With no object model, training set or per-object trajectory, it runs faster than real time on Raspberry Pi class hardware. Two counting rules are described: a constant average speed rule, whose expected accuracy is derived analytically as about 86% under a Gaussian speed distribution, and a self-calibrating pre-calibration rule that recovers the lane geometry from blob statistics and counts edges of lane occupancy, additionally yielding per-vehicle average speed at no extra cost. Over four videos the latter counts with 83.3%-100% accuracy; in a field deployment it reaches 91% against 37.5% for a blob-tracking baseline under the same compute budget. We report the observations of that period in detail: the resolution floor below which accuracy collapses, the frame rate floor at which vehicles alias past the counting line, the gap between short curated clips and long uncontrolled footage, and the trade-off between Python (easier to tune, 100% CPU) and C++ (40% CPU, thermally viable). These are properties of the sampling geometry, not of the hardware of the time, and still constrain edge deployments. We close by arguing where motion-based, class-agnostic detection remains the right tool: open-set classes with no annotated data, tight power budgets, privacy-constrained installations, and the cold start of mining training crops to bootstrap a learned detector.

Continuous parameterization of medical data has emerged as a powerful paradigm for resolution-independent image representation. While Implicit Neural Representations offer high fidelity and compact storage, their reliance on global Multi-Layer Perceptrons incurs sizeable computational costs, large memory requirements, and extensive optimization times. As medical imaging trends towards ever-more detailed, high-resolution volumes, these costs impose significant bottlenecks in the applicability of implicit approaches. Recently, explicit Gaussian-based primitives have revolutionized the representation learning paradigm by trading deep network evaluations for localized, rasterization-friendly primitives. In this paper, we present a comprehensive, cross-dimensional evaluation of Gaussian representations against implicit approaches for medical imaging applications. First, we outline a theoretical overview on the mathematical properties offered by explicit primitives beyond what is capable under the implicit neural paradigm. Subsequently, we benchmark the computational performance on two demanding image datasets: 2D microscopy histology and 3D lung Computed Tomography (CT). Our experiments demonstrate that Gaussian representations consistently match or surpass reconstruction metrics compared to implicit methods across all compression factors, while displaying significantly lower optimization times, and memory requirements. Together with the compelling mathematical properties offered by explicit primitives, these findings motivate the wider adoption of Gaussian representations and position them as an attractive direction for future research in medical imaging.

Feed-forward 3D Gaussian Splatting (3DGS) enables efficient and generalizable 3D reconstruction, but current feed-forward 3DGS methods for scene understanding remain largely category-oriented. In contrast, instance-aware 3DGS methods typically rely on per-scene optimization and often decouple reconstruction from instance and semantic learning, limiting reciprocal interactions among them. We present InstanceSplat, a unified feed-forward 3DGS framework for generalizable 3D reconstruction and instance-aware scene understanding from pose-free multi-view images. In a single forward pass, InstanceSplat constructs an instance-aware Gaussian representation that jointly encodes appearance, geometry, instance identity, and language-aligned semantics. Shared 3D Gaussians ground instance identities across views, producing renderable and cross-view-consistent instance features. To allow reconstruction and scene understanding to benefit from each other, we further design an instance-centric learning strategy that connects reconstruction, instance learning, and semantic learning through shared instance structure. Specifically, instance cues guide reconstruction, language-aligned semantics strengthen the discrimination of confusing same-category instances, and instance regions aggregate semantic evidence into coherent object-level predictions. Experiments on novel-view synthesis, instance segmentation, and open-vocabulary semantic understanding under varying input-view settings and on an unseen dataset demonstrate state-of-the-art performance, practical efficiency, and strong generalization.

