NeurIPS 2026 论文列表

Bayesian Additive Regression Trees (BART) is a nonparametric Bayesian regression technique based on an ensemble of decision trees. It is part of the toolbox of many statisticians. The overall statistical quality of the regression is typically higher than other generic alternatives, and it requires less manual tuning, making it a good default choice. However, it is a niche method compared to natural competitors such as XGBoost, due to the longer running time, making sample sizes above 10000–100000 a nuisance. We present a GPU-enabled implementation of BART, faster by up to 100x in a given GPU vs. CPU comparison, making BART fast enough to be a viable alternative to non-Bayesian algorithms on large datasets, and showing that BART parallelizes better than its non-Bayesian counterparts. This implementation is available in the Python package bartz.

In this paper, we propose UniGS, a unified map representation and differentiable framework for high-fidelity multimodal 3D reconstruction based on 3D Gaussian Splatting. Our framework integrates a CUDA-accelerated rasterization pipeline capable of rendering photo-realistic RGB images, geometrically accurate depth maps, consistent surface normals, and semantic logits simultaneously. We redesign the rasterization to render depth via differentiable ray-ellipsoid intersection rather than using Gaussian centers, enabling effective optimization of rotation and scale attribute through closed-form analytic depth gradients. Furthermore, we derive the analytic gradient formulation for surface normal rendering, ensuring geometric consistency among the reconstructed 3D scenes. To improve computational and storage efficiency, we introduce a learnable attribute that enables differentiable pruning of Gaussians with minimal contribution during training. Quantitative and qualitative experiments demonstrate the state-of-the-art reconstruction accuracy across several datasets, validating the efficacy and robust optimization stability of our geometry-aware paradigm.

Multinomial logistic regression (MLR) is the default last-layer classifier in fully supervised recognition, while prototype classifiers are central to few-shot recognition. Although they are usually presented as different principles, we show that both can be organized by a geometric notion of class boundaries. A Euclidean MLR logit is a signed distance to a class hyperplane, so ordinary MLR is already the hyperplane decision-boundary case of Umbilic Multinomial Logistic Regression (UMLR). Classical submanifold geometry supplies the matching spherical decision boundary: in Euclidean space, the complete connected totally umbilic hypersurfaces are hyperplanes and spheres. The spherical UMLR form keeps a prototype-like center but adds a learnable radius; its signed squared-distance form contains squared prototype scoring as the radius-zero case. Thus UMLR is not a separate replacement for MLR or prototypes, but a boundary-aware family that places hyperplane logits, spherical logits, mixed heads, and prototype scoring in one framework. Experiments on low-shot vision head swaps, prototype comparisons, and mixed hyperplane--sphere heads support this organization and show how the different decision boundaries behave across data regimes. UMLR provides a compact geometric language for studying when class evidence is better modeled by flat boundaries, spherical boundaries, or their mixture.

We present UltraVoxelGS, a 3D ultrasound reconstruction method that achieves both fast reconstruction and physically faithful rendering, bringing live spatial feedback during 2D ultrasound scanning within reach. This is made possible by a feed-forward design that predicts a complete Gaussian scene representation from posed ultrasound images directly, entirely bypassing the per-scene optimization bottleneck that has confined prior methods to offline use. Realizing such feed-forward prediction in this setting is non-trivial: unlike natural images, ultrasound slices share at most one-dimensional intersections and exhibit view-dependent appearance due to acoustic propagation and attenuation, violating the dense overlap and photometric consistency assumed by existing feed-forward Gaussian methods. To achieve fast reconstruction, we introduce a feed-forward voxel-to-Gaussian pass that decouples representation size from input count by lifting posed slices into a fixed-size voxel support and predicting Gaussian parameters directly. For faithful rendering, we propose an ultrasound-aware appearance rendering strategy that factorizes reflection from cumulative attenuation during training and exploits appearance continuity among spatially adjacent slices for efficient Render-time Appearance Adaptation. On both real-world and simulated datasets, UltraVoxelGS achieves the best PSNR/SSIM compared with per-scene optimization baselines, while reducing inference from 10--20 minutes to approximately 10 seconds, over 60× faster, and scaling to sequences exceeding 1,000 frames.

