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.

Apr 27, 2026

PathMoG: A Pathway-Centric Modular Graph Neural Network for Multi-Omics Survival Prediction

Cancer survival prediction from multi-omics data remains challenging because prognostic signals are high-dimensional, heterogeneous, and distributed across interacting genes and pathways. We propose PathMoG, a pathway-centric modular graph neural network for multi-omics survival prediction. PathMoG reorganizes genome-scale inputs into 354 KEGG-informed pathway modules, introduces a Hierarchical Omics Modulation module to condition gene-expression representations on mutation, copy number variation, pathway, and clinical context, and uses dual-level attention to capture both intra-pathway driver signals and inter-pathway clinical relevance. We evaluated PathMoG on 5,650 patients across 10 TCGA cancer types and observed consistent improvements over representative survival baselines. The framework further provides gene-level, pathway-level, and patient-level interpretability, supporting biologically grounded and clinically relevant risk stratification.

Di Wang, Chupei Tang, Junxiao Kong +3

1Cuiying Honors College, Lanzhou University, China · School of Mathematics and Statistics, Lanzhou University, China · School of Mathematics and Statistics, Lanzhou University, China and Shanghai Innovation Institute +1

Cancer Genomics Graph Neural Networks Cancer Survival Prediction Survival Analysis Oncology Modular Neural Networks

Apr 27, 2026

Latent-Hysteresis Graph ODEs: Modeling Coupled Topology-Feature Evolution via Continuous Phase Transitions

Graph neural ordinary differential equations (Graph ODEs) extend graph learning from discrete message-passing layers to continuous-time representation flows. While it supports adaptive long-range propagation, we show that Graph ODEs with strictly positive irreducible mixing operators face an inherent monostability trap: in the long-time regime, information leakage is unavoidable and the dynamics converge to a single global consensus attractor. We propose the Hysteresis Graph ODE (HGODE), which couples feature evolution with a latent topological potential driven by a learned pairwise force. A double-well edge potential and bipolarized gate allow edge states to polarize into connected or insulated phases while preserving differentiability. We provide asymptotic analysis of the collapse mechanism and the proposed hysteretic topology dynamics, and validate HGODE on theory-driven synthetic diagnostics and real-world graph benchmarks.

Qinhan Hou, Jing Tang

Doctoral Program of Computer Science, University of Helsinki, Helsinki, Finland · Research Program in Systems Oncology, Faculty of Medicine, University of Helsinki, Helsinki, Finland

Dynamical Systems Graph Structure Learning Graph Neural Networks Graph Representation Learning Phase Transitions Neural ODEs

Apr 27, 2026

Graph-augmented Segmentation of Complex Shapes in Laser Powder bed Fusion for Enhanced In Situ Inspection

The technological maturity of in situ inspection and monitoring methods in additive manufacturing is steadily increasing, enabling more efficient and practical qualification procedures. In this context, image segmentation of powder bed images in Laser Powder Bed Fusion (L-PBF) has been investigated by various authors, leveraging both edge detection and machine learning approaches to identify deviations from nominal geometry. Despite these developments, several challenges remain, including the sensitivity of segmentation performance to industrial illumination conditions and layer-to-layer variability in pixel intensity patterns. The study addresses these limitations by proposing a graph-augmented segmentation approach. The underlying principle consists of preserving the geometrical information at a global level rather than at pixel-wise level, modeling dependencies and relational information among spatial regions with a Graph Neural Network bottleneck embedded into a U-Net architecture. This allows enhancing the consistency and accuracy of the geometry reconstruction in the presence of spatial and layer-wise photometric variability systematically faced in real data. The method is evaluated against benchmark techniques for the in situ reconstruction of lattice structures produced by L-PBF, demonstrating its potential as a scalable solution for robust in situ inspection and geometric verification in industrial environments.

