3D Gaussian Splatting

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

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

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

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

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

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

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

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

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

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

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

Quantum Circuit Born Machines (QCBMs) offer a natural approach to generative machine learning by leveraging the Born rule. Recent work has provided a method to classically train QCBMs with Instantaneous Quantum Polynomial (IQP) circuits via the Maximum Mean Discrepancy (MMD) loss. Despite the assumed intractability of sampling from IQP circuits classically, their expectation values can be computed classically, enabling training of these IQP QCBMs. However, quantum machine learning (QML) models have various other challenges, including trainability issues caused by exponential concentration or barren plateaus. While these issues have been explored for parameters sampled from a uniform distribution, little work has been done to rigorously treat the use of arbitrary Gaussian initialization schemes. This work leverages Stein's lemma and Lipschitz concentration bounds for Gaussian random variables to provide an analytical lower bound of the variance of the gradient and a probabilistic concentration bound of the deviation of the gradient from its mean. It discusses strategies to either avoid or encourage exponential concentration, as well as the conditions under which barren plateaus are more likely to occur.

Averaging a neural network over its random parameters and marginalizing a Gaussian sector are the same operation, the Schur complement of the eliminated block, and when that block is closed it returns a covariance and its inverse. That is all a network ensemble produces, the closed case. The open case is missing, and nuclear reaction theory has it worked out. Projecting a scattering problem onto a chosen set of channels, with the rest carrying probability irreversibly to a continuum, leaves a non-Hermitian effective generator that conserves and itemizes exactly what it loses: the nuclear optical model and its generalized optical theorem. I set the two cases side by side using only the moments of a distribution, the algebra of Gaussians, and block inversion, no field theory, and give the closed-case dictionary in full: the neural tangent kernel is the Fisher sensitivity kernel, the infinite-width Gaussian limit is the Gaussian-process emulator, and the lazy-to-feature transition is the validity boundary of a reduced-basis emulator. I then test the open export on a truncated attention map, a token-level transfer operator, and a sparse expert router, and report a mostly negative result. The conserved flux ledger ports wherever openness is genuinely present, but its distinctive content is absent, an artifact of the chosen partition, or pinned near a floor by the training objective, and the operationally useful uncertainty turns out to be epistemic, living in the closed half of the correspondence, not the open one. The negative has a structural reason this note makes precise: the open case needs an eliminated sector with a continuous spectrum and wave-like, not relaxational, dynamics, which mainstream learning's finite or dissipative objects do not supply. This is a note, not a result; its main finding is that negative one, and its value is the map that locates it.

Social Learning is a decentralized decision-making paradigm in which spatially dispersed agents collect streaming observations regulated by one of a finite number of models (the hypotheses). The agents are interested in assigning probability scores (the beliefs) to the possible hypotheses. To this end, the agents exchange their beliefs according to a certain communication graph. It has been shown that, under reasonable conditions on the identifiability of the decision model and the network connectivity, each agent ultimately places all the belief mass on the true hypothesis governing the data. However, several questions remain unanswered regarding the evaluation of the social learning performance. One recently adopted performance metric is the rejection rate, i.e., the rate at which the beliefs about the erroneous hypotheses vanish. One contribution of this work is to establish that the rejection rate leads to several paradoxes, which make it unsuitable as a valid performance measure. We then focus on studying the error probability measure. For a binary Gaussian problem, we derive an analytical formula characterizing the ratio between the individual agents' probabilities and the optimal Bayesian probability. The formula shows that this ratio is expressed by the product of two terms quantifying the effect of the network connectivity and the role of the prior information. As a result, an irreducible gap emerges between the decentralized and the centralized error probabilities, which is agent-dependent and does not disappear asymptotically.

Neural radiance field (NeRF) and 3D Gaussian splatting (3DGS) are two mainstream approaches for novel view synthesis. They often show complementary performance, i.e., 3DGS demonstrating faster rendering speed and NeRF demonstrating higher rendering quality. Motivated by this, we propose leveraging NeRF-rendered images for 3DGS. Specifically, we target street scenes and utilize a pre-trained street-specific NeRF method to produce training images for a target 3DGS method. In our 3DGS training, NeRF-rendered images are used to remove transient objects in street-level input views and to generate bird's-eye views as additional views, inheriting the higher-quality rendering of NeRF into 3DGS. We further incorporate a diffusion-based image enhancement to improve the image quality of the additional views. Experimental results on one synthetic and two real datasets demonstrate that our proposed method improves street-scene rendering while preserving the speed of 3DGS and the quality of NeRF.

We prove a variance-aware pointwise majorizing-measure theorem for centered Gaussian processes. Classical generic chaining characterizes the scalar quantity $\mathbb E\sup_{x\in T}X_x$; the theorem here gives a simultaneous high-probability envelope for the entire field. For an ambient prior $μ$, the envelope at $x$ is governed by a pointwise Fernique-Talagrand functional $$Φ_μ(x):=\int_0^{4σ(x)}\sqrt{\log\frac{1}{μ(B_d(x,\varepsilon))}}\,d\varepsilon,$$ together with the corresponding Gaussian tail term. The theorem provides a reusable field-level refinement of classical generic chaining and a Gaussian-process counterpart of pointwise empirical-process bounds for deep neural networks. We also record a Bayesian algorithmic lower envelope from the interactive Fano/data-processing principle. For a known prior $π$, an observation channel, and a concrete estimator $\widehat t(Y)$, the lower bound is expressed through the exact ghost small-ball mass $\mathbb E_{Y\sim Q}π(B_d(\widehat t(Y),Δ))$, rather than a worst-case covering number. In Gaussian location experiments, comparison decoders convert Bayes location error into lower bounds on decision-aligned Gaussian ranges. We then construct an elementary example separating the usual Fano relaxation, the Bayesian algorithmic lower envelope, the pointwise Gaussian envelope, and the full-class minimax risk. Together, these results show that algorithmic lower bounds provide local-geometric validations of pointwise complexity for fixed estimators in overparameterized ambient classes, precisely in regimes where classical minimax theory becomes either too coarse or oracle-dependent. This separation can also be recast in minimax language as penalty-range information relaxation, highlighting an important question of algorithmic robustness for classical high-dimensional models and regularized algorithms.

We present RPC-GS, the first Gaussian Splatting framework for satellite imagery that operates natively with Rational Polynomial Camera (RPC) models. The RPC model is the de facto standard for representing the complex imaging geometry of modern pushbroom satellite sensors. To simplify rendering, prior satellite Gaussian Splatting methods replace the RPC model with perspective or affine camera approximations, leading to geometric errors during reconstruction. RPC-GS avoids these approximations by projecting Gaussian means and covariances directly through the RPC model during the splatting process. We embed the RPC model in a chain of carefully selected geo-coordinate transformations representing a mapping from splatting-suitable scene coordinates to image coordinates. To map the Gaussian covariance matrices, we derive a numerically robust Jacobian-based covariance projection for the (partially nonlinear) coordinate transformations. Since RPCs lack an explicit notion of camera depth, we integrate a metric ray-based depth formulation. We benchmark RPC, perspective, and affine camera models in a unified framework, with our native RPC renderer consistently achieving the lowest reconstruction error on leading satellite benchmark datasets, improving mean altitude error over perspective and affine approximations by 29.6% and 63.8% on DFC2019, and by 9.9% and 37.9% on IARPA2016. We release our code to support future research of Gaussian Splatting in the satellite imaging domain.