Multi-view transformers for feed-forward 3D reconstruction must jointly solve two tasks. They need to extract precise per-view features and reason about cross-view geometric correspondences. Existing architectures apply cross-view attention throughout the network, leaving each layer to handle both objectives together. We revisit this design through a layer-wise probing analysis of feed-forward geometry transformers and observe that trained models tend to divide these two roles across layers. Early layers tend to specialize in per-frame feature extraction, while spatial cognition and cross-view reasoning emerge predominantly in later layers. This suggests that separating the two roles across the network can allocate compute more effectively. Building on this observation, we propose U-MVP, a U-shaped multi-view transformer for feed-forward 3D Gaussian Splatting that reflects this structure in the architecture itself. The encoder applies frame-wise attention to preserve per-view detail, the decoder introduces multi-view attention for cross-view geometric reasoning, and skip connections fuse the two streams so that appearance and geometry are recombined at decoding time. To scale to dense view regimes, we replace several global interaction blocks at the bottleneck with a grouping and swapping scheme that preserves cross-view information flow at lower cost. U-MVP performs competitively with feed-forward and optimization-based baselines from 16 to 256 views, generalizes to unseen datasets, and achieves strong results on 3D reconstruction and novel-view synthesis in posed and unposed settings.

Transmissive scenes are ubiquitous in daily life, yet reconstructing and rendering them remains highly challenging due to the inherent entanglement between near-field reflections from the surrounding environment on the transmissive surface, and the transmitted content of the scene behind it. This coupling gives rise to dual surface geometries and dual radiance components within each observation, posing ambiguities for standard methods. We present TransmissiveGS, a novel framework for disentangled reconstruction and rendering of transmissive scenes. Specifically, we model the scene with a dual-Gaussian representation and introduce a deferred shading function to jointly render the two Gaussian components. To separate reflection and transmission, we exploit the inherent multi-view inconsistency of reflections and leverage the residuals from reconstructing multi-view consistent content as cues for disentangled geometry and appearance modeling. We further propose a reflection light field that enables high-fidelity estimation of near-field reflections. During training, we introduce a high-frequency regularization to preserve fine details. We also contribute a new synthetic dataset for evaluating transmissive surface reconstruction. Experiments on both synthetic and real-world scenes demonstrate that TransmissiveGS consistently outperforms prior Gaussian Splatting-based methods in both reconstruction and rendering quality for transmissive scenes.

3D Gaussian Splatting (3DGS) has emerged as a mainstream representation for real-time novel view synthesis and 3D reconstruction. However, existing 3DGS rendering pipelines are poorly aligned with modern GPU architectures: depth-sorted alpha compositing introduces strong per-pixel sequential dependencies, limiting parallelism and resulting in scalar Fused Multiply-Add (FMA)-dominated execution that underutilizes high-throughput matrix units such as Tensor Cores. This mismatch becomes more severe for multimodal and semantically enriched 3DGS, where high-dimensional features must be accumulated from millions of Gaussians, leading to rapidly increasing computation and memory costs. To address these challenges, we propose a matrix-parallel rendering framework for feature-scalable 3DGS on modern GPUs. We first identify the sequential dependency of alpha compositing as the key obstacle to efficient high-dimensional feature rendering, and derive an order-independent weighted accumulation formulation that transforms feature rendering into matrix-oriented computation. Our framework features three key designs: i: a tile-based splatting pipeline that maps feature accumulation to warp-level matrix-multiply-accumulate execution on Tensor Cores; ii: a warp-granularity Gaussian packing strategy that mitigates visibility irregularity and improves feature reuse; and iii: a lazy channel-batched feature-fetching pipeline that reduces shared-memory pressure, maintains high warp occupancy, and overlaps memory access with matrix execution for high-dimensional features. Extensive experiments on Mip-NeRF 360, LERF, and 3DOVS demonstrate that our approach enables both high performance and strong scalability for feature-rich 3DGS rendering. Particularly, our method achieves up to 3.8$\times$ speedup over 3DGS and 2$\times$ over TC-GS while preserving rendering quality and semantic accuracy, and further reduces kernel render time by up to 36.7$\times$ for high-dimensional features.

