NeurIPS 2025 Papers

The non-Euclidean geometry inherent in graph structures fundamentally impedes cross-graph knowledge transfer. Drawing inspiration from texture transfer in computer vision, we pioneer topological primitives as transferable semantic units for graph structural knowledge. To address three critical barriers - the absence of specialized benchmarks, aligned semantic representations, and systematic transfer methodologies - we present G²SN-Transfer, a unified framework comprising: (i) TopoGraph-Mapping that transforms non-Euclidean graphs into transferable sequences via topological primitive distribution dictionaries; (ii) G²SN, a dual-stream architecture learning text-topology aligned representations through contrastive alignment; and (iii) AdaCross-Transfer, a data-adaptive knowledge transfer mechanism leveraging cross-attention for both full-parameter and parameter-frozen scenarios. Particularly, G²SN is a dual-stream sequence network driven by ordinary differential equations, and our theoretical analysis establishes the convergence guarantee of G²SN. We construct STA-18, the first large-scale benchmark with aligned topological primitive-text pairs across 18 diverse graph datasets. Comprehensive evaluations demonstrate that G²SN achieves state-of-the-art performance on four structural learning tasks (average 3.2\% F1-score improvement), while our transfer method yields consistent enhancements across 13 downstream tasks (5.2\% average gains) including 10 large-scale graph datasets. The datasets and code are available at https://anonymous.4open.science/r/UGSKT-C10E/.

Graph Neural Networks (GNNs) have achieved strong performance across a range of graph representation learning tasks, yet their adversarial robustness in graph classification remains underexplored compared to node classification. While most existing defenses focus on the message-passing component, this work investigates the overlooked role of pooling operations in shaping robustness. We present a theoretical analysis of standard flat pooling methods (sum, average and max), deriving upper bounds on their adversarial risk and identifying their vulnerabilities under different attack scenarios and graph structures. Motivated by these insights, we propose Robust Singular Pooling (RS-Pool), a novel pooling strategy that leverages the dominant singular vector of the node embedding matrix to construct a robust graph-level representation. We theoretically investigate the robustness of RS-Pool and interpret the resulting bound leading to improved understanding of our proposed pooling operator. While our analysis centers on Graph Convolutional Networks (GCNs), RS-Pool is model-agnostic and can be implemented efficiently via power iteration. Empirical results on real-world benchmarks show that RS-Pool provides better robustness than the considered pooling methods when subject to state-of-the-art adversarial attacks while maintaining competitive clean accuracy.

Tubular-like system shape analysis is quite difficult in geometry and topology, while it is widely used in plants and organs analysis in practice. However, traditional discrete representations such as voxels and point clouds often require substantial storage and may lead to the loss of fine-grained geometric and topological details. To address these challenges, we propose SE(3)-BBSCformerGCN, a novel framework for learning shape-aware representations from continuous tubular topological manifolds with equivariance to rotations and translations. Our approach leverages Ball B-Spline Curve (BBSC) to define tubular manifolds and its functional space. We provide a formal mathematical definition and analysis of the resulting manifolds and the BBSC functional space, and incorporate an equivariant mapping that preserves geometric and topological stability. Compared to the point cloud and voxel based representations, our manifold-based formulation significantly reduces data complexity while preserving geometric attributes together with topological features. We validate our method on the branch classification task for Circle of Willis (CoW) on the TopCoW 2024 dataset and the clinical dataset. Our method consistently outperforms voxel and point cloud based baselines in terms of classification performance, generalization ability, convergence speed, and robustness to overfitting.

Graph Neural Networks (GNNs) often encounter significant performance degradation under distribution shifts between training and test data, hindering their applicability in real-world scenarios. Recent studies have proposed various methods to address the out-of-distribution (OOD) generalization challenge, with many methods in the graph domain focusing on directly identifying an invariant subgraph that is predictive of the target label. However, we argue that identifying the edges from the invariant subgraph directly is challenging and error-prone, especially when some spurious edges exhibit strong correlations with the targets. In this paper, we propose $\texttt{PrunE}$, the first pruning-based graph OOD method that eliminates spurious edges to improve OOD generalizability. By pruning spurious edges, $\texttt{PrunE}$ retains the invariant subgraph more comprehensively, which is critical for OOD generalization. Specifically, $\texttt{PrunE}$ employs two regularization terms to prune spurious edges: 1) _graph size constraint_ to exclude uninformative spurious edges, and 2) _$\epsilon$-probability alignment_ to further suppress the occurrence of spurious edges. Through theoretical analysis and extensive experiments, we show that $\texttt{PrunE}$ achieves superior OOD performance and outperforms previous state-of-the-art methods significantly.