Beamforming plays a key role in multiple-input-multiple-output (MIMO) communication systems. However, conventional beamforming design normally requires accurate instantaneous channel state information (CSI) and iterative optimization, which incur substantial pilot overhead and computational complexity. Recognizing that radio propagation is intrinsically governed by the physical geometry, we develop a 3D Gaussian splatting for environment-aware beamforming (GSBF) pipeline based on multi-modal data, which characterizes the environment through a persistent 3D Gaussian representation. Specifically, GSBF models the environmental scattering response with reciprocity-preserving bidirectional spherical Gaussian (Bi-SG) kernels and performs two-sided electromagnetic rasterization to render an angular propagator map. The rendered map is then aggregated through an over-complete array-manifold dictionary and projected to the constant-modulus beamformers, thereby synthesizing beams directly from the access point (AP) pose and user position without online instantaneous CSI. Simulations demonstrate that GSBF consistently outperforms baselines such as exhaustive beam alignment (EBA) with lower latency.

Modern image models provide strong cues about \emph{what} should be segmented in each view, but their masks do not by themselves determine \emph{where} those labels should persist in 3D. We present Cross-Domain Segmentation via Gaussian Splatting (CDSeg), a label-transfer interface that requires no task-specific 3D segmentation training and uses Gaussian primitives as a renderable label carrier. An external mask source supplies the labels, while renderer-derived visibility determines which 3D primitives receive them. The carrier is instantiated either by completing each input point into one Gaussian, preserving its index, or by reusing the native primitives of an optimized Gaussian scene. CDSeg records pixel--primitive associations during rendering and fuses multi-view masks through voting and a local filter. The resulting labels can be returned to the original points, retained on the native Gaussian scene, or rendered into other views. CDSeg covers promptable, automatic instance, semantic, and LiDAR settings and processes scenes with millions of primitives in seconds. It obtains 92.35% mIoU on DesktopObjects-360, 95.89% on NeRDS-360, and 65.77% on the full ScanNet-v2 validation split using the provided 2D semantic annotations. CDSeg thereby provides one interface for reusing 2D masks across point clouds, Gaussian scenes, and image views without a task-specific 3D segmentation network.

Creating photorealistic 3D human avatars with realistic upper-body motion remains challenging. Existing approaches either focus on the head and overlook hand gestures, or reconstruct the full body but fail to preserve fine-grained facial fidelity and hand pose accuracy. As a result, current methods struggle to capture the subtle dynamics of facial expressions and hand gestures that are crucial for natural human communication. While methods based on full-body parametric models enable avatar reconstruction from monocular or multi-view inputs, they often lack accurate facial animation and detailed hand articulation. To address these limitations, we propose MVFGA, a novel multi-view-consistent pipeline for generating realistic upper-body avatars. Our approach models the face and hands separately and fuses them with a parametric upper-body mesh model, enabling the capture of fine-grained facial expressions and hand poses for accurate upper-body avatar reconstruction. We then splat 3D Gaussians onto the obtained mesh, enabling high-quality rendering of dynamic avatars from novel viewpoints. Furthermore, we introduce MVFGA-MoCap, a multi-view upper-body motion capture dataset featuring controlled facial expression sequences, diverse hand gestures, and free-form communication. Experiments show that MVFGA generates visually realistic avatars with high-fidelity facial expressions and hand motions, outperforming baselines for upper-body avatar animation. Project page: https://dfki-av.github.io/MVFGA/

Recent advances in 4D Gaussian Splatting (4DGS) enable high-fidelity, real-time spatiotemporal rendering, but expose a fundamental trade-off between motion expressiveness and storage efficiency. While anchor-based designs achieve compactness through anchor-level parameter sharing, their rigid uniform parametrization enforces fixed Neural Gaussian counts and feature budgets per anchor. Consequently, insufficient fidelity is addressed by excessive anchor density, rather than lightweight, targeted increases in Neural Gaussian count or feature capacity, resulting in memory waste. To overcome this rigidity, we introduce an adaptive-capacity anchor-based framework that dynamically allocates the representational capacity based on local spatiotemporal demands. Adaptive Anchor Cardinality varies the number of Neural Gaussians per anchor, concentrating primitives in regions of high geometric or motion complexity while suppressing redundancy. In parallel, Adaptive Anchor Feature Masking modulates anchor-level feature channels, assigning rich features to complex regions and lightweight representations to simpler ones. Experiments on MPEG, Panoptic Sports, and N3DV datasets demonstrate substantial storage reduction without degrading visual quality. Notably, on challenging MPEG sequences with complex motion, our method achieves up to 1.5x higher compression than state-of-the-art anchor-based methods while preserving comparable quality.

