NeurIPS 2025 论文列表

Reinforcement Learning (RL) is a continuously growing field that has the potential to revolutionize many areas of artificial intelligence. However, despite its promise, RL research is often hindered by the lack of standardization in environment and algorithm implementations. This makes it difficult for researchers to compare and build upon each other's work, slowing down progress in the field. Gymnasium is an open-source library that provides a standard API for RL environments, aiming to tackle this issue. Gymnasium's main feature is a set of abstractions that allow for wide interoperability between environments and training algorithms, making it easier for researchers to develop and test RL algorithms. In addition, Gymnasium provides a collection of easy-to-use environments, tools for easily customizing environments, and tools to ensure the reproducibility and robustness of RL research. Through this unified framework, Gymnasium significantly streamlines the process of developing and testing RL algorithms, enabling researchers to focus more on innovation and less on implementation details. By providing a standardized platform for RL research, Gymnasium helps to drive forward the field of reinforcement learning and unlock its full potential. Gymnasium is available online at \url{https://github.com/Farama-Foundation/Gymnasium}.

Recent advances in large language models (LLMs) have intensified efforts to fuse heterogeneous open-source models into a unified system that inherits their complementary strengths. Existing logit-based fusion methods maintain inference efficiency but treat vocabulary dimensions independently, overlooking semantic dependencies encoded by cross-dimension interactions. These dependencies reflect how token types interact under a model's internal reasoning and are essential for aligning models with diverse generation behaviors. To explicitly model these dependencies, we propose \textbf{InfiGFusion}, the first structure-aware fusion framework with a novel \textit{Graph-on-Logits Distillation} (GLD) loss. Specifically, we retain the top-$k$ logits per output and aggregate their outer products across sequence positions to form a global co-activation graph, where nodes represent vocabulary channels and edges quantify their joint activations. To ensure scalability and efficiency, we design a sorting-based closed-form approximation that reduces the original $O(n^4)$ cost of Gromov-Wasserstein distance to $O(n \log n)$, with provable approximation guarantees. Experiments across multiple fusion settings show that GLD consistently improves fusion quality and stability. InfiGFusion outperforms SOTA models and fusion baselines across 11 benchmarks spanning reasoning, coding, and mathematics. It shows particular strength in complex reasoning tasks, with +35.6 improvement on Multistep Arithmetic and +37.06 on Causal Judgement over SFT, demonstrating superior multi-step and relational inference.

Recently, Gaussian Splatting (GS) has shown great potential for urban scene reconstruction in the field of autonomous driving. However, current urban scene reconstruction methods often depend on multimodal sensors as inputs, $\textit{i.e.}$ LiDAR and images. Though the geometry prior provided by LiDAR point clouds can largely mitigate ill-posedness in reconstruction, acquiring such accurate LiDAR data is still challenging in practice: i) precise spatiotemporal calibration between LiDAR and other sensors is required, as they may not capture data simultaneously; ii) reprojection errors arise from spatial misalignment when LiDAR and cameras are mounted at different locations. To avoid the difficulty of acquiring accurate LiDAR depth, we propose ${D}^2GS$, a LiDAR-free urban scene reconstruction framework. In this work, we obtain geometry priors that are as effective as LiDAR while being denser and more accurate. $\textbf{First}$, we initialize a dense point cloud by back-projecting multi-view metric depth predictions. This point cloud is then optimized by a Progressive Pruning strategy to improve the global consistency. $\textbf{Second}$, we jointly refine Gaussian geometry and predicted dense metric depth via a Depth Enhancer. Specifically, we leverage diffusion priors from a depth foundation model to enhance the depth maps rendered by Gaussians. In turn, the enhanced depths provide stronger geometric constraints during Gaussian training. $\textbf{Finally}$, we improve the accuracy of ground geometry by constraining the shape and normal attributes of Gaussians within road regions. Extensive experiments on the Waymo dataset demonstrate that our method consistently outperforms state-of-the-art methods, producing more accurate geometry even when compared with those using ground-truth LiDAR data.

