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.

May 27, 2026

A Generalized Tikhonov Layer for Interpretable-by-design Graph Neural Networks

We propose the Tikhonov layer, a graph neural network layer that is interpretable by design: once trained, its learned parameters directly reveal which node features and which aspects of the graph topology were leveraged for prediction. In practice, the layer's propagation matrix takes the closed-form

R = (p(L)+Q)^{-1} Q

, where

L

is the normalized graph Laplacian,

Q = diag(q_1,...,q_n)

a learnable diagonal matrix of positive node-importance scores, and

p(\cdot)

a learnable polynomial. For any input feature

x

, the layer output

Rx

is the exact minimizer of a generalized graph Tikhonov problem that trades off node-level data fidelity against a topology-driven regularization penalty. The learned pair

\{\{q_i\},p\}

constitutes a built-in explanation: large

q_i

indicates that node

i

's own features drive the prediction, while small

q_i

signals reliance on the local graph topology; the shape of

p

reveals whether homophily, heterophily, or a band-pass response is exploited. Expressivity is preserved by routing complexity through a dedicated, arbitrarily deep Q-network that produces the importance scores, while the Tikhonov layer itself remains transparent. We prove that distinct node-importance matrices yield distinct propagation operators, structurally coupling the explanation to the computation. Additionally, the Tikhonov layer provides, in a single layer, a global receptive field, mitigating both oversmoothing and oversquashing. Experiments on standard graph classification benchmarks confirm that the model matches (and sometimes outperforms) opaque baselines while producing interpretable and faithful explanations.

Nicolas Tremblay, Benjamin Ricaud, Filippo Maria Bianchi

UiT the Arctic University of Norway · & CNRS, France · & NORCE Norwegian Research Centre

Graph Neural Networks Graph Classification GNN Explainability

May 27, 2026

Let Relations Speak: An End-to-End LLM-GNN Soft Prompt Framework for Fraud Detection

In recent years, Large Language Models (LLMs) have shown great capability in processing graph tasks such as fraud detection. However, most existing methods rely heavily on rich text attributes, which poses difficulties for this domain due to the lack of textual data. Although some pioneering methods attempt to overcome it, their textualization of graph structures via hard prompts easily leads to feature distortion. Additionally, fraud detection often exhibits multi-relational complexity, where current methods struggle to capture this deep semantic information. To address these challenges, we propose LLM-GNN Soft Prompt Framework (LGSPF). Specifically, LGSPF bridges the graph structure and semantic space using soft prompt to eliminate reliance on text. We further introduce a parallel Graph Neural Network (GNN) encoder to translate multi-relational topologies into graph tokens for fine-grained LLM fraud comprehension. Through end-to-end optimization, LGSPF enhances deep semantic alignment between LLM and GNN. Experiments across diverse fraud detection benchmarks demonstrate our method achieves state-of-the-art performance. Moreover, we further validate the contribution of LGSPF on enhancing the semantic interpretability of fraud behaviors.

Zhixing Zuo, Huilin He, Jiasheng Wu +1

School of Computer Science and Technology, Tongji University

Graph Neural Networks Graph Representation Learning Financial Fraud Detection Prompt Tuning LLMs for Graph Learning

May 27, 2026

From Detection to Mechanism: Cross-Attention Graph Neural Networks Enable Drug-Drug Interaction Type Prediction An Ablation Study with Acetylsalicylic Acid Validation

Predicting whether two drugs interact (binary detection) is a substantially dif- ferent task from predicting the mechanism type of that interaction (multi-class classification). This study presents a systematic ablation study of three Graph Neural Network (GNN) architectures for drug-drug interaction (DDI) prediction on a publicly available benchmark dataset comprising 38,337 positive pairs across 86 interaction types. Three architectures are compared under identical training conditions (n = 61,339 pairs): a siamese dual Message Passing Neural Network (MPNN) with concatenation (Concat), a dual MPNN with four-head cross-attention (CrossAtt), and a ternary MPNN incorporating an interaction graph (Ternary). CrossAtt improves multi-class F1-macro by +0.186 absolute (+45%) over Concat, while improving binary AUC by only +0.012 (+1.3%) - confirming that atom-level inter-molecular communication specifically enables mechanism-type classification. The ternary architecture underperforms despite equivalent training data, with its failure consistent with a training instability hypothesis. Validation on ten acetylsali- cylic acid (ASA) drug pairs, held out prior to training, demonstrates 10/10 correct DDI-type predictions for CrossAtt versus 0/10 for Ternary. Two consistent failure cases are identified across all architectures, linking to structural limits established in a companion toxicity study.

