NeurIPS 2025 Papers

This work proposes a novel framework based on nested evolving set processes to accelerate Personalized PageRank (PPR) computation. At each stage of the process, we employ a localized inexact proximal point iteration to solve a simplified linear system. We show that the time complexity of such localized methods is upper bounded by $\min\{\tilde{\mathcal{O}}(R^2/\epsilon^2), \tilde{\mathcal{O}}(m)\}$ to obtain an $\epsilon$-approximation of the PPR vector, where $m$ denotes the number of edges in the graph and $R$ is a constant defined via nested evolving set processes. Furthermore, the algorithms induced by our framework require solving only $\tilde{\mathcal{O}}(1/\sqrt{\alpha})$ such linear systems, where $\alpha$ is the damping factor. When $1/\epsilon^2\ll m$, this implies the existence of an algorithm that computes an $\epsilon$-approximation of the PPR vector with an overall time complexity of $\tilde{\mathcal{O}}(R^2 / (\sqrt{\alpha}\epsilon^2))$, independent of the underlying graph size. Our result resolves an open conjecture from existing literature. Experimental results on real-world graphs validate the efficiency of our methods, demonstrating significant convergence in the early stages.

Recent advances in 3D Gaussian Splatting have shown remarkable potential for novel view synthesis. However, most existing large-scale scene reconstruction methods rely on the divide-and-conquer paradigm, which often leads to the loss of global scene information and requires complex parameter tuning due to scene partitioning and local optimization. To address these limitations, we propose MixGS, a novel holistic optimization framework for large-scale 3D scene reconstruction. MixGS models the entire scene holistically by integrating camera pose and Gaussian attributes into a view-aware representation, which is decoded into fine-detailed Gaussians. Furthermore, a novel mixing operation combines decoded and original Gaussians to jointly preserve global coherence and local fidelity. Extensive experiments on large-scale scenes demonstrate that MixGS achieves state-of-the-art rendering quality and competitive speed, while significantly reducing computational requirements, enabling large-scale scene reconstruction training on a single 24GB VRAM GPU.

Neural population activity exhibits complex, nonlinear dynamics, varying in time, over trials, and across experimental conditions. Here, we develop *Conditionally Linear Dynamical System* (CLDS) models as a general-purpose method to characterize these dynamics. These models use Gaussian Process priors to capture the nonlinear dependence of circuit dynamics on task and behavioral variables. Conditioned on these covariates, the data is modeled with linear dynamics. This allows for transparent interpretation and tractable Bayesian inference. We find that CLDS models can perform well even in severely data-limited regimes (e.g. one trial per condition) due to their Bayesian formulation and ability to share statistical power across nearby task conditions. In example applications, we apply CLDS to model thalamic neurons that nonlinearly encode heading direction and to model motor cortical neurons during a cued-reaching task.

Post-training processes are essential phases in grounding pre-trained language models to real-world tasks, with learning from demonstrations or preference signals playing a crucial role in this adaptation. We present a unified theoretical framework bridging Supervised Fine-Tuning (SFT) and preference learning in Large Language Model (LLM) post-training. Through rigorous mathematical derivation, we demonstrate that both SFT and preference learning methods like Direct Preference Optimization (DPO) operate within the same optimal policy-reward subspace, with SFT representing a special case of implicit reward learning. Our analysis reveals a critical limitation in conventional SFT: the KL divergence term in distribution matching becomes constant with respect to the policy during optimization, failing to constrain model updates. To address this, we propose a simple yet effective learning rate reduction approach that yields significant performance improvements (up to \textbf{25\%} relative gain and \textbf{6\%} absolute win rate increase in instruction following tasks. Additionally, we derive alternative SFT objectives from various f-divergence functions that preserve the KL term during optimization, further enhancing post-DPO model performance. Finally, we extend the theoretical relationship between LLM logits and Q-functions from preference learning to the SFT context, providing mathematical derivations and experimental validation.

In classification tasks, softmax functions are ubiquitously used as output activations to produce predictive probabilities. Such outputs only capture aleatoric uncertainty. To capture epistemic uncertainty, approximate Gaussian inference methods have been proposed. We develop a common formalism to describe such methods, which we view as outputting Gaussian distributions over the logit space. Predictives are then obtained as the expectations of the Gaussian distributions pushed forward through the softmax. However, such softmax Gaussian integrals cannot be solved analytically, and Monte Carlo (MC) approximations can be costly and noisy. We propose to replace the softmax activation with element-wise normCDF or sigmoid, which allows for the accurate sampling-free approximation of predictives. This also enables the approximation of the Gaussian pushforwards by Dirichlet distributions with moment matching. This approach entirely eliminates the runtime and memory overhead associated with MC sampling. We evaluate it combined with several approximate Gaussian inference methods (Laplace, HET, SNGP) on large- and small-scale datasets (ImageNet, CIFAR-100, CIFAR-10), demonstrating improved uncertainty quantification capabilities compared to softmax MC sampling. Our code is available at https://github.com/bmucsanyi/probit.