The limited availability of high-quality training data poses a major obstacle in data-driven PDE solving, where expensive data collection and resolution constraints severely impact the ability of neural operator networks to learn and generalize the underlying physical system. To address this challenge, we propose DeltaPhi, a novel learning framework that transforms the PDE solving task from learning direct input-output mappings to learning the residuals between similar physical states, a fundamentally different approach to neural operator learning. This reformulation provides implicit data augmentation by exploiting the inherent stability of physical systems where closer initial states lead to closer evolution trajectories. DeltaPhi is architecture-agnostic and can be seamlessly integrated with existing neural operators to enhance their performance. Extensive experiments demonstrate consistent and significant improvements across diverse physical systems including regular and irregular domains, different neural architectures, multiple training data amount, and cross-resolution scenarios, confirming its effectiveness as a general enhancement for neural operators in data-limited PDE solving.

Hebbian learning is a biological principle that intuitively describes how neurons adapt their connections through repeated stimuli. However, when applied to machine learning, it suffers serious issues due to the unconstrained updates of the connections and the lack of accounting for feedback mediation. Such shortcomings limit its effective scaling to complex network architectures and tasks. To this end, here we introduce the Structural Projection Hebbian Representation (SPHeRe), a novel unsupervised learning method that integrates orthogonality and structural information preservation through a local auxiliary nonlinear block. The loss for structural information preservation backpropagates to the input through an auxiliary lightweight projection that conceptually serves as feedback mediation while the orthogonality constraints account for the boundedness of updating magnitude. Extensive experimental results show that SPHeRe achieves SOTA performance among unsupervised synaptic plasticity approaches on standard image classification benchmarks, including CIFAR-10, CIFAR-100, and Tiny-ImageNet. Furthermore, the method exhibits strong effectiveness in continual learning and transfer learning scenarios, and image reconstruction tasks show the robustness and generalizability of the extracted features. This work demonstrates the competitiveness and potential of Hebbian unsupervised learning rules within modern deep learning frameworks, demonstrating the possibility of efficient and biologically inspired learning algorithms without the strong dependence on strict backpropagation. Our code is available at https://github.com/brain-intelligence-lab/SPHeRe.

A phenomenon known as ``Neural Collapse (NC)'' in deep classification tasks, in which the penultimate-layer features and the final classifiers exhibit an extremely simple geometric structure, has recently attracted considerable attention, with the expectation that it can deepen our understanding of how deep neural networks behave. The Unconstrained Feature Model (UFM) has been proposed to explain NC theoretically, and there emerges a growing body of work that extends NC to tasks other than classification and leverages it for practical applications. In this study, we investigate whether a similar phenomenon arises in deep Ordinal Regression (OR) tasks, via combining the cumulative link model for OR and UFM. We show that a phenomenon we call Ordinal Neural Collapse (ONC) indeed emerges and is characterized by the following three properties: (ONC1) all optimal features in the same class collapse to their within-class mean when regularization is applied; (ONC2) these class means align with the classifier, meaning that they collapse onto a one-dimensional subspace; (ONC3) the optimal latent variables (corresponding to logits or preactivations in classification tasks) are aligned according to the class order, and in particular, in the zero-regularization limit, a highly local and simple geometric relationship emerges between the latent variables and the threshold values. We prove these properties analytically within the UFM framework with fixed threshold values and corroborate them empirically across a variety of datasets. We also discuss how these insights can be leveraged in OR, highlighting the use of fixed thresholds.

Multi-objective optimization problems (MOPs) are prevalent in numerous real-world applications. Recently, Pareto Set Learning (PSL) has emerged as a powerful paradigm for solving MOPs. PSL can produce a neural network for modeling the set of all Pareto optimal solutions. However, applying PSL to black-box objectives, particularly those exhibiting non-separability, high dimensionality, and/or other complex properties, remains very challenging. To address this issue, we propose leveraging evolution strategies (ESs), a class of specialized black-box optimization algorithms, within the PSL paradigm. Traditional ESs capture the complex dimensional dependencies less efficiently, which can significantly hinder their performance in PSL. To tackle this issue, we suggest encapsulating the dependencies within a neural network, which is then trained using a novel gradient estimation method. The proposed method, termed Neural-ES, is evaluated using a bespoke benchmark suite for black-box PSL. Experimental comparisons with other methods demonstrate the efficiency of Neural-ES, underscoring its ability to learn the Pareto sets of challenging black-box MOPs.