Functional flow matching is posed on distributions of functions but implemented from finitely many coefficients or point values. Under scattered or adaptive refinement, the resulting conditioning sigma-algebras need not be nested, so martingale convergence does not justify the sensor limit. We prove strong $L^2$ convergence of finite conditional velocity targets for every strongly consistent sequence of finite-rank reconstructions, with quantitative bounds for orthogonal projections and a point-sensor extension through a regularity space. For learned flows, coupling directly to a population superposition path yields an end-to-end Wasserstein bound without assuming uniqueness of the population finite-dimensional ODE. We verify sensor-independent constants for a normalized quadrature neural operator, including globally Lipschitz activations through an explicit magnitude recurrence. A noncommuting trace-class Gaussian example gives boundary multiplier $0$ under projected restriction and $0.72$ under exact conditioning. A spatial regularity--cubature certificate closes the operator-realization term, a Bernstein argument gives a $\widetilde{O}(n^{-1})$ excess-risk term for fixed model dimension and envelopes, and an exactly realizable clipped Gaussian scaling specialization yields an explicit end-to-end rate.

We give a negative solution to MAIS-O60. We first construct an example in which an initially active ReLU neuron becomes completely inactive in finite time and thereafter remains frozen at a limit whose Fourier energy is equally distributed among all nonzero real frequency classes. The counterexample holds on an open set of initial conditions and therefore occurs with positive probability under Gaussian initialization. An appendix prepared by GPT-5.6 Sol strengthens the counterexample by showing that the same failure can occur for every Clarke trajectory from an open set of initial conditions, under the convention $\mathrm{ReLU}'(0)=0$, for smooth dead-zone approximations of ReLU, and for fixed-step full-batch gradient descent. Thus, single-frequency alignment is not a general consequence of training a single neuron on modular addition.

Existing studies on self-supervised learning for white-box networks typically decouple the derivation of white-box networks via optimization algorithms from self-supervised learning paradigms. In this work, we instead revisit the two components from a joint perspective. The LeJEPA-based self-supervised framework assumes an isotropic Gaussian distribution as the optimal embedding distribution for downstream tasks, which is conceptually equivalent to the expansion term $R(Z)$ in the sparse rate reduction objective guiding white-box Transformer optimization. Building on this observation, we use the LeJEPA self-supervised paradigm to optimize $R(Z)$, and derive the remaining terms $R^{c}(Z\mid U_{[K]})+λ\lVert Z\rVert_{0}$ via the alternating direction method of multipliers (ADMM) into an attention-only Transformer that dispenses with the ISTA structure or MLP layers of the original design. Experimental results demonstrate that our attention-only white-box Transformer achieves classification accuracies of $88.88\%$ on CIFAR-10 and $63.54\%$ on CIFAR-100 at the Base scale under the LeJEPA self-supervised paradigm, while the original white-box Transformer CRATE achieves classification accuracies of $89.18\%$ on CIFAR-10 and $63.56\%$ on CIFAR-100. Our model achieves competitive performance while reducing the parameter count by roughly $31\%$. Beyond the white-box setting, we further investigate standard ViTs and find that replacing all MLP blocks with ReLU activations under knowledge distillation removes approximately 66% of the parameters while preserving competitive accuracy, motivating further investigation into the potential redundancy of MLP modules in standard ViT architectures.

For $n$ unit vectors $x_1,\ldots,x_n \in \mathbb{R}^d$, we study the continuous ReLU derivative Gram matrix $H$, whose entries are obtained by averaging pairwise gated inner products over a standard Gaussian direction. Writing $Δ_\pm := \min_{i \neq j} \min\{ \|x_i-x_j\|_2, \|x_i+x_j\|_2 \}$ for their projective separation, we prove the universal dimension-free lower bound $λ_{\min}(H) = Ω( Δ_\pm/\sqrt{\log n} )$. Conversely, we construct worst-case families satisfying the matching upper bound $λ_{\min}(H) = O( Δ_\pm/\sqrt{\log n} )$, showing that this rate is tight up to universal constants.