ICML 2026 论文列表

We prove that Thompson sampling exhibits $\tilde{O}(\sigma d \sqrt{T} + d r \sqrt{\mathrm{Tr}(\Sigma_0)})$ Bayesian regret in the linear-Gaussian bandit with a $\mathcal{N}(\mu_0, \Sigma_0)$ prior distribution on the coefficients, where $d$ is the dimension, $T$ is the time horizon, $r$ is the maximum $\ell_2$ norm of the actions, and $\sigma^2$ is the noise variance. In contrast to existing regret bounds, this shows that to within logarithmic factors, the prior-dependent ''burn-in'' term $d r \sqrt{\mathrm{Tr}(\Sigma_0)}$ decouples additively from the minimax (long run) regret \sigma d \sqrt{T}. Previous regret bounds exhibit a multiplicative dependence on these terms. We establish these results via a new ''elliptical potential'' lemma, and also provide a lower bound indicating that the burn-in term is unavoidable.

Federated learning (FL) offers a promising framework for collaborative digital pathology by enabling model training across institutions. However, real-world deployments face heterogeneity arising from diverse multiple instance learning (MIL) architectures and heterogeneous feature extractors across institutions. We propose FedHD, a novel FL framework that performs local Gaussian-mixture feature alignment tailored for WSI analysis. Instead of exchanging model parameters, each client independently distills semantically rich synthetic feature representations aligned with the distribution of real WSIs. To preserve diagnostic diversity, FedHD adopts a one-to-one distillation strategy, generating a synthetic counterpart for each real slide to avoid over-compression. During federation, a curriculum-based integration strategy progressively incorporates cross-site synthetic features into local training once performance plateaus. Furthermore, an optional interpretation module reconstructs pseudo-patches from synthetic embeddings, enhancing transparency. FedHD is architecture-agnostic, privacy-preserving, and supports personalized yet collaborative training across diverse institutions. Experiments on TCGA-IDH, CAMELYON16, and CAMELYON17 show that FedHD consistently outperforms state-of-the-art federated and distillation baselines.

Belief Propagation (BP) is a powerful algorithm for distributed inference in probabilistic graphical models, however it quickly becomes infeasible for practical compute and memory budgets. Many efficient, non-parametric forms of BP have been developed, but the most popular is Gaussian Belief Propagation (GBP), a variant that assumes all distributions are locally Gaussian. GBP is widely used due to its efficiency and empirically strong performance in applications like computer vision or sensor networks – even when modelling non-Gaussian problems. In this paper, we seek to provide a theoretical guarantee for when Gaussian approximations are valid in highly non-Gaussian, sparsely-connected factor graphs performing BP (common in Spatial AI). We leverage the Central Limit Theorem to prove mathematically that variables’ beliefs under BP converge to a Gaussian distribution in complex, loopy factor graphs obeying our 4 key assumptions. We then confirm experimentally that variable beliefs become increasingly Gaussian after just a few BP iterations in a stereo depth estimation task.

The trajectory prediction of N-body systems is of great significance and remains challenging with broad applications across various fields such as physics, chemistry and biology. Recent advances in generative models including flow matching and diffusion models have emerged as effective solutions to this problem, owing to their capacity to model the stochasticity and underlying distributions of complex system trajectories. However, existing approaches typically adopt trivial prior distributions that neglect the temporal correlations and spatial symmetries of N-body trajectories, which not only complicates the generation process but also limits model performance. To address these limitations, we propose GP-EquiFlow, an SE(3)-equivariant flow matching model incorporating vector-valued Gaussian processes. Based on observed trajectories, we employ vector-valued Gaussian processes to construct SE(3)-equivariant prior distributions, which exhibit enhanced consistency with the target data distribution in both spatial and temporal dynamics. Extensive experiments on N-body simulations and molecular dynamics demonstrate that the proposed GP-EquiFlow delivers more accurate predictions while requiring fewer sampling steps, underscoring the effectiveness of integrating Gaussian process-based SE(3)-equivariant prior distributions in geometric trajectory prediction.

Modeling the learning curve is critical for cost-effective data collection in deep learning systems. Most prior approaches assume a specific parametric learning curve, but these can be inappropriate when no reliable parametric form can be assumed for the learning curve. While Gaussian processes offer flexible nonparametric modeling, existing GP approaches that enforce monotonicity typically introduce intractable factors or require derivative observations. To address this, we propose a Monotonic Variational Gaussian Process for Efficient Data Collection (MOVE), which (i) introduces a novel monotonic variational GP formulation with virtual-derivative factors to enable tractable posterior inference, and (ii) develops an expected shortfall based objective for target-driven data collection. Furthermore, our theoretical analysis shows that expected shortfall provides non-vanishing gradient signals that enable reliable gradient-based optimization. Extensive experiments on classification, segmentation, and detection benchmarks demonstrate consistent improvements over the prior method.

