NeurIPS 2026 Papers

Modern datasets across many disciplines increasingly consist of time-evolving, potentially infinite-dimensional random objects, such as dynamic functional data, which are naturally modeled in Hilbert spaces. In these settings, characterizing probability measures, for example, through densities, can be ill-defined or technically challenging. Motivated by clustering applications, we propose a Gaussian mixture framework for Hilbert-space-valued data based on kernel mean embeddings and develop efficient optimization algorithms for estimation. We establish theoretical guarantees showing that the proposed algorithm is well defined and that the model yields a dense class of approximations in infinite-dimensional spaces. We evaluate the framework through extensive experiments on diverse structures and data geometries, including $L^2$-functional data and random graphs in Laplacian spaces arising in modern medical applications.

This paper proposes a novel crowd counting approach, the Gaussian Density Splatting Network (GDSNet). Unlike methods that rely on conventional, grid-based density maps and are sensitive to spatial resolution, GDSNet represents a crowd as a superposition of continuous 2D Gaussian primitives. Our approach is built upon two key contributions. First, we introduce a control-point-based fitting mechanism to structure the prediction of the Gaussian parameters. We design a method to allocate a set of control points that define local regions, from which features are pooled to regress each primitive's parameters. Second, we adapt a differentiable Gaussian Splatting framework to the counting task by parameterizing each primitive with geometric parameters and a scalar density mass. This formulation allows the network to be trained end-to-end via spatial matching of differentiably rendered density maps, naturally providing both local density supervision and global count optimization. Extensive evaluations on four standard benchmarks show GDSNet consistently outperforms the state of the art. Code will be released upon acceptance.

Electromagnetic inverse scattering (EIS), which aims to recover object permittivity from measured scattered fields, is central to a wide range of applications, from medical diagnostics to security screening. However, it is a highly nonlinear and ill-posed problem. Despite substantial progress, existing approaches face a fundamental trade-off between physical fidelity, efficiency, and generalization: data-driven methods are fast but tied to training geometries and sensor setups, while physics-based optimization is accurate but computationally expensive. We introduce a Gaussian-Galerkin (GauGal) method that reformulates EIS from a dense point-wise field reconstruction to a compact, primitive-level physical solving. Rather than using Gaussian primitive merely as a material representation, GauGal take it as the computational units for wave scattering. By projecting the continuous EIS scattering equation into a Gaussian primitive space, the material modulation, Green propagation, source excitation, and receiver observation are all realized as primitive-level operators. This yields a compact differentiable forward solver for physics-consistent reconstruction. Our method achieves state-of-the-art accuracy on synthetic and real benchmarks while reducing runtime from over 30 minutes by leading physics-driven baselines to under 10 seconds. It also generalizes significantly better to unseen geometries and sensor configurations than leading data-driven baselines. Overall, this framework establishes an accurate, efficient, and generalizable paradigm for electromagnetic inverse imaging, enabling fast, physics-consistent imaging in practical settings.

Feed-forward 4D Gaussian Splatting (4DGS) offers an efficient paradigm for reconstructing dynamic scenes from monocular videos, bypassing the need for lengthy per-scene optimization. However, existing methods suffer from three fundamental bottlenecks: redundant frame-wise grid-aligned Gaussian representations, suboptimal single-step 2D-to-4D regression architectures, and restrictive dependencies on 3D/4D signals during training or inference. In response to these limitations, we introduce a novel Gaussian-Grounded Query Refinement (GGQR) framework. To reduce representation redundancy, GGQR learns a compact set of Gaussian queries equipped with a newly designed plateau-shaped temporal kernel, enabling single primitives to persistently model motion-consistent regions across extended frames. To alleviate regression ambiguity, these queries are iteratively refined through a Gaussian-grounded attention mechanism operating in 3D space. Specifically, GGQR leverages foundation models to lift 2D observations into a shared 3D space, explicitly grounds the 3D attention in intermediate Gaussian states, and residually updates those Gaussian states. Trained entirely self-supervised on casual videos, GGQR achieves a new state-of-the-art on dynamic reconstruction benchmarks among feed-forward 4DGS methods, delivering superior performance in novel view-time rendering alongside downstream motion modeling tasks.