A central error measure in Gaussian DDPMs is the path-space KL divergence between the exact reverse chain and the learned Gaussian reverse process. This quantity is especially relevant for procedures such as classifier guidance, which perturb the entire reverse trajectory rather than only the terminal sample. Prior analyses show that standard isotropic reverse covariances suffer an unavoidable $\Omega(1/T)$ path-KL error as the number of denoising steps $T$ grows. We show that matching the full posterior covariance breaks this barrier, yielding an order-wise improvement that reduces the path KL to $O(1/T^2)$. To make full covariance matching practical, we introduce the Lanczos Gaussian sampler, a training-free, matrix-free method for sampling from the optimal reverse covariance using only covariance-vector products, which are available through Jacobian-vector products of the posterior mean. The sampler avoids dense covariance storage and auxiliary covariance models. We prove that its approximation error decays exponentially in the number of Lanczos steps, where each Lanczos step requires a single Jacobian-vector product. Empirically, using only just three such steps improves sample quality over strong diagonal-covariance baselines, including OCM-DDPM, across standard image benchmarks. This identifies full covariance matching as both theoretically valuable and practically accessible for fast DDPM sampling.

We study classification and regression tasks under label differential privacy (label-DP), a setting where only the labels are considered sensitive information. We quantify the "price of locality" by revealing fundamental statistical gaps between local and central privacy models. For classification, we establish a strict separation in accuracy. Specifically, we prove that the minimax excess risk in the local model is lower bounded by $\Omega(\frac{1}{\epsilon}\sqrt{\text{VC}(\mathcal{H})/n})$ for classification on size-$n$ dataset, a fundamental limitation that holds even under relaxed approximate $(\epsilon, \delta)$-local DP. Overcoming this barrier, we propose the first *efficient* central-model algorithm that operates under the stricter pure $\epsilon$-DP, yet achieves a significantly improved upper bound of $\tilde{O}(\sqrt{\text{VC}(\mathcal{H})/(\epsilon n)})$. For linear regression, we show that local randomizers or naive central-DP approach algorithms are statistically inefficient. Instead, we turn to the Matrix Mechanism and use an encoder-decoder framework built on ridge regression, which projects the data into a spherical latent space before injecting noise. This structural design effectively isolates and exponentially suppresses the severe noise inflation typically caused by ill-conditioned feature covariance matrices in full-DP (Cai et al., The Annals of Statistics, 49(5)), achieving an optimal privacy penalty of $\tilde{O}({d^2}/({n^2\epsilon^2}))$ where $d$ is the feature dimension.

We characterize the minimax rate of estimating the second-order calibration error for binary classification, which quantifies whether a higher-order predictor's epistemic-uncertainty estimate matches the conditional variance of the label probability on its level sets. Our key observation is that the sech perturbation kernel, previously used only to enforce smoothness of calibration functions, in fact makes them \emph{analytic} in a strip of half-width $h\pi/2$. Polynomial regression then estimates the calibration error at rate $\tilde{O}(1/\sqrt{n})$, with explicit constants, a qualitative improvement over the $O(n^{-1/4})$ rate achievable by bucketing or kernel smoothing. A matching $\Omega(1/\sqrt{n})$ lower bound establishes minimax optimality up to logarithmic factors. As a corollary, we give the first finite-sample guarantee for second-order Platt scaling, yielding a post-hoc procedure that recalibrates both the mean prediction and the epistemic-variance estimate of any higher-order predictor. Along the way, we provide a bucket-free definition of second-order calibration and relate it quantitatively to the bucketed formulation of Ahdritz et al. [2025]. Our experiments confirm the predicted rate and the quality of the recalibrated uncertainties.