Juergen Dietrich

Graph Neural Networks Cross-Attention Molecular Representation Learning

May 26, 2026

Sampling Triangulations and Calabi-Yau Threefolds with Autoregressive GNNs

We introduce

dualGNN', an autoregressive message-passing GNN for sampling fine, regular triangulations of lattice polytopes. dualGNN operates on a generalization of the dual graph of a triangulation, with edges labeled by

signed circuits' -- combinatorial invariants from the theory of oriented matroids. We show that these circuits are necessary and sufficient to determine a triangulation's regularity from the graph, provided certain magnitude information is retained. The model is independent of the polytope's point count and invariant under its orientation-preserving symmetries (

\mathrm{SL}(d,\mathbb{Z}) \ltimes \mathbb{Z}^d

), and our masking procedure further guarantees that every rollout produces a fine triangulation (in 2D). On unseen polygons with

N_\mathrm{pts} \leq 40

, dualGNN is the only sampler we tested that is consistent with uniform sampling across all our diagnostics (KL divergence from uniformity, collision counts, and sample autocorrelation). The model is small (

\sim92

k parameters) and trains in

\sim7.5

hours on a single consumer GPU. We apply dualGNN to string theory, sampling Calabi-Yau threefolds uniformly at

h^{1,1}=86

; we also sample CYs at

h^{1,1}=128

, observing no deviations from uniformity, but our diagnostics are weaker here. Code, training scripts, and pretrained models are available at https://github.com/natemacfadden/dualGNN (pip install dualgnn), and dualGNN is integrated into CYTools.

Nate MacFadden

Department of Physics, Cornell University, Ithaca, NY 14853 USA

Graph Neural Networks Generative Modeling

May 26, 2026

Outage Detection in Self-Healing Smart Grids Using Reinforcement Learning with Spectral Graph Neural Networks

Self-healing smart grids can quickly adjust their network configuration during outages to minimize power disruptions. During an outage, several actions can be taken, such as network reconfiguration through switching operations and emergency load shedding. However, traditional machine learning methods for outage mitigation are not well suited for smart grids due to their slow response time and high computational cost. To address these challenges, recent studies have explored reinforcement learning to automatically perform network reconfiguration. In these approaches, the control policy is typically modeled using a graph neural network (GNN). However, conventional GNNs operate in the spatial domain and may fail to capture important relationships in the frequency domain. Frequency-domain information is particularly useful for modeling global structural patterns and system-wide interactions in power networks. In this paper, we propose a spectral graph reinforcement learning framework for outage management in distribution networks to enhance system resilience. Our model learns the optimal power restoration policy using a spectral graph neural network. We evaluate the proposed method on three modified IEEE test systems: the 13-bus, 34-bus, and 123-bus networks. Experimental results show that our approach achieves near-optimal performance in real time and generalizes well across a wide range of outage scenarios.

Lihui Liu, Mucun Sun, Caisheng Wang

Wayne State University, Detroit, MI, USA

RL Control Graph Neural Networks Spectral Graph Convolution Power Systems

May 26, 2026

RAPNet: Accelerating Algebraic Multigrid with Learned Sparse Corrections

The scalable solution of large sparse linear systems is a bottleneck in scientific computing and graph analysis. While algebraic multigrid (AMG) offers optimal linear scaling, its performance is severely constrained by the trade-off between the sparsity and convergence quality of coarse-grid operators. Classical AMG heuristics struggle to balance these objectives, often sacrificing stability or performance for sparsity. We propose RAPNet, a graph neural network (GNN) framework that resolves this trade-off by learning to generate sparse, robust coarse operators directly from the sparse algebraic system. Key to our approach is a level-wise training strategy that enables learning from small subgraphs and generalization to million-node domains, bypassing the bottlenecks of prior neural AMG attempts. RAPNet executes exclusively during the solver setup phase, ensuring that the solve phase retains its favorable computational properties. We show that our method outperforms classical non-Galerkin baselines on diverse PDE discretizations and graph Laplacians, making it particularly effective for multi-query tasks such as eigenproblems, time-dependent simulations, and inverse or design problems.

Yali Fink, Ido Ben-Yair, Lars Ruthotto +1

Institute for Interdisciplinary Computational Sciences, Faculty of Computer and Information Science, Ben-Gurion University of the Negev, Be’er Sheva, Israel · Department of Mathematics and Computer Science, Emory University, Atlanta, GA, USA.

Graph Neural Networks

May 25, 2026

Dynamic Link Prediction with Temporally Enhanced Signed Graph Neural Networks

Temporal signed networks (TSNs) model the time evolution of cooperative and adversarial relationships that arise in applications such as social media analysis, trust and reputation systems, and financial transaction networks. While graph neural networks (GNNs) perform well for static or unsigned link prediction, effective learning in temporal signed graphs remains challenging due to the interaction of signed relations, evolving structure, and balance-theoretic constraints. To address this gap, we propose a modular temporal enhancement framework for signed GNNs that integrates historical context into otherwise static architectures. The framework introduces a Historical Context Integration Module (HCIM) that combines learnable recency-aware temporal weighting, LSTM-based embedding trajectory modeling, and multi-head temporal attention to capture both short- and long-term signed interaction dynamics. Historical information is fused with current node representations using either global or node-adaptive weighting, allowing the architecture-agnostic framework to accommodate heterogeneous temporal behaviors. We instantiate the approach on the Self-Explainable Signed Graph Transformer (SE-SGformer), preserving interpretability while extending it with temporal awareness. Experiments on real-world and synthetic TSNs, including Bitcoin OTC, Bitcoin Alpha, Reddit, and small-world network models, demonstrate consistent and statistically significant improvements over the static baseline.

