NeurIPS 2026 Papers

Cross-device deployment of a single reconstructed avatar often requires adaptation to varying Gaussian budgets with minimal degradation in visual quality. Motivated by the need for a robust budget-adaptive 3D representation, we propose RobustAvatar, a train-once Level-of-Detail (LoD) adaptation framework for dynamic Gaussian avatars based on sequential selection and compensation. RobustAvatar supports flexible compression-ratio control within a single trained avatar, without requiring fine-tuning at each compression ratio. The framework consists of two coordinated modules: Semantic Distribution-Regularized Selection (SDS) and Canonical Budget-Conditioned Compensation (CBC). SDS performs budget-aware Gaussian selection guided by semantic distribution regularization, preserving the coverage of perceptually salient facial regions relative to the full avatar under constrained budgets. CBC refines the selected primitives in a canonical, expression- and pose-neutral space by predicting ratio-conditioned attribute residuals, reducing detail loss from Gaussian removal and improving robustness to decreasing Gaussian budgets. Experiments on the NeRSemble dataset show that RobustAvatar achieves more robust budget adaptation than state-of-the-art methods, with slower quality degradation as Gaussian budgets decrease. The code will be made publicly available.

Training-free weighted aggregation is widely used to lift 2D semantic features onto 3D Gaussians for open-vocabulary scene understanding, yet its theoretical role remains insufficiently understood. Existing analyses typically justify this operation from the rendering side, treating Gaussian features as linearly composable Euclidean variables for reconstructing 2D feature maps. However, this view does not match downstream 3D usage, where each Gaussian is often queried independently in a cosine-based embedding space. We revisit feature lifting from the 3D side and formulate per-Gaussian assignment as a cosine alignment problem on the CLIP unit sphere. Under this objective, the $\ell_2$-normalized semantic back-projected feature emerges as the closed-form solution, providing a complementary interpretation of the standard lifting rule from the perspective of per-Gaussian semantic assignment. The same formulation further yields a norm decomposition into intra-view and inter-view consistency, suggesting that feature magnitude itself can serve as a semantic reliability signal. Calibrated by effective multi-view support, this reliability score guides a mode-voting refinement that preserves CLIP feature validity by avoiding linear averaging. Experiments on open-vocabulary 3D semantic segmentation show that NormLift is an efficient, training-free framework that achieves strong performance across evaluation protocols.

Inference in nonlinear continuous stochastic processes on trees is challenging, particularly when observations are sparse and the topology is complex. Exact smoothing via Doob's $h$-transform is intractable for general nonlinear dynamics. We propose Neural Backward Filtering Forward Guiding (NBFFG), a unified framework for both discrete transitions and continuous diffusions. Our method constructs a variational posterior by leveraging a proxy linear-Gaussian process. This proxy process yields a closed-form backward filter that serves as a guide, steering the generative path toward high-likelihood regions. We then learn a neural residual to capture the non-linear discrepancies. This formulation allows for an unbiased pathwise subsampling scheme, reducing the training complexity from tree-size dependent to path-length dependent. Empirical results show that NBFFG outperforms baselines on synthetic benchmarks, and we demonstrate the method on a high-dimensional inference task in phylogenetic analysis with reconstruction of ancestral butterfly wing shapes.