Continuous-time SLAM provides a principled framework for fusing heterogeneous sensors while estimating smooth trajectories, and is particularly well-suited for handling heterogeneous, asynchronous sensor streams with non-uniform readout patterns, such as rolling shutter cameras, LiDAR scanners, radar sweeps, or event-based sensors. In this work, we introduce G-solver, a fully Gaussian and distributed framework that combines Gaussian Belief Propagation (GBP) with Gaussian Process (GP) motion priors for continuous-time trajectory estimation. Our GP model provides a probabilistic representation of the trajectory, enabling consistent interpolation and the use of data-driven hyperparameters, while GBP offers a scalable message-passing formulation well-suited for decentralized settings. The resulting solver naturally extends to multi-camera scenarios without specialized synchronization or engineering effort. We evaluate the approach on synthetic and real data, including rolling shutter and distributed multi-camera optimization, demonstrating accurate and stable estimation with runtimes comparable to existing continuous-time methods. An open-source implementation is released.

Modeling dynamic facial expressions using 3D Gaussian representations remains challenging due to their unstructured nature. Conventional Gaussian avatar pipelines require extensive multiview and sequential expression data, limiting scalability and accessibility. In this work, we introduce Self-Adaptive Gaussian Expression (SAGE), a framework for self-learning expression-induced Gaussian deformations that enables high-fidelity, animatable avatars from minimal input data. Our method jointly optimizes 2D Gaussian surfels and a Signed Distance Field (SDF) to enforce compact, surface-aligned Gaussian distributions, while a self-supervised expression learning phase replaces long training sequences with geometric and appearance consistency constraints. This design allows flexible deployment across multiple reconstruction regimes: in the multiview setting, only a single frame (timestep) is required instead of thousands; in the monocular setting, only head rotations are needed without expression sequences; and in the one-shot setting, no pretraining or priors are necessary. Experiments demonstrate that our approach achieves reconstruction and animation quality comparable to state-of-the-art methods, while reducing data requirements by several orders of magnitude. Our results highlight the potential of self-supervised Gaussian deformation learning as a step toward accessible, data-efficient avatar creation.

After the success of 3D Gaussian Splatting (3DGS) for novel view synthesis, many works have explored how to also use it for geometric surface representation. However, extracting accurate geometric information directly from 3DGS remains challenging and can often reduce the appearance rendering quality. In this work, we show that 3DGS in its default form is inheritedly unsuited to represent texture and geometry at the same time, by training with complete ground-truth texture and geometry information. We also propose a simple solution by applying a single additional geometry opacity parameter to each splat, together with an optional transparency-curated optimization pipeline. Our experiments, both with ground-truth and vision foundation model geometric input, show that this change leads to improved rendering and geometry performance on a wide variety of dataset, and especially complex scenes with transparent objects benefit significantly from our method.

Feed-forward 3D Gaussian Splatting methods reconstruct a scene from posed or pose-free images in a single forward pass, yet current approaches predict one Gaussian per input pixel, tying the representation budget to camera resolution rather than scene complexity. A flat wall and a richly textured object thus produce equally many Gaussians despite very different geometric needs. We propose ZipSplat, a token-based feed-forward model that decouples Gaussian placement from the pixel grid. A multi-view backbone extracts dense visual tokens, and k-means clustering compresses them into a compact set of scene tokens. Cross- and self-attention refine these tokens, and a lightweight MLP decodes each into a group of Gaussians with unconstrained 3D positions. Because clustering is applied at inference, a single trained model spans the quality-efficiency curve without retraining. ZipSplat operates without ground-truth poses or intrinsics, yet sets a new state of the art on DL3DV and RealEstate10K with ${\sim}6{\times}$ fewer Gaussians than pixel-aligned methods, surpassing the best pose-free baseline by 2.1dB and 1.2dB PSNR, respectively. It further generalizes zero-shot to Mip-NeRF360 and ScanNet++, outperforming all comparable baselines. Our project page is at https://veichta.com/zipsplat.

For nonconvex optimization problems whose objective is the prediction function of a trained Support Vector Regression (SVR) model with the Gaussian radial basis function (RBF) kernel (RBF-SVR), we present a framework that applies the difference of convex functions (DC) algorithm (DCA) by exploiting the analytical structure of the RBF kernel to construct an explicit DC decomposition. Specifically, we derive in closed form both the lower bound $μ$ of the strong convexity parameter of the DC components and the upper bound $L$ of the gradient Lipschitz constant of the subproblem. Both $μ$ and $L$ are determined solely by the post-training dual-coefficient sum $C_α$ and the RBF kernel parameter $γ$, together with the DC decomposition parameter $ρ$, and they share a common leading term $C_αρ$. Through numerical experiments on six benchmark functions, we show that $C_αρ$ is the primary single quantity characterizing both the convergence properties and the initial-point dependence of DCA, and further demonstrate that it decomposes into two independent pathways, $C \to C_α$ and $γ\to ρ$, with its primary variation governed by the SVR hyperparameters $(C, γ)$. Together, these results allow the convergence properties of DCA on RBF-SVR to be assessed in advance through the single scalar quantity $C_αρ$: approximately from $(C, γ)$ before training, and exactly in closed form after training.

Dynamic 3D Gaussian Splatting (3DGS) methods reconstruct time-varying scenes from synchronized multi-camera video using photometric supervision. When a moving object becomes fully occluded from all training cameras, this supervision vanishes: the Gaussians representing it receive no gradient signal and degrade. Existing approaches to incomplete observations in neural reconstruction rely on learned generative priors that prioritize visual plausibility over physical correctness. We propose $\textbf{PersistGS}$, a method that restores object permanence during occlusion by coupling differentiable rigid body simulation with 3D Gaussian Splatting. Our approach decomposes the scene into per-object Gaussians and collision meshes, estimates friction and velocity from the observed pre-occlusion trajectory via differentiable simulation, and uses the resulting SE(3) trajectory to position object Gaussians throughout the occlusion period. Because the predicted trajectory satisfies the governing equations of rigid body dynamics, it faithfully captures contact events (bounces, friction-based deceleration, direction changes) that kinematic extrapolation cannot model. We introduce a centroid silhouette loss that isolates positional gradients from appearance noise, yielding 40% lower trajectory error than photometric supervision. We evaluate using cameras withheld from training that observe the object during its occlusion. Experiments on synthetic scenes show that PersistGS outperforms constant velocity extrapolation by +2.46dB PSNR and comes within 0.19dB of a ground-truth trajectory upper bound.