Derek Regier, Andrew Polyak, Aresh Dadlani +1

Temporal GNNs Graph Neural Networks Temporal Link Prediction Temporal Attention

May 25, 2026

Provably Communication-Efficient and Privacy-Preserving Federated Graph Neural Networks

Graph neural networks (GNNs) achieve strong performance on relational data, but real-world graphs are often distributed across organizations that cannot share raw data due to privacy and policy constraints. Existing federated GNN methods either ignore cross-client links, leading to degraded accuracy, or require frequent embedding exchanges, incurring substantial communication and privacy costs. We propose CE-FedGNN, a communication-efficient and privacy-preserving federated GNN framework for learning over such coupled graphs. Our approach avoids sharing raw data or per-round embeddings by infrequently exchanging aggregated node representations. To handle cross-client dependency and staleness, we introduce a moving-average estimator that continuously tracks node representations and enables their stable reuse across rounds. To provide formal privacy guarantees for the released representations, we adopt the metric differential privacy (metric-DP) framework, which measures privacy with respect to distances in the learned embedding space rather than worst-case input perturbations. This yields meaningful guarantees at noise levels where standard differential privacy becomes overly conservative. We establish convergence to a stationary point at a rate of

O(1/\sqrt{T})

with

O(T^{3/4})

communication complexity. In addition, we derive

(\varepsilon,δ)

-metric-DP guarantees via Rényi differential privacy composition under a public-cohort threat model. Experiments on synthetic interbank anti-money laundering benchmarks and citation networks demonstrate that CE-FedGNN achieves strong performance while significantly reducing communication and maintaining robustness under privacy-preserving noise.

Zhishuai Guo, Wenhan Wu, Chen Chen +3

Department of Computer Science Northern Illinois University · Department of Computer Science University of North Carolina at Charlotte · Department of Computer Science University of Central Florida +2

Graph Neural Networks Communication-Efficient Distributed Training Federated Graph Learning Federated Learning

May 25, 2026

Invariant-Based Weight Sharing for Message Passing

Message-passing neural networks (MPNNs) are a powerful framework for learning representations of graph-structured domains. However, weights in MPNNs act on features only, limiting their ability to capture structural patterns. We introduce a novel structure-aware weight sharing principle that explicitly incorporates information inherent to the graph structure. Weights are indexed directly by user-chosen graph invariants, i.e., functions preserved under node permutations, enabling systematic reuse across structurally equivalent subgraphs. We present ShareGNNs, which instantiate this principle within a simple encoder-decoder architecture, resulting in an MPNN with learnable adjacency and transformer-like connectivity. We show that their expressivity is at least as strong as the discriminative power of the chosen invariants, providing explicit control over the model complexity. Experiments on synthetic and real-world data, as well as subgraph counting tasks, demonstrate consistent improvements over standard MPNNs, competitive expressivity beyond the 1-WL test, and scalability to large datasets.

Florian Seiffarth

University of Bonn, Bonn, Germany · Lamarr Institute for Machine Learning and Artificial Intelligence, Bonn, Germany

Graph Neural Networks GNN Expressivity Message Passing Neural Networks

May 25, 2026

Evaluating passing decision-making in professional football: An enhanced MPNN approach to Receiver Selection

The process of decision-making in football is characterized by a complex interplay between spatial positioning, opponent pressure, and player intent. This work introduces a Graph Neural Network (GNN) framework designed to predict Receiver Selection, the optimal passing target, by modeling on-field interactions as dynamic graphs. Each player is represented as a node with positional and contextual features, while potential passing lines form weighted edges characterized by distance, angle, and pressure metrics. A Message-Passing Neural Network (MPNN) has been developed and trained using a combination of tracking data and event data from professional matches, synchronized through a robust pipeline based on an optimized version of the Needleman-Wunsch Algorithm. The model achieves competitive accuracy in identifying the actual chosen receiver and state-of-the-art accuracy within its top three suggestions. Our model further offers quantification of each option's likelihood, threat, and creativity, enabling performance analysts to evaluate over 1,000 passes in seconds.

Gabriel Masella, Giuseppe Alessio D'Inverno, Max Goldsmith +1

Department of Mathematics, Informatics and Geoscience, University of Trieste, via Weiss 2, Trieste, 34128, Italy. · MathLab, International School for Advanced Studies (SISSA), Via Bonomea 265, Trieste, 34136, Italy. · Royal Belgium Football Association, Rue de Bruxelles 480, Tubize, 1480, Belgium.

Graph Neural Networks Message Passing Neural Networks

May 25, 2026

ARMA-C3: A Contrastive ARMA Convolutional Framework for Unsupervised and Semi-supervised Classification

In biomedical and neurodegenerative disorders, accurate and early disease identification remains challenging due to the scarcity of labeled data and the complexity of imaging patterns. To address these challenges, we introduce ARMA-C3, a unified unsupervised and semi-supervised graph learning framework for node classification based on contrastive learning and graph-cut regularization to learn structurally meaningful and discriminative representations. By modeling samples or images as graph nodes and exploiting inter-sample relationships, the proposed framework captures subject-level dependencies that conventional machine learning methods typically overlook. We conduct extensive binary classification experiments across five clinically relevant datasets: the Alzheimer's Disease Neuroimaging Initiative (ADNI), the Neuroimaging in Frontotemporal Dementia (NIFD) dataset, and three medical imaging benchmarks (BreastMNIST, PneumoniaMNIST, and a liver ultrasound dataset). Experimental results demonstrate that ARMA-C3 achieves competitive and frequently superior performance compared to classical clustering techniques, state-of-the-art machine learning models, and existing graph-based deep learning approaches across multiple evaluation settings, particularly under limited supervision and severe class imbalance. The proposed framework further demonstrates robust representation learning and strong cross-modal generalization across diverse biomedical imaging modalities.