We present GAMMA, a scalable feed-forward model that reconstructs 4D Gaussian Splatting from monocular videos, enabling dynamic novel view synthesis in real-time. Most existing approaches for dynamic scene modeling require multi-view videos as input or costly per-scene optimization. In contrast, GAMMA learns a unified 4D scene representation from monocular videos and generatively predicts 4D Gaussian primitives within seconds. The key insight of GAMMA lies in its unified Gaussian reconstruction model, which jointly estimates temporally consistent geometry, appearance, and motion from the input video. We further explore its scalability through large-scale training on a comprehensive dataset encompassing both synthetic and real-world videos. The reconstructed GAMMA representation supports interactive scene exploration via real-time rendering across timesteps and local viewpoints. Extensive experiments demonstrate that GAMMA outperforms existing methods in both reconstruction fidelity and efficiency.

Rough path signatures provide a universal feature map for continuous paths and, via the expected signature, a principled characterisation of path distributions. These results do not directly extend to \clag paths of Temporal Point Processes (TPPs), limiting the use of signature methods for event sequences. Furthermore, neural TPP models, including recent generative approaches, optimise per-event objectives with no global sequence-level loss, while evaluation of variable-length event sequences lacks distributional discrepancy measures. This paper proposes a common pathwise framework for addressing these limitations. We introduce the interarrival embedding, a stable (homeomorphic) lift from jump paths to continuous paths of bounded variation, enabling signature methods to discrete event sequences. Our theoretical contributions give rise to \sigTPP, the first signature-based generative model for TPPs, trained using a path-level loss on complete trajectories. We further analyse the space of counting paths and derive three distributional discrepancies, providing mathematically justified tools for evaluating generative TPP models. Across synthetic and real-world datasets, \sigTPP~achieves the best average rank based on 8 complementary metrics, outperforms or is within one standard error of the strongest baseline in $64\%$ of the dataset-metric pairs, and according to a relative score, improves against every baseline by at least $19\%$ on average.

Implicit-process priors define distributions over functions through flexible generative mechanisms, making them attractive for Bayesian function-space modelling. However, performing posterior inference with such priors is challenging because their induced function-space distributions are typically not available in closed form. One practical strategy is to approximate the prior using a finite collection of sampled functions, and then represent posterior functions as learned combinations of these samples. Existing approaches commonly place a Gaussian variational distribution over the combination weights. While tractable, this choice limits the shapes of posterior uncertainty that can be represented, especially when the true posterior is asymmetric, heavy-tailed, or multimodal. We propose Flow-Transformed Implicit Processes (FTIP), a variational inference method that makes this finite-dimensional function-space approximation more expressive. Instead of using a Gaussian distribution over the combination weights, FTIP uses a normalizing flow to define a richer variational distribution. This induces a flexible posterior distribution over functions while preserving tractable optimization. We train the model using a Black-Box $\alpha$ objective, allowing us to compare mass-covering and mode-seeking variational behaviour. Experiments show that FTIP captures asymmetric and multimodal posterior structure in function space that Gaussian coefficient approximations tend to smooth or collapse.

Temporal point processes (TPPs) are the canonical framework for event sequence data, with applications spanning seismology, social media, and electronic health records. Recent neural extensions have been reported to substantially outperform classical baselines such as Hawkes processes, but a systematic comparison across model families and intensity parameterizations is lacking, and large-scale medical benchmarks — arguably one of the most promising application domains — have not been considered. Here, we revisit this comparison through a systematic benchmark of neural and non-neural TPPs on existing datasets and on two large-scale medical benchmarks derived from UK Biobank disease histories and MIMIC-IV ICU records. First, our results show that the previously reported gap between Hawkes processes and neural TPPs largely disappears once Hawkes processes are equipped with flexible and learnable kernels. Second, we find that the flexibility of the intensity parameterization also limits prior neural TPPs: a transformer with a spline-based intensity head outperforms prior neural TPP implementations. Third, our benchmark underscores the value of complex datasets when assessing the performance of TPPs. In fact, exclusively on the MIMIC-IV ICU records did we find clear evidence for structures — time-varying or higher-order interactions — beyond what pairwise flexible Hawkes process kernels can capture. Our results guide both future method development and practitioners’ model choice. Our TPP framework is released as an open-source package, providing consistent and feature rich implementations of classical and neural TPPs.