We consider classification in high-dimensional feature spaces where only a vanishing fraction of features are useful and the number of classes may be large. While this rare-useful-feature regime is well understood in the binary setting, its multiclass version raises new questions: a feature can be useful for class discrimination without separating any specific pair of classes. We focus on a rare feature diversity model, in which most features are useless, but a small fraction promote discrimination among classes in a way that can be detected by a per-feature diversity test, such as one-way ANOVA or the Kruskal--Wallis test. For this setting, we propose Diversity Pursuit Higher Criticism (DP-HC), a feature-screening procedure that applies a higher-criticism threshold to the collection of p-values obtained from per-feature diversity tests. We justify DP-HC under a multiclass rare/weak Gaussian feature model with class-mean contrasts of fixed magnitude in random directions, extending the binary model of Donoho and Jin (2008). When the number of classes is fixed, our model recovers the binary phase transition. When the number of classes grows logarithmically with the number of features, however, we derive a new and strictly harder phase transition, driven by a second-order variance term that the fixed-class analysis does not capture. We show that whenever classification beyond chance is possible, DP-HC with ANOVA, followed by a simple classifier based on similarity to class means, achieves asymptotically perfect accuracy. Experiments on real multiclass classification benchmarks demonstrate substantial improvements, and numerical simulations confirm that the derived phase-transition curve accurately predicts the finite-sample behavior of DP-HC in the growing-class regime.

Most FDR-controlled feature selection methods are designed for coordinate-wise hypotheses, where each feature has a single weight or importance score. This abstraction fails in sequential and grouped models, where one original feature is represented by a block of sub-features, such as lags, recurrent states, or attention-based interactions. We propose a grouped-feature FDR control framework for such settings. For grouped linear models, we construct null-symmetric block-level mirror statistics with matrix-valued perturbations. For neural sequential models, we combine Permutation SHAP derivatives as model-agnostic block-level importance scores with kernel-based dependence measure. The framework is model-agnostic across network architectures, does not require specifying the covariate distribution, and reduces to Gaussian Mirror or Neural Gaussian Mirror when the block size is one. We prove FDR control for low- and high-dimensional grouped linear models and asymptotic symmetry of smoothed Permutation SHAP derivatives under fixed fitted nonlinear models. Experiments on simulated and real-world datasets show reliable FDR control and improved power under correlated grouped-feature signals.

In overparameterised classification, training data can be linearly separable even when the underlying distribution is not. In this setting, gradient descent (GD) on the logistic loss diverges in norm while converging in direction to a max-margin interpolating classifier, whose implicit bias can be statistically suboptimal. In this work, we show that early stopping can overcome this suboptimality: in a Gaussian mixture model with label-flipping noise, GD stopped at an appropriate oracle time achieves minimax-optimal excess zero-one risk for covariance spectra with fast and continuous decay, including polynomial and exponential spectral decays. Our analysis combines a sharp upper bound for the early-stopped iterate with a matching statistical lower bound over arbitrary classifiers, yielding optimal rates that are validated by experiments. A central technical contribution is a new calibration result that converts excess logistic risk into excess zero-one risk; it handles the model misspecification induced by the label-flipping noise, and removes the square-root rate in standard bounds. We also establish a lower bound for linear interpolators, showing that interpolation can require exponentially more samples than early stopping to achieve the same excess risk.

We introduce mesh-invariant adaptive Markov chain Monte Carlo methods for Gaussian-process posteriors arising in infinite-dimensional Bayesian inference. In function-space MCMC, posterior distributions are defined by a change of measure with respect to a Gaussian prior, making absolute continuity essential for valid proposal construction. Standard adaptive schemes that modify means or scales in the full discretized space can destroy this property, leading to proposal measures that become singular in the infinite-dimensional limit. To avoid this, we adapt only an active finite-dimensional subspace of the Gaussian-process representation while preserving the prior dynamics on inactive coordinates. This yields two adaptive proposals, pCNLV and pCNMV, which extend preconditioned Crank--Nicolson and Crank--Nicolson Langevin methods by learning posterior scale, and in pCNMV also posterior mean structure, on the data-informed subspace without introducing discretization-dependent Gaussian density ratios. The resulting samplers retain the mesh robustness of function-space methods while improving efficiency through local adaptation. Experiments on a Darcy-flow inverse problem and Bayesian logistic regression demonstrate consistent efficiency gains, including an approximately fourfold improvement in effective sampling efficiency for Darcy flow.