3D Gaussian Splatting enables high-fidelity, real-time novel view synthesis, yet adapting it to dynamic, evolving scenes remains challenging. Existing methods rely on fixed static-dynamic partitioning, which suffers from persistent partitioning errors and cannot adapt during optimization. To tackle this issue, we introduce SynGS, a unified 3D Gaussian framework for continual scene updating and multi-view change detection. We cast static-dynamic decomposition as a learnable task, jointly optimizing per-Gaussian change probabilities and scene representations for iterative refinement. We further propose a change-guided update strategy that modulates illumination-aware photometric corrections via learned probabilities, separating transient appearance variations from authentic scene changes. Projecting Gaussian-level probabilities to the image plane yields 3D-consistent change masks, enabling mutual optimization between reconstruction and change localization. An illumination-decoupled refinement step further improves mask quality. Evaluations on standard benchmarks show that SynGS outperforms baseline methods on scene update and change detection tasks, while fully retaining the real-time rendering capability of 3D Gaussian Splatting. Code will be released upon acceptance.

Programmable photonic circuits are a natural platform for physical learning, where the learned computation is performed by the hardware itself rather than by a digital model. We propose a physical learning algorithm and architecture for continuous-variable quantum systems where a photonic circuit is configured in situ to invert an unknown lossless Gaussian quantum operation. Our contributions are threefold. (i) Theory: we prove that generic $S \in \mathrm{Sp}(2 N, \mathbb{R})$ admits a triangular decomposition into two-mode and single-mode symplectic gates. (ii) Architecture: we introduce the symplectic Reck mesh, a triangular array of two-mode symplectic gates that physically realizes this factorization, generalizing the unitary Reck mesh widely used in optical neural networks. (iii) Physical learning: when placed after an unknown Gaussian unitary, the mesh is trained in situ by nulling local response blocks one at a time using simple optical probes and measurements. We identify a measure that predicts when training becomes hard and numerically demonstrate finite-shot training and robustness to gate errors. Our work extends self-configuring optical networks from unitary to symplectic transformations, bringing physical learning to continuous-variable quantum photonic hardware.

This paper characterizes the sharp asymptotics of the $\ell_{\infty}$-norm estimation error for estimating the coefficient vector in linear regression under proportional asymptotics. While $\ell_2$-error is well-documented, we demonstrate that the $\ell_{\infty}$-error exhibits a distinct phase transition governed by the structure of the underlying signal. We explore this through the lens of a class of estimators that include ridge-regularized estimators, a method-of-moments estimator, and the ordinary least squares estimator for the under-parametrized regime. Our results provide a comparative study of these estimators and characterize regimes (as identified by the maximal signal component, number of large signals, total signal strength, and noise variance) where one estimator is preferable to the others. As a by-product, we obtain new double descent curves in $\ell_{\infty}$-error metric for the ridgeless regression, as well as ingredients for uniform confidence intervals for the signal coordinates. Our theoretical results are supported by extensive numerical simulations that confirm the predicted phase transitions and error limits.

Constrained Markov decision processes (CMDPs) extend standard MDPs by incorporating a cost function and enforcing constraints---most commonly by requiring that the expected cumulative cost over the entire trajectory remains below a prescribed threshold. While this global, expectation-based formulation is natural and widely studied, it is insufficient for many safety- and reliability-critical applications, where guarantees are required not only from the initial state but also for every subprocess starting at any intermediate time step. Motivated by this need, we introduce \emph{subprocess-constrained MDPs} (S-CMDPs), in which the expected cumulative cost must satisfy a constraint not only from the initial state, but from every intermediate step onward along the trajectory. We investigate the algorithmic aspects of this model and characterize the limitations of classical solution concepts. In particular, we show that stationary policies can be both suboptimal and computationally intractable to optimize in S-CMDPs. Leveraging a value-set iteration framework, we further demonstrate that history-dependent policies surprisingly overcome both obstacles. Building on this insight, we develop a polynomial-time algorithm that computes the action distribution of a (near-)optimal history-dependent policy for any given history.

We investigate the problem of uncertainty quantification in the mean estimation framework. Given an i.i.d. sample from a distribution with unknown mean $\mu$ and variance $\sigma^2$, we want to construct an estimator $\hat{\mu}_n$ and provide a computable and size-optimal upper bound for the error $|\hat{ \mu}_n - \mu|$. While estimators possessing strong deviation guarantees are well known, no data-dependent non-asymptotic upper bounds for their performance exist in general. We show that this gap can be bridged by introducing a parameter that characterizes the "effective sample size" available for uncertainty quantification. This parameter captures the difficulty of the problem, interpolating between "easy" cases where sub-Gaussian confidence intervals exist and "hard" cases where their construction is impossible. Using this characterization, we design confidence intervals of optimal length that are fully adaptive to the unknown variance. Numerical experiments confirm that our approach maintains nominal coverage even in asymmetric and heavy-tailed regimes where other existing methods fail.