We consider the parameter estimation problem in logistic regression with Gaussian design: the estimation of a fixed unknown parameter $\theta^* \in \mathbb{R}^d$ ($\lVert\theta^*\rVert_2\geq$ 1) from $n$ i.i.d. samples $\{(x_i,y_i)\}_{i=1}^n$, where $x_i\sim N(0,I_d)$ and $y_i\mid x_i \sim \mathrm{Bernoulli}$ (1/ (1+exp($-x_i^T$ $\theta^*~$ ))). Our main aim is to characterize the finite-sample estimation performance and convergence behavior of gradient descent (GD) on the maximum likelihood objective (i.e., the logistic loss). Under small $O(1)$ stepsize and $0$ initialization, it is shown that GD linearly converges to a small neighborhood of the true parameter and achieves $\ell_2$ error of order $O(\sqrt{\lVert \theta \rVert_2^5 d/n}).$ This substantially goes beyond existing theoretical results that lack non-asymptotic estimation error rate and exhibit much slower parameter convergence. We also establish a faster local linear convergence to the same statistical error under a large stepsize. The main technical component is to show that the gradient of the logistic loss satisfies a certain approximate invertibility condition (AIC). To that end, we bound the concentration term via covering and peeling arguments, and show that the bias term is a contraction by a delicate eigenvalue analysis of the population Hessian matrices. Finally, we build upon the recent work Matsumoto and Mazumdar (2025) and devise a novel efficient estimator that attains a sharper rate in high dimensions. This indicates that the existing non-asymptotic guarantees exhibit sub-optimal dependence on $\lVert\theta\rVert_2$, and that in many regimes $\Theta(\sqrt{\lVert\theta\rVert_2d/n})$ is the tight estimation error rate. Numerical examples are provided to corroborate our theoretical results for GD.

Recent hand avatar reconstruction methods achieve high-quality results through multi-view observations or per-subject optimization, limiting scalability and practical applicability. We present \emph{FF3DGS-Hand}, a feed-forward framework that reconstructs animatable hand avatars from a single monocular image using 3D Gaussian Splatting. Our method establishes a stable canonical geometry for thin and articulated hand structures, then reconstructs appearance by leveraging source image evidence instead of relying solely on global latent features. We further introduce a rendering-aware, source-conditioned appearance framework that selectively updates Gaussians according to their rendering contribution, recovering input-specific details while suppressing artifacts in unobserved regions. The resulting representation is animatable via standard hand pose parameters and supports efficient rendering. Experiments demonstrate strong visual quality and quantitative performance in the single-image setting.

We study the problem of propagating the mean and covariance of a general multivariate Gaussian distribution through a deep (residual) neural network using layer-by-layer moment matching. We close a longstanding gap by deriving exact moment matching for the probit, GeLU, ReLU (as a limit of GeLU), Heaviside (as a limit of probit), and sine activation functions; for both feedforward and generalized residual layers. On random networks, we find orders-of-magnitude improvements in the KL divergence error metric, up to a millionfold, over popular alternatives. On a variational Bayesian neural network, we show that our method attains hundredfold improvements in KL divergence from Monte Carlo ground truth over a state-of-the-art deterministic inference method. We also give an smooth-distance error bound showing that, under regularity assumptions, moment matching removes the leading low-variance errors and propagates higher-order local accuracy through the layers of a network.

Modern machine learning depends heavily on massive datasets, but obtaining high-quality annotations at scale is often expensive. As a result, learning from noisily-labeled data has become common, making accurate estimation of the label-noise transition matrix crucial. However, existing transition matrix estimators rely on the fragile estimation of class-posteriors and do not provide finite-sample performance guarantees. In this work, we propose a novel methodology to estimate the transition matrix based on one-sided selective classification. This approach bypasses class-posterior estimation, provides finite-sample performance guarantees, and leverages flexible learning methods for binary classification. Moreover, we introduce effective algorithms to implement the proposed methodology and provide their refined finite-sample performance bounds.