Federated learning (FL) is a distributed machine learning paradigm that enables multiple clients to collaboratively train a shared model without exposing their raw data. However, existing FL research has primarily focused on optimizing learning performance based on the assumption of uniform client participation, with few studies delving into performance fairness under inconsistent client participation, particularly in model-heterogeneous FL environments. In view of this challenge, we propose PHP-FL, a novel model-heterogeneous FL method that explicitly addresses scenarios with varying client participation probabilities to enhance both model accuracy and performance fairness. Specifically, we introduce a Dual-End Aligned ensemble Learning (DEAL) module, where small auxiliary models on clients are used for dual-end knowledge alignment and local ensemble learning, effectively tackling model heterogeneity without a public dataset. Furthermore, to mitigate update conflicts caused by inconsistent participation probabilities, we propose an Importance-driven Selective Parameter Update (ISPU) module, which accurately updates critical local parameters based on training progress. Finally, we implement PHP-FL on a lightweight FL platform with heterogeneous clients across three different client participation patterns. Extensive experiments under heterogeneous settings and diverse client participation patterns demonstrate that PHP-FL achieves state-of-the-art performance in both accuracy and fairness. Our code is available at: https://github.com/Siyuan01/PHP-FL-main.

We consider the two-sample testing problem for networks, where the goal is to determine whether two sets of networks originated from the same stochastic model. Assuming no vertex correspondence and allowing for different numbers of nodes, we address a fundamental network testing problem that goes beyond simple adjacency matrix comparisons. We adopt the stochastic block model (SBM) for network distributions, due to their interpretability and the potential to approximate more general models. The lack of meaningful node labels and vertex correspondence translate to a graph matching challenge when developing a test for SBMs. We introduce an efficient algorithm to match estimated network parameters, allowing us to properly combine and contrast information within and across samples, leading to a powerful test. We show that the matching algorithm, and the overall test are consistent, under mild conditions on the sparsity of the networks and the sample sizes, and derive a chi-squared asymptotic null distribution for the test. Through a mixture of theoretical insights and empirical validations, including experiments with both synthetic and real-world data, this study advances robust statistical inference for complex network data.

Routing Problems are central to many real-world applications, yet remain challenging due to their (NP-)hard nature. Amongst existing approaches, heuristics often offer the best trade-off between quality and scalability, making them suitable for industrial use. While Reinforcement Learning (RL) offers a flexible framework for designing heuristics, its adoption over handcrafted heuristics remains incomplete. Existing learned methods still lack the ability to adapt to specific instances and fully leverage the available computational budget. Current best methods either rely on a collection of pre-trained policies, or on RL fine-tuning; hence failing to fully utilize newly available information within the constraints of the budget. In response, we present MEMENTO, an approach that leverages memory to improve the search of neural solvers at inference. MEMENTO updates the action distribution dynamically based on the outcome of previous decisions. We validate its effectiveness on Traveling Salesman and Capacitated Vehicle Routing problems, demonstrating its superiority over tree-search and policy-gradient fine-tuning; and showing that it can be zero-shot combined with diversity-based solvers. We successfully train all RL auto-regressive solvers on large instances, and verify MEMENTO's scalability and data-efficiency: pushing the state-of-the-art on 11 out of 12 evaluated tasks.

Neural rendering techniques, including NeRF and Gaussian Splatting (GS), rely on photometric consistency to produce high-quality reconstructions. However, in real-world driving scenarios, it is challenging to guarantee perfect photometric consistency in acquired images. Appearance codes have been widely used to address this issue, but their modeling capability is limited, as a single code is applied to the entire image. Recently, the bilateral grid was introduced to perform pixel-wise color mapping, but it is difficult to optimize and constrain effectively. In this paper, we propose a novel multi-scale bilateral grid that unifies appearance codes and bilateral grids. We demonstrate that this approach significantly improves geometric accuracy in dynamic, decoupled autonomous driving scene reconstruction, outperforming both appearance codes and bilateral grids. This is crucial for autonomous driving, where accurate geometry is important for obstacle avoidance and control. Our method shows strong results across four datasets: Waymo, NuScenes, Argoverse, and PandaSet. We further demonstrate that the improvement in geometry is driven by the multi-scale bilateral grid, which effectively reduces floaters caused by photometric inconsistency.