Graph neural networks have achieved strong performance on graph-structured data, but their effectiveness depends heavily on the quality of the observed graph. In real applications, graph topology is often imperfect: noisy edges may connect unrelated nodes, while missing edges may prevent useful information from being propagated. Existing robust graph learning methods mainly address this problem by removing suspicious edges or by learning a new graph structure during training. However, edge removal alone cannot recover missing connections, and graph structure learning may introduce additional optimization complexity. In this paper, we propose Topology-Aware Gaussian Repair (TAGR), a simple graph repair framework for robust message passing in graph neural networks. Instead of learning a dense adjacency matrix, TAGR constructs a sparse feature-neighborhood graph using an adaptive Gaussian kernel and combines it with a topology-aware residual correction of the observed graph. The Gaussian repair component introduces auxiliary edges between feature-similar nodes, while the residual correction preserves and reweights the original topology according to local feature and structural consistency. The repaired graph can be used directly with standard graph neural networks without changing their architectures. Extensive experiments on benchmark citation networks show that TAGR improves the robustness of GNNs under both noisy-edge and missing-edge settings. The analysis further show that Gaussian feature-neighborhood repair provides the main robustness gain, while topology-aware residual correction improves stability when the observed graph is incomplete. These results suggest that effective graph robustness can be achieved through lightweight sparse graph repair rather than dense graph structure learning.

We present a hierarchical model for ball action anticipation in football broadcast video. Given a 30-second observation window, the system predicts actions occurring in the subsequent 5-second window across 10 classes. A shared local Transformer encodes clip-level features within each 5-second sub-window; a GRU then aggregates temporal context across all sub-windows; finally, a Transformer decoder with K input-conditioned event slots decodes the anticipation target via three decoupled heads (objectness, class, temporal offset). We introduce frequency-reweighted Hungarian matching that systematically favours rare action classes, and Gaussian soft targets for temporal bin supervision. On the SoccerNet Ball Action Anticipation benchmark, our method achieves 17.91% mAP on the test server.

Multi-view video recordings are increasingly used to capture the 3D movements of animals in experimental settings, yet extracting rich 3D representations from these recordings remains challenging. Supervised pose estimation requires extensive manual annotation, while general-purpose 3D reconstruction models trained on generic scene datasets fail on the specialized imagery and sparse-view setting of laboratory experiments. We address these limitations with BEAST3D, a self-supervised pretraining framework that learns 3D visual representations from unlabeled, calibrated multi-view video. BEAST3D uses a vision transformer to predict 3D Gaussian splats that reconstruct held-out views through differentiable rendering, while simultaneously segmenting the animal from the background. BEAST3D reconstructs 3D structure with as few as four views by conditioning directly on known camera parameters--unlike general-purpose models, which must estimate camera geometry from dense overlapping viewpoints that are seldom available in lab settings. Through comprehensive evaluation across four species, we demonstrate that BEAST3D produces rich, viewpoint-invariant features that transfer effectively to three downstream tasks: novel view synthesis, which validates the quality of the learned 3D representations; multi-view pose estimation, which provides the sparse keypoint trajectories widely used in behavioral analysis; and neural encoding, which relates 3D behavioral features to simultaneously recorded neural activity. BEAST3D thus establishes a versatile framework for behavioral analysis that leverages 3D structure in modern multi-view laboratory recordings.

Gradient observations can substantially improve Gaussian process (GP) surrogates, particularly in high-dimensional settings where function evaluations are expensive. However, exact inference with $n$ function values and $n$ full gradients in $d$ dimensions scales cubically in the joint state size, imposing an intractable $\mathcal{O}(n^3 d^3)$ computational bottleneck. We introduce TERA, a highly scalable derivative GP method based on target-specific exact gradient reduction. We prove that for stationary kernels, the gradient components orthogonal to the directions connecting the target and conditioning points are conditionally independent of the target function value; consequently, the exact conditional density is fully characterized by at most $m^2$ directional derivatives once a conditioning set of size $m$ is specified. By using these reduced, dimension-free conditionals as local factors in a Vecchia approximation, TERA effectively decouples $n$ and $d$ from the dense matrix inversion. This reduces the per-target evaluation cost to $\mathcal{O}(dm^2 + m^6)$ time and $\mathcal{O}(dm^2 + m^4)$ memory, leaving the underlying derivative GP model mathematically unchanged. Empirical evaluations demonstrate that TERA achieves state-of-the-art predictive accuracy while operating orders of magnitude faster than standard derivative GPs. Crucially, both computation time and peak GPU memory remain essentially flat with respect to $d$, enabling highly scalable inference in high-dimensional spaces.

Reward guidance algorithms steer a learned generative process toward the reward-tilted measure at inference time. While empirically powerful, these methods are prone to reward hacking: the guided model over-optimizes the reward at the cost of fidelity to the learned distribution. Prior work has attributed this to the complexity of neural reward functions or implicit biases in diffusion training, but its fundamental origins remain poorly understood. We show that reward hacking arises from an approximation made in most practical implementations of reward-guided diffusion -- finite-particle plug-in estimation of the Doob h-function -- even in the simplest non-trivial settings of Gaussian and Gaussian mixture targets with quadratic rewards. In closed form, we isolate two distinct failure modes of the plug-in estimator: it leads to reward hacking within each mode and it cannot select high-reward modes. We propose a closed-form reward damping schedule that corrects the within-mode bias with no additional compute, and clarify the role of best-of-n sampling in compensating for the mode selection failure. Experiments on Gaussian mixture targets, a 2D checkerboard, and FLUX.1 text-to-image generation confirm that our theoretical insights carry over to practical settings.

World models enable intelligent agents to predict the consequences of their actions on the environment. In this paper, we propose Multi Rigid Object Gaussian World Model (MRO-GWM), a novel model that learns action-conditional dynamics of rigid objects in 3D. By representing the scene by object-centric Gaussians, we can represent arbitrary object shapes and multi-object scenes. We develop a novel spatio-temporal transformer architecture that predicts future rigid body motion from a history of object Gaussians and future actions. Objects are represented by their Gaussians in a canonical frame, which allows for describing object motion as rigid body transformation. Our model is trained on reconstructions from multiple viewpoints, which requires the model to handle partial observations of objects due to occlusions. We analyze prediction performance of our approach on synthetic datasets composed of typical household objects with multi-object dynamics and interactions by a robot end effector. We also evaluate our model in model-predictive control for non-prehensile manipulation in simulation.