Log-Gaussian Cox Processes (LGCP) are essential for modeling spatial point patterns but suffer from high computational costs and intractable likelihoods. We propose VoGCAM, an efficient Variational Voronoi Gaussian Coordinate Ascent Maximization framework for fitting LGCPs. Our approach first approximates the intractable integral in the LGCP likelihood using a flexible Voronoi tessellation, which incorporates observed points as integration nodes. By applying variational Gaussian approximation, we derive an Evidence Lower Bound (ELBO) that admits an explicit and closed-form expression. To optimize this objective, we develop a novel coordinate ascent algorithm that updates parameter blocks via Newton and fixed-point methods. We further enhance scalability by adopting a Nearest Neighbor Gaussian Process (NNGP) prior and utilizing the Woodbury formula to reduce matrix inversion costs. Theoretically, we prove the existence and uniqueness of the optimal solution and establish the convergence of our algorithm. Numerical experiments on synthetic and real-world data demonstrate that VoGCAM offers superior computational efficiency and inferential accuracy over state-of-the-art methods like INLA and VIFRK.

Neural Processes (NPs) are flexible meta-learning models capable of uncertainty quantification across diverse applications. However, the standard NP framework assumes access to noise-free inputs. This is unrealistic in many practical settings, where sensor noise or measurement errors are unavoidable. This discrepancy between model assumptions and real-world data can significantly degrade prediction quality and uncertainty estimates. We introduce Denoising Neural Processes (DnNPs), a principled extension of the NP framework that explicitly models input uncertainty. We train DnNPs via variational inference. DnNPs jointly learn to denoise corrupted inputs and perform meta-learning, making them robust to noisy training data. We demonstrate DnNPs' effectiveness on both synthetic and real-world datasets, showing consistent improvements in prediction and uncertainty quantification compared to standard NPs. On PM$_{2.5}$ spatial interpolation from real-world air quality sensors, DnNPs reduces RMSE by up to 43% and NLL by up to 80% relative to standard NPs. We also provide theoretical grounding: we show that the Bayes optimal predictor under noisy inputs belongs to the DnNPs model class, and that plug-in models with fixed observation variance incur an irreducible KL divergence gap that DnNPs provably avoids.

While Gaussian Splatting-based Feature Fields (GSFFs) have shown promise for visual localization, this paper highlights that photometrically optimized GSFFs are inherently ill-suited for 2D-3D matching. The volumetric extent of each Gaussian induces many-to-one pixel-to-point mappings that destabilize PnP-based pose estimation, while photometric optimization gives rise to superfluous Gaussians devoid of multi-view consistency. To address these issues, we propose SplitGS-Loc, a localization-specialized GSFFs construction framework that disambiguates 2D-3D correspondences by exploiting Gaussian attributes. Our key design, Mixture-of-Gaussians-based splitting, decomposes each Gaussian into smaller Gaussians, replacing ambiguous many-to-one with precise one-to-one correspondences. In parallel, we exploit composition weights from GS rasterization to select Gaussians that significantly and consistently contribute across multiple views and aggregate discriminative features through strong pixel-Gaussian associations, enforcing multi-view consistency. The resulting compact yet discriminative feature fields enable stable PnP convergence, achieving state-of-the-art performance on localization benchmarks. Extensive experiments validate that SplitGS-Loc extends the utility of photometric GSFFs to accurate and efficient localization by exploiting Gaussian attributes, without per-scene training or iterative pose refinement.

3D Gaussian Splatting (3DGS) has emerged as an effective solution for real-time novel view synthesis (NVS) with high rendering quality, but training memory scales with image resolution, making downsampled supervision common and leading to loss of sharp, high-frequency details and degraded perceptual quality. Moreover, uniform supervision assigns equal weight to all pixels, resulting in weak emphasis on detail-rich regions such as edges and thin structures. We propose \textbf{OT-3DGS}, which leverages optimal transport in screen space to reparameterize the image domain prior to downsampling, inducing importance-based non-uniform supervision that redistributes pixel budget toward geometry-critical regions and strengthens supervision on high-frequency content. Our method remains fully compatible with the original 3DGS pipeline, requiring no modification to loss functions, rendering settings, or pruning, cloning, and splitting strategies. Experiments across diverse datasets show that OT-3DGS produces sharper structures, clearer reflectance, and reduced over-smoothing; while PSNR and SSIM may slightly decrease due to deviation from downsampled references, reference-free metrics including BRISQUE, NIQE, and Laplacian Variance (LV) improve significantly, better reflecting perceptual quality and high-frequency detail. These results demonstrate that OT-3DGS aligns with the fundamental goal of NVS: generating perceptually realistic, high-quality unseen views.