VSS Tejaswi Abburi, Saurabh J. Shigwan, Nitin Kumar

Department of Computer Science and Engineering, Shiv Nadar Institute of Eminence Deemed to be University, Delhi NCR, India

Graph Neural Networks Unsupervised Representation Learning Medical Image Classification Graph-Based Semi-Supervised Learning Graph Contrastive Learning Semi-Supervised Learning+1

May 25, 2026

PHGNet: Prototype-Guided Hypergraph Construction for Heterogeneous Spatiotemporal Forecasting

As a core task in intelligent transportation systems, traffic forecasting plays a critical role in urban traffic management. Accurate traffic forecasting relies on modeling complex spatiotemporal dependencies, which is inherently challenging due to spatial heterogeneity in traffic systems.Despite significant progress, most existing methods are still limited to pairwise spatial dependency modeling, making it difficult to capture dynamic high-order interactions among nodes with similar traffic patterns. To address this issue, we propose PHGNet, a novel spatiotemporal forecasting framework based on prototype-guided hypergraph construction. At the core of PHGNet, a prototype learning mechanism is designed to adaptively assign pattern-similar nodes to hyperedges, thereby capturing high-order interactions with time-varying structures. To improve the reliability of dynamic hypergraph construction, we further develop a global-local node representation module to extract time-consistent features. For forecasting, iterative residual refinement and Temporal Query Attention are introduced to improve forecasting accuracy while supporting efficient parallel decoding. Extensive experiments on multiple real-world datasets demonstrate that PHGNet achieves superior predictive performance compared with state-of-the-art methods.

Ruiwen Gu, Yahao Liu, Zhenyu Liu +2

Shenzhen Ubiquitous Data Enabling Key Lab Shenzhen International Graduate School, Tsinghua University, Shenzhen, China · School of Computer Science and Engineering University of Electronic Science and Technology of China, Chengdu, China

Graph Neural Networks Intelligent Transportation Systems Spatiotemporal Forecasting Traffic Forecasting Hypergraph Learning

May 25, 2026

Different Statistical Perspectives for Understanding Generalisation in Graph Neural Networks

Graph Neural Networks (GNN) are currently the most popular approach for learning and prediction on graph-structured data and are deployed in various fields, from social network analysis to drug discovery. However, there is limited mathematical understanding of the performance of GNNs. We discuss the various perspectives used to study statistical generalisation in GNNs. We identify three broad frameworks. The first approach, rooted in learning theory, relies on uniform convergence bounds and the complexity of the hypothesis class of specific GNN architectures. This approach also builds on the expressivity of GNNs, typically studied through the lens of graph isomorphism tests. The second principle is to simplify the neural architecture by analysing GNNs under the asymptotics of infinitely many parameters or infinite graph size. This approach approximates GNNs using Gaussian processes, neural tangent kernels or graphon neural network operators, which allow studying the generalisation or stability of trained GNNs. The third framework studies GNNs under random graph models, often the contextual stochastic block model, and derives non-asymptotic error rates using tools from high-dimensional statistics. We highlight some key theoretical results and discuss a few limitations and open research questions for each perspective.

Nil Ayday, Mahalakshmi Sabanayagam, Debarghya Ghoshdastidar

Technical University of Munich, School of Computation, Information and Technology, Boltzmannstr. 3, Garching, 85748, Germany. · Australian Institute for Machine Learning, Adelaide University,2026 Adelaide, SA 5000, Australia.

Neural Network Generalization Graph Neural Networks GNN Expressivity Statistical Learning Theory

May 24, 2026

Revisiting Pre-Propagation GNNs: Robust Diffusion Operators and Hidden-State Re-Propagation

Pre-propagation graph neural networks (PPGNNs) decouple node feature propagation from transformation: graph diffusion is performed once as preprocessing, and training reduces to dense per-node transformations. This design enables mini-batch training without inter-node dependencies, avoids repeated sparse matrix--matrix multiplications, and better matches modern accelerators optimized for dense compute. However, their expressivity remains unclear, and empirical results show a gap between PPGNNs and their message-passing counterparts on commonly used graph benchmarks, especially heterophilic ones. In this paper, we propose a suite of robust graph diffusion operators for preprocessing and a few-shot hidden-state re-propagation scheme during training. Our methods improve the validation and test accuracy of PPGNNs, enabling them to match the accuracy of message-passing GNNs while maintaining training efficiency.

Zichao Yue, Zhiru Zhang

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

Graph Neural Networks Graph Diffusion

May 24, 2026

GL-LFGNN:A Global-Local Dual-branch Causal Graph Neural Network Based on Liang-Kleeman Information Flow for EEG Emotion Recognition

EEG-based emotion recognition holds significant promise for objective diagnosis of mood disorders. Graph neural networks (GNNs) have emerged as the dominant paradigm for modeling inter-channel dependencies in EEG, yet existing approaches rely on symmetric adjacency matrices derived from spatial proximity or functional correlations that fundamentally capture statistical associations rather than directed causal influences, which conflicts with the inherently asymmetric, causally-driven nature of neural information flow. To bridge this gap, we propose GL-LFGNN, a Global-Local Dual-branch Causal Graph Neural Network grounded in Liang-Kleeman information flow theory. Unlike Granger causality that merely assesses temporal precedence, our approach rigorously quantifies causal strength from a dynamical systems perspective, yielding neurophysiologically interpretable directed graphs. A dual-branch architecture further integrates whole-brain connectivity with region-specific processing aligned to established functional neuroanatomy. On the MEEG dataset, GL-LFGNN achieves 86.17% (Arousal) and 86.71% (Valence) accuracy with only 37K parameters -- approximately 10% of the current state-of-the-art -- demonstrating that principled causal modeling can simultaneously enhance interpretability, generalization, and computational efficiency. Code will be released.