Spatial interpolation from sparse irregular observations is a recurring task across the environmental and health sciences. Neural processes amortise this inference into a single forward pass at test time. Joint-predictive variants capture correlations across query locations but typically rely on self-attention over context and query points, incurring $O(K^2)$ compute in the combined point count $K$ and capping practical use at a few thousand points. State-space models offer a linear-time alternative, but existing state-space NPs compress the context into a single hidden state before reading queries, reducing the information available to the decoder. We propose MambaFlowNP, a joint-predictive NP with linear compute trained with a conditional flow-matching objective. A multi-directional Mamba-2 scan reads context and query tokens in a single shared sequence, so each query's velocity is read from its own scan position rather than from a compressed context summary. MambaFlowNP is competitive with the strongest attention-based joint-predictive baselines on synthetic Gaussian-process benchmarks, and across regional and continental-scale NOAA temperature interpolation tasks it attains the lowest RMSE on every tier and the lowest CRPS at the California and continental US tiers, while running $170$--$760{\times}$ faster than the strongest joint-predictive baseline. A single forward pass scales to $10^6$ points on one GPU in under a second. This scalability unlocks amortised joint-predictive inference for continental-scale, irregularly sampled sensor networks, spanning climate monitoring to disease vector surveillance.

3D Gaussian Splatting (3DGS) achieves real-time photorealistic novel-view synthesis but is vulnerable to adversarial perturbations of its training images. Recent attacks inflate the Gaussian count to exhaust GPU memory or corrupt rendered scenes to mislead downstream classifiers. We find that both attacks have the same structural signature: 2D image adversarial perturbations are not 3D-consistent by design. The Gaussians generated to match them provide erroneous contributions in some views while making significant contributions in others. We propose Multi-View Photometric Inconsistency (MVPI) Defense that scores each Gaussian by the variance of its opacity-weighted local $\mathcal{L}_1$ contribution across a stratified set of training views. The most inconsistent are soft-pruned via 3DGS's existing opacity threshold method. We evalute our approach on two different datasets. MVPI reduces peak Gaussian count by up to $1.90\times$ and training time by $1.22{-}1.50\times$ under Poison-Splat attack. It also restores top-1 classification accuracy on adversarially perturbed renders from $57.4\%$ to $66.5\%$. Our code is available at https://anonymous.4open.science/r/PruneDefense-2876/README.md.

Modeling event sequences requires understanding when future events will occur and how event types causally influence one another over time. Existing temporal point process (TPP) models typically assume static or first-order dependence structures, which limits their ability to capture the dynamic and multi-order causal mechanisms commonly observed in real-world systems. We propose MOCHA, a Multi-Order Causal Hierarchical Architecture for multivariate TPP that jointly models time-varying causal structure and multi-hop influence propagation in continuous time. MOCHA learns latent dynamic weighted directed acyclic graphs (DAG) over event types, where acyclicity and sparsity constraints promote structurally valid causal graphs. Based on the learned graph, the model decomposes event dynamics into multi-order causal paths, and incorporate both direct influence and indirect propagation into the intensity function. The entire framework is end-to-end differentiable and optimized jointly for event prediction and causal structure discovery. Experiments on seven real-world datasets from different domains show that MOCHA consistently achieves superior negative log-likelihood, while also recovering dynamic causal patterns that align with domain knowledge. These results demonstrate that MOCHA provides an effective framework for dynamic causal structure learning in TPP.

Driving-scene reconstruction via feed-forward Gaussian splatting from sparse multi-view images remains challenging due to two factors. First, cross-camera photometric inconsistency—caused by variations in exposure, ISP, and illumination—can be incorrectly absorbed into Gaussian geometry. Second, unreliable local geometric supervision arises from normal-based constraints near depth discontinuities. To address these issues, we present **MCSplat**, a multi-view consistent feed-forward Gaussian splatting framework for driving scenes. MCSplat constructs a canonical appearance space from depth-guided multi-camera correspondences to decouple geometry learning from camera-specific appearance. A multi-scale Bilateral Grid Transformer restores raw camera appearance from canonical renderings, enabling photometric supervision without contaminating Gaussian geometry. To improve local geometric reliability, we estimate Fisher-information based uncertainty from photometric sensitivity and use it to adaptively weight surface-oriented self-supervision. Experiments on the Waymo Dataset show that MCSplat achieves state-of-the-art performance on both the full validation set and an appearance-challenging subset with strong cross-camera photometric inconsistency, demonstrating improved reconstruction quality and more consistent novel-view geometry. Code will be released.