Shortcut models represent a promising, non-adversarial paradigm for generative modeling, uniquely supporting one-step, few-step, and multi-step sampling from a single trained network. However, their widespread adoption has been stymied by critical performance bottlenecks. This paper tackles the five core issues that held shortcut models back: (1) the hidden flaw of compounding guidance, which we are the first to formalize, causing severe image artifacts; (2) inflexible fixed guidance that restricts inference-time control; (3) a pervasive frequency bias driven by a reliance on low-level distances in the direct domain, which biases reconstructions toward low frequencies; (4) divergent self-consistency arising from a conflict with EMA training; and (5) curvy flow trajectories that impede convergence. To address these challenges, we introduce iSM, a unified training framework that systematically resolves each limitation. Our framework is built on four key improvements: Intrinsic Guidance provides explicit, dynamic control over guidance strength, resolving both compounding guidance and inflexibility. A Multi-Level Wavelet Loss mitigates frequency bias to restore high-frequency details. Scaling Optimal Transport (sOT) reduces training variance and learns straighter, more stable generative paths. Finally, a Twin EMA strategy reconciles training stability with self-consistency. Extensive experiments on ImageNet 256x256 demonstrate that our approach yields substantial FID improvements over baseline shortcut models across one-step, few-step, and multi-step generation, making shortcut models a viable and competitive class of generative models.

We introduce learning to condition (L2C), a scalable, data-driven framework for accelerating Most Probable Explanation (MPE) inference in Probabilistic Graphical Models (PGMs)—a fundamentally intractable problem. L2C trains a neural network to score variable-value assignments based on their utility for conditioning, given observed evidence. To facilitate supervised learning, we develop a scalable data generation pipeline that extracts training signals from the search traces of existing MPE solvers. The trained network serves as a heuristic that integrates with search algorithms, acting as a conditioning strategy prior to exact inference or as a branching and node selection policy within branch-and-bound solvers. We evaluate L2C on challenging MPE queries involving high-treewidth PGMs. Experiments show that our learned heuristic significantly reduces the search space while maintaining or improving solution quality over state-of-the-art methods.

Clustering is a fundamental problem that has been extensively studied over past few decades, with most research focusing on point-based clustering such as $k$-means, $k$-median, and $k$-center. However, numerous real-world applications, such as motion analysis, computer vision, and missing data analysis, require clustering over structured data, including lines, time series and affine subspaces (flats), where traditional point-based clustering algorithms often fall short. In this paper, we study the $k$-means of lines problem, where the input is a set $L$ of lines in $\mathbb{R}^d$, and the goal is to find $k$ centers $C$ in $\mathbb{R}^d$ such that the sum of squared distances from each line in $L$ to its nearest center in $C$ is minimized. The local search algorithm is a well-established strategy for point-based $k$-means clustering, known for its efficiency and provable approximation guarantees. However, extending local search algorithm to the $k$-means of lines problem is nontrivial, as the capture relation used in point-based clustering does not generalize to the line setting. This is because that the point-to-line distance function lack the triangle inequality property that supports geometric analysis in point-based clustering. Moreover, since lines extend infinitely in space, it is difficult to identify effective swap points that can significantly reduce the clustering cost. To overcome above obstacles, we introduce a *proportional capture relation* that links optimal and current centers based the assignment proportions of lines, enabling a refined analysis that bypasses the triangle inequality barrier. We also introduce a *CrossLine* structure, which provides a principled discretization of the geometric space around line pairs, and ensures coverage of high-quality swap points essential for local search, thereby enabling effective execution of the local search process. Consequently, based on the proposed components, we develop the first single-swap local search algorithm for the $k$-means of lines problem, achieving a $(500+\varepsilon)$-approximation in polynomial time for low-dimensional Euclidean space.

Premise selection is a critical bottleneck in interactive theorem proving, particularly with large libraries. Existing methods, primarily relying on semantic embeddings, often fail to effectively leverage the rich structural information inherent in mathematical expressions. This paper proposes a novel framework for premise selection based on the structure of expression trees. The framework enhances premise selection ability by explicitly utilizing the structural information of Lean expressions and by means of the simplified tree representation obtained via common subexpression elimination. Our method employs a multi-stage filtering pipeline, incorporating structure-aware similarity measures including the Weisfeiler-Lehman kernel, tree edit distance, $\texttt{Const}$ node Jaccard similarity, and collapse-match similarity. An adaptive fusion strategy combines these metrics for refined ranking. To handle large-scale data efficiently, we incorporate cluster-based search space optimization and structural compatibility constraints. Comprehensive evaluation on a large theorem library extracted from Mathlib4 demonstrates that our method significantly outperforms existing premise retrieval tools across various metrics. Experimental analysis, including ablation studies and parameter sensitivity analysis, validates the contribution of individual components and highlights the efficacy of our structure-aware approach and multi-metric fusion.