Ziyi Wang, Dongyang Kuang

Graph Neural Networks EEG Emotion Recognition

May 23, 2026

Beyond the Aggregation Dilemma: Prior-Retaining Decoupled Learning for Multimodal Graphs

Multimodal Attributed Graph Learning (MAGL) integrates intrinsic node attributes with structural topology via graph aggregation. However, as pretrained encoders evolve into Large Foundation Models (LFMs), the landscape of MAGL fundamentally shifts: under high-confidence LFM priors, mandatory aggregation introduces topological noise that overwhelms discriminative signals, triggering a counter-intuitive performance inversion where sophisticated MAGL architectures underperform simple topology-agnostic MLPs. Through systematic empirical and theoretical analysis, we identify that this inversion stems from a fundamental aggregation dilemma characterized by two concurrent pathologies: (1) Representational Pathology (SNR Degradation) - mandatory aggregation dilutes robust intrinsic features with topological noise, causing the noise penalty to outweigh its collaborative benefit; and (2) Optimization Pathology (Gradient Starvation) - topological aggregation attenuates gradient flow, while a shared task loss causes dominant modalities to prematurely suppress weaker ones. To resolve this dilemma, we propose SUPRA (Shared-Unique Prior-Retaining Architecture), a decoupled dual-pathway paradigm. SUPRA processes modality-specific features through topology-agnostic MLPs while capturing structural synergy via a lightweight shared GNN, with auxiliary deep supervision counteracting gradient starvation. Extensive evaluations demonstrate that SUPRA achieves state-of-the-art performance while requiring 3.5x lower peak GPU memory and up to 4.4x faster training time than Multimodal Graph Transformers.

Hao Yan, Xuanru Wang, Jun Yin +3

School of Computer Science and Engineering, Central South University, Changsha, China · Department of Data Science and Artificial Intelligence, The Hong Kong Polytechnic University, Hong Kong SAR, China · School of Information and Communication Technology, Griffith University, Brisbane, Australia

Graph Neural Networks Multimodal Graph Learning Multimodal Fusion Multimodal Learning

May 23, 2026

Gaussian Rank-Based Neighborhood Degree for Graph Neural Networks in Image Classification

The exponential growth of data has intensified the gap between the availability of unlabeled data and the high cost of manual annotation. Graph Neural Networks (GNNs) have emerged as a promising solution, as they exploit relational structures and learn from both labeled and unlabeled data, performing semi-supervised learning. A crucial component of many of these models is degree-based normalization, which influences message propagation but typically assumes uniform importance among neighboring nodes. In image classification, graphs are usually constructed from feature similarity, where treating all neighbors equally may overlook important variations in relevance. Motivated by this gap, we propose GRaNDe (Gaussian Rank-based Neighborhood Degree). This novel degree measure integrates neighborhood ranking with Gaussian distance weighting to better capture node importance. Experiments on five public image classification datasets show consistent accuracy improvements and competitive or superior results compared to state-of-the-art methods.

Rafael Mendonça Duarte, Jean Roberto Ponciano, Lucas Pascotti Valem

Institute of Mathematics and Computer Science (ICMC) University of São Paulo (USP) São Carlos – SP – Brazil

Graph Neural Networks Graph-Based Semi-Supervised Learning Image Classification

May 23, 2026

Whole-Body Inverse Kinematics with Graph Diffusion

Inverse kinematics (IK) is a fundamental problem in robotics, requiring the generation of joint configurations that satisfy target end-effector poses. Existing approaches often struggle to generalize across diverse robot morphologies and to effectively model the multi-modal nature of IK, particularly in articulated systems with multiple kinematic branches. In this work, we propose GraphDiff-IK, a structure-aware graph diffusion framework for inverse kinematics. Specifically, we represent the robot as a kinematic graph constructed from the robot URDF, where nodes correspond to actuated joints and edges encode kinematic dependencies. Building upon this representation, we formulate IK as a conditional graph diffusion process that directly generates joint configurations on the robot graph. To better capture structural dependencies in articulated systems, we further introduce a structure-aware graph reasoning framework with hierarchical stage-wise message passing and torso-aware conditioning for multi-branch robots. In addition, we incorporate noisy forward kinematics feedback and task-space supervision to improve geometric consistency during denoising. The proposed framework provides a unified formulation that naturally supports single-arm robots, dual-arm systems, and articulated robots with torso or waist structures. Extensive experiments on diverse robotic platforms demonstrate that the proposed method achieves accurate and stable IK performance while preserving the ability to generate multiple feasible solutions for redundant robotic systems.

Helong Huang, Kai Tan, Feng Wen +2

Large Model Algorithm Lab, Huawei

Graph Neural Networks Inverse Kinematics Graph Diffusion

May 22, 2026

S $^3$ GNN: Efficient Global Mixing and Local Message Passing for Long-Range Graph Learning

Message-passing neural networks (MPNNs) often suffer from an information bottleneck when capturing long-range dependencies, leading to the oversquashing (OSQ) phenomenon. Alongside spatial connectivity enrichment (e.g., rewiring), recent studies have shown that spectral filtering can yield strong long-range learning outcomes, as spectral operators enable global information mixing that alleviates OSQ. These approaches achieve this either by stabilizing the Jacobian energies in deep propagation or by guaranteeing OSQ mitigation under strong theoretical assumptions. We revisit these conclusions and show that the associated Jacobian sensitivity lower bound is generally difficult to achieve in practice. We then propose S

^3

GNN, which mitigates OSQ without such restrictive assumptions by lightweightly reintroducing omitted components with substantially lower computational complexity, while standard stability constraints on feature transformations remain effective under our new dynamics. Extensive experiments across diverse domains (e.g., long-range benchmarks, KGQA, and mesh-based fluid dynamics) demonstrate that S

^3

GNN achieves up to an order-of-magnitude error reduction with up to 50% fewer parameters. Our code can be found in https://github.com/EEthanShi/S3-GNN.git.

Dai Shi, Luke Thompson, Linhan Luo +4

Department of Engineering, University of Cambridge, Cambridge, UK · University of Sydney, Australia

Graph Neural Networks Graph Representation Learning Message Passing Neural Networks

May 22, 2026

Weisfeiler-Leman Is Incomplete on Simple Spectrum Graphs, so Canonicalize Them

Graphs with a simple spectrum admit cubic-time isomorphism testing, yet we prove that for every natural number

k

, the

k

-Weisfeiler-Leman (

k

-WL) test cannot distinguish all non-isomorphic graphs with a simple spectrum. As the WL hierarchy upper-bounds the distinguishing power of widely-used Graph Neural Networks (GNNs), this incompleteness applies to all such GNNs, ruling out completeness for every

k

-WL-aligned GNN family. To close this gap, we introduce PRiSM (Partition, Refine, Solve, Match), the first provably complete canonicalization of simple-spectrum eigendecompositions. PRiSM obtains the completeness guarantee that prior canonicalizations provably lack, and resolves the open problem of achieving complete expressivity on simple-spectrum graphs. When composed with DeepSets or a Transformer, PRiSM achieves universal approximation on simple-spectrum graphs, justifying the use of canonicalized Laplacian positional encodings. Empirically, PRiSM performs comparably to or outperforms existing spectral canonicalizations on graph regression, classification, and expressivity

Snir Hordan, Nadav Dym, Tim Seppelt

Faculty of Mathematics Technion - Israel Institute of Technology · IT University of Copenhagen

Graph Neural Networks GNN Expressivity

May 22, 2026

Self-supervised Adversarial Purification for Graph Neural Networks

Defending Graph Neural Networks (GNNs) against adversarial attacks requires balancing accuracy and robustness, a trade-off often mishandled by traditional methods like adversarial training that intertwine these conflicting objectives within a single classifier. To overcome this limitation, we propose a self-supervised adversarial purification framework. We separate robustness from the classifier by introducing a dedicated purifier, which cleanses the input data before classification. In contrast to prior adversarial purification methods, we propose GPR-GAE, a novel graph auto-encoder (GAE), as a specialized purifier trained with a self-supervised strategy, adapting to diverse graph structures in a data-driven manner. Utilizing multiple Generalized PageRank (GPR) filters, GPR-GAE captures diverse structural representations for robust and effective purification. Our multi-step purification process further facilitates GPR-GAE to achieve precise graph recovery and robust defense against structural perturbations. Experiments across diverse datasets and attack scenarios demonstrate the state-of-the-art robustness of GPR-GAE, showcasing it as an independent plug-and-play purifier for GNN classifiers.

Woohyun Lee, Hogun Park

Department of Computer Science and Engineering, Sungkyunkwan University, Suwon, South Korea.

Graph Neural Networks Adversarial Robustness

May 21, 2026

Do Deep Ensembles Actually Capture Uncertainty in Graph Neural Networks?

While deep ensembles are widely considered to be the default method for uncertainty quantification in deep learning, their effectiveness for graph-structured data is often simply assumed based on successes in domains like computer vision. We investigate standard deep ensembles specifically for message-passing graph neural networks. Benchmarking across eight datasets representing varied tasks and complexities, we reveal that ensembles provide only marginal improvement over a single model. These marginal gains stem primarily from averaging out optimization noise in point predictions rather than from meaningfully better uncertainty estimates. Through an aleatoric-epistemic decomposition, we identify epistemic collapse: independently trained networks consistently converge to overly similar predictions. Because disagreement is the fundamental mechanism through which ensembles capture epistemic uncertainty, this lack of diversity neutralizes their key advantage. Towards explaining this phenomenon, we derive a bound on epistemic variance in terms of the graph topology and Dirichlet energy budget, linking epistemic collapse to the smoothing bias of message passing. Our results suggest that deep ensemble success does not seamlessly transfer to graph machine learning.

Pedro C. Vieira, Pedro Ribeiro, Viacheslav Borovitskiy

University of Edinburgh · DCC/FCUP, University of Porto

Graph Neural Networks Deep Ensembles Epistemic Uncertainty

May 21, 2026

Implicit Regularization of Mini-Batch Training in Graph Neural Networks

Mini-batch training of Graph Neural Networks (GNNs) is fundamentally different from training on i.i.d. data: sampling a subgraph alters the topology and introduces boundary effects, leading prior work to develop structure-aware samplers that preserve local connectivity and reduce embedding variance. Surprisingly, we demonstrate that the simplest possible scheme, Random Node Sampling (RNS), training on the induced subgraph of uniformly sampled nodes, matches or outperforms full-graph training on 8 of 10 datasets at a fraction of the wall-clock time and memory. To explain this, we apply backward error analysis to graph mini-batch Stochastic Gradient Descent (SGD) and show that it implicitly minimizes the sampled loss plus a regularizer proportional to the mini-batch gradient variance, a quantity directly shaped by the sampler. Although RNS discards local structure, it produces mini-batches whose expected loss is closer to the full-graph loss, and whose per-batch gradients have lower variance, yielding a better implicit objective. Our analysis reframes the choice of graph sampler as a form of implicit regularization, and identifies RNS as a strong, theoretically grounded method for scalable GNN training.

Clement Wang, Antoine Vialle, Robin Vaysse +1

Institut Polytechnique de Paris · Mirakl

Graph Neural Networks Implicit Regularization Stochastic Gradient Descent

May 21, 2026

Ex-GraphRAG: Interpretable Evidence Routing for Graph-Augmented LLMs

GraphRAG conditions language models on subgraphs retrieved from knowledge graphs, encoded via message-passing GNNs. Because these encoders entangle node contributions through iterated neighborhood aggregation, there is no closed-form way to determine how much each retrieved entity influenced the encoder's output, and therefore no way to faithfully audit what structural evidence actually reached the model. We introduce Ex-GraphRAG, which replaces the GNN encoder with a Multivariate Graph Neural Additive Network (M-GNAN), an extension of additive graph models to high-dimensional embedding spaces that yields an exact decomposition of the encoder's output across individual nodes and feature groups, without post-hoc approximation. On STaRK-Prime, this auditable encoder matches black-box performance. Using it to audit evidence routing, we uncover a semantic-structural mismatch: the nodes that dominate the encoder's output are structurally disconnected in the retrieved subgraph, held together by low-attribution intermediaries whose removal degrades multi-hop QA by up to 28%. This mismatch, invisible to any opaque encoder, reveals that semantic importance and structural connectivity are governed by disjoint sets of nodes, with direct implications for retrieval pruning, context construction, and failure diagnosis in graph-augmented LLMs.

Yoav Kor Sade, Arvindh Arun, Rishi Puri +2

Tel Aviv University · Institute for AI, University of Stuttgart · NVIDIA +1

Graph Neural Networks LLM Reasoning with Graphs Graph Retrieval-Augmented Generation Knowledge Graph Question Answering GNN Explainability

May 20, 2026

Is Fixing Schema Graphs Necessary? Full-Resolution Graph Structure Learning for Relational Deep Learning

Relational prediction tasks are fundamental in many real-world applications, where data are naturally stored in relational databases (RDBs). Relational Deep Learning (RDL) addresses this problem by modeling RDBs as graphs and applying graph neural networks (GNNs) for end-to-end learning. However, the full-resolution property is commonly adopted as a design principle in graph construction for RDBs to preserve relational semantics, which leads most existing methods to rely on fixed graph structures. In this paper, we propose FROG, a Full-Resolution and Optimizable Graph Structure Learning} framework for RDL that formulates relational structure learning as a learnable table role modeling problem, allowing tables to contribute as nodes and edges in message passing. We further design role-driven message passing mechanisms to capture relational semantics, enabling joint optimization of graph structure and GNN representations. To ensure semantic consistency, we introduce functional dependency constraints that regularize representations across table and entity levels. Extensive experiments demonstrate that our method outperforms existing approaches and reveal how table roles impact downstream tasks, offering new insights into graph construction for RDL

Yi Huang, Qingyun Sun, Jia Li +2

SKLCCSE, School of Computer Science and Engineering, Beihang University, Beijing, China · Key Lab of Education Blockchain and Intelligent Technology, Ministry of Education, Guangxi Normal University, Guilin, China

Graph Structure Learning Graph Neural Networks Relational Deep Learning Relational Databases

May 20, 2026

Gaussian Sheaf Neural Networks

Graph Neural Networks (GNNs) have become the de facto standard for learning on relational data. While traditional GNNs' message passing is well suited for vector-valued node features, there are cases in which node features are better represented by probability distributions than real vectors. Concretely, when node features are Gaussians, characterized by a mean and a covariance matrix, naively concatenating their parameters into a single vector and applying standard message passing discards the geometric and algebraic structure that governs means and covariances. We propose Gaussian Sheaf Neural Networks (GSNNs), a principled framework that incorporates these inductive biases into graph-based learning. Building on the theory of cellular sheaves, we derive a new Laplacian operator that generalizes the sheaf Laplacian to this setting and preserves its key properties. We complement our theoretical contributions with experiments on synthetic and real-world data that illustrate the practical relevance of GSNNs.

André Ribeiro, Ana Luiza Tenório, Tiago da Silva +1

Getulio Vargas Foundation · MBZUAI

Graph Neural Networks Sheaf Neural Networks Sheaf Theory

May 20, 2026

Graph Navier Stokes Networks

Graph Neural Networks (GNNs) have emerged as a cornerstone of deep learning, with most existing methods rooted in graph signal processing and diffusion equations to model message passing. However, these approaches inherently suffer from the oversmoothing problem, where node features become indistinguishable as the network depth increases. Inspired by the Navier Stokes equations, we introduce Graph Navier Stokes Networks (GNSN), a novel architecture that transcends conventional diffusion-based message passing by incorporating convection into graph structures. GNSN defines a dynamic velocity field on the graph to govern convection, enabling more efficient and direct message propagation. By adaptively balancing convection and diffusion, GNSN is able to efficiently handle datasets with varying levels of homophily. Extensive evaluations across twelve real-world datasets demonstrate that GNSN consistently outperforms state-of-the-art baselines in classification accuracy. Moreover, experimental results further emphasize its effectiveness in alleviating the oversmoothing problem.

Zexing Zhao, Guangsi Shi, Yu Gong +4

Northwest A&F University Yangling, Shaanxi, China · Corporate Research Center, Midea Group Shanghai, China · Bosch Shanghai, China

Graph Neural Networks Graph Diffusion

May 19, 2026

WaveGraphNet: Physics-Consistent Guided-Wave Damage Localization through Coupled Inverse-Forward Graph Learning

Guided-wave structural health monitoring enables damage localization in composite plates using sparse networks of bonded piezoelectric transducers. However, supervised localization remains weakly constrained when measurements are available from only a limited set of damage locations. Because exhaustive spatial coverage is impractical, models trained at observed locations may generalize poorly to unseen regions. We propose WaveGraphNet, an inverse-forward graph-learning framework for guided-wave damage localization in carbon-fiber-reinforced polymer (CFRP) plates. The sensing network is represented as a graph, with transducers as nodes and measured pitch-catch paths as edges. The inverse branch uses order-invariant message passing and a geometry-constrained decoder to map path-wise energy deviations to a damage coordinate. An independently trained forward branch predicts the energy-deviation pattern associated with a candidate coordinate. At test time, gradients propagated through the forward branch update only the inverse-predicted coordinate to reduce the discrepancy between the measured and predicted response patterns. The framework is evaluated on the OGW-1 benchmark using three spatial hold-out splits in which complete damage regions are excluded from training. Comparisons include non-graph and graph-learning baselines together with the training-free Reconstruction Algorithm for Probabilistic Inspection of Damage (RAPID). Under the validation-selected settings, refined WaveGraphNet achieves the lowest reported test mean absolute error on all three splits. Refinement reduces the standalone localization error by 23.6 percent-67.9 percent, with an average relative reduction of 50.4 percent. These results demonstrate that learned forward-response consistency can improve guided-wave localization under limited spatial training coverage.

Vinay Sharma, Aditya Bharade, Olga Fink

EPFL, Intelligent Maintenance and Operations Systems, Lausanne, Switzerland

Graph Neural Networks Inverse Problems Structural Health Monitoring

May 19, 2026

B-cos GNNs: Faithful Explanations through Dynamic Linearity

We introduce B-cos GNNs, an inherently explainable class of graph neural networks whose predictions decompose exactly into per-node, per-feature contributions via a single input-dependent linear map. B-cos GNNs use linear (sum-based) aggregation and replace non-linear message and update functions with B-cos transforms. This induces meaningful, task-specific weight-input alignment that is directly accessible through the model's dynamic linearity. Instance-level explanations follow from a single forward and backward pass, requiring no auxiliary explainer, modified learning objective, or perturbation procedure. Instantiated as a GIN, our approach trades small losses in predictive accuracy for state-of-the-art explainability across diverse synthetic and real-world benchmarks, producing explanations orders of magnitude faster than post-hoc baselines.

Joschka Groß, Mohammad Shaique Solanki, Verena Wolf

Saarland Informatics Campus, Saarland University · DFKI

Feature Attribution Graph Neural Networks GNN Explainability

May 19, 2026

BrainDyn: A Sheaf Neural ODE for Forecasting and Generating Brain Dynamics

Brain activity unfolds as coordinated patterns across regions over time, and modeling these dynamics is a central goal in computational neuroscience. Because activity is distributed over connected brain regions, it is naturally represented on a graph whose nodes are brain regions or recording electrodes and whose edges capture relationships between these nodes, with message-passing modeling regional communication. However, standard message-passing networks place every node in a single shared feature space and typically aggregate messages from neighbors by scalar summation, which does not align with neurobiological evidence of brain communication. In order to model the heterogeneous nature of the brain, we introduce BrainDyn, a graph ordinary differential equation (ODE) network built on a cellular sheaf with dynamic restriction maps, recomputed from the forecasting context window rather than fixed once, mediating region-to-region communication through learned linear transformations that drive the time evolution of neural activity. We evaluate BrainDyn on resting-state fMRI, EEG, and simulated activity from the NEST simulator. Across these modalities, we test multi-region forecasting and autoregressive generation of brain transients, and, using NEST, prediction of altered transients following controlled perturbations. BrainDyn outperforms competing models across modalities, while analysis of the learned features shows that they are expressive, interpretable, and biologically aligned.

Siddharth Viswanath, Panayiotis Ketonis, Cassidy All +10

Yale University · Boise State University · University of Wisconsin–Madison

Graph Neural Networks Sheaf Neural Networks Neuroimaging Neural ODEs Spatiotemporal GNNs Brain Network Analysis