Graph Neural Networks (GNNs) are increasingly deployed in mission-critical tasks, yet they often encounter inputs that lie outside their training distribution, leading to unreliable or overconfident predictions. To address this limitation, we present RAGNOR (Robust Aggregation Graph Norm for Outlier Recognition), a post-hoc approach that leverages embedding norms for robust out-of-distribution (OOD) detection on both node-level and graph-level tasks. Unlike previous methods designed primarily for image domains, RAGNOR directly tackles the relational challenges intrinsic to graphs: local contamination by anomalous neighbors, disparate norm scales across classes or roles, and insufficient references for boundary or low-degree nodes. By combining global Z-score normalization, median-based local aggregation, and multi-hop blending, RAGNOR effectively refines raw norm signals into robust OOD scores while incurring minimal overhead and requiring no retraining of the original GNN. Experimental evaluations on multiple benchmarks demonstrate that RAGNOR not only achieves competitive or superior detection performance compared to alternative techniques, but also provides an intuitive, modular design that can be readily integrated into existing graph pipelines.

Brain disorders have been consistently associated with abnormalities in specific brain regions or neural circuits. Identifying key brain regional activities and functional connectivity patterns is essential for discovering more precise neurobiological biomarkers. However, previous studies have primarily emphasized alterations in functional connectivity while overlooking abnormal neuronal population activity within brain regions. To bridge this gap, we propose a novel Local-Global Coupling Spiking Graph Transformer (LGC-SGT) that jointly models both inter-regional connectivity differences and deviations in neuronal population firing rates within brain regions, enabling a dual-perspective neuropathological analysis. The global pathway leverages spike-based computation in LGC-SGT to model biologically plausible aberrant neural firing dynamics, while the local pathway adaptively captures abnormal graph-based representations of brain connectivity learned by local plasticity in the liquid state machine module. Furthermore, we design a shortcut-enhanced output strategy in LGC-SGT with the hybrid loss function to suppress outlier interference caused by inter-individual and inter-center variability, enabling a more robust decision boundary. Extensive experiments on three brain disorder datasets demonstrate that our model consistently outperforms state-of-the-art graph methods in brain disorder diagnosis. Moreover, it facilitates the extraction of interpretable neurobiological biomarkers by jointly analyzing regional neural activity and functional connectivity, offering a more comprehensive framework for brain disorder understanding and diagnosis.

Geometric graph neural networks (GNNs) that respect E(3) symmetries have achieved strong performance on small molecule modeling, but they face scalability and expressiveness challenges when applied to large biomolecules such as RNA and proteins. These systems require models that can simultaneously capture fine-grained atomic interactions, long-range dependencies across spatially distant components, and biologically relevant hierarchical structure—such as atoms forming residues, which in turn form higher-order domains. Existing geometric GNNs, which typically operate exclusively in either Euclidean or Spherical Harmonics space, are limited in their ability to capture both the fine-scale atomic details and the long-range, symmetry-aware dependencies required for modeling the multi-scale structure of large biomolecules. We introduce DualEquiNet, a Dual-Space Hierarchical Equivariant Network that constructs complementary representations in both Euclidean and Spherical Harmonics spaces to capture local geometry and global symmetry-aware features. DualEquiNet employs bidirectional cross-space message passing and a novel Cross-Space Interaction Pooling mechanism to hierarchically aggregate atomic features into biologically meaningful units, such as residues, enabling efficient and expressive multi-scale modeling for large biomolecular systems. DualEquiNet achieves state-of-the-art performance on multiple existing benchmarks for RNA property prediction and protein modeling, and outperforms prior methods on two newly introduced 3D structural benchmarks demonstrating its broad effectiveness across a range of large biomolecule modeling tasks.