A central difficulty in training Joint-Embedding Predictive Architectures (JEPAs) is preventing representation collapse. LeJEPA addresses this by enforcing an isotropic Gaussian target on the embeddings via Sketched Isotropic Gaussian Regularization (SIGReg). This target is in tension with the manifold hypothesis, which expects embeddings to concentrate on a low-dimensional subset of the ambient space. We propose \emph{UR-JEPA}, which targets a uniformly $n$-rectifiable measure of local tangent dimension $n$ at small scales, realized through a Gaussian-kernel smoothed Carleson-type square function $\mathcal{L}^{\text{CGLT}}$, with a complementary Jones $β$-number formulation. On Inet10, UR-JEPA($\mathcal{L}^{\text{CGLT}}$) attains $0.9141 \pm 0.0014$ for a $+0.83$,pp gain over LeJEPA($\mathcal{L}^{\text{SIGReg}}$) with $\sim 30\%$ lower seed standard deviation; on matched-recipe Galaxy10~SDSS, a single-seed ImageNet-$100$ run, and a $3$-seed EuroSAT remote-sensing run, the two methods lie in the same peak-accuracy band at convergence, with UR-JEPA retaining its lower-seed-variance signature. On EuroSAT the in-domain pair is competitive at $96.0$ to $96.1\%$ with large remote-sensing foundation-model transfer at a $25\times$ smaller backbone. The distinction is geometric: direct visualization of the projector output distribution shows that on all four datasets UR--JEPA($\mathcal{L}^{\text{CGLT}}$) produces a global PCA spectrum with a $4$ to $5$ order-of-magnitude drop at index $\sim 20$ to $25$ out of $D = 32$, while LeJEPA's spectrum is near-flat (top-to-bottom ratio at most $3.6$). Per-dimension marginals are simultaneously near-Gaussian for both methods (mean Shapiro-Wilk $W \in [0.992, 0.996]$) as a Diaconis-Freedman consequence. At matched accuracy the two regularizers therefore yield structurally distinct projected representations.

Recent publications have suggested using the Shap- ley value for sensor anomaly/attack localization. We study the performance of such an approach by using mathematically de- fined optimum binary classifiers in the Shapley value calculation. To judge localization performance, we study the ability of the Shapley value of a given sensor observation to determine if that observation is anomalous. First, we prove that for cases with independent sensor observations, an optimized anomaly test using the Shapley value is equivalent to an optimized lower-complexity anomaly test using a single term in the Shapley value calculation, yielding the exact same probability of error. For some popular dependent observation cases involving two sensors, including correlated bivariate Gaussian/Laplacian probability density functions and constant/Gaussian at- tacks/anomalies, we prove that these two tests are fundamentally different, yielding different decision regions and error probabil- ities. Further, we prove that the Shapley value test is sometimes strictly inferior to the other (single term in Shapley calculation) test in certain statistically dependent bivariate Gaussian scenarios with large correlation magnitude and additive attacks/anomalies, while it is strictly superior in others, depending on the sign of the correlation. One can combine these two approaches to obtain a strictly better approach in these cases. These results, which provide the first theoretical statistical analysis of Shapley-based localization, seem very interesting based on the wide acceptance of the Shapley value by many researchers and should encourage further research on this topic. Numerical results are provided which illustrate our findings.

3D Gaussian Splatting (3DGS) renders new views of a scene in real time. Like every rasterizer, it answers only primary rays, the rays from the camera through the image. It cannot trace the secondary rays that shadows, ambient occlusion, and global illumination need. We turn a trained 3DGS scene into a ray oracle by distilling a Directed Distance Function (DDF). The DDF is a small neural field. It takes a ray, given by an origin and a direction, and returns the distance to the first surface and whether the ray hits anything. Each query is one forward pass. The field is 52MB, and its size does not depend on the number of Gaussians, so its cost and memory stay flat as the scene grows. We make three points. First, we study what supervision a DDF needs. Depth rendered from the Gaussians is too blurry to teach thin parts, while clean distance supervision recovers them. Second, we measure speed. The DDF is 26 to 72 times faster than sphere tracing an equivalent signed distance field, and unlike a bounding volume hierarchy built over the Gaussians, even on dedicated RT-core hardware, its query time and memory do not grow with the scene. Third, we show a pipeline that needs no mesh: images give a 3DGS scene, a neural surface gives clean distances, and the DDF learns from them. We use the DDF as a secondary-ray oracle for global illumination. It reproduces reference ray-traced shadows at 30.3dB and ambient occlusion at 21.3~dB across 142 objects, and on real captured scenes. Our codes are available at https://github.com/smlab-niser/ddf-gs.

Dynamic scene reconstruction via 3D Gaussian Splatting (3DGS) has emerged as a compelling approach for representing evolving environments, yet understanding trade-offs between methodologies remains crucial. This paper presents a comprehensive analysis of dynamic 3DGS methods, categorizing them into two paradigms: structure-guided methods employing auxiliary representations (deformation fields, canonical spaces, grids) to model temporal changes, and gaussian-centric methods encoding dynamics directly into primitives via continuous functions or 4D representations. We evaluate representative methods from both paradigms on the D-NeRF benchmark. Our findings reveal that structure-guided methods achieve superior reconstruction fidelity and compact model sizes, while gaussian-centric approaches demonstrate significantly higher rendering speeds enabling real-time performance, though with greater quality variability and potentially substantial storage overhead. This analysis highlights a fundamental trade-off between reconstruction quality/compactness versus rendering speed, providing insights to guide future research and application development in dynamic scene reconstruction.

3D Gaussian Splatting (3DGS) is a technique for creating and rendering 3D scenes, however its performance depends heavily on the quality of initial seed points. To improve 3DGS initialization, this study presents and evaluates several point cloud upsampling approaches: linear interpolation, triangular interpolation, spline-based surface reconstruction, moving least squares surface fitting, and Voronoi-based point generation. Additionally, this research introduces a depth-guided point lifting method that leverages depth maps to maintain geometric consistency with Structure-from-Motion (SfM) reconstructions. Through extensive experiments on the Mip-NeRF360 and Replica datasets, the proposed methods demonstrate improvements in reconstruction quality across diverse scene types. Results indicate that different upsampling strategies excel in different scenarios: surface reconstruction methods perform better with organic, detailed scenes, while simpler interpolation approaches are more suited for scenes dominated by piecewise-smooth geometries. In comparison, the depth-guided approach shows promise for adding geometry-aware points across the entire scene, importantly in texture-less regions. These findings, which provide preliminary practical guidelines for selecting appropriate upsampling methods based on scene characteristics and computational constraints, advances the understanding of how point cloud initialization affects 3DGS quality.

Dynamic scene reconstruction from monocular video remains a fundamental challenge in computer vision. Existing feed-forward methods predict 3D Gaussians pixel-wise for each frame, suffering from duplicated Gaussians and view-dependent biases that hinder effective learning of scene motion. We present C4G, a feed-forward 4D reconstruction framework built upon a compact set of timestamp-conditioned learnable Gaussian query tokens. Each token aggregates corresponding features across the full temporal context and decodes a 3D Gaussian whose position is modulated by the target timestamp, enabling globally coherent motion modeling without per-scene optimization. To capture fine-grained details, we further introduce a video diffusion model-based rendering enhancement module. Since our framework effectively aggregates features into Gaussians, we extend this capability to feature lifting, producing a 4D feature field that supports point tracking and dynamic scene understanding. C4G achieves strong novel-view synthesis performance using significantly fewer Gaussians and without requiring camera poses, while exhibiting stronger motion modeling and robustness to large temporal gaps.