Reconstructing complete yet compact 3D Gaussian Splatting (3DGS) representations from sparse-view monocular videos remains a significant challenge. While hierarchical training with Video Frame Interpolation (VFI) improves coverage, its correlated pseudo-views and repeated merging accumulate structured, non-i.i.d. redundancy, violating the implicit independence assumptions of standard pruning methods and rendering global thresholding ineffectual. We propose CoverPruneGS, a coverage-preserving structured pruning framework specifically designed for hierarchical 3DGS. Our approach implements a coarse-to-fine pruning pipeline using voxel-based local diversity selection and ground-truth-guided lazy refinement via randomized dropout rendering. To ensure reliable refinement, we introduce a footprint-aware CUDA attribution mechanism. By aggregating ground-truth-aligned error degradation across Gaussian-influenced pixels, we generate faithful importance scores that enable precise, quantile-based "rescue" of essential primitives. Experimental results across multiple datasets demonstrate that CoverPruneGS substantially reduces Gaussian counts by 56.8\% and significantly accelerates inference speeds, all while enhancing or maintaining the quality of novel view synthesis.

In truncated linear regression, samples $(x,y)$ are shown only when the outcome $y$ falls inside a certain survival set $S^\star$ and the goal is to estimate the unknown $d$-dimensional regressor $w^\star$. This problem has a long history of study in Statistics and Machine Learning going back to the works of (Galton, 1897; Tobin, 1958) and more recently in, e.g., (Daskalakis et al., 2019; 2021; Lee et al., 2023; 2024). Despite this long history, however, most prior works are limited to the special case where $S^\star$ is precisely known. The more practically relevant case, where $S^\star$ is unknown and must be learned from data, remains open: indeed, here the only available algorithms require strong assumptions on the distribution of the feature vectors (e.g., Gaussianity) and, even then, have a $d^{\mathrm{poly} (1/\varepsilon)}$ run time for achieving $\varepsilon$ accuracy. In this work, we give the first algorithm for truncated linear regression with unknown survival set that runs in $\mathrm{poly} (d/\varepsilon)$ time, by only requiring that the feature vectors are sub-Gaussian. Our algorithm relies on a novel subroutine for efficiently learning unions of a bounded number of intervals using access to positive examples (without any negative examples) under a certain smoothness condition. This learning guarantee adds to the line of works on positive-only PAC learning and may be of independent interest.

Existing offline feed-forward methods for joint scene understanding and reconstruction on long image streams often perform global computation over an ever-growing set of past observations, causing runtime and GPU memory to increase rapidly with sequence length. We propose Streaming Semantic Gaussian Splatting (S2GS), a strictly causal and incremental framework that builds a 3D Gaussian semantic field from image streams without accessing future frames or reprocessing historical observations. S2GS continuously updates scene geometry, appearance, and instance-level semantics through a geometry--semantic decoupled dual-backbone design. The geometry branch performs causal modeling for incremental Gaussian updates, while the semantic branch leverages a 2D foundation vision model and a query-driven decoder to predict masks and identity embeddings. Query-level contrastive alignment and lightweight online association with an instance memory further stabilize temporal identities. Experiments show that S2GS matches or outperforms strong offline baselines, while substantially improving long-horizon scalability: it processes over 1,000 frames with much slower runtime and GPU memory growth, whereas offline global-processing baselines typically run out of memory at around 80 frames under the same setting. Project Page: https://stdcoutzrh.github.io/projects/s2gs/.

Multi-Output Gaussian Processes (MOGPs) provide a principled probabilistic framework for modelling correlated outputs but face scalability bottlenecks when applied to datasets with high-dimensional output spaces. To maintain tractability, existing methods typically resort to restrictive assumptions, such as employing low-rank or sum-of-separable kernels, which can limit expressiveness. We propose the Transformed Latent Variable MOGP (T-LVMOGP), a novel framework that scales MOGPs to a massive number of outputs while preserving the capacity to capture meaningful inter-output dependencies. T-LVMOGP constructs a flexible multi-output deep kernel by mapping inputs and output-specific latent variables into an embedding space using a Lipschitz-regularised neural network. Combined with stochastic variational inference, our model effectively scales to high-dimensional output settings. Across diverse benchmarks, including climate modelling with over $10,000$ outputs and zero-inflated spatial transcriptomics data, T-LVMOGP outperforms baselines in both predictive accuracy and computational efficiency.