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 algorithm, it can dramatically slow 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. We then 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.

Gaussian processes are a cornerstone of modern probabilistic machine learning, providing principled uncertainty quantification and flexible nonparametric modeling. While the Gaussian kernel is widely used in Euclidean spaces, many real-world problems involve data residing on non-Euclidean domains, particularly compact Lie groups that naturally encode \emph{symmetries}. In this work, we construct a local Gaussian kernel on arbitrary compact Lie groups by decomposing the group into a \emph{maximal torus} and its orthogonal complement. For the prominent Lie groups $\mathbf{SO}(3)$ and $\mathbf{SU}(2)$, we derive closed-form kernel expressions using the Rodrigues formula. Extensive experiments verify the positive definiteness of the proposed kernel and demonstrate its effectiveness in Gaussian process regression, achieving accurate predictions across the entire manifold.

Discrete diffusion language models (DLMs) enable parallel generation but usually rely on fixed forward processes, such as masking, uniform noise, or precomputed hierarchies. We investigate whether the hierarchical forward process can instead be learned while preserving continuous-time tractability. We propose \textbf{Learnable Hierarchical Diffusion Language Model (LHDLM)}, which extends a learnable column-stochastic token-cluster map. This many-to-many hierarchy preserves a CTMC with block-conditional transition and closed-form CT-ELBO, while recovering HDLM in the one-hot limit and masked diffusion in the collapsed limit. We identify degenerate hierarchy maps caused by learning the same map used in both forward targets and model-induced cluster predictions, and mitigate them with an information-retention regularizer. Empirically, LHDLM is competitive with discrete diffusion approaches and reveals soft token structures --- cluster-agnostic function tokens and sharp content-token assignments --- that cannot be represented by hard partitions.

Recent work has demonstrated surprisingly good performance of pre-trained LLMs on regression tasks (for example, time-series prediction), with the ability to incorporate expert prior knowledge and the information contained in textual metadata. However we observe major error cascades even in short sequences $\lesssim 100$ points; these models are also computationally intensive and difficult to parallelise. Marginal LLM predictions do not suffer this issue and are trivially parallelised, but can predict over-broad densities. To address this, we propose combining these densities with a lightweight (diffusion-based) neural process. We show that this combination leads to better-calibrated predictions overall, outputs locally consistent trajectories, and leads to text-conditioned function space selection in the meta-learner. As part of this work we propose a gradient-free (and non-Monte Carlo) method for sampling from a product-of-experts of a score model and an `expert' (here the LLM predictive densities). We believe this general method is of independent interest as it is applicable whenever an expert can be convolved with a Gaussian in closed form.

Foundational marked temporal point process (MTPP) models, such as the Hawkes process, often use inexpressive model families in order to offer interpretable parameterizations of event data. On the other hand, neural MTPPs models forego this interpretability in favor of absolute predictive performance. In this work, we present a new family MTPP models: the hyper Hawkes process (HHP), which aims to be as flexible and performant as neural MTPPs, while retaining interpretable aspects. To achieve this, the HHP extends the classical Hawkes process to increase its expressivity by first expanding the dimension of the process into a latent space, and then introducing a hypernetwork to allow time- and data-dependent dynamics. These extensions define a highly performant MTPP family, achieving state-of-the-art performance across a range of benchmark tasks and metrics. Furthermore, by retaining the linearity of the recurrence, albeit now piecewise and conditionally linear, the HHP also retains much of the structure of the original Hawkes process, which we exploit to create direct probes into how the model creates predictions. HHP models therefore offer both state-of-the-art predictions, while also providing an opportunity to ``open the box'' and inspect how predictions were generated.