The tasks of object removal and inpainting 3D Gaussian Splatting (3DGS) scenes face challenges such as 3D consistency across camera views. In comparing 2D inpainters and their suitability for the 3D domain, we find that reconstruction-based inpainters outperform generative diffusion models in 3D consistency. Integrating these 2D inpainters into different single-step methods for creating and finetuning 3DGS scenes, our results indicate that initializing the scene from scratch produces higher quality results than finetuning the existing scene. Using a state-of-the-art generative 2D inpainter, we create a straightforward baseline to underline the importance of object removal before inpainting in the 3D setting. Since 360° datasets rarely include real-world ground truths, and challenging occlusion scenarios are equally sparse, we introduce a novel multi-object scene with recorded ground truth data and many views with object occlusions.

We formulate data propagation through the Transformer, the machine learning architecture powering large language models, as a nonlinear control system on the space of probability measures. For the mean-field Transformer model with self-attention and affine feed-forward layers, we prove that Gaussian distributions remain exactly Gaussian along the induced flow. This invariance reduces the infinite-dimensional measure dynamics to a finite-dimensional bilinear control system governing the evolution of the mean and covariance, reformulates the expressive capacity of Transformers as a reachability problem for prescribed Gaussian moments, and reveals a novel connection with Riccati-type equations from classical filtering and control. For time-varying controls, we prove exact finite-time reachability of any target Gaussian distribution whose covariance matrix has the same rank as the initial one, this rank constraint being an intrinsic invariant of the dynamics. For time-invariant parameters, we derive explicit spectral conditions leading either to asymptotic stability toward positive-definite equilibria or to finite-time blow-up of the covariance. Numerical experiments complement the theory by showing that practical Transformers with Gaussian inputs remain close to moment-matched Gaussian distributions through early and intermediate layers, while Transformers with prescribed attention matrices reproduce the predicted covariance regimes: bounded evolution in stabilizing configurations and blow-up in destabilizing ones.

Two recent results have reshaped quantum Gaussian processes (QGPs). On the one hand, \citet{lowe2025assessing} rule out the exponential speedups claimed by HHL-based QGP regression in the typical, well-conditioned regime; on the other, an independent line of work shows that highly expressive quantum kernels suffer posterior pathologies that break Bayesian optimization. We show that these seemingly unrelated phenomena are governed by the same quantity: the normalized spectral entropy $S(K)/\log n$ of the kernel Gram matrix. We prove a Cauchy--Schwarz tail bound on Nyström approximation error, a finite-sample variance-contraction identity in terms of Bach's degrees of freedom $d_σ(K)$, and a characterization of the \emph{target-dependent} optimal entropy via the intrinsic dimension of the target in the kernel eigenbasis. Empirically, the diagnostic is kernel-agnostic: hardware-efficient, matchgate, IQP \emph{and} RBF/Matérn/RFF/deep-kernel families all collapse onto identical $S/\log n$ curves on dequantization, ECE, and variance-contraction panels. The NLL sweet spot lives at high entropy for smooth targets and at low entropy for band-limited quantum-data targets. The diagnostic transfers from simulator to IBM Heron hardware with median absolute error $3.2\%$ and mean $5.2\%$ in $S/\log n$ across $24$ configurations at $n_q = 4$, with matchgate and IQP within $5\%$ mean and a single HE configuration returning a $30\%$ outlier that drops to $0.5\%$ on rerun (attributed to calibration drift); the same diagnostic transfers to a second Heron backend (mean error $2.7\%$) and to a $n_q = 6$ scale-up on the original backend (mean error $1.7\%$). No error mitigation is applied throughout.

We study the problem of learning Gaussian mixture models under overparameterization. Prior work has shown that while overparameterization is essential for avoiding spurious local optima and enables global recovery of the ground-truth model using the gradient-EM (expectation-maximization) algorithm, it can dramatically slow down the local rate of convergence. Under certain assumptions on the mixture weights, we show that a standard divergence measure minimized by statistical learning procedures possesses a manifold of slow growth on which the well-known Polyak stepsize reduces the loss geometrically, and design a gradient-based method that converges to minimizers at a locally linear rate. Additionally, we show that our method converges to nearly optimal solutions -- up to a natural misspecification threshold -- for mixtures with arbitrary weights. At a high level, the method alternates between several "short" gradient descent steps that approach the manifold and "long" Polyak steps that contract the distance to minimizers. Our results suggest that slow convergence is not an intrinsic challenge of overparameterization, but can be overcome by exploiting the favorable structure of the loss landscape.

Efficient and robust 3D scene representation is crucial in autonomous driving, robotics, and related fields. While RGB images provide valuable content for 3D reconstruction, other modalities like thermal or depth can enable additional information on the environment. Lately, novel view synthesis methods like 3D Gaussian Splatting have started using multiple modalities to further boost their performance. But fusing or combining multimodal data can make the process slower and can bring in additional challenges. Therefore, our project aims to use single modality based on thermal infrared domain, by removing the reliance on visible light as much as possible. This single modality can be expected to be faster as it does not rely on multimodal data. We propose a method, Thermal-to-Depth Gaussian Splatting (TDg), that uses only thermal images and depth estimation in its architecture to derive the radiance fields. Our TDg method outperforms the MSMG (Multiple Single-Modal Gaussians) baseline in most cases on our test datasets, RGBT-Scenes and ThermalMix. On average, the rendering quality metrics such as learned perceptual image patch similarity (LPIPS), structural similarity index measure (SSIM), and peak signal-to-noise ratio (PSNR) of TDg are 1.12%, 0.034%, and 0.01% better than the baseline MSMG values. It also reduces the training time significantly, by 12 mins 47 secs (55% improvement). Overall, our method is successful in deriving these thermal radiance fields, which can ultimately have several applications, such as identifying heat sources critical in surveillance, search or rescue operations, and industrial inspections where temperature is widely used to monitor machines.

In this work, we focus on zero-shot 3D style transfer that can generate multi-view consistent stylized views of the 3D scene given an arbitrary style image. We primarily tackle the issue of data scarcity in 3D style transfer, which arises when each model is trained on only a single scene, thereby limiting the number of available content images. This scarcity significantly hampers stylization performance, as model optimization relies on a sufficient number of content-style image pairs to provide supervisory signals. Our core idea is to integrate a decoder pre-trained on large-scale 2D image datasets into the 3D style transfer pipeline, thereby leveraging the prior knowledge encoded in the decoder from learning over numerous content-style image pairs. Our method combines feature Gaussian splatting and deferred stylization, enabling high-quality stylization with the data-sufficient decoder network while ensuring view consistency by unifying view-dependent operations into a view-invariant process. Experiments demonstrate that our Data-Sufficient StyleGaussian (DS-StyleGaussian) model outperforms existing zero-shot 3D style transfer methods in terms of visual quality across various datasets. This work also suggests that 2D pre-training can serve as a strong enhancement for 3D tasks, bridging the data gap between 2D and 3D.