This work introduces a family of generative diffusion models based on the stochastic heat equation. The deterministic heat equation has natural connections with kernels over discrete structures and has been successfully applied in machine learning to discriminative tasks for various types of data such as graphs. We extend it to a stochastic version by formulating our diffusion as a Gaussian process whose transition kernel can be written in closed form for both the forward- and reverse-time processes. Our diffusion process propagates noise smoothly among neighbours under the guidance of a Laplacian matrix that describes the global structure of the input. Following a flow matching-based approach, we train a denoising neural network that takes noisy representations as input and gradually removes noise to generate clean samples. We experimentally show that, by exploiting the Laplacian during training, our decoder is able to recover the global structure of the input.

We present StereoSplat, a feed-forward 3D Gaussian Splatting architecture designed explicitly for stereo videos to achieve reliable, metric-scale novel-view synthesis. Unlike monocular approaches that neglect the nature of binocular pairs, StereoSplat adopts a native stereo architecture that extracts dense multi-scale latent features and disparity from a foundation stereo backbone and feeds them into a dedicated Gaussian decoder. Our decoder utilizes cross-view feature fusion and gated spatial refinement to directly translate these rich representations into per-pixel 3D Gaussians. To resolve the high redundancy of per-pixel predictions across overlapping views, we propose a learnable depth-adaptive aggregation mechanism that clusters and aggregates primitives in inverse-depth space while preserving fine-grained details. To support robust training and generalization, we introduce XRStereo, a large-scale synthetic dataset of stereo video featuring various rig configurations tailored to match the physical hardware of real-world platforms. Trained exclusively on synthetic data and evaluated across challenging benchmarks, StereoSplat yields substantial improvements in the depth accuracy of rendered novel views over established baselines while maintaining high-fidelity novel view synthesis. By overcoming prior geometric limitations, our framework enables robust zero-shot transfer to real-world domains, offering a scalable geometric foundation for spatial computing in mixed reality, autonomous driving, and robotics.

Active view selection for 3D Gaussian Splatting (3DGS) requires information-theoretic grounding, computational efficiency, and strong reconstruction quality, yet existing methods satisfy these only partially. Information-theoretic approaches quantify gain over the full parameter space via costly Fisher computation under a Laplace approximation; faster alternatives sacrifice the grounding they started from. We propose SpheriBED, a Bayesian experimental design framework that defines the information objective over per-Gaussian spherical appearance—the quantity each observation fundamentally measures—rather than the full parameter vector, yielding exact closed-form posteriors without Laplace approximation. Scoring a candidate view requires only a single forward rasterization pass with no backward pass or per-candidate optimization. Extensive experiments across benchmarks demonstrate that SpheriBED consistently improves active reconstruction performance and provides more reliable uncertainty quantification compared to state-of-the-art methods.

Time series, spatial data, and images are natural applications of Neural Processes. However, when such data exhibit strong periodicity and quasi-periodicity, existing methods often suffer from underfitting and generalise poorly beyond the training distribution. In this work, we propose Spectral Transformer Neural Processes (STNPs), a frequency-aware extension of Transformer Neural Processes (TNPs). STNPs introduce a Spectral Aggregator that estimates an empirical context spectrum, compresses it into a spectral mixture, samples task-adaptive spectral features, and concatenates them with time-domain embeddings, thereby injecting a spectral-mixture-kernel bias into TNPs. This design reshapes the similarity geometry, allowing inputs that are distant in Euclidean space to remain close in an induced periodic manifold while enhancing time--frequency interactions. Extensive experiments on synthetic regression tasks, real-world time-series datasets, and an image dataset demonstrate that STNPs consistently improve predictive performance over existing baselines, extending Neural Processes beyond translation equivariance toward effective modelling of periodicity and quasi-periodicity.