Compositional priors describe the generic properties of layered functions in deep Bayesian models, where deep neural networks with random weights are a canonical example. In the wide-network limit, the prior is a Gaussian process with a depth-dependent kernel, and its behaviour as depth grows has been extensively studied through this kernel. Here, we study another case, where each layer itself is a vector valued Gaussian process, and our aim is similarly to understand the limiting behaviour of the prior as depth grows. Previous GP work has established that for the RBF kernel and a certain range of bandwidths $r$, the prior degenerates in the limit, converging to the set of constant functions --- which is not useful as a probabilistic model. In this paper we establish several new results. First, we identify a sharp bandwidth threshold $r_c(d) = \Theta(\sqrt{d})$ above which the limit is degenerate, strengthening the earlier bounds. Second, and more importantly, we show that for $r$ below the threshold $r_c(d)$ the prior converges to a limit distribution $\pi_{\bar{Z}}$. We also prove that these distributions are non-degenerate and non-Gaussian, with non-vanishing dependence between coordinates. In contrast to the previously known degenerate regime, deep Gaussian process priors can therefore admit non-trivial limits. Empirically, we verify the threshold across a range of dimensions $d$, and demonstrate a complex multimodal behaviour of the limit distributions $\pi_{\bar{Z}}$ --- a regime that becomes increasingly narrow with $d$ and would be hard to identify without knowing the threshold.

Many real-world high-dimensional time series exhibit long-memory, but Gaussian graphical model testing in this regime remains understudied. We develop a direct, data-adaptive test statistic for assessing conditional independence in the graph structure of stationary Gaussian time series. We establish a finite-sample, Berry--Esseen type Gaussian approximation bound for the statistic, which applies to both short-memory and long-memory time series. The testing procedure is fully data-adaptive using block bootstrap method, on which we provide a finite-sample validity result including in the ultra-high-dimensional scenario, and can be extended to comparing graphical structures in two-sample tests. We also develop a consistency-empowered correction to the statistic and show that such tests attain asymptotic consistency in both size and power. Our proposed method is applied to a real-world fMRI data to understand functional connectivities within brain in different periods.

The recent breakthrough Score-Repellent Monte Carlo (SRMC) method improves MCMC sampling by tilting the target density $\pi$ in $\mathbb{R}^d$ with the factor $\exp(-\alpha\,\theta_n^\top s(x))$, where the score function $s(x) = \nabla_x \log \pi(x)$, and $\theta_n$ is the score average from past samples. However, a single scalar repellence strength $\alpha\ge0$ cannot handle both the steep and the flat directions in anisotropic energy landscapes at once. We introduce Geometry-Aware SRMC (GA-SRMC), which generalizes the Euclidean alignment to $\theta^\top M s(x)$ for any symmetric positive-definite matrix $M$. A stochastic-approximation central limit theorem under a trace constraint on $M$ identifies the trace-normalized inverse Fisher $M_{\rm opt}\propto S^{-1}$ as the unique minimizer of the worst-direction covariance bound, elevating the Fisher information $S=\text{Cov}_\pi(s,s)$ from a proposal-side preconditioner (e.g., FisherMALA, natural gradient) to the optimal repulsion-side matrix, with a single online estimate $\widehat S_n$ serving both roles at no additional cost. On an $8$-target simulation spanning the condition number $\kappa\in[1.3,100]$ and dimension $d\in[2,785]$, GA-SRMC dominates SRMC by $4.4\times$ on anisotropic Gaussian ($\kappa=100$) and $6.8\times$ on MNIST under the MALA baseline, by $18\text{ - }32\\%$ on the well-conditioned Bayesian logistic-regression posteriors, and by up to $+48\\%$ under FisherMALA; the advantage scales monotonically with the condition number $\kappa$.