High-density electroencephalography (HD-EEG) enables fine-grained measurement of cortical activity but requires expensive hardware and lengthy setup times, limiting its clinical and research accessibility. We propose EMAG (EEG Mixture of Anisotropic Gaussians), a differentiable framework that reconstructs HD-EEG signals from a sparse subset of low-density (LD) electrodes by representing brain electrical sources as a mixture of anisotropic 4D space-time Gaussians. EMAG places a mixture of multiple Gaussians at each point of a spherical brain grid, each parameterized by a full 4 x 4 precision matrix, enabling anisotropic spatial spreads and explicit coupling between spatial and temporal dimensions. The forward model renders scalp EEG via differentiable Gaussian field contributions at electrode locations, enabling end-to-end training without explicit source localization supervision. We evaluate EMAG on three public EEG benchmarks (Localize-MI, SEED, and SEED-IV) at super-resolution factors of 2x through 8/16x. EMAG outperforms the current state-of-the-art EEG super-resolution method at most super-resolution factors on three standard benchmarks (Localize-MI, SEED, SEED-IV). The explicit Gaussian parameterization further enables direct visualization and interpretability of learned brain source configurations, potentially opening avenues for clinical and neuroscientific applications, such as source localization or biomarker discovery.

3D Gaussian Splatting (3DGS) is a recent approach for scene rendering. Although primarily designed for view synthesis, its potential for scene understanding tasks remains underexplored. In this work, we conduct a comparative evaluation of various geometric deep learning architectures for the classification of 3D scenes represented using Gaussian Splatting. We benchmark point-based and graph-based models across both traditional point cloud datasets and dedicated Gaussian Splatting datasets. Scenes are embedded into latent representations, which are evaluated through end-to-end classification, linear probing, and clustering analysis. Our study provides insight into the suitability of different geometry-aware architectures and input feature configurations for learning effective 3D Gaussian Splat representations. The results highlight consistent differences between architectural families and reveal the impact of Gaussian-specific attributes on the quality of representation.

We introduce a probabilistic splat-based radiance field framework that retains the fast rasterization and test-time efficiency of 3D Gaussian Splatting (3DGS) while replacing heuristic primitive manipulation with gradient-based optimization of a volumetric probability density. Rather than relocating, splitting, or culling Gaussians via hand-tuned densification (e.g., ADC), we treat primitive locations as samples drawn from a persistent, learnable density. We instantiate this density using a novel, memory-efficient multi-scale hierarchical grid that enables end-to-end gradient-based optimization. To stabilize the optimization, we derive an unbiased gradient estimator with control variates that markedly reduces variance. By allowing probability mass to flow to where the loss demands, our framework eliminates brittle priors and naturally explores the volume, achieving state-of-the-art reconstruction quality on mip-NeRF 360 while preserving 3DGS-level rendering speed.

We design a class of additive noise mechanisms that satisfy $(\varepsilon, δ)$-differential privacy (DP) for scalar, real-valued query functions with known sensitivities, with a particular focus on moderate and low-privacy regimes. These mechanisms, which we call \textit{mixture mechanisms}, are constructed by mixing multiple Gaussian distributions that share the same variance but differ in their means and mixture weights. The resulting distributions can be interpreted as convex combinations of a zero-mean Gaussian (as used in the analytic Gaussian mechanism) and additional Gaussians whose means depend on the sensitivity of the query function. We derive tight conditions on the variances required for $(\varepsilon, δ)$-DP and provide efficient algorithms to compute them. Compared to the analytic Gaussian mechanism, our mechanisms yield substantially lower expected noise amplitudes ($l_1$-loss) and variances ($l_2$-loss for zero-mean distributions). In the low-privacy regime that motivates our design, our mechanisms approach optimality, mitigating nearly all of the optimality gap of the analytic Gaussian mechanism.

We study the problem of computationally efficient proper agnostic learning of multidimensional concept classes under the Gaussian distribution. In this setting, given i.i.d. labeled samples from an unknown distribution over $\mathbb{R}^d \times \{\pm 1\}$ whose marginal on $\mathbb{R}^d$ is Gaussian, the goal is to output a hypothesis from a target class $\mathcal{F}$ whose 0-1 loss is within $ε$ of that of the best classifier in $\mathcal{F}$. We give the first efficient proper agnostic learning algorithm for arbitrary Boolean functions of $K$ halfspaces under Gaussian marginals. Our algorithm runs in time $d^{O(K^2 \log(1/ε)/ε^2)} + (K/ε)^{O(K^3/ε^{2.5})}$. Prior to our work, the only known algorithm for $K \geq 2$ was brute-force search, with run-time exponential in $d$. Moreover, the dependence of our run-time on the dimension $d$ matches that of the best known improper learning algorithm, namely $d^{\widetilde{O}(K^2/ε^2)}$. For the special case of a single halfspace ($K=1$), the best previous run-time was $d^{O(1/ε^4)} + (1/ε)^{O(1/ε^6)}$. Our algorithm improves this to $d^{O(1/ε^2)} + (1/ε)^{O(1/ε^{2.5})}$. Once again, the dependence on $d$ matches that of the best known improper algorithm, namely $d^{O(1/ε^2)}$. Furthermore, the dependence of our run-time on the dimension $d$ is essentially optimal in the statistical query model.

This short note presents a dimension-independent subgaussian concentration bound for Gaussian vectors under coordinate-wise nonlinear mappings. Discovered by Gemini 3.5 Flash, this result applies to any bounded function under a well-conditioned covariance. We apply this tool to answer a question of Simone Bombari on sign-quantized linear maps $Y = \text{sgn}(Wx)$.

Modern intrusion detection systems generate thousands of alerts daily, but alert fatigue severely limits security operations effectiveness due to too many false positives or low-impact events. We address this by proposing a principled framework for alert prioritization based on subnormal Gaussian fuzzy numbers, explicitly modeling three sources of uncertainty: threat severity, detection confidence, and organizational risk attitude. Each alert is represented as a fuzzy number with the core indicating severity, spread indicating uncertainty, and height reflecting detection reliability. We apply ranking indices to prioritize alerts, allowing organizations to tune security posture through a risk-attitude parameter. Experimental validation on CIC-IDS2017 and NSL-KDD demonstrates greater robustness than baselines under detector degradation (0.9963 vs 0.8215 NDCGrel@100), with distinct differentiation in mid-confidence alerts and near-parity with baselines under robust detectors. The framework is theoretically grounded, computationally efficient, provides interpretable reasoning, and remains robust across detector families and miscalibration scenarios.

In probabilstic supervised learning of an input-output relationship - as a sample function of a Gaussian Process (GP) - priors are typically specified for the hyperparameters of the kernel that parametrises the covariance function of the GP, where the induced covariance matrix of the (resulting multivariate Normal) likelihood, governs the learning and prediction. When the sought function is highly multivariate, multiple lengthscale parameters must be learnt simultaneously, making inference difficult. We develop a ``self-assembled'' Wishart prior for the covariance matrix, while undertaking Bayesian inference on the kernel hyperparameters using MCMC. The construction uses a look-back window over recent MCMC iterations to define a time-step dependent scale matrix, thereby introducing adaptiveness to the chain. Results suggest that direct prior specification on the covariance matrix can be useful for diagnosing weakly informative inputs within the GP-based learning paradigm. We support our prior development with two distinct empirical illustrations - one on synthetic data, and another on a real-world dataset.