Graph-based recommender systems have achieved remarkable effectiveness by modeling high-order interactions between users and items. However, such approaches are significantly undermined by popularity bias, which distorts the interaction graph’s structure—referred to as topology bias. This leads to overrepresentation of popular items, thereby reinforcing biases and fairness issues through the user-system feedback loop. Despite attempts to study this effect, most prior work focuses on the embedding or gradient level bias, overlooking how topology bias fundamentally distorts the message passing process itself. We bridge this gap by providing an empirical and theoretical analysis from a Dirichlet energy perspective, revealing that graph message passing inherently amplifies topology bias and consistently benefits highly connected nodes. To address these limitations, we propose Test-time Simplicial Propagation (TSP), which extends message passing to higher-order simplicial complexes. By incorporating richer structures beyond pairwise connections, TSP mitigates harmful topology bias and substantially improves the representation and recommendation of long-tail items during inference. Extensive experiments across five real-world datasets demonstrate the superiority of our approach in mitigating topology bias and enhancing recommendation quality. The implementation code is available at https://github.com/sotaagi/TSP.

Deep neural networks (DNNs) have been shown to memorize their training data, but similar analyses for graph neural networks (GNNs) remain under-explored. We introduce NCMemo (Node Classification Memorization), the first framework to quantify label memorization in semi-supervised node classification. We establish an inverse relationship between memorization and graph homophily, i.e the tendency of connected nodes to share labels or features. Lower homophily significantly increases memorization, indicating that GNNs rely on label memorization when learning less homophilic graphs. We then analyze GNN training dynamics and find that increased memorization in low-homophily graphs is tightly coupled to GNNs' implicit bias toward using graph structure. When structure is less informative, models instead memorize node labels to minimize training loss. Finally, we show that nodes with higher label inconsistency in their feature-space neighborhood are more prone to memorization. Based on these insights, we investigate graph rewiring as a mitigation strategy. Our results show that rewiring reduces memorization without harming model performance, while also lowering the privacy risk for previously memorized data points. Thus, our work advances understanding of GNN learning and supports more privacy-preserving GNN deployment.

Cutting planes (cuts) are essential for solving mixed-integer linear programming (MILP) problems, as they tighten the feasible solution space and accelerate the solving process. Modern MILP solvers offer diverse cutting plane separators to generate cuts, enabling users to leverage their potential complementary strengths to tackle problems with different structures. Recent machine learning approaches learn to configure separators based on problem-specific features, selecting effective separators and deactivating ineffective ones to save unnecessary computing time. However, they ignore the dynamics of separator efficacy at different stages of cut generation and struggle to adapt the configurations for the evolving problems after multiple rounds of cut generation. To address this challenge, we propose a novel **dyn**amic **sep**arator configuration (**DynSep**) method that models separator configuration in different rounds as a reinforcement learning task, making decisions based on an incremental triplet graph updated by iteratively added cuts. Specifically, we tokenize the incremental subgraphs and utilize a decoder-only Transformer as our policy to autoregressively predict when to halt separation and which separators to activate at each round. Evaluated on synthetic and large-scale real-world MILP problems, DynSep speeds up average solving time by 64% on easy and medium datasets, and reduces primal-dual gap integral within the given time limit by 16% on hard datasets. Moreover, experiments demonstrate that DynSep well generalizes to MILP instances of significantly larger sizes than those seen during training.

Current semi-supervised graph anomaly detection (GAD) methods utilizes a small set of labeled normal nodes to identify abnormal nodes from a large set of unlabeled nodes in a graph. These methods posit that 1) normal nodes share a similar level of homophily and 2) the labeled normal nodes can well represent the homophily patterns in the entire normal class. However, this assumption often does not hold well since normal nodes in a graph can exhibit diverse homophily in real-world GAD datasets. In this paper, we propose RHO, namely Robust Homophily Learning, to adaptively learn such homophily patterns. RHO consists of two novel modules, adaptive frequency response filters (AdaFreq) and graph normality alignment (GNA). AdaFreq learns a set of adaptive spectral filters that capture different frequency components of the labeled normal nodes with varying homophily in the channel-wise and cross-channel views of node attributes. GNA is introduced to enforce consistency between the channel-wise and cross-channel homophily representations to robustify the normality learned by the filters in the two views. Experiments on eight real-world GAD datasets show that RHO can effectively learn varying, often under-represented, homophily in the small labeled node set and substantially outperforms state-of-the-art competing methods. Code is available at \url{https://github.com/mala-lab/RHO}.