Regression trees have emerged as a preeminent tool for solving real-world regression problems due to their ability to deal with nonlinearities, interaction effects and sharp discontinuities. In this article, we rather study regression trees applied to well-behaved, differentiable functions, and determine the relationship between node parameters and the local gradient of the function being approximated. We find a simple estimate of the gradient which can be efficiently computed using quantities exposed by popular tree learning libraries. This allows tools developed in the context of differentiable algorithms, like neural nets and Gaussian processes, to be deployed to tree-based models. To demonstrate this, we study measures of model sensitivity defined in terms of integro-differential quantities and demonstrate how to compute them for regression trees using the proposed gradient estimates. Quantitative and qualitative numerical experiments reveal the capability of gradients estimated by regression trees to improve predictive analysis, solve tasks in uncertainty quantification, and provide interpretation of model behavior.

We study value-iteration (VI) algorithms for solving general (a.k.a. multichain) Markov decision processes (MDPs) under the average-reward criterion, a fundamental but theoretically challenging setting. Beyond the difficulties inherent to all average-reward problems posed by the lack of contractivity and non-uniqueness of solutions to the Bellman operator, in the multichain setting an optimal policy must solve the navigation subproblem of steering towards the best connected component, in addition to optimizing long-run performance within each component. We develop algorithms which better solve this navigational subproblem in order to achieve faster convergence for multichain MDPs, obtaining improved rates of convergence and sharper measures of complexity relative to prior work. Many key components of our results are of potential independent interest, including novel connections between average-reward and discounted problems, optimal fixed-point methods for discounted VI which extend to general Banach spaces, new sublinear convergence rates for the discounted value error, and refined suboptimality decompositions for multichain MDPs. Overall our results yield faster convergence rates for discounted and average-reward problems and expand the theoretical foundations of VI approaches.

Recent advances in radiance fields and novel view synthesis enable creation of realistic digital twins from photographs. However, current methods struggle with flat, texture-less surfaces, creating uneven and semi-transparent reconstructions, due to an ill-conditioned photometric reconstruction objective. Surface reconstruction methods solve this issue but sacrifice visual quality. We propose a novel hybrid 2D/3D representation that jointly optimizes constrained planar (2D) Gaussians for modeling flat surfaces and freeform (3D) Gaussians for the rest of the scene. Our end-to-end approach dynamically detects and refines planar regions, improving both visual fidelity and geometric accuracy. It achieves state-of-the-art depth estimation on ScanNet++ and ScanNetv2, and excels at mesh extraction without overfitting to a specific camera model, showing its effectiveness in producing high-quality reconstruction of indoor scenes.

Squared families of probability distributions have been studied and applied in numerous machine learning contexts. Typically, they appear as likelihoods, where their advantageous computational, geometric and statistical properties are exploited for fast estimation algorithms, representational properties and statistical guarantees. Here, we investigate the use of squared families as prior beliefs in Bayesian inference. We find that they can form helpful conjugate families, often allowing for closed-form and tractable Bayesian inference and marginal likelihoods. We apply such conjugate families to Bayesian regression in feature space using end-to-end learnable neural network features. Such a setting allows for a rich multi-modal alternative to Gaussian processes with neural network features, often called deep kernel learning. We demonstrate our method on few shot learning, outperforming existing neural methods based on Gaussian processes and normalising flows.

Dynamic 4D Gaussian Splatting (4DGS) effectively extends the high-speed rendering capabilities of 3D Gaussian Splatting (3DGS) to represent volumetric videos. However, the large number of Gaussians, substantial temporal redundancies, and especially the absence of an entropy-aware compression framework result in large storage requirements. Consequently, this poses significant challenges for practical deployment, efficient edge-device processing, and data transmission. In this paper, we introduce a novel end-to-end RD-optimized compression framework tailored for 4DGS, aiming to enable flexible, high-fidelity rendering across varied computational platforms. Leveraging Fully Explicit Dynamic Gaussian Splatting (Ex4DGS), one of the state-of-the-art 4DGS methods, as our baseline, we start from the existing 3DGS compression methods for compatibility while effectively addressing additional challenges introduced by the temporal axis. In particular, instead of storing motion trajectories independently per point, we employ a wavelet transform to reflect the real-world smoothness prior, significantly enhancing storage efficiency. This approach yields significantly improved compression ratios and provides a user-controlled balance between compression efficiency and rendering quality. Extensive experiments demonstrate the effectiveness of our method, achieving up to 91$\times$ compression compared to the original Ex4DGS model while maintaining high visual fidelity. These results highlight the applicability of our framework for real-time dynamic scene rendering in diverse scenarios, from resource-constrained edge devices to high-performance environments. The source code is available at https://github.com/HyeongminLEE/RD4DGS.