Stefano Raimondo, Matteo Bugatti, Marco Grasso

Department of Mechanical Engineering, Politecnico di Milano, Milan, Italy · Department of Mechanical Engineering, Politecnico di Milano, Via La Masa 1, 20156 Milan, Italy

Graph Neural Networks U-Net Industrial Inspection Convolutional Neural Networks Additive Manufacturing

Apr 27, 2026

Crystal structure prediction using graph neural combinatorial optimization

Crystalline materials are widely used in technological applications, yet their discovery remains a significant challenge. As their properties are driven by structure, crystal structure prediction (CSP) methods play a central role in computational approaches aiming to accelerate this process. Previously, CSP has been approached from a combinatorial optimization perspective, with the core challenge of allocating atoms on a fine grid of predefined discrete positions within a unit cell while minimizing their interaction energy. Exact mathematical optimization methods provide guaranteed solutions, but they become computationally expensive for large-scale instances, where the atomic configuration space grows rapidly, particularly in the absence of additional symmetry constraints. In this work, we introduce a neural combinatorial optimization approach to the atom allocation challenge and, subsequently, CSP, based on graph neural networks (GNNs), which can effectively sample from the distribution of feasible structures in an unsupervised manner. We leverage expander graphs to construct computational graphs over discrete positions that capture both short- and long-range interactions between atoms, and employ the Gumbel-Sinkhorn approach to enforce the desired stoichiometry of the generated structures. We demonstrate that our method outperforms classical heuristic approaches and is competitive with a commercial optimization solver across a range of chemical compositions. This enables the use of ever-expanding GPU infrastructure to tackle the inherent combinatorial challenges of CSP, paving the way for scaling beyond current capabilities.

Stavros Gerolymatos, J. Kyle Brubaker, Martin J. A. Schuetz +1

School of Computer Science and Informatics, University of Liverpool, Liverpool, England, UK · Amazon Advanced Solutions Lab, Seattle, Washington 98170, USA · Arm Inc., San Jose, California 95134

Graph Neural Networks Crystal Structure Prediction Combinatorial Optimization Crystal Structure Generation Neural Combinatorial Optimization

Apr 26, 2026

Graph Memory Transformer (GMT)

We investigate whether the Feed-Forward Network (FFN) sublayer in a decoder-only transformer can be replaced by an explicit learned memory graph while preserving the surrounding autoregressive architecture. The proposed Graph Memory Transformer (GMT) keeps causal self-attention intact, but replaces the usual per-token FFN transformation with a memory cell that routes token representations over a learned bank of centroids connected by a learned directed transition matrix. In the base GMT v7 instantiation studied here, each of 16 transformer blocks contains 128 centroids, a 128 * 128 edge matrix, gravitational source routing, token-conditioned target selection, and a gated displacement readout. The cell therefore returns movement from an estimated source memory state toward a target memory state, rather than a retrieved value. The resulting model is a fully decoder-only language model with 82.2M trainable parameters and no dense FFN sublayers, compared with a 103.0M-parameter dense GPT-style baseline used in the evaluation. The base v7 model trains stably and exposes centroid usage, transition structure, and source-to-target movement as directly inspectable quantities of the forward computation. It remains behind the larger dense baseline in validation loss and perplexity (3.5995/36.58 vs. 3.2903/26.85), while showing close zero-shot benchmark behavior under the evaluated setting. These results are not intended as a state-of-the-art claim; they support the viability and structural interpretability of replacing dense within-token transformation with graph-mediated memory navigation. Broader scaling, optimized kernels, and more extensive benchmark evaluation are left for subsequent work.