Graph Neural Networks learn on graph-structured data by iteratively aggregating local neighborhood information. While this local message passing paradigm imparts a powerful inductive bias and exploits graph sparsity, it also yields three key challenges: (i) oversquashing of long-range information, (ii) oversmoothing of node representations, and (iii) limited expressive power. In this work we inject randomized global embeddings of node features, which we term Sketched Random Features, into standard GNNs, enabling them to efficiently capture long-range dependencies. The embeddings are unique, distance-sensitive, and topology-agnostic---properties which we analytically and empirically show alleviate the aforementioned limitations when injected into GNNs. Experimental results on real-world graph learning tasks confirm that this strategy consistently improves performance over baseline GNNs, offering both a standalone solution and a complementary enhancement to existing techniques such as graph positional encodings.

Graph Convolutional Networks (GCNs) based on linear aggregation have been widely applied across various domains due to their exceptional performance. To enhance performance, these networks often utilize the graph Laplacian norm to suppress the propagation of information from first-order neighbors. However, this approach may dilute valuable interaction information and make the model slowly learn sparse interaction relationships from neighbors, which increases training time and negatively affects performance. To address these issues, we introduce BoostGCN, a novel linear GCN model that focuses on amplifying significant interactions with first-order neighbors, which enables the model to accurately and quickly capture significant relationships. BoostGCN has relatively fixed parameters, making it user-friendly. Experiments on four real-world datasets demonstrate that BoostGCN outperforms existing state-of-the-art GCN models in both performance and efficiency.

Graph coarsening aims to diminish the size of a graph to lighten its memory footprint, and has numerous applications in graph signal processing and machine learning. It is usually defined using a reduction matrix and a lifting matrix, which, respectively, allows to project a graph signal from the original graph to the coarsened one and back. This results in a loss of information measured by the so-called Restricted Spectral Approximation (RSA). Most coarsening frameworks impose a fixed relationship between the reduction and lifting matrices, generally as pseudo-inverses of each other, and seek to define a coarsening that minimizes the RSA. In this paper, we remark that the roles of these two matrices are not entirely symmetric: indeed, putting constraints on the *lifting matrix alone* ensures the existence of important objects such as the coarsened graph's adjacency matrix or Laplacian. In light of this, in this paper, we introduce a more general notion of reduction matrix, that is *not* necessarily the pseudo-inverse of the lifting matrix. We establish a taxonomy of ``admissible'' families of reduction matrices, discuss the different properties that they must satisfy and whether they admit a closed-form description or not. We show that, for a *fixed* coarsening represented by a fixed lifting matrix, the RSA can be *further* reduced simply by modifying the reduction matrix. We explore different examples, including some based on a constrained optimization process of the RSA. Since this criterion has also been linked to the performance of Graph Neural Networks, we also illustrate the impact of this choices on different node classification tasks on coarsened graphs.

We consider the graph alignment problem, wherein the objective is to find a vertex correspondence between two graphs that maximizes the edge overlap. The graph alignment problem is an instance of the quadratic assignment problem (QAP), known to be NP-hard in the worst case even to approximately solve. In this paper, we analyze Birkhoff relaxation, a tight convex relaxation of QAP, and present theoretical guarantees on its performance when the inputs follow the Gaussian Wigner Model. More specifically, the weighted adjacency matrices are correlated Gaussian Orthogonal Ensemble with correlation $1/\sqrt{1+\sigma^2}$. Denote the optimal solutions of the QAP and Birkhoff relaxation by $\Pi^\star$ and $X^\star$ respectively. We show that $\|X^\star-\Pi^\star\|_F^2 = o(n)$ when $\sigma = o(n^{-1})$ and $\|X^\star-\Pi^\star\|_F^2 = \Omega(n)$ when $\sigma = \Omega(n^{-0.5})$. Thus, the optimal solution $X^\star$ transitions from a small perturbation of $\Pi^\star$ for small $\sigma$ to being well separated from $\Pi^\star$ as $\sigma$ becomes larger than $n^{-0.5}$. This result allows us to guarantee that simple rounding procedures on $X^\star$ align $1-o(1)$ fraction of vertices correctly whenever $\sigma = o(n^{-1})$. This condition on $\sigma$ to ensure the success of the Birkhoff relaxation is state-of-the-art.