We study the noise-free Gaussian Process (GP) bandit problem, in which a learner seeks to minimize regret through noise-free observations of a black-box objective function that lies in a known reproducing kernel Hilbert space (RKHS). The Gaussian Process Upper Confidence Bound (GP-UCB) algorithm is a well-known approach for GP bandits, where query points are adaptively selected based on the GP-based upper confidence bound score. While several existing works have reported the practical success of GP-UCB, its theoretical performance remains suboptimal. However, GP-UCB often empirically outperforms other nearly-optimal noise-free algorithms that use non-adaptive sampling schemes. This paper resolves the gap between theoretical and empirical performance by establishing a nearly-optimal regret upper bound for noise-free GP-UCB. Specifically, our analysis provides the first constant cumulative regret bounds in the noise-free setting for both the squared exponential kernel and the Matérn kernel with some degree of smoothness.

Gaussian processes (GPs) are widely used for regression and optimization tasks such as Bayesian optimization (BO) due to their expressiveness and principled uncertainty estimates. However, in settings with large datasets corrupted by outliers, standard GPs and their sparse approximations struggle with computational tractability and robustness. We introduce Robust Computation-aware Gaussian Process (RCaGP), a novel GP model that jointly addresses these challenges by combining a principled treatment of approximation-induced uncertainty with robust generalized Bayesian updating. The key insight is that robustness and approximation-awareness are not orthogonal but intertwined: approximations can exacerbate the impact of outliers, and mitigating one without the other is insufficient. Unlike previous work that focuses narrowly on either robustness or approximation quality, RCaGP combines both in a principled and scalable framework, thus effectively managing both outliers and computational uncertainties introduced by approximations such as low-rank matrix multiplications. Our model ensures more conservative and reliable uncertainty estimates, a property we rigorously demonstrate. Additionally, we establish a robustness property and show that the mean function is key to preserving it, motivating a tailored model selection scheme for robust mean functions. Empirical results confirm that solving these challenges jointly leads to superior performance across both clean and outlier-contaminated settings, both on regression and high-throughput Bayesian optimization benchmarks.

3D Gaussian Splatting (3DGS) has emerged as a high-fidelity and efficient paradigm for online free-viewpoint video (FVV) reconstruction, offering viewers rapid responsiveness and immersive experiences. However, existing online methods face challenge in prohibitive storage requirements primarily due to point-wise modeling that fails to exploit the motion properties. To address this limitation, we propose a novel Compact Gaussian Streaming (ComGS) framework, leveraging the locality and consistency of motion in dynamic scene, that models object-consistent Gaussian point motion through keypoint-driven motion representation. By transmitting only the keypoint attributes, this framework provides a more storage-efficient solution. Specifically, we first identify a sparse set of motion-sensitive keypoints localized within motion regions using a viewspace gradient difference strategy. Equipped with these keypoints, we propose an adaptive motion-driven mechanism that predicts a spatial influence field for propagating keypoint motion to neighboring Gaussian points with similar motion. Moreover, ComGS adopts an error-aware correction strategy for key frame reconstruction that selectively refines erroneous regions and mitigates error accumulation without unnecessary overhead. Overall, ComGS achieves a remarkable storage reduction of over 159 × compared to 3DGStream and 14 × compared to the SOTA method QUEEN, while maintaining competitive visual fidelity and rendering speed. Project page: https://chenjiacong-1005.github.io/ComGS/.

Neural radiance fields (NeRF) and 3D Gaussian Splatting (3DGS) are popular techniques to reconstruct and render photorealistic images. However, the prerequisite of running Structure-from-Motion (SfM) to get camera poses limits their completeness. Although previous methods can reconstruct a few unposed images, they are not applicable when images are unordered or densely captured. In this work, we propose a method to train 3DGS from unposed images. Our method leverages a pre-trained 3D geometric foundation model as the neural scene representation. Since the accuracy of the predicted pointmaps does not suffice for accurate image registration and high-fidelity image rendering, we propose to mitigate the issue by initializing and fine-tuning the pre-trained model from a seed image. The images are then progressively registered and added to the training buffer, which is used to train the model further. We also propose to refine the camera poses and pointmaps by minimizing a point-to-camera ray consistency loss across multiple views. When evaluated on diverse challenging datasets, our method outperforms state-of-the-art pose-free NeRF/3DGS methods in terms of both camera pose accuracy and novel view synthesis, and even renders higher fidelity images than 3DGS trained with COLMAP poses.