Growing data privacy demands, driven by regulations like GDPR and CCPA, require machine unlearning methods capable of swiftly removing the influence of specific training points. Although verified approaches like SISA, using data slicing and checkpointing, achieve efficient unlearning for single models by reverting to intermediate states, these methods struggle in teacher-student knowledge distillation settings. Unlearning in the teacher typically forces costly, complete student retraining due to pervasive information propagation during distillation. Our primary contribution is PURGE (Partitioned Unlearning with Retraining Guarantee for Ensembles), a novel framework integrating verified unlearning with distillation. We introduce constituent mapping and an incremental multi-teacher strategy that partitions the distillation process, confines each teacher constituent’s impact to distinct student data subsets, and crucially maintains data isolation. The PURGE framework substantially reduces retraining overhead—requiring only partial student updates—when teacher-side unlearning occurs. We provide both theoretical analysis, quantifying significant speed-ups in the unlearning process, and empirical validation on multiple datasets, demonstrating that PURGE achieves these efficiency gains while maintaining student accuracy comparable to standard baselines.

Node tokenized graph Transformers (GTs) have shown promising performance in node classification. The generation of token sequences is the key module in existing tokenized GTs which transforms the input graph into token sequences, facilitating the node representation learning via Transformer. In this paper, we observe that the generations of token sequences in existing GTs only focus on the first-order neighbors on the constructed similarity graphs, which leads to the limited usage of nodes to generate diverse token sequences, further restricting the potential of tokenized GTs for node classification. To this end, we propose a new method termed SwapGT. SwapGT first introduces a novel token swapping operation based on the characteristics of token sequences that fully leverages the semantic relevance of nodes to generate more informative token sequences. Then, SwapGT leverages a Transformer-based backbone to learn node representations from the generated token sequences. Moreover, SwapGT develops a center alignment loss to constrain the representation learning from multiple token sequences, further enhancing the model performance. Extensive empirical results on various datasets showcase the superiority of SwapGT for node classification. Code is available at https://github.com/JHL-HUST/SwapGT.

Optical flow estimation has achieved promising results in conventional scenes but faces challenges in high-speed and low-light scenes, which suffer from motion blur and insufficient illumination. These conditions lead to weakened texture and amplified noise and deteriorate the appearance saturation and boundary completeness of frame cameras, which are necessary for motion feature matching. In degraded scenes, the frame camera provides dense appearance saturation but sparse boundary completeness due to its long imaging time and low dynamic range. In contrast, the event camera offers sparse appearance saturation, while its short imaging time and high dynamic range gives rise to dense boundary completeness. Traditionally, existing methods utilize feature fusion or domain adaptation to introduce event to improve boundary completeness. However, the appearance features are still deteriorated, which severely affects the mostly adopted discriminative models that learn the mapping from visual features to motion fields and generative models that generate motion fields based on given visual features. So we introduce diffusion models that learn the mapping from noising flow to clear flow, which is not affected by the deteriorated visual features. Therefore, we propose a novel optical flow estimation framework Diff-ABFlow based on diffusion models with frame-event appearance-boundary fusion. Inspired by the appearance-boundary complementarity of frame and event, we propose an Attention-Guided Appearance-Boundary Fusion module to fuse frame and event. Based on diffusion models, we propose a Multi-Condition Iterative Denoising Decoder. Our proposed method can effectively utilize the respective advantages of frame and event, and shows great robustness to degraded input. In addition, we propose a dual-modal optical flow dataset for generalization experiments. Extensive experiments have verified the superiority of our proposed method. The code is released at <https://github.com/Haonan-Wang-aurora/Diff-ABFlow>.

The problem of optimally covering a given compact subset of $\mathbb{R}^N$ with a preassigned number $n$ of Euclidean metric balls has a long-standing history and it is well-recognized to be computationally hard. This article establishes a numerically viable algorithm for obtaining optimal covers of compact sets via two key contributions. The first is a foundational result establishing Lipschitz continuity of the marginal function of a certain parametric non-convex maximization problem in the optimal covering problem, and it provides the substrate for numerical gradient algorithms to be employed in this context. The second is an adaptation of a stochastically smoothed numerical gradient-based (zeroth-order) algorithm for a non-convex minimization problem, that, equipped with randomized restarts, spurs global convergence to an optimal cover. Several numerical experiments with complicated nonconvex compact sets demonstrate the excellent performance of our techniques.