Nicola Zanarini, Niccolò Ferrari, Evelina Lamma

Bonfiglioli Engineering s.r.l. · Department of Engineering, University of Ferrara, Via Saragat 1, 44122 Ferrara, Italy · NAIS s.r.l., Via Maria Callas 4, 40131 Bologna, Italy

Memory-Augmented Neural Networks Transformer FFNs Graph Neural Networks Memory-Augmented Language Models Transformer Decoder-Only Language Models

Apr 26, 2026

Scalable Production Scheduling: Linear Complexity via Unified Homogeneous Graphs

Efficiently solving the Job Shop Scheduling Problem in real-world industrial applications requires policies that are both computationally lean and topologically robust. While Reinforcement Learning has shown potential in automating dispatching rules, existing models often struggle with a scalability bottleneck caused by quadratic graph complexity or the architectural overhead of heterogeneous layers. We introduce a unified graph framework that employs feature-based homogenization to project distinct node roles into a shared latent space. This allows a standard homogeneous Graph Isomorphism Network to capture complex resource contention with linear complexity, ensuring low-latency inference for large-scale industrial applications. Our empirical results demonstrate that our framework achieves state-of-the-art performance while exhibiting consistent zero-shot generalization. We identify the job-to-machine ratio as the primary driver of policy effectiveness, rather than absolute problem size. Based on this, we propose a hypothesis of structural saturation, demonstrating that policies trained on critically congested instances (

\mathcal{J} \approx \mathcal{M}

) learn scale-invariant resolution strategies. Agents trained at this saturation point internalize invariant conflict-resolution logic, allowing them to treat massive rectangular instances as a sequential concatenation of saturated sub-problems. This approach eliminates the need for expensive scale-specific retraining and prevents overfitting to statistical shortcuts, providing a robust and efficient pathway for deploying RL solutions in dynamic production environments.

Jonathan Hoss, Moritz Link, Noah Klarmann

Faculty of Management and Engineering, Rosenheim Technical University of Applied Sciences, Germany

Graph Neural Networks Reinforcement Learning Graph Representation Learning Job Shop Scheduling

Apr 26, 2026

Crystal Fractional Graph Neural Network for Energy Prediction of High-Entropy Alloys

High-entropy alloys (HEAs) have attracted growing attention for their exceptional mechanical and thermal properties arising from complex atomic configurations. In this paper, we propose crystal fractional graph neural network for predicting the energy of high-entropy alloys by explicitly integrating both local atomic environments and global compositional information. The model consists of three components: a crystal graph neural network, which employs graph attention network layers to learn local interactions among 16 on-site atoms within the crystal lattice; fractional neural network, a fully connected network that embeds the global fraction of constituent elements; and feature fusion neural network, which fuses the outputs of the two submodels to predict the total crystal energy. We train the model on a dataset of 1,049 crystal structures and validate it on 198 quaternary structures, optimizing all hyperparameters via Optuna. Our results show that our model achieves an RMSE comparable to first-principles calculations and maintains high accuracy even for low-energy configurations. However, the model exhibits limitations in handling large crystal cells, which we aim to address in future work to extend its applicability to more complex systems.

Takanori Kotama, Yang Huang

School of Informatics, Nagoya University, Nagoya 4648601, Japan · University of Science and Technology of China, Hefei 230026, China · Suzhou Institute for Advanced Research, University of Science and Technology of China, Suzhou 215213, China

Graph Neural Networks Materials Property Prediction Materials Science

Apr 26, 2026

Hamiltonian Graph Inference Networks: Joint structure discovery and dynamics prediction for lattice Hamiltonian systems from trajectory data

Lattice Hamiltonian systems underpin models across condensed matter, nonlinear optics, and biophysics, yet learning their dynamics from data is obstructed by two unknowns: the interaction topology and whether node dynamics are homogeneous. Existing graph-based approaches either assume the graph is given or, as in

α

-separable graph Hamiltonian network, infer it only for separable Hamiltonians with homogeneous node dynamics. We introduce the Hamiltonian Graph Inference Network (HGIN), which jointly recovers the interaction graph and predicts long-time trajectories from state data alone, for both separable and non-separable Hamiltonians and under heterogeneous node dynamics. HGIN couples a structure-learning module -- a learnable weighted adjacency matrix trained under a Hamilton's-equations loss -- with a trajectory-prediction module that partitions edges into physically distinct subgraphs via

k

-means clustering, assigning each subgraph its own encoder and thereby breaking the parameter-sharing bottleneck of conventional GNNs. On three benchmarks -- a Klein--Gordon lattice with long-range interactions and two discrete nonlinear Schrödinger lattices (homogeneous and heterogeneous) -- HGIN reduces long-time energy prediction error and trajectory prediction error by six to thirteen orders of magnitude relative to baselines. A symmetry argument on the Hamiltonian loss further shows that the learned weights encode the parity of the underlying pair potential, yielding an interpretable readout of the system's interaction structure.