Building upon the real-time rendering capability of 3D Gaussian Splatting (3DGS), 2D Gaussian Splatting (2DGS) achieves improved surface reconstruction and geometric fidelity for novel view synthesis through explicit planar Gaussian primitives. However, the smooth falloff inherent to Gaussian kernels fundamentally limits the reconstruction of high-frequency shape signals, causing over-smoothed edges and loss of fine geometric detail. Prior works have explored alternative kernel functions to address this limitation, yet through systematic evaluation across signal fitting tasks, we find that all existing kernels suffer from the Gibbs phenomenon — producing oscillatory artifacts near sharp discontinuities. This observation motivates a fundamentally different strategy: rather than replacing the kernel, we make it deformable. This study presents *Deformable 2D Gaussian Splatting*, which augments each Gaussian surfel with a learnable, monotonic coordinate remapping in its local tangent plane. With only a single free control point per axis (two extra parameters), the remapping enables asymmetric radial profiles, allowing each primitive to reliably capture sharp edges and irregular structures that symmetric kernels inherently cannot represent. The deformation operates on the 2D tangent plane of 2DGS, preserving the differentiable rasterization pipeline with negligible overhead, and is optimized end-to-end through rendering loss alone. Experiments on MipNeRF 360 and Tanks&Temples demonstrate that our method effectively suppresses Gibbs artifacts at sharp boundaries and achieves state-of-the-art performance among 2DGS-based approaches in PSNR, SSIM, and LPIPS.

Phylogenetic inference plays a central role in understanding evolutionary relationships, with applications ranging from tracking pathogen spread to reconstructing the history of life. Conventionally, practitioners obtain posteriors over the phylogenetic tree of species using MCMC methods. However, such likelihood-based methods are only tractable for simple evolutionary models with restrictive assumptions. For more complex and realistic evolutionary models, conventional methods are prohibitively expensive, inaccurate, or even impossible. We instead advocate for a simulation-based inference approach, by using simulated data from an evolutionary model to train a neural network that predicts tree topologies conditioned on sequences. To accurately represent the complex posterior distributions over tree topologies that can arise, we present flexible models that iteratively generate trees using three natural paradigms: top-down, middle-out, and bottom-up. We use a discrete diffusion framework to train these models efficiently on large-scale simulated datasets of phylogenetic trees. For all three generative paradigms, our models fit the data substantially better than the previous state-of-the-art simulation-based method, Phyloformer 2, and obtain more accurate posteriors on real datasets. Finally, our models outperform misspecified conventional methods on data following complex evolutionary processes.

Many real world processes can be represented as compositions of functions along a Directed Acyclic Graph (DAG). In causal modelling these correspond to the underlying mechanisms, in engineering to the multiple fidelities present, and in gene-regulatory networks to the transcription factors. These functions are partially observed across the DAG, with noisy and heterogeneously sampled measurements, posing significant challenges for reconstruction, uncertainty propagation, and inference. To tackle these we place priors over functions and naturally arrive at Deep Gaussian Processes over DAGs. We theoretically study their prior-collapse behaviour, and the effect of graph topology and intermediate observations on the preservation of information. We obtain almost-sure lower bounds on the asymptotic frequency of depths at which distinction between inputs is preserved, identify broad kernel classes for which these hold, and prove an observation by \citep{dunlop2018} on the role of input connections. We offer a structured variational approximation that retains graph dependencies, satisfies compositional uncertainty, and captures the explaining-away behaviour of colliders. Finally, we empirically validate our theoretical results and our methodology, and model a latent-collider DAG, a protein signalling network, and a multi-fidelity heavy-ion collision task, attaining state-of-the-art performance while recovering the low-fidelity contributions and yielding explainability over the simulator hierarchy.