While 3D Gaussian Splatting has achieved remarkable success in photorealistic novel view synthesis, its pursuit of fast and high-fidelity 3D reconstruction has long been constrained by a trade-off between geometric accuracy and optimization efficiency. Methods specialized in image rendering converge quickly at the cost of imperfect geometry caused by superfluous primitives overfitting training views, while methods integrating neural signed-distance field (SDF) for better geometry incur prohibitive training costs. In this paper, we attempt to strike a better trade-off by tethering scaffold-anchored Gaussians to a jointly optimized sparse voxel scaffold. This hybrid Gaussian-Voxel representation explicitly confines anchored Gaussians to a narrow band around surfaces defined by voxelized SDFs, which effectively improves representation efficiency and condenses floating Gaussians without sacrificing geometry quality. An implicit surface tethering loss further pulls individual Gaussian primitives closer to SDF-induced surfaces in a mutually regularized manner for improved reconstruction accuracy. Extensive experiments on diverse real-world indoor scenes from ScanNet++, ScanNetv2, and DeepBlending datasets demonstrate that our method achieves state-of-the-art surface reconstruction quality as well as superior novel view synthesis against leading baselines, while maintaining fast training convergence and real-time rendering. Code will be available at https://github.com/duzh11/VoxelGS.

Underwater scene reconstruction is essential for immersive exploration of aquatic environments, yet remains challenging due to complex participating-media effects such as absorption and scattering, as well as the limited field of view (FoV) of conventional cameras. Although combining panoramic imaging with 3D Gaussian Splatting (3DGS) offers a promising direction for photorealistic underwater rendering, traditional 3DGS struggles with both spherical projection distortion and underwater medium degradation. In this paper, we propose \textbf{Underwater360}, a physics-informed omnidirectional 3DGS framework for underwater panoramic scene reconstruction. First, we introduce an Omnidirectional Gaussian Splatting module that performs ray casting directly in spherical camera space instead of relying on 2D projection approximations, thereby reducing geometric distortions under 360$^\circ$ FoV. Second, we design a physics-based appearance-medium modeling architecture with pose-conditioned appearance embeddings to explicitly decouple intrinsic scene radiance from depth-dependent backscatter and attenuation, enabling physically grounded scene appearance restoration. Finally, we establish a new panoramic underwater benchmark dataset containing both synthetic and real-world scenes. Extensive experiments demonstrate that Underwater360 achieves superior performance in underwater novel view synthesis and scene appearance restoration, delivering improved rendering quality and cross-view consistency in complex underwater environments. The code and datasets are released at https://github.com/SwcK423/Underwater360

The detection of unmanned aerial vehicles (UAVs) is important for the protection of civilian and military infrastructure. In this paper we propose a cost effective UAV detection system using sound signals obtained from microphones. The recorded signals are passed through a signal processing pipeline which employs interpretable adaptive feature extractors using so-called rational Gaussian wavelets. These adaptive wavelet transformations are embedded into and trained together with an underlying small neural network which detects and classifies UAVs based on the obtained features. This leads to a physically interpretable machine learning algorithm that in addition to classifying UAVs is also capable of detecting UAV swarms. We demonstrate our results using data collected in indoor studio and noisy outdoor environments. We conclude that the proposed method outperforms traditional machine learning approaches for detecting and classifying single UAVs as well as drone swarms, while retaining a high degree of interpretability. Our implementation of the proposed methods is made publicly available for reproducibility.

Collaborative navigation of heterogeneous robots in unknown environments poses significant challenges due to sensing, communication, and computational limitations. In this work, a lead robot navigates toward a target while a mobile sensor robot (e.g., a drone) assists by transmitting information about its locally observed map under bandwidth constraints. We propose a framework that enables the sensor to jointly select its transmitted map points and navigation actions online, while also predicting unexplored regions of the environment. To this end, we present $β$-Sparse Gaussian Processes, a robust variational sparse Gaussian Process model for task-aware inducing point selection under cardinality constraints. Furthermore, we develop an action-selection strategy that balances task relevance with exploration. Simulations on Mars and Earth maps show that the framework can reduce path cost by 18% relative to no communication and decrease transmitted information by 76% compared to raw-data transmission baselines.

Capturing relightable 3D assets from real-world objects is a widely researched problem. Several per-scene optimization-based methods, based on 3D Gaussian splatting (3DGS), support relighting; however, they usually require dense input views, and their overfitting nature makes it difficult to generalize across scenes. Unlike per-scene optimization methods, generalized feed-forward models can directly reconstruct Gaussians from sparse input views. However, the resulting assets have baked-in illumination and cannot be easily used for relighting. In this paper, we present F-RNG, a feed-forward framework that directly generates relightable 3DGS assets from sparse-view inputs. Training such a model from scratch can require massive data and computing resources, and it is especially challenging to generate relightable assets in a feed-forward manner with acceptable cost. We develop F-RNG upon an existing large reconstruction model (LRM) to extract relightable representations, while also utilizing priors from an intrinsic decomposition model (IDM). Specifically, we first introduce a latent-interpolated fine-grained geometry synthesis to enhance the LRM's geometry representation. Second, we propose a prior-guided relightable appearance distillation to extract relightable neural representations by incorporating IDM priors. Finally, a universal neural renderer enables flexible and high-fidelity relighting. F-RNG requires neither re-training nor fine-tuning of the underlying LRMs, thus can automatically benefit from better LRMs and IDMs in the future. With only small networks that can be trained with affordable data and computational resources, F-RNG avoids the repetitive inference of large models under different light conditions. By comparison to the state-of-the-art LRM-based relighting method, F-RNG achieves 25x faster relighting, as well as superior quality (+2.0 dB).

Reconstructing dynamic 3D scenes from multi-view videos is a foundational task for robotics, AR/VR, and digital twins. While 3D Gaussian Splatting (3DGS) provides state-of-the art scene representation, its dynamic adaptations (4DGS) face significant challenges. Early MLP-based deformation models excel at interpolating within training frames but fail at temporal extrapolation --- important feature for forecasting in predictive systems. To address this, physically grounded approaches have been proposed to enable robust future forecasting, while, concurrently, semantic 4DGS methods have been developed for scene analysis and language-driven prompting. However, there is currently no framework that unites both physical consistency and semantic understanding. In this paper, we propose the first, to the best of our knowledge, unified 4DGS approach that is both physically grounded and semantically aware. Furthermore, to optimize computational efficiency, we introduce a novel rigid-body constraint mechanism. Instead of predicting the physical dynamics for every Gaussian particle, our model predicts the motion of a single anchor Gaussian per semantic object, updating the remaining Gaussians via relative transformations. This architectural design significantly accelerates novel view synthesis compared to an unconstrained baseline, while enabling object-accurate extrapolation and intuitive semantic interaction. Our project page: https://be2rlab.github.io/r5dgs/.