Traditional recommender systems have relied heavily on positive feedback for learning user preferences, while the abundance of negative feedback in real-world scenarios remains underutilized. To address this limitation, recent years have witnessed increasing attention on leveraging negative feedback in recommender systems to enhance recommendation performance. However, existing methods face three major challenges: limited model compatibility, ineffective information exchange, and computational inefficiency. To overcome these challenges, we propose a model-agnostic Signed Dual-Channel Graph Contrastive Learning (SDCGCL) framework that can be seamlessly integrated with existing graph contrastive learning methods. The framework features three key components: (1) a Dual-Channel Graph Embedding that separately processes positive and negative graphs, (2) a Cross-Channel Distribution Calibration mechanism to maintain structural consistency, and (3) an Adaptive Prediction Strategy that effectively combines signals from both channels. Building upon this framework, we further propose a Dual-channel Feedback Fusion (DualFuse) model and develop a two-stage optimization strategy to ensure efficient training. Extensive experiments on four public datasets demonstrate that our approach consistently outperforms state-of-the-art baselines by substantial margins while exhibiting minimal computational complexity.

Deep graph clustering (DGC) aims to partition graph nodes into distinct clusters in an unsupervised manner. Despite rapid advancements in this field, DGC remains inherently challenging due to the absence of ground-truth, which complicates the design of effective algorithms and impedes the establishment of standardized benchmarks. The lack of unified datasets, evaluation protocols, and metrics further exacerbates these challenges, making it difficult to systematically assess and compare DGC methods. To address these limitations, we introduce $\texttt{DGCBench}$, the first comprehensive and unified benchmark for DGC methods. It evaluates 12 state-of-the-art DGC methods across 12 datasets from diverse domains and scales, spanning 6 critical dimensions: $\textbf{discriminability}$, $\textbf{effectiveness}$, $\textbf{scalability}$, $\textbf{efficiency}$, $\textbf{stability}$, and $\textbf{robustness}$. Additionally, we develop $\texttt{PyDGC}$, an open-source Python library that standardizes the DGC training and evaluation paradigm. Through systematic experiments, we reveal persistent limitations in existing methods, specifically regarding the homophily bottleneck, training instability, vulnerability to perturbations, efficiency plateau, scalability challenges, and poor discriminability, thereby offering actionable insights for future research. We hope that $\texttt{DGCBench}$, $\texttt{PyDGC}$, and our analyses will collectively accelerate the progress in the DGC community. The code is available at https://github.com/Marigoldwu/PyDGC.

Graph attention has demonstrated superior performance in graph learning tasks. However, learning from global interactions can be challenging due to the large number of nodes. In this paper, we discover a new phenomenon termed over-aggregating. Over-aggregating arises when a large volume of messages is aggregated into a single node with less discrimination, leading to the dilution of the key messages and potential information loss. To address this, we propose Wideformer, a plug-and-play method for graph attention. Wideformer divides the aggregation of all nodes into parallel processes and guides the model to focus on specific subsets of these processes. The division can limit the input volume per aggregation, avoiding message dilution and reducing information loss. The guiding step sorts and weights the aggregation outputs, prioritizing the informative messages. Evaluations show that Wideformer can effectively mitigate over-aggregating. As a result, the backbone methods can focus on the informative messages, achieving superior performance compared to baseline methods.

Graph Neural Networks (GNNs) have shown significant success for graph-based tasks. Motivated by the prevalence of large datasets in real-world applications, pooling layers are crucial components of GNNs. By reducing the size of input graphs, pooling enables faster training and potentially better generalisation. However, existing pooling operations often optimise for the learning task at the expense of discarding fundamental graph structures, thus reducing interpretability. This leads to unreliable performance across dataset types, downstream tasks and pooling ratios. Addressing these concerns, we propose novel graph pooling layers for structure-aware pooling via edge collapses. Our methods leverage diffusion geometry and iteratively reduce a graph’s size while preserving both its metric structure and its structural diversity. We guide pooling using *magnitude*, an isometry-invariant diversity measure, which permits us to control the fidelity of the pooling process. Further, we use the *spread* of a metric space as a faster and more stable alternative ensuring computational efficiency. Empirical results demonstrate that our methods (i) achieve top performance compared to alternative pooling layers across a range of diverse graph classification tasks, (ii) preserve key spectral properties of the input graphs, and (iii) retain high accuracy across varying pooling ratios.