Scene reconstruction from casually captured videos has wide real-world applications. Despite recent progress, existing methods relying on traditional cameras tend to fail in high-speed scenarios due to insufficient observations and inaccurate pose estimation. Event cameras, inspired by biological vision, record pixel-wise intensity changes asynchronously with high temporal resolution and low latency, providing valuable scene and motion information in blind inter-frame intervals. In this paper, we introduce the event cameras to aid scene construction from a casually captured video for the first time, and propose Event-Aided Free-Trajectory 3DGS, called EF-3DGS, which seamlessly integrates the advantages of event cameras into 3DGS through three key components. First, we leverage the Event Generation Model (EGM) to fuse events and frames, enabling continuous supervision between discrete frames. Second, we extract motion information through Contrast Maximization (CMax) of warped events, which calibrates camera poses and provides gradient-domain constraints for 3DGS. Third, to address the absence of color information in events, we combine photometric bundle adjustment (PBA) with a Fixed-GS training strategy that separates structure and color optimization, effectively ensuring color consistency across different views. We evaluate our method on the public Tanks and Temples benchmark and a newly collected real-world dataset, RealEv-DAVIS. Our method achieves up to 3dB higher PSNR and 40% lower Absolute Trajectory Error (ATE) compared to state-of-the-art methods under challenging high-speed scenarios.

In this paper, we study the quantitative convergence of shallow neural networks trained via gradient descent to their associated Gaussian processes in the infinite-width limit. While previous work has established qualitative convergence under broad settings, precise, finite-width estimates remain limited, particularly during training. We provide explicit upper bounds on the quadratic Wasserstein distance between the network output and its Gaussian approximation at any training time $t \ge 0$, demonstrating polynomial decay with network width. Our results quantify how architectural parameters, such as width and input dimension, influence convergence, and how training dynamics affect the approximation error

Fitting Gaussian Processes (GPs) provides interpretable aleatoric uncertainty quantification for estimation of spatio-temporal fields. Spatio-temporal deep learning models, while scalable, typically assume a simplistic independent covariance matrix for the response, failing to capture the underlying correlation structure. However, spatio-temporal GPs suffer from issues of scalability and various forms of approximation bias resulting from restrictive assumptions of the covariance kernel function. We propose STACI, a novel framework consisting of a variational Bayesian neural network approximation of non-stationary spatio-temporal GP along with a novel spatio-temporal conformal inference algorithm. STACI is highly scalable, taking advantage of GPU training capabilities for neural network models, and provides statistically valid prediction intervals for uncertainty quantification. STACI outperforms competing GPs and deep methods in accurately approximating spatio-temporal processes and we show it easily scales to datasets with millions of observations.

A key challenge in automated formal reasoning is the intractable search space, which grows exponentially with the depth of the proof. This branching is caused by the large number of candidate proof tactics which can be applied to a given goal. Nonetheless, many of these tactics are semantically similar or lead to an execution error, wasting valuable resources in both cases. We address the problem of effectively pruning this search, using only synthetic data generated from previous proof attempts. We first demonstrate that it is possible to generate semantically aware tactic representations which capture the effect on the proving environment, likelihood of success, and execution time. We then propose a novel filtering mechanism which leverages these representations to select semantically diverse and high quality tactics, using Determinantal Point Processes. Our approach, 3D-Prover, is designed to be general, and to augment any underlying tactic generator. We demonstrate the effectiveness of 3D-Prover on the miniF2F and LeanDojo benchmarks by augmenting popular open source proving LLMs. We show that our approach leads to an increase in the overall proof rate, as well as a significant improvement in the tactic success rate, execution time and diversity. We make our code available at https://github.com/sean-lamont/3D-Prover.

We propose 4DGT, a 4D Gaussian-based Transformer model for dynamic scene reconstruction, trained entirely on real-world monocular posed videos. Using 4D Gaussian as an inductive bias, 4DGT unifies static and dynamic components, enabling the modeling of complex, time-varying environments with varying object lifespans. We proposed a novel density control strategy in training, which enables our 4DGT to handle longer space-time input. Our model processes 64 consecutive posed frames in a rolling-window fashion, predicting consistent 4D Gaussians in the scene. Unlike optimization-based methods, 4DGT performs purely feed-forward inference, reducing reconstruction time from hours to seconds and scaling effectively to long video sequences. Trained only on large-scale monocular posed video datasets, 4DGT can outperform prior Gaussian-based networks significantly in real-world videos and achieve on-par accuracy with optimization-based methods on cross-domain videos.