We study an algorithm-independent, worst-case lower bound for the Gaussian process (GP) bandit problem in the frequentist setting, where the reward function is fixed and has a bounded norm in the known reproducing kernel Hilbert space (RKHS). Specifically, we focus on the squared exponential (SE) kernel, one of the most widely used kernel functions in GP bandits. One of the remaining open questions for this problem is the gap in the *dimension-dependent* logarithmic factors between upper and lower bounds. This paper partially resolves this open question under a hyperspherical input domain. We show that any algorithm suffers $\Omega(\sqrt{T (\ln T)^{d} (\ln \ln T)^{-d}})$ cumulative regret, where $T$ and $d$ represent the total number of steps and the dimension of the hyperspherical domain, respectively. Regarding the simple regret, we show that any algorithm requires $\Omega(\epsilon^{-2}(\ln \frac{1}{\epsilon})^d (\ln \ln \frac{1}{\epsilon})^{-d})$ time steps to find an $\epsilon$-optimal point. We also provide the improved $O((\ln T)^{d+1}(\ln \ln T)^{-d})$ upper bound on the maximum information gain for the SE kernel. Our results guarantee the optimality of the existing best algorithm up to *dimension-independent* logarithmic factors under a hyperspherical input domain.

Reliable uncertainty quantification for causal effects is crucial in high-stakes applications, but remains challenging when the target is an entire function rather than a scalar estimand. In this work, we introduce a GP-based approach for uncertainty quantification of interventional functions. The central idea is to build on recent work representing *interventional* functions as an inner-product of *observational* functions in a reproducing kernel Hilbert space (RKHS), by constructing appropriate GP priors for such functions and inferring posteriors from observational data. Our approach yields closed-form posterior moments and tractable training and inference, while avoiding pathologies of previous GP prior constructions for RKHS functions. We further derive a practical procedure for posterior coverage calibration. Across synthetic benchmarks, causal Bayesian optimization tasks, and a large-scale real dataset, our method improves uncertainty quantification while remaining competitive in causal effect estimation.

Bayesian optimization (BO) is a method commonly used for policy search in problems with low-dimensional policy parameterizations. While it is generally considered data-efficient, existing BO approaches are agnostic to the sequential structure of the optimization objective induced by policy roll-outs. Thereby, valuable information is discarded that could improve the convergence of BO. We address this inefficiency by developing and rigorously analyzing a novel approach for BO that relies on a temporal difference learning formulation for discounted infinite-horizon value functions based on Gaussian process (GP) regression. We derive learning error bounds for the proposed temporal difference GPs, such that we can exploit upper confidence bounds to analyze the cumulative regret of our BO approach. This analysis is further refined by bounding the maximal information gain for our temporal difference GP model. In a comparison with relevant baseline methods, we demonstrate the practical advantages of our method.

Accelerating diffusion models via feature caching has progressed from static feature reuse to polynomial extrapolation, yet current cache-then-forecast strategies still rely on hand-crafted approximation families (e.g., Taylor or Hermite bases) that can misalign with the non-stationary, layer-specific dynamics of generative features. This paper introduces EigenCache, a training-free framework that re-frames diffusion acceleration as covariance-adaptive feature forecasting and uncertainty-aware temporal design. EigenCache models cached feature trajectories as time-indexed stochastic processes and estimates layer-wise temporal kernels from a small calibration set. Under the resulting scalar temporal-kernel approximation, the Gaussian-process posterior mean, i.e., Kriging, is risk-optimal within the scalar-weighted linear predictor class; under joint Gaussianity, it further coincides with the MMSE estimator. This formulation generalizes fixed-basis forecasting from a covariance-adaptive perspective while providing a closed-form posterior-variance proxy for prediction uncertainty. Leveraging this proxy, EigenCache selects computation anchors by maximizing a log-determinant information-gain objective over denoising timesteps, a monotone submodular objective with a near-optimal greedy solution. Across image, video, transformer, U-Net, and LoRA-adapted diffusion models, EigenCache achieves a strong speed--fidelity Pareto frontier and provides a principled mechanism for robust compute allocation.