Vision-Language-Action (VLA) models reach high success rates on clean inputs but collapse under small adversarial perturbations: a $16/255$ PGD attack drops OpenVLA-7B's LIBERO success from $95\%$ to under $5\%$. Whether this trade-off has a theoretical floor was open. We prove that it does. For any VLA policy, capability $I(\Astar;\Api)$ and robustness $I(\Api;\Atildepi)-I(\Api;δ)$ sum to at most $H(\Astar)+I(X;\Xtilde)$, the task entropy plus adversarial channel capacity. The proof reduces to two applications of the Data Processing Inequality. The pixel-level bound is loose by $\sim 10^3$ nats and serves as a ceiling guarantee; an encoder-specific corollary tightens it by over an order of magnitude, into a regime where realized capability already consumes $5$--$9\%$ of the budget. We validate Theorem~\ref{thm:main} with zero violations across $308$ cells: $252$ closed-form Gaussian-VLA, $48$ OpenVLA-7B$+$LIBERO$+$PGD ($4$ suites $\times$ $4$ $\eps$ $\times$ $3$ seeds), $4$ Square-Attack, and $4$ multi-step ($T{=}10$). A complementary measurability inequality $\Rob_{\text{disc}} \le \Cap_{\text{disc}}$ further holds across $144$ cross-architecture cells spanning OpenVLA, OpenVLA-OFT (continuous-$L_1$), and SmolVLA (flow-matching). The same construction yields three label-free diagnostics: a pre-flight encoder ceiling, a defense-forensics probe that localizes input-side vs.\ language-model intervention, and a head-agnostic robustness ratio comparable across discrete-token, $L_1$-regression, and flow-matching policies. Together these provide the cross-setting axis defense and architecture comparisons currently lack.

3D Gaussian Splatting (3DGS) provides an efficient method for high-quality scene reconstruction using anisotropic Gaussians. Recently, 3DGS-based methods have significantly improved the rendering quality of human avatars while enabling real-time performance. However, existing methods suffer from a magnitude mismatch in the number of Gaussians generated by image-based and 3DMM-based approaches. This discrepancy results in reconstructed expressions that lack fine-grained detail. In this paper, we introduce a novel method for reconstructing an animatable head avatar from a single image. We propose a Graph splitting network to progressively generate Gaussians from coarse to fine using an autoregressive architecture. To address the graph inconsistency caused by split Gaussians, we employ a mesh topology extension method to align the GNN's connectivity with the increased Gaussian count. Furthermore, we introduce a novel density control method that includes a gating mechanism that generates soft masks for Gaussians, preventing over-densification after the splitting operation. This allows for dynamic control over Gaussian density across different facial regions. For smooth and rapid training, we employ a delayed filtering strategy to avoid re-computing the graph topology during training. Experimental results demonstrate that our autoregressive structure effectively improves expression representation ability by progressively splitting Gaussians. This process, enabled by the GNN-guided splitting, synthesizes more precise facial details and achieves higher reconstruction quality.

While feed-forward 3D Gaussian splatting reconstructs renderable Gaussian primitives from sparse context views without per-scene optimization, existing pipelines do not provide a compact scene representation for storage or transmission. A natural solution is to apply existing 3DGS compression methods to the generated Gaussian primitives. However, this approach operates on the final irregular 3D representation and is decoupled from the internal feature-to-Gaussian generation process, which limits compression efficiency. To address this, we introduce CodecSplat, an ultra-compact latent coding framework for feed-forward 3D Gaussian splatting. CodecSplat first encodes an intermediate 2D Gaussian-generation feature into an entropy-coded scene bitstream. At the decoder, the latent feature is reconstructed and used to predict depth and Gaussian parameters, which are then mapped to 3D Gaussian primitives. Note that, by integrating compression into the feed-forward Gaussian generation pipeline, CodecSplat avoids inefficient compression over irregular 3D Gaussian primitives and allows the codec to exploit the structured intermediate feature representation. We instantiate CodecSplat on a feed-forward Gaussian splatting backbone with depth-guided multi-view feature refinement and a hierarchical learned feature codec. On DL3DV and RealEstate10K datasets, CodecSplat achieves 23.56-26.36 dB and 24.76-27.05 dB PSNR with only 20.00-107.77 KiB and 3.37-12.51 KiB per scene, respectively. This is roughly one order of magnitude smaller than compressing feed-forward generated Gaussian primitives, while preserving controllable rate-distortion behavior.

Competitive resource allocation problems over frequency and space can be formulated as minimax interaction between transmit power and worst-case interference. This formulation naturally arises in multi-operator low Earth orbit (LEO) satellite spectrum sharing, where transmissions from competing constellations interfere in real-time. Under Gaussian channels, the corresponding power-allocation problem admits a convex-concave formulation with a unique saddle point. Discrete constellations yield generally nonconvex mercury/water-filling formulations. In this paper we propose the adversarial water-filling (AWF) problem with corresponding theory and algorithms for these settings. In addition, we develop a domain-specific wireless foundation model for AWF to learn the AWF search dynamics. The architecture incorporates permutation-invariant channel representations, a constraint-aware graph neural network (GNN) with sparse message passing, and global latent variables capturing the low-dimensional water level implied by the AWF optimality. Through learned projected extragradient iterations, the model approximates stationary solutions of the constrained minimax problem arising under mercury/water-filling. We further establish projected-stationarity/Karush-Kuhn-Tucker consistency and conditional local convergence of the learned AWF dynamics under local regularity and stability conditions. Experiments demonstrate empirical generalization across unseen problem sizes, constraint structures, discrete constellations, and channel-weighted objectives, while achieving a median speedup exceeding one order of magnitude over Mirror-Prox on matched instances at comparable first-order solution quality. The related code can be found at https://github.com/convexsoft/AWF.

We introduce a user defined probabilistic polygonal representation for plane curves. Given a curve, we select vertices on the curve and connect consecutive vertices by line segments to obtain a polygonal approximation. Each segment is equipped with a user defined uncertainty parameter in the normal direction. This yields a collection of thin probabilistic geometric primitives that retain the geometrz of the underlying curve while extending it beyond the idealized deterministic one dimensional formulation. For each segment, we define a Random Variable that is uniform distributed in the tangent direction of the segment and Gaussian distributed in the normal direction of the segment. By matching the first and the second central moments, this construction induces a Gaussian component whose mean lies at the segment midpoint and whose covariance encodes both tangential and normal uncertainty. Combining the segment wise components with appropriate weights yields a Gaussian Mixture Model (GMM) representation of the user defined probabilistic polygonal representation of the plane curve. The proposed framework provides an analytically tractable probabilistic model that preserves local geometry, and uncertainty in the normal direction. It applies to smooth, closed, open, non regular, and self intersecting plane curves, allows adaptive discretization and varying uncertainty in the normal direction, and as a result supports uncertainty aware geometric modeling. Experiments on a collection of canonical plane curves show that the resulting GMM capture local tangent, local normal, and local arc length; resulting in the global shape of the underlying curves to be truthfully captured as well. The representation is particularly relevant for applications in uncertainty aware CAD and digital twins, probabilistic obstacle modeling in robotics, and probabilistic trajectory planning.