Graph Neural Networks

Also known as GNN

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Latest papers 686

88 papers in the last four weeks, up 31% on the four weeks before. 0.5% of all new papers.

Jun 4, 2026

The Post-GCN Decade Revisited: Curvature-Stratified Evaluation of Relational Learning

Current evaluation practices in relational learning rely heavily on flat leaderboards that average performance across heterogeneous datasets, implicitly assuming a uniform underlying structure. We show that this assumption introduces systematic bias: it obscures geometry-dependent performance variations and can lead to misleading conclusions about model generalization. In this work, we identify intrinsic geometry as a key latent factor governing model effectiveness. We demonstrate that conventional aggregated metrics mask critical performance trade-offs that only become visible when datasets are stratified by their geometric properties. To address this issue, we introduce a curvature-stratified evaluation framework that partitions datasets into positive, negative, and near-zero curvature regimes. Our benchmark evaluates 18 representative models including Graph Convolutional Networks (GCNs), Graph Foundation Models (GFMs), and tabular learning methods across 14 datasets. We find that model rankings are highly stable within each curvature regime but shift significantly across regimes, indicating that performance is fundamentally geometry-dependent rather than universally transferable. Notably, we identify regimes where GFMs offer diminishing returns compared to geometry-aligned GNNs. Based on these findings, we propose a geometry-aware evaluation protocol that yields more reliable and interpretable comparisons than standard aggregated benchmarks. We release all code, curvature-stratified dataset splits, and evaluation tools to support reproducible and rigorous assessment of future relational learning methods. Code and datasets are provided in our project homepage: https://sirbabbage.github.io/CurvBench_HOME/.

Shuo Wang, Xiangyu Wang, Quanxin Wang +9

University of Electronic Science and Technology of China · Tsinghua University · Western University +1

Graph Neural Networks Graph Representation Learning Geometric Representation Learning Graph Foundation Models

Jun 4, 2026

AttackPathGNN: Cross-function vulnerability detection in smart contracts using state interference graphs and conjunction pooling

Existing learning-based detectors for Solidity smart-contracts reduce vulnerability detection to syntactic pattern matching within single functions, yet many of the most consequential exploits (The DAO, Cream Finance) exist not in any individual function but in the relationship between functions and in the combination of conditions that made the attack feasible. Thus, we propose AttackPathGNN, a graph neural network (GNN) that reframes detection as reasoning over explicit attack paths. Two architectural choices distinguish it from prior GNN-based detectors: (1)a State Interference Graph that links every pair of functions sharing mutable storage through typed, weighted edges and through directed reentrancy-path edges defined by an explicit five-condition predicate; (2)conjunction pooling, a differentiable AND-aggregator over eight named exploit preconditions whose log-sigmoid form causes the per-function exploit score to collapse whenever any single mitigation (a reentrancy guard, an access-control modifier or SafeMath) is in place. Across five independent training runs, AttackPathGNN attains 92.3+/-0.2% F1 on the SmartBugs Wild held-out test partition (4.3+/-0.3% false-negative rate, 90.8+/-2.5% detection rate on the independently human-labelled SmartBugs Curated benchmark), recovering 6/10 DASP10 categories at 100% on every seed and Reentrancy at 98.7+/-1.8%. Each prediction is emitted with a structured remediation report, turning each verdict into an actionable, function-level audit finding.

Gabriela Dobrita, Simona-Vasilica Oprea, Adela Bara

Bucharest University of Economic Studies, Department of Economic Informatics and Cybernetics, no.6 Piața Romană, Bucharest, 010374, Romania

Graph Neural Networks Software Vulnerability Detection

Jun 4, 2026

Q-GNN: Query-Conditioned Graph Neural Networks with Type Awareness for Knowledge Graph Completion

Knowledge Graph Completion (KGC) aims at predicting missing triplets from incomplete knowledge graphs, which is crucial for downstream applications. Recently, Graph Neural Network (GNN)-based methods have achieved remarkable success by performing message passing over query-centered local subgraphs. However, in practice, a query is jointly defined by both the entity and the relation, with both carrying information indispensable for reasoning, yet these methods rely solely on the query relation as the guiding signal, while the information inherent in the query entity is not leveraged to guide inference - the entity serves merely as a structural anchor for subgraph extraction. To this end, we incorporate query entity information into the reasoning process from two perspectives: the first is structural context, i.e., the neighboring structure and relation patterns around the entity, which is encoded by a dedicated context encoder and used to modulate messages; the second is semantic type of the entity, inferred by a large language model, which is incorporated into attention computation and final scoring to provide type-level prior constraints. Together, these two sources of information enable the reasoning process to be guided by both the query relation and the query entity. Experimental results on standard benchmarks demonstrate the effectiveness of the proposed Q-GNN.

Dongxiao He, Ruqiong Zhang, Zhizhi Yu +4

College of Intelligence and Computing, Tianjin University

Graph Neural Networks KG Completion

Jun 3, 2026

Graph Set Transformer

We introduce the Graph Set Transformer (GST), a neural network architecture for learning on sets of graphs, designed for tasks in which per-element predictions depend on set-wide context as well as local structure. Existing architectures, including DeepSets and SetTransformer, require pre-encoded graph embeddings from a separate GNN, creating a bottleneck between feature extraction and set-level contextualisation. In contrast, GST interleaves node-level feature propagation and cross-graph contextual modelling at every layer, fusing the two levels of information through a gating mechanism. We evaluate GST on a controlled synthetic suite designed to isolate set-conditional structural reasoning and on three real-data benchmarks spanning per-atom reaction-centre identification, reaction yield prediction, and image classification. Under matched parameter budgets, GST performs better than the baselines across these settings. An architectural ablation strongly suggests that the interleaving of local and set context contributes substantially to this advantage.