Covariance matrices serve as compact descriptors of feature distributions in many machine-learning pipelines, including domain adaptation and Gaussian embeddings. Under a centered Gaussian approximation, the *unregularized* Wasserstein-2 *optimal transport* (OT) discrepancy admits a closed form on covariances given by the *Bures--Wasserstein* (BW) objective on the *symmetric positive definite* (SPD) cone. We propose **ITSPACE** (Iterative Transport for Stable Proximal Alignment of Covariance Embeddings), a proximal majorization-minimization method that directly optimizes this exact BW objective through closed-form updates in a square-root factorization. In exact arithmetic, each iteration satisfies a sufficient-decrease inequality for the BW objective; under inexact polar computations, we provide an explicit certificate-gap bound controlling deviations from exact descent. The resulting iterations preserve PSD structure by construction and naturally support rank-restricted factors, making **ITSPACE** well-suited as a lightweight inner-loop primitive in settings where adaptation must be performed from unlabeled target batches under strict step and compute budgets. Across real-world covariance-alignment benchmarks, **ITSPACE** reaches low-BW-gap solutions substantially faster than BW-gradient descent, methods based on other covariance geometries, and entropically regularized sample-OT baselines.

Single-cell RNA sequencing provides insights into gene expression at single-cell resolution, yet inferring temporal processes from these static snapshot measurements remains a fundamental challenge. Current approaches utilizing neural differential equations and flows are sensitive to overfitting and lack careful considerations of biological variability. In this work, we propose a generative framework that models population trends using a latent heteroscedastic Gaussian process (GP) approximated by Hilbert space methods. To address the absence of genuine cell trajectories, we leverage an optimal transport (OT) objective that aligns generated and observed population distributions. Our method explicitly captures biological heterogeneity by incorporating cell-specific latent time and cell type conditioning to disentangle temporal asynchrony and trajectories to different cell types. We demonstrate state-of-the-art performance on complex interpolation and extrapolation benchmarks and introduce a novel gradient-based strategy for inferring perturbation trajectories.

Conventional dynamic SLAM approaches typically treat dynamic objects as outliers based on pre-defined categories, creating perceptual blind spots that limit the comprehensive environmental perception required for embodied agents. Although integrating Gaussian Splatting into SLAM enables holistic scene representation, it introduces an optimization paradox: without categorical priors, flexible dynamic primitives rapidly overfit static residuals. This phenomenon undermines the self-supervised error signals necessary for distinguishing motion. In response, we present De4D-SLAM, a novel framework designed for decoupled 4D reconstruction from monocular video. Our approach features a Gradient-Isolated Decoupling strategy, which leverages static reconstruction residuals to supervise a Spatially-Aware Kolmogorov-Arnold Network (SA-KAN), ensuring robust, category-agnostic motion segmentation. Additionally, we propose a Flow-Induced Initialization prior to stabilize the non-convex optimization of 4D Gaussian primitives using dense optical flow. Extensive evaluations on the TUM and Bonn benchmarks demonstrate that De4D-SLAM achieves competitive performance in both tracking and dynamic reconstruction, successfully reconciling the tension between robust localization and high-fidelity 4D mapping.

Recent neural methods, such as 3D Gaussian Splatting, have achieved state-of-the-art rendering quality and speed. However, these methods frequently encounter challenges in regions with overlapping Gaussians, leading to blurring and artifacts in the rendered images. We observed that widely used view-space positional gradients are insufficient for handling such circumstances. To address this, we introduce PCGS, a Patch Comparison Gaussian Splatting method to control the densification of corresponding Gaussians adaptively. Specifically, PCGS divides the rendered image into patches and identifies those with significant errors by comparing the loss between the rendered and ground truth images. Additional densification operations are then applied to the Gaussians in these error-prone regions. Furthermore, to prevent over-densification and redundant Gaussians, we design a Gaussian control strategy to regulate the densification process. Specifically, we set a Gaussian number budget that dynamically changes according to the progress of densification, and sample the Gaussians required for each densification step based on their importance scores. Our method results in significantly fewer artifacts and less blur while maintaining a Gaussian count approximately equal to that of 3DGS. Extensive experiments on multiple standard benchmarks demonstrate the superiority of our approach.

Surface reconstruction with differentiable rendering has achieved impressive performance in recent years, yet the pervasive photometric ambiguities have strictly bottlenecked existing approaches. This paper presents AmbiSuR, a framework that explores an intrinsic solution upon Gaussian Splatting for the photometric ambiguity-robust surface reconstruction with high performance. Started by revisiting the foundation, our investigation uncovers two built-in primitive-wise ambiguities in representation, while revealing an intrinsic potential for ambiguity self-indication in Gaussian Splatting. Stemming from these, a photometric disambiguation is first introduced, constraining ill-posed geometry solution for definite surface formation. Then, we propose an ambiguity indication module that unleashes the self-indication potential to identify and further guide correcting underconstrained reconstructions. Extensive experiments demonstrate our superior performance in surface reconstruction compared to existing methods across various challenging scenarios, while excelling in broad compatibility. Our code will be made open-source upon acceptance.