Ru Geng, Panayotis Kevrekidis, Yixian Gao +2

School of Mathematics and Statistics, Changchun University, Changchun, 130022, China · Department of Mathematics and Statistics, University of Massachusetts, Amherst, 01003, MA, USA · Department of Physics, University of Massachusetts, Amherst, 01003, MA, USA +2

Dynamical Systems Graph Structure Learning Graph Neural Networks Graph Representation Learning System Identification Physics-Informed ML+2

Apr 26, 2026

Probabilistic Graphical Model using Graph Neural Networks for Bayesian Inversion of Discrete Structural Component States

The health condition of components in civil infrastructures can be described by various discrete states according to their performance degradation. Inferring these states from measurable responses is typically an ill-posed inverse problem. Although Bayesian methods are well-suited to tackle such problems, computing the posterior probability density function (PDF) presents challenges. The likelihood function cannot be analytically formulated due to the unclear relationship between discrete states and structural responses, and the high-dimensional state parameters resulting from numerous components severely complicates the computation of the marginal likelihood function. To address these challenges, this study proposes a novel Bayesian inversion paradigm for discrete variables based on Probabilistic Graphical Models (PGMs). The Markov networks are employed as modeling tools, with model parameters learned from data and structural topology prior. It has been proved that inferring this PGM produces the same probabilistic estimation as the posterior PDF derived from Bayesian inference, which effectively solves the above challenges. The inference is accomplished by Graph Neural Networks (GNNs), and a graph property-based GNN training strategy is developed to enable accurate inference across varying graph scales, thereby significantly reducing the computational overhead in high-dimensional problems. Both synthetic and experimental data are used to validate the proposed framework

Teng Li, Stephen Wu, Yong Huang +2

Key Lab of Smart Prevention and Mitigation of Civil Engineering Disasters of the Ministry of Industry and Information Technology, Harbin Institute of Technology, Harbin 150090, China · Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education, School of Civil Engineering, Harbin, Institute of Technology, Harbin 150090, China · The Institute of Statistical Mathematics, Research Organization of Information and Systems, 10-3 Midori-cho, Tachikawa, Tokyo 190-8562, Japan +2

Graph Neural Networks Bayesian Inverse Problems Probabilistic Graphical Models Structural Health Monitoring

Apr 25, 2026

Layer Embedding Deep Fusion Graph Neural Network

Graph Neural Networks (GNNs) have demonstrated impressive performance in learning representations from graph-structured data. However, their message-passing mechanism inherently relies on the assumption of label consistency among connected nodes, limiting their applicability to low-homophily settings. Moreover, since message passing operates as a hierarchical diffusion process, GNNs face challenges in capturing long-range dependencies. As network depth increases, the structural noise along heterophilic edges tends to be amplified, resulting in over-smoothing. This issue becomes especially prominent in highly heterophilic graphs, where the propagation of inconsistent semantics across the topology continually exacerbates misaggregation. To address this issue, we propose a novel framework named Layer Embedding Deep Fusion Graph Neural Network (LEDF-GNN). Specifically, we design a Layer Embedding Deep Fusion (LEDF) operator that nonlinearly fuses multi-layer embeddings to capture inter-layer dependencies and effectively alleviate deep propagation degradation. Meanwhile, to mitigate structural heterophily, LEDF-GNN employs a Dual-Topology Parallel Strategy (DTPS) that simultaneously leverages the original and reconstructed topologies, allowing for adaptive structure-semantics co-optimization under diverse homophily conditions. Extensive semi-supervised classification experiments on the citation and image benchmarks demonstrate that, under both homophilic and heterophilic settings, LEDF-GNN consistently outperforms state-of-the-art baselines, validating its effectiveness and generalization capability across diverse graph types.

Taihua Xu, Genhao Tian, Jicong Fan +3

Jiangsu University of Science and Technology · The Chinese University of Hong Kong, Shenzhen · Chongqing University of Post and Telecommunications

Graph Structure Learning Graph Neural Networks Graph Representation Learning Multi-Scale Feature Fusion Graph Heterophily

Apr 25, 2026

HBGSA: Hydrogen Bond Graph with Self-Attention for Drug-Target Binding Affinity Prediction

Accurate prediction of drug-target binding affinity accelerates drug discovery by prioritizing compounds for experimental validation. Current methods face three limitations: sequence-based approaches discard spatial geometric constraints, structure-based methods fail to exploit hydrogen bond features, and conventional loss functions neglect prediction-target correlation, a key factor for identifying high-affinity compounds in virtual screening. We developed HBGSA (Hydrogen Bond Graph with Self-Attention), a 3.06M-parameter model that encodes hydrogen bond spatial features. HBGSA uses graph neural networks to model hydrogen bond spatial topology with self-attention enhancement and Pearson correlation loss. Experimental results on PDBbind Core Set and CSAR-HiQ dataset demonstrate that HBGSA outperforms baseline methods with strong generalization capability. Ablation studies confirm the effectiveness of hydrogen bond modeling and Pearson correlation loss.

Junxiao Kong, Chupei Tang, Di Wang +4

School of Mathematics and Statistics, Lanzhou University, 222 South Tianshui Road, 730000, Gansu, China · Department of Computer Science, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong 999077, China

Protein-Ligand Binding Affinity Prediction Graph Neural Networks Molecular Property Prediction Drug Discovery

Apr 24, 2026

STEM: Structure-Tracing Evidence Mining for Knowledge Graphs-Driven Retrieval-Augmented Generation

Knowledge Graph-based Question Answering (KGQA) plays a pivotal role in complex reasoning tasks but remains constrained by two persistent challenges: the structural heterogeneity of Knowledge Graphs(KGs) often leads to semantic mismatch during retrieval, while existing reasoning path retrieval methods lack a global structural perspective. To address these issues, we propose Structure-Tracing Evidence Mining (STEM), a novel framework that reframes multi-hop reasoning as a schema-guided graph search task. First, we design a Semantic-to-Structural Projection pipeline that leverages KG structural priors to decompose queries into atomic relational assertions and construct an adaptive query schema graph. Subsequently, we execute globally-aware node anchoring and subgraph retrieval to obtain the final evidence reasoning graph from KG. To more effectively integrate global structural information during the graph construction process, we design a Triple-Dependent GNN (Triple-GNN) to generate a Global Guidance Subgraph (Guidance Graph) that guides the construction. STEM significantly improves both the accuracy and evidence completeness of multi-hop reasoning graph retrieval, and achieves State-of-the-Art performance on multiple multi-hop benchmarks.

Peng Yu, En Xu, Bin Chen +2

AI Product Center, Kingsoft Corporation, Beijing, China

Graph Neural Networks Graph Retrieval-Augmented Generation Knowledge Graph Question Answering Multi-Hop Reasoning

Apr 23, 2026

Towards Understanding the Expressive Power of GNNs with Global Readout

We study the expressive power of message-passing aggregate-combine-readout graph neural networks (ACR-GNNs). Particularly, we focus on the first-order (FO) properties expressible by this formalism. While a tight logical characterisation remains a difficult open question, we make two contributions towards answering it. First, we show that sum aggregation and readout suffice for GNNs to capture FO properties that cannot be expressed in the logic C2 on both directed and undirected graphs. This strengthens known results by Hauke and Wał{\k e}ga (2026) where aggregation and readout functions are specially crafted for the task. Second, we identify two natural ways of restoring characterisability (with regard to C2) for ACR-GNNs. One option is to limit local aggregation (without imposing restrictions on global readout), whilst the second is to run ACR-GNNs over graphs of bounded degree (but unbounded size). In both cases, the FO properties captured by GNNs are exactly those definable by a formula in graded modal logic with global counting modalities. Our results thus establish an innate lower- and upper-bound in terms of how far (fragments of) C2 can be taken to characterise GNNs, and imply that is indeed the unbounded interaction of aggregation and readout that pushes the logical expressive power of GNNs above C2.

Maurice Funk, Daumantas Kojelis

Leipzig University, Germany

Graph Neural Networks GNN Expressivity Message Passing Neural Networks Neural Network Expressivity

Apr 23, 2026

Drug Synergy Prediction via Residual Graph Isomorphism Networks and Attention Mechanisms

In the treatment of complex diseases, treatment regimens using a single drug often yield limited efficacy and can lead to drug resistance. In contrast, combination drug therapies can significantly improve therapeutic outcomes through synergistic effects. However, experimentally validating all possible drug combinations is prohibitively expensive, underscoring the critical need for efficient computational prediction methods. Although existing approaches based on deep learning and graph neural networks (GNNs) have made considerable progress, challenges remain in reducing structural bias, improving generalization capability, and enhancing model interpretability. To address these limitations, this paper proposes a collaborative prediction graph neural network that integrates molecular structural features and cell-line genomic profiles with drug-drug interactions to enhance the prediction of synergistic effects. We introduce a novel model named the Residual Graph Isomorphism Network integrated with an Attention mechanism (ResGIN-Att). The model first extracts multi scale topological features of drug molecules using a residual graph isomorphism network, where residual connections help mitigate over-smoothing in deep layers. Subsequently, an adaptive Long Short-Term Memory (LSTM) module fuses structural information from local to global scales. Finally, a cross-attention module is designed to explicitly model drug-drug interactions and identify key chemical substructures. Extensive experiments on five public benchmark datasets demonstrate that ResGIN-Att achieves competitive performance, comparing favorably against key baseline methods while exhibiting promising generalization capability and robustness.

Jiyan Song, Wenyang Wang, Chengcheng Yan +2

College of Sciences, Shihezi University, 221 North 4th Road, Shihezi, 832003, Xinjiang, China · School of Mathematics and Computational Science, Xiangtan University, North 2nd Ring Road, Xiangtan, 411105, Hunan, China

Graph Neural Networks Graph Representation Learning Molecular Representation Learning

Apr 23, 2026

Graph Neural Network-Informed Predictive Flows for Faster Ford-Fulkerson and PAC-Learnability

We propose a learning-augmented framework for accelerating max-flow computation and image segmentation by integrating Graph Neural Networks (GNNs) with the Ford-Fulkerson algorithm. Rather than predicting initial flows, our method learns edge importance probabilities to guide augmenting path selection. We introduce a Message Passing GNN (MPGNN) that jointly learns node and edge embeddings through coupled updates, capturing both global structure and local flow dynamics such as residual capacity and bottlenecks. Given an input image, we propose a method to construct a grid-based flow network with source and sink nodes, extract features, and perform a single GNN inference to assign edge probabilities reflecting their likelihood of belonging to high-capacity cuts. These probabilities are stored in a priority queue and used to guide a modified Ford-Fulkerson procedure, prioritizing augmenting paths via an Edmonds-Karp-style search with bottleneck-aware tie-breaking. This avoids repeated inference over residual graphs while leveraging learned structure throughout optimization. We further introduce a bidirectional path construction strategy centered on high-probability edges and provide a theoretical framework relating prediction quality to efficiency via a weighted permutation distance metric. Our method preserves max-flow/min-cut optimality while reducing the number of augmentations in practice. We also outline a hybrid extension combining flow warm-starting with edge-priority prediction, establishing a foundation for learning-guided combinatorial optimization in image segmentation.

Eleanor Wiesler, Trace Baxley

1Harvard Department of Mathematics. · 2Harvard Department of Computer Science.

Image Segmentation Graph Neural Networks Combinatorial Optimization Learning-Augmented Algorithms

Apr 22, 2026

Robustness of Spatio-temporal Graph Neural Networks for Fault Location in Partially Observable Distribution Grids

Fault location in distribution grids is critical for reliability and minimizing outage durations. Yet, it remains challenging due to partial observability, given sparse measurement infrastructure. Recent works show promising results by combining Recurrent Neural Networks (RNNs) and Graph Neural Networks (GNNs) for spatio-temporal learning. Still, many modern GNN architectures remain untested for this grid application, while existing GNN solutions have not explored GNN topology definitions beyond simply adopting the full grid topology to construct the GNN graph. We address these gaps by (i) systematically comparing a newly proposed graph-forming strategy (measured-only) to the traditional full-topology approach, and (ii) introducing STGNN (Spatio-temporal GNN) models based on GraphSAGE and an improved Graph Attention (GATv2), for distribution grid fault location; (iii) benchmarking them against state-of-the-art STGNN and RNN baselines on the IEEE 123-bus feeder. In our experiments, all evaluated STGNN variants achieve high performance and consistently outperform a pure RNN baseline, with improvements up to 11 percentage points F1. Among STGNN models, the newly explored RGATv2 and RGSAGE achieve only marginally higher F1 scores. Still, STGNNs demonstrate superior stability, with tight confidence intervals (within +/- 1.4%) compared to the RNN baseline (up to +/- 7.5%) across different experiment runs. Finally, our proposed reduced GNN topology (measured-only) shows clear benefits in both (i) model training time (6-fold reduction) and (ii) model performance (up to 11 points F1). This suggests that measured-only graphs offer a more practical, efficient, and robust framework for partially observable distribution grids.

Burak Karabulut, Carlo Manna, Chris Develder

Ghent University – imec · VITO

Graph Attention Networks Graph Neural Networks Anomaly Localization Spatiotemporal GNNs Power Systems

Apr 22, 2026

Sheaf Neural Networks on SPD Manifolds: Second-Order Geometric Representation Learning

Graph neural networks face two fundamental challenges rooted in the linear structure of Euclidean vector spaces: (1) Current architectures represent geometry through vectors (directions, gradients), yet many tasks require matrix-valued representations that capture relationships between directions-such as how atomic orientations covary in a molecule. These second-order representations are naturally captured by points on the symmetric positive definite matrices (SPD) manifold; (2) Standard message passing applies shared transformations across edges. Sheaf neural networks address this via edge-specific transformations, but existing formulations remain confined to vector spaces and therefore cannot propagate matrix-valued features. We address both challenges by developing the first sheaf neural network operates natively on the SPD manifold. Our key insight is that the SPD manifold admits a Lie group structure, enabling well-posed analogs of sheaf operators without projecting to Euclidean space. Theoretically, we prove that SPD-valued sheaves are strictly more expressive than Euclidean sheaves: they admit consistent configurations (global sections) that vector-valued sheaves cannot represent, directly translating to richer learned representations. Empirically, our sheaf convolution transforms effectively rank-1 directional inputs into full-rank matrices encoding local geometric structure. Our dual-stream architecture achieves SOTA on 6/7 MoleculeNet benchmarks, with the sheaf framework providing consistent depth robustness.

Yuhan Peng, Junwen Dong, Yuzhi Zeng +6

School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore · Chern Institute of Mathematics, Nankai University, Tianjin, China · Department of Mathematics, Faculty of Science, National University of Singapore, Singapore +3

Graph Neural Networks Geometric Representation Learning Manifold Learning Sheaf Neural Networks Sheaf Theory Molecular Representation Learning

Apr 22, 2026

Concept Graph Convolutions: Message Passing in the Concept Space

The trust in the predictions of Graph Neural Networks is limited by their opaque reasoning process. Prior methods have tried to explain graph networks via concept-based explanations extracted from the latent representations obtained after message passing. However, these explanations fall short of explaining the message passing process itself. To this aim, we propose the Concept Graph Convolution, the first graph convolution designed to operate on node-level concepts for improved interpretability. The proposed convolutional layer performs message passing on a combination of raw and concept representations using structural and attention-based edge weights. We also propose a pure variant of the convolution, only operating in the concept space. Our results show that the Concept Graph Convolution allows to obtain competitive task accuracy, while enabling an increased insight into the evolution of concepts across convolutional steps.

Lucie Charlotte Magister, Pietro Lio

University of Cambridge

Graph Neural Networks Message Passing Neural Networks Concept-Based Explanations GNN Explainability

Apr 21, 2026

When Graph Structure Becomes a Liability: A Critical Re-Evaluation of Graph Neural Networks for Bitcoin Fraud Detection under Temporal Distribution Shift

The consensus that GCN, GraphSAGE, GAT, and EvolveGCN outperform feature-only baselines on the Elliptic Bitcoin Dataset is widely cited but has not been rigorously stress-tested under a leakage-free evaluation protocol. We perform a seed-matched inductive-versus-transductive comparison and find that this consensus does not hold. Under a strictly inductive protocol, Random Forest on raw features achieves F1 = 0.821 and outperforms all evaluated GNNs, while GraphSAGE reaches F1 = 0.689 +/- 0.017. A paired controlled experiment reveals a 39.5-point F1 gap attributable to training-time exposure to test-period adjacency. Additionally, edge-shuffle ablations show that randomly wired graphs outperform the real transaction graph, indicating that the dataset's topology can be misleading under temporal distribution shift. Hybrid models combining GNN embeddings with raw features provide only marginal gains and remain substantially below feature-only baselines. We release code, checkpoints, and a strict-inductive protocol to enable reproducible, leakage-free evaluation.

Saket Maganti

Graph Neural Networks Distribution Shift Graph Representation Learning Financial Fraud Detection Temporal Distribution Shift

Apr 21, 2026

The Logical Expressiveness of Topological Neural Networks

Graph neural networks (GNNs) are the standard for learning on graphs, yet they have limited expressive power, often expressed in terms of the Weisfeiler-Leman (WL) hierarchy or within the framework of first-order logic. In this context, topological neural networks (TNNs) have recently emerged as a promising alternative for graph representation learning. By incorporating higher-order relational structures into message-passing schemes, TNNs offer higher representational power than traditional GNNs. However, a fundamental question remains open: what is the logical expressiveness of TNNs? Answering this allows us to characterize precisely which binary classifiers TNNs can represent. In this paper, we address this question by analyzing isomorphism tests derived from the underlying mechanisms of general TNNs. We introduce and investigate the power of higher-order variants of WL-based tests for combinatorial complexes, called

k

-CCWL test. In addition, we introduce the topological counting logic (TC

_k

), an extension of standard counting logic featuring a novel pairwise counting quantifier

\exists^{N}(x_i,x_j)\, \varphi(x_i,x_j),

which explicitly quantifies pairs

(x_i, x_j)

satisfying property

\varphi

. We rigorously prove the exact equivalence:

\text{k-CCWL} \equiv \text{TC}_{k{+}2} \equiv \text{Topological }(k{+}2)\text{-pebble game}.

These results establish a logical expressiveness theory for TNNs.

Amirreza Akbari, Amauri H. Souza, Vikas Garg

Aalto University · Federal Institute of Cear´a, 2δ AI · YaiYai Ltd

Graph Neural Networks GNN Expressivity Neural Network Expressivity

Apr 21, 2026

Inductive Subgraphs as Shortcuts: Causal Disentanglement for Heterophilic Graph Learning

Heterophily is a prevalent property of real-world graphs