Jose E. Escrig Molina, Baoquan Chen, Daniel Probst

Bioinformatics Group Wageningen University Droevendaalsesteeg 6708 PB Wageningen The Netherlands · Department of Physics Technical University of Munich 85748 Garching Germany

Graph Neural Networks Graph Representation Learning Graph Transformer

Jun 3, 2026

Treat Traffic Like Trees: A Semantic-Preserving Hierarchical Graph-Based Expert Framework for Encrypted Traffic Analysis

Graph-based deep learning methods have been widely employed in encrypted traffic analysis to exploit latent correlations across different granularities. However, while complex preprocessing pipelines and sophisticated model structures often achieve strong performance, they may obscure inherent protocol semantics during representation learning. Moreover, the hierarchical structure of protocol layers and their corresponding fields, defined by protocol specifications and routinely utilized in manual traffic analysis, remains underexplored in existing learning frameworks. In this paper, we propose Protocol Tree Graph Attention with Mixture of Experts (PTGAMoE), a semantic-preserving hierarchical graph-based expert framework for encrypted traffic analysis. The field-based graph construction and expert committee design enable PTGAMoE to quantify the model's preferences for specific fields and protocols. Extensive experimental results on representative benchmark datasets under strict no-data-leakage settings demonstrate that PTGAMoE significantly outperforms state-of-the-art (SOTA) models. Furthermore, the semantic-preserving design provides interpretable insights into protocol-level feature importance and expert-level contributions, reflecting the model's decision-making logic in encrypted traffic classification tasks.

Yuantu Luo, Jun Tao, Linxiao Yu +1

School of Cyber Science and Engineering, Southeast University, Nanjing 211189, China · Purple Mountain Laboratories, Nanjing 210096, China · Engineering Research Center of Blockchain Application, Supervision and Management (Southeast University), MoE, Nanjing 211189, Jiangsu, China +1

Graph Neural Networks Encrypted Network Traffic Analysis Cybersecurity Mixture-of-Experts Models

Jun 2, 2026

Contrastive Neural Algorithmic Reasoning for Graph Coloring

Graph coloring seeks to assigns colors to a graph's nodes so that adjacent nodes receive different colors, using as few colors as possible. Here, we study approximate

k

-coloring, where the goal is to use at most

k

colors while minimizing the number of monochromatic edges. This problem is central to graph theory and has applications in areas such as scheduling and resource allocation. Recent unsupervised GNN approaches optimize each instance directly, precluding generalization across graph sizes and distributions. We instead propose a contrastive learning framework that learns transferable coloring geometry where the embeddings of same-color nodes align, while adjacent nodes' representations are pushed toward distinct directions. We analyze the resulting population objective over bounded-size graphs. For unit-norm embeddings, we show that its optima have a line-prototype structure: Representations of nodes of the same color collapse to a shared one-dimensional subspace, and edges connect orthogonal subspaces. This geometry yields stationarity conditions in the supervised setting and is preserved by projected subgradient dynamics under a balanced-coloring assumption. In an unnormalized variant, gradient descent has a max-margin bias governed by a quotient-graph hard-margin problem. Experiments on synthetic and real-world graphs show that contrastive GNN encoders generalize effectively and produce low-conflict colorings, matching and sometimes improving on greedy approaches.

Thien Le, Tianyu Zhao, Melanie Weber

Harvard University SEAS · Harvard University T.H. Chan School of Public Health

Graph Neural Networks Graph Representation Learning Neural Algorithmic Reasoning Combinatorial Optimization Graph Contrastive Learning Algorithmic Reasoning

Jun 2, 2026

Text-attributed Graph Condensation via Text Selection and Attribute Matching

Text-Attributed Graph (TAG) is an important type of graph structured data, where each node has a text description. TAG models usually train a Graph Neural Network (GNN) and language model jointly, which leads to high space and time consumption, especially on large datasets. To mitigate this, we propose TAGSAM, a condensation method that compresses TAGs while preserving training accuracy. TAGSAM comes with two key designs, i.e., subgraph text Selection and Attribute similarity Matching, which compress the text description and graph topology of TAG, respectively. For the texts, subgraph text selection selects and merges representative text chunks from multiple related text descriptions by maximizing mutual information. For the graph topology, popular condensation methods based on Matching Training Trajectories (MTT) suffer from high variance, which hinders accuracy. Our attribute similarity matching mitigates this issue by aligning stable similarity matrices. We evaluate TAGSAM against six state-of-the-art baselines, where it showcases superior performance. For the same compressed size, TAGSAM improves upon the best-performing baseline by an average of 4.9% in accuracy. Furthermore, it maintains competitive training accuracy even when the TAG is condensed to just 1% size. Our code is available at https://github.com/SundayVHan/TAGSAM

Haowei Han, Yuxiang Wang, Guojia Wan +5

School of Computer Science Wuhan University Wuhan, China · Institute for Math & AI Wuhan University Wuhan, China

Graph Neural Networks Text-Attributed Graph Learning Dataset Condensation

Jun 2, 2026

Limit Analysis of Graph Neural Networks with Wireless Conflict Graphs

Graph Neural Networks (GNNs) have emerged as a powerful tool for wireless resource allocation that leverages the underlying graph structure of communication networks. Their transferability property enables models trained on small-scale graphs to generalize to large-scale deployments with little performance deterioration, a desirable property for currently growing networks. Wireless networks are sparse regimes, where a single node is connected to a small number of other users. This work establishes theoretical results for transferability of GNNs over graphs derived from sparse Random Geometric Graphs (RGGs). In particular, we focus on conflict graphs of RGGs used to model interference among links. Our approach considers the closeness between RGGs and Deterministic Grid Graphs (DGG) to establish bounds in the performance loss when a model is transferred across scales. We validate our theoretical findings through the problem of link scheduling, demonstrating that our learned policies consistently outperform existing benchmarks at scale. Finally, we examine the impact of our theoretical assumptions on empirical performance.

Romina Garcia Camargo, Zhiyang Wang, Alejandro Ribeiro

Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA · Halıcıoğlu Data Science Institute, UCSD, La Jolla, CA

Graph Neural Networks Wireless Resource Allocation

Jun 2, 2026

Bayesian Membership Privacy for Graph Neural Networks

Existing privacy analyses for Graph Neural Networks (GNNs) largely inherit assumptions from non-graph settings, overlooking structural correlations and stochastic training-graph sampling. In particular, node-dependent priors make type-I and type-II errors alone insufficient to characterize the best membership inference test. To address this, we introduce Bayesian Membership Privacy (BMP), a sampling-aware formulation of node-level membership privacy that incorporates node-dependent priors and treats graph sampling probabilities as part of the adversary's knowledge. BMP casts membership inference as a Bayesian hypothesis test and accordingly quantifies membership privacy in terms of posterior membership probability. We explore theoretical properties of BMP in relation to the existing definitions in the literature. We further propose a practical, sampling-aware auditing mechanism to estimate the parameters of BMP as a measure of node-level privacy leakage in GNNs. We conduct experiments on benchmark graph datasets and show that BMP yields fine-grained privacy insights that are not visible through global attack accuracy alone.

Sinan Yıldırım, Megha Khosla

Faculty of Engineering and Natural Sciences Sabancı University Istanbul, Turkey · Intelligent Systems Department Delft University of Technology (TU Delft) Delft, The Netherlands

Privacy Auditing Graph Neural Networks Membership Inference Attacks Privacy-Preserving ML

Jun 2, 2026

Topology-Aware Gaussian Graph Repair for Robust Graph Neural Networks

Graph neural networks have achieved strong performance on graph-structured data, but their effectiveness depends heavily on the quality of the observed graph. In real applications, graph topology is often imperfect: noisy edges may connect unrelated nodes, while missing edges may prevent useful information from being propagated. Existing robust graph learning methods mainly address this problem by removing suspicious edges or by learning a new graph structure during training. However, edge removal alone cannot recover missing connections, and graph structure learning may introduce additional optimization complexity. In this paper, we propose Topology-Aware Gaussian Repair (TAGR), a simple graph repair framework for robust message passing in graph neural networks. Instead of learning a dense adjacency matrix, TAGR constructs a sparse feature-neighborhood graph using an adaptive Gaussian kernel and combines it with a topology-aware residual correction of the observed graph. The Gaussian repair component introduces auxiliary edges between feature-similar nodes, while the residual correction preserves and reweights the original topology according to local feature and structural consistency. The repaired graph can be used directly with standard graph neural networks without changing their architectures. Extensive experiments on benchmark citation networks show that TAGR improves the robustness of GNNs under both noisy-edge and missing-edge settings. The analysis further show that Gaussian feature-neighborhood repair provides the main robustness gain, while topology-aware residual correction improves stability when the observed graph is incomplete. These results suggest that effective graph robustness can be achieved through lightweight sparse graph repair rather than dense graph structure learning.

Anubha Goel, Juho Kanniainen

Computing Science/Financial Computing and Data Analytics Group, Tampere University, Tampere, 33720, Finland

Graph Structure Learning Graph Neural Networks

Jun 2, 2026

Multi-Modal Graph Neural Network with Transformer-Guided Adaptive Diffusion for Preclinical Alzheimer Classification

The graphical representation of the brain offers critical insights into diagnosing and prognosing neurodegenerative disease via relationships between regions of interest (ROIs). Despite recent emergence of various Graph Neural Networks (GNNs) to effectively capture the relational information, there remain inherent limitations in interpreting the brain networks. Specifically, convolutional approaches ineffectively aggregate information from distant neighborhoods, while attention-based methods exhibit deficiencies in capturing node-centric information, particularly in retaining critical characteristics from pivotal nodes. These shortcomings reveal challenges for identifying disease-specific variation from diverse features from different modalities. In this regard, we propose an integrated framework guiding diffusion process at each node by a downstream transformer where both short- and long-range properties of graphs are aggregated via diffusion-kernel and multi-head attention respectively. We demonstrate the superiority of our model by improving performance of pre-clinical Alzheimer's disease (AD) classification with various modalities. Also, our model adeptly identifies key ROIs that are closely associated with the preclinical stages of AD, marking a significant potential for early diagnosis and prevision of the disease.

Jaeyoon Sim, Minjae Lee, Guorong Wu +1

Pohang University of Science and Technology, Pohang, South Korea · University of North Carolina at Chapel Hill, Chapel Hill, USA

Graph Neural Networks Alzheimer's Disease Classification Multimodal Graph Learning Graph Transformer Graph Diffusion

Jun 2, 2026

A Graph Foundation Model with Spectral Parsing and Prototype-Guided Spatial Propagation

Graph foundation models aim to learn transferable knowledge from diverse graphs for generalization to unseen graphs and tasks. Unlike text and images, graphs lack a shared vocabulary or regular spatial grid, making cross-graph transfer challenging. This challenge comes from both feature discrepancies and, more critically, diverse graph structures. Existing GFMs mainly improve transferability by unifying feature spaces or incorporating structural tokens and vocabularies. However, existing topology-aware designs still have limitations. Structural tokens are usually discrete, while structural vocabularies often rely on predefined substructures such as trees and cycles, whose limited coverage may miss richer relational patterns across graphs. Moreover, graph signals contain both high-frequency local patterns and smoother low-frequency patterns, which require different propagation behaviors. These components are often entangled in raw graph signals, while this spectral perspective is rarely explored in existing GFMs. To address these challenges, we propose SPG, a graph foundation model with spectral parsing and prototype-guided spatial propagation. SPG applies learnable Chebyshev filters to decompose node features into multiple spectral responses, reducing the mismatch between frequency-specific graph signals and propagation behaviors. It then constructs a Gromov-Wasserstein prototype geometry to distill transferable pairwise relations beyond predefined substructures into a shared structural space. The learned prototype geometry is further projected back as a prototype-guided propagation operator. Experiments demonstrate consistent improvements in cross-domain generalization.

Ankang Yang, Jitao Zhao, Dongxiao He +3

School of Computer Science and Technology Tianjin University Tianjin, China · School of Artificial Intelligence Hebei University of Technology Tianjin, China · Department of Health Technology and Informatics Department of Data Science and Artificial Intelligence The Hong Kong Polytechnic University Kowloon, Hong Kong

Graph Neural Networks Cross-Domain Generalization Graph Foundation Models Spectral Graph Convolution

Jun 2, 2026

GFFMERGE: Efficient Merging of Graph Neural Force Fields and Beyond

Graph Neural Networks (GNNs) have revolutionized Neural Force Fields for atomistic simulations, achieving near-quantum accuracy at reduced cost, yet adapting these models to new chemical systems requires expensive retraining of foundation models. Inspired by model merging in vision and language processing, we introduce GFFMERGE, the first principled framework for closed-form model merging in GNNs. We exploit the linear structure of message-passing layers and formulate merging as a convex embedding-alignment problem with an analytical solution. Through the first systematic benchmarking of model merging for GNNs, we show that existing methods designed for vision and language catastrophically fail on force field regression, while GFFMERGE recovers performance approaching gold standard joint training. Across molecular (MD17, MD22), solid-state (LiPS20), and large-scale graph benchmarks, GFFMERGE and GNNMERGE (its generic GNN counterpart) achieve 5-27

\times

speedups while enabling modular composition of specialized models. Remarkably, our closed-form solution alone outperforms all baseline methods before fine-tuning and provides superior initialization for faster, data-efficient convergence.

Parth Verma, Parv P. Singh, Vipul Garg +3

Department of Computer Science, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, India · Yardi School of Artificial Intelligence, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, India · Department of Civil Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, India

Graph Neural Networks Machine Learning Interatomic Potentials Message Passing Neural Networks Model Merging

Jun 2, 2026

Learn When and Where to Connect: Adaptive Virtual Nodes for Dynamic Message Passing on Graphs

While Virtual Nodes (VNs) are often utilized in Message Passing Neural Networks (MPNNs) to facilitate effective message passing, existing VN-based methods have limitations, such as constraining all nodes to connect to the same number of VNs, fixing the connections before applying MPNNs, and connecting a node to a VN independently of the other nodes that connect to the same VN. We propose MAVN, an end-to-end differentiable MPNN framework that allows non-constrained connections between nodes and VNs and dynamically introduces VNs on demand in response to evolving node representations across layers. Specifically, MAVN learns to adaptively determine when (at which layer) and where (to which nodes) to introduce and connect VNs based on the relative importance of connections. From a pool of candidate VNs, MAVN selects the necessary VNs in each layer, where each selected VN is connected to a nonempty subset of nodes, guided by a dual-perspective scoring mechanism that jointly captures the nodes' preferences for VNs and the VNs' preferences for nodes. We theoretically prove that for any node-VN connectivity pattern, there exists a set of MAVN's parameters that can simulate the pattern. Experiments on nine real-world datasets demonstrate that MAVN consistently improves the performance of backbone MPNNs, achieving up to 46.5% improvement over the backbones and outperforms the baselines.

Jaejun Lee, Joyce Jiyoung Whang

School of Computing KAIST Daejeon, Republic of Korea · Department of AI Computing KAIST Daejeon, Republic of Korea

Graph Structure Learning Graph Neural Networks Graph Representation Learning Message Passing Neural Networks

Jun 1, 2026

Uncertainty-Aware Graph Neural Reconstruction of Urban Temperature Fields from Sparse Sensors under Deployment Constraints

Reconstructing spatially continuous daily temperature fields from sparse observations is important for urban climate monitoring and heat-risk analysis, but practical deployments are limited by sensor budgets and spacing constraints. This study proposes an uncertainty-aware graph neural network (GNN) framework for reconstructing daily maximum temperature fields from sparse sensors while supporting distance-constrained sensor placement and probabilistic exceedance mapping. The model predicts both the temperature field and a spatially varying predictive uncertainty field using a graph-attention-based mean-residual architecture trained with a Gaussian negative log-likelihood. Sensor placement is addressed using a Proper Orthogonal Decomposition with QR factorization (POD-QR) strategy with a 4 km minimum inter-sensor distance constraint and is compared with random feasible placement and farthest-point sampling. The framework is evaluated over a Montreal-area polygon using Daymet v4.1 daily temperature data (1 km resolution) under a strict temporal hold-out protocol (training: 2020-2023; testing: 2024). Across sensor budgets (10-40 sensors), the proposed GNN consistently outperforms inverse distance weighting and ordinary kriging in RMSE and MAE on unobserved nodes. Sensor-placement effects are most pronounced at low budgets and diminish at higher budgets, with a practical saturation regime emerging around 30 sensors under the imposed spacing constraint. Probabilistic evaluation further shows improved uncertainty calibration with increasing sensor density and a better sharpness-calibration trade-off than kriging. These results support the proposed framework as an effective tool for uncertainty-aware temperature field reconstruction and decision-oriented heat-risk mapping.

Reda Snaiki, Abdelatif Merabtine

Department of Construction Engineering, École de Technologie Supérieure, Université du Québec, Montréal, Québec, Canada

Graph Neural Networks Uncertainty Quantification

Jun 1, 2026

Structure-Aware Prediction of PROTAC-Mediated Protein Degradability via Graph Neural Networks

Proteolysis-targeting chimeras (PROTACs) can selectively degrade disease-causing proteins, yet predicting which targets are amenable to degradation remains a critical bottleneck: existing computational methods require the complete PROTAC molecular structure, information unavailable before synthesis. We present DegradoMap, a graph neural network that predicts PROTAC-mediated degradability from protein structure and E3 ligase identity alone -- the minimal information available at the target selection stage. The model encodes biophysical priors through lysine-weighted graph pooling with per-protein normalization, models protein-E3 compatibility via cross-attention, and integrates cellular context from the Cancer Dependency Map. On the PROTAC-8K benchmark (3,101 samples, 155 targets, 10 E3 ligases), DegradoMap achieves 0.646+-0.124 AUROC on target-unseen evaluation (best seed: 0.7449) and 0.811 AUROC on CRBN->VHL E3-unseen transfer, outperforming GNN and machine learning baselines. The model additionally recommends optimal E3 ligases with 74% Hit@3 accuracy. Two findings carry broader implications: E(3)-equivariant architectures underperform the simpler invariant design for this scalar prediction task, and ESM-2 embeddings improve peak performance only with careful regularization -- naive integration fails. DegradoMap provides pre-synthesis computational guidance for degradability assessment; its well-calibrated confidence scores (ECE = 0.029, target-unseen) enable practitioners to prioritize high-confidence predictions for experimental follow-up. However, the high seed variance (std = 0.124) and limited E3 coverage require ensembling for reliable deployment.

Bryan Cheng, Austin Jin

Independent Researcher USA

Graph Neural Networks Molecular Property Prediction Drug Discovery

Jun 1, 2026

Gate the Filter, Not the Message: Node-Channel Mixtures for Pre-Propagation GNNs

Pre-propagation graph neural networks (PPGNNs) push all graph-dependent computation into a preprocessing step and train only on the resulting dense hop features, which makes them highly scalable. A puzzle in this regime is that more complex hop aggregators do not reliably outperform simpler ones: on many benchmarks, a plain MLP-based aggregator matches or beats hop-attention variants. We revisit this behavior from a graph-filter perspective. Over a precomputed diffusion basis, existing PPGNNs differ mainly in how filter coefficients are shared across nodes and feature channels, rather than simply in raw aggregator capacity. MLP-based architectures learn channel-dependent filters that are largely shared across nodes, while hop-attention-based architectures learn node-dependent mixtures that are largely shared across channels. This reveals a missing regime in standard PPGNN designs: joint node- and channel-adaptive filtering under the pre-propagation computational contract. We propose FilterMoE, a mixture-of-experts PPGNN in which a small bank of learnable Chebyshev filter experts is routed jointly over nodes and channels by a 3D gating tensor. Across eleven homophilic and heterophilic benchmarks, FilterMoE outperforms strong PPGNN baselines on nine datasets and ranks first on all three large-scale benchmarks, improving the average test score by 1.53 points. These results establish joint node-channel filter routing as a robust alternative to dataset-specific hop-aggregator selection.

Zichao Yue, Zhiru Zhang

School of Electrical and Computer Engineering, Cornell University Ithaca, New York, USA

Graph Neural Networks Mixture of Experts

Jun 1, 2026

GJDNet: Robust Graph Neural Networks via Joint Disentangled Learning Against Adversarial Attacks

Graph Neural Networks (GNNs) are vulnerable to adversarial attacks, which inherently invert connectivity patterns by introducing disassortative edges in assortative graphs and assortative edges in disassortative graphs. This structural inversion creates structure-feature mismatches that disrupt neighborhood aggregation across different graph types. However, we find that existing defenses are limited, as they either treat neighborhoods as monolithic under fixed assortativity assumptions or rely on standard softmax classifiers that fail to account for perturbation-induced representation shifts. To further exploit this observation, we adopt a robustness perspective that jointly disentangles node representations and decision spaces, isolating perturbation effects while enforcing well-separated decision regions. Based on this principle, we propose Graph Joint Disentanglement Network (GJDNet), a unified framework for robust node classification across diverse graph assortativity regimes. GJDNet enhances robustness at both representation and decision levels: it employs feature-driven soft structural disentanglement with skewness-aware neighbor filtering to suppress perturbation-induced structure-feature mismatches, and introduces a Spherical Decision Boundary (SDB) to promote intra-class compactness and inter-class separation in the embedding space, thereby stabilizing decision boundaries under perturbations. Theoretical analysis provides insights into the effectiveness of the proposed disentangled representation and decision mechanisms, while extensive experiments demonstrate that GJDNet consistently achieves strong robustness across graphs with different connectivity regimes.

Canyixing Cui, Tao Wu, Xingping Xian +3

School of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing, China · School of Cyber Security and Information Law, Chongqing University of Posts and Telecommunications, Chongqing, China · Computational Communication Research Center, Beijing Normal University, Zhuhai, China +2

Disentangled Representation Learning Graph Neural Networks Adversarial Robustness Node Classification

May 31, 2026

Learning-based Directed Graph Abstraction of Combinatorial Spaces for Order-Preserving Search in Mixed-Combinatorial Nonlinear Optimization

Mixed-combinatorial nonlinear programming (MCNLP) problems arise in many engineering design and planning applications, e.g., due to categorical, component, and geometric design choices, as well as joint task and motion planning. Traditional representations of combinatorial spaces, such as integer or binary encoding, often introduce spurious relations, increase dimensionality, and require additional compatibility constraints. Instead, this paper draws on recent developments in robot planning and vehicle/network routing domains that aim to learn search heuristics over combinatorial spaces using graph neural networks (GNNs). More specifically, this paper presents a first-of-its-kind structured abstraction of the combinatorial space by learning a mapping from an undirected fully connected graph of combinations to a directed graph indicating improvement directions using an Edge Field Graph Network (EFGN). To demonstrate the utility of this new way of abstracting the combinatorial space in solving MCNLPs, we adopt a recent optimization framework that purely searches over the non-combinatorial (e.g., continuous) variables and retrieves the best-suited combination for each candidate design by using the abstraction model, akin to a recommender system. The presented direction-aware abstraction model provides a potentially more scalable and interpretable retrieval of combinations compared to the original recommendation system in that framework. For evaluation, the proposed method is integrated with a well-known particle swarm optimization and genetic algorithm solvers on three benchmark nonlinear problems with varying numbers of combinations and variables. Compared to baseline solvers using indexified combinations, the GNN-based recommender consistently achieves better mean optimum values and robustness across multiple runs.

Gishnu Madhu, Feng Liu, Souma Chowdhury

University at Buffalo Buffalo, New York, 14260

Graph Structure Learning Graph Neural Networks Nonconvex Optimization Neural Combinatorial Optimization

May 30, 2026

RADE: Random Add-Drop Edge as a Regularizer

Graph Neural Networks (GNNs) suffer from overfitting and over-squashing of long-range information. Stochastic graph augmentations (e.g., edge deletion) regularize training against overfitting but can introduce train-inference misalignment and do not improve over-squashing. In contrast, rewiring methods improve connectivity to mitigate over-squashing, but are not designed to regularize training. We propose Random Add-Drop Edge (RADE), a stochastic graph augmentation method that jointly drops and adds edges to address both overfitting and over-squashing simultaneously. RADE is provably designed to align training and inference so that random augmentations regularize training without distribution shift, while supporting long-range communication at inference. We further propose and study a mini-batch gradient-norm balancing algorithm that adapts deletion and addition rates during training, rendering RADE hyperparameter-free in practice. Experiments on node- and graph-classification benchmarks show that RADE is a strong regularizer and mitigates over-squashing. Ablations support the roles of train-inference alignment, adaptive rate selection, and the complementary effects of random edge deletion and edge addition.

Danial Saber, Amirali Salehi-Abari

Ontario Tech University, Oshawa, Ontario, Canada.

Neural Network Generalization Graph Neural Networks Graph Rewiring Data Augmentation

May 30, 2026

Graph Neural Networks for Predicting Solvability of Finite Groups

We present a Graph Neural Network (GNN) framework for the classification of finite groups according to their solvability. Using graph representations associated with finite groups, including Cayley graphs (CG), the proposed model is trained to distinguish solvable and non-solvable groups using structural graph information alone. The framework is evaluated on groups outside the training dataset in order to investigate the extent to which GNNs can learn algebraic properties arising in group theory. More broadly, the present work explores the relationship between algebraic structure and graph-based geometric representations of finite groups. The present study is intended as a proof-of-concept investigation of whether GNNs can learn algebraic properties of finite groups from graph-based representations

Tal Weissblat

Graph Neural Networks

May 29, 2026

Scaling Higher-Order Graph Learning with Maximal Clique Complexes

Graph neural networks (GNNs) are limited to modeling pairwise interactions, while higher-order models based on cell complexes achieve greater expressivity but often suffer from poor scalability. We introduce simplified and factored cellular Weisfeiler Leman tests (sCWL and fCWL), which preserve the expressivity of the CWL test while improving computational efficiency. We further introduce the maximal clique complex, enabling scalable CWNs with reduced time and memory complexity while retaining strong empirical performance. To avoid explicit clique enumeration, we propose CliqueWalk, a biased random walk that samples maximal cliques and scales linearly with graph size. These contributions yield a scalable topological learning framework for higher-order graph representation.

Antoine Vialle, Aref Einizade, Fragkiskos D. Malliaros +1

LTCI, Télécom Paris · Institut Polytechnique de Paris · Palaiseau, France +4

Graph Neural Networks Graph Representation Learning

May 29, 2026

Graph Neural Networks Are Not Continuous Across Graph Resolutions

We show that contrary to conventional wisdom in the community, graph neural networks (GNNs) are not continuous with respect to all natural modes of graph convergence. As a result, GNNs may generate substantially different latent representations for graphs that are very similar. In particular they assign vastly different latent embeddings to graphs that represent the same underlying object at different resolution scales. We trace this failure of continuity back to a structural obstruction arising from commonly used information-propagation schemes. Building on this insight we then derive a principled modification to standard GNN architectures which equips models with continuity across scales. The proposed modification enables consistent integration of distinct resolutions and reliable generalization between them. We systematically validate our theoretical findings in a wide range of numerical experiments.

Christian Koke, Yuesong Shen, Abhishek Saroha +4

AITHYRA · Munich Center for Machine Learning · Technical University of Munich, Munich +3

Neural Network Generalization Graph Neural Networks Graph Representation Learning

May 29, 2026

An Efficient and Scalable Graph Condensation with Structure-Preserving

Graph condensation (GC) is pivotal for enabling Graph Neural Networks (GNNs) deployment in resource-constrained scenarios by compressing large-scale graphs into compact synthetic counterparts. Existing GC methods commonly suffer from computational inefficiency due to coupled optimization as well as encountering poor generalization across GNN architectures. To address these challenges, this study proposes an Efficient and Scalable Graph Condensation with Structure-Preserving (SP-ESGC), which possesses a decoupled design that separates node condensation from graph structure generation. Specifically, it first employs heat kernel feature propagation to generate node representation via spectral graph theory-inspired diffusion. Further, a novel hybrid clustering strategy is designed to extracts discriminative intra-class centroids from the node representation. Finally, a pre-trained edge predictor infers transferable structural patterns from the original graph, ensuring accurate synthetic graph generation. Extensive experiments on real-world graph datasets demonstrate that the proposed SP-ESGC implementes a precise GC with significantly high computational efficiency. Moreover, SP-ESGC also generalizes well across diverse GNN architectures.

Yulin Hu, Fuyan Ou, Ye Yuan

Southwest University Chongqing, China

Graph Neural Networks

May 29, 2026

Physics-Informed Coarsening for Multigrid Graph Neural Surrogates

Learning-based surrogates for partial differential equations have recently matched the accuracy of classical solvers while achieving orders-of-magnitude speedups, predominantly in fluid settings and structured geometries. In contrast, robust surrogates for deformable solids remain underexplored, despite the presence of nonlinear elasticity, plasticity, and transient behavior that challenge standard architectures. We introduce a multigrid graph neural network for solid mechanics that couples an encoder-processor-decoder backbone with a physics-informed coarsening strategy. Instead of downsampling via geometric heuristics, our method scores nodes using a residual-based measure of local physical activity and preferentially retains regions of high strain or stress concentration, allocating multiscale capacity where it is most needed. This preserves long-range interactions through hierarchical message passing while improving stability over long rollouts. We evaluate on multiple datasets covering linear, nonlinear, and transient regimes, and observe consistent gains in accuracy and rollout stability compared to standard sampling baselines. Our results highlight the importance of physics-informed coarsening for scalable surrogate modeling in solid mechanics.

Amir Bazzi, David Cardinaux, Ramy Nemer +3

1CEMEF, Mines Paris – PSL, Sophia Antipolis, France · 2Aubert et Duval, France · 3Transvalor, Mougins, France.

Graph Neural Networks Neural PDE Solvers Structural Mechanics PDE Surrogate Modeling Physics-Informed ML

May 29, 2026

A Topological Characterization of Graph Neural Networks via Stochastic Block Model Embeddings on the n-Sphere

We propose a topological framework for comparing trained Graph Neural Networks (GNNs) by mapping the Stochastic Block Models (SBMs) induced on the graphon-signal space of a Message Passing Neural Network (MPNN) onto the unit

n

-sphere

\sphere^{n-1}\subset\R^n

. The construction rests on three classical pillars: the compactness of the cut-distance graphon space

(\Wo,\cutdist)

\citep{lovasz2006limits,lovasz2012large}, the Frieze--Kannan weak regularity lemma together with its graphon-signal extension due to \citet{levie2023graphon}, and the Lipschitz continuity of MPNNs with respect to the cut-distance. We show that, for any prescribed tolerance

\varepsilon>0

, a trained MPNN

Φ

acting on a sufficiently large graph factors (up to

\varepsilon

) through a step-graphon-signal of bounded complexity, and we construct an explicit measure-preserving map

Ψ_n\colon[0,1]\to\sphere^{n-1}

that places the SBM regions on disjoint spherical caps. This produces a problem-agnostic, low-dimensional ``fingerprint'' of a trained GNN that is amenable to visual inspection and to nearest-neighbour search across model zoos, enabling transfer-learning candidate retrieval without retraining. We discuss the obstruction posed by concentration of measure in high dimension -- a phenomenon directly relevant to LLM-scale embeddings. We close with five concrete future research directions: hyperbolic and Grassmannian alternatives to the spherical model, Gromov--Wasserstein distances on graphon-signals as an isometry-free alternative to the

n

-sphere map, an information-geometric (Fisher) reformulation of the SBM manifold, persistent-homology fingerprints of layer-wise embedding clouds, and a spectral-distance baseline derived from the graphon eigendecomposition.

Gopal Anantharaman

KnotTheory.ai Inc. · Dept. of Mathematics, Emporia State University

Graph Neural Networks Neural Representation Geometry Topological Mapping

May 29, 2026

AbstainGNN: Teaching Graph Neural Networks to Abstain for Graph Classification

Graph classification is a core task in graph data mining with widespread real-world applications. Recent advances in graph neural networks (GNNs) have led to substantial performance improvements for graph classification. However, existing GNNs are typically forced to make predictions even under high uncertainty or unknown conditions, resulting in unreliable decisions that can severely impact downstream tasks, particularly in safety-critical scenarios. To address this critical limitation, we propose AbstainGNN, a novel and theory-driven framework for graph classification with abstention, which enables GNNs to reject uncertain predictions instead of producing incorrect decisions. Specifically, AbstainGNN explicitly models both the predictive function and the abstention function, allowing for effective utilization of graph structural information. Moreover, unlike existing heuristic abstention methods, we theoretically characterize the trade-off between classification errors and rejection costs from a PAC-Bayesian generalization perspective, and derive a unified learning objective for model optimization. Guided by this theoretical insight, we further develop an efficient two-stage training strategy consisting of predictive function warm-start and abstention function calibration. Extensive experiments on five benchmark datasets show that AbstainGNN outperforms existing abstention methods, achieving superior classification performance under the same rejection rates.

Xixun Lin, Zhiheng Zhou, Zhengyin Zhang +9

Institute of Information Engineering, Chinese Academy of Sciences · School of Mathematics and Statistics, Shandong University · China University of Mining and Technology-Beijing +6

Graph Neural Networks Selective Prediction Graph Classification

May 28, 2026

Can Subgraph Explanations Be Weaponized to Steal Graph Neural Networks?

Graph Machine Learning as a Service (GMLaaS) platforms increasingly implement explainability interfaces to meet regulatory transparency requirements. However, this transparency creates exploitable vulnerabilities for model extraction attacks. We present the first model extraction attack specifically designed for graph classification under strict black-box constraints where the attacker observes only discrete class labels and binary explanation masks (no probability scores, gradients, or confidence values). Our method (1) uses model explanation outputs to guide Monte Carlo edge sensitivity estimation toward decision boundaries, with Hoeffding concentration guarantees on estimation accuracy and (2) exploits explanation subgraphs to efficiently narrow the boundary search space. Extensive experiments on benchmark graph datasets across multiple domains demonstrate our method's superiority over comparable baselines. These findings demonstrate that such explainability interfaces create exploitable attack surfaces, informing both defensive mechanisms and policy frameworks for explainable AI mandates. The implementation code is provided in https://github.com/LabRAI/XSTEAL/.

Ojas Nimase, Jiate Li, Yue Zhao +1

University of Southern California Los Angeles, USA · Florida State University Tallahassee, USA

Graph Neural Networks Model Extraction Attacks Graph Classification GNN Explainability

May 28, 2026

SAHG: Sector-Anisotropic Hyperbolic Graph Model for Social Bot Detection

LLM-driven social bots can generate fluent, human-like text, reducing the discriminative advantage of content-based detection alone. However, coordinated campaigns still leave relational patterns -- interactions, behavioral similarity, shared neighborhoods, community positions, and coordinated activity -- that graph-based methods can exploit. Existing graph detectors face two challenges when exploiting such evidence. First, Euclidean GNNs distort hierarchical and scale-free social graphs; while hyperbolic geometry addresses this volume-growth mismatch, fixed-curvature models still assign uniform geometric resolution to structural directions with different densities and separation needs. Second, relational evidence is not always reliable: sophisticated bots forge heterophilic connections with genuine users, causing neighborhood aggregation to mix bot and human signals and dilute account-level evidence. We propose SAHG (Sector-Anisotropic Hyperbolic Graph), addressing both challenges. SAHG learns a direction-dependent curvature field

γ(u)

that adapts geometric resolution across structural directions, and uses sector prototypes to convert angular concentration and alignment into classifier-readable features. To prevent contaminated aggregation from overwhelming account-level evidence, SAHG encodes per-account features and graph-neighborhood representations in two independent SAH channels, fusing them only at the classifier. Experiments on Fox8-23, BotSim-24, and MGTAB show that SAHG achieves the highest accuracy and F1 on all three benchmarks, outperforming feature-based, graph-based, LLM-based, and isotropic hyperbolic baselines. Ablation and geometric analyses confirm the effectiveness of the anisotropic geometry and dual-channel design.

Hanning Lu, Yingguang Yang, Jinwei Su +8

University of Leeds · University of Science and Technology of China · 3South China Normal University +6

Social Media Analysis Graph Neural Networks Hyperbolic Representation Learning

May 28, 2026

Gated Graph Attention Networks with Learnable Temperature

Graph attention networks learn neighbor importance through data-dependent coefficients, but standard layers lack explicit control over unreliable feature dimensions and use fixed sharpness of attention coefficient distributions. This paper proposes gated graph attention and learnable temperature for common graph attention mechanisms. Gated graph attention filters feature or message responses to reduce the influence of unreliable dimensions, while learnable temperature dynamically adjusts the sharpness of the attention coefficient distribution. Experiments on homogeneous and heterophilic heterogeneous benchmarks show that the proposed variants consistently improve the corresponding graph attention backbones, and controlled noise studies further verify their behavior under feature perturbations. Theoretical analysis explains these results by showing that gating improves robustness when only part of the feature coordinates are reliable, while temperature is beneficial when global noise weakens the discriminability of node features.

Zhongtian Ma, Hao Wu, Yexin Zhang +2

School of Cybersecurity, Northwestern Polytechnical University, Xi’an 710072, China · Shanghai Artificial Intelligence Laboratory, Shanghai 200232, China

Graph Attention Networks Graph Neural Networks Gated Attention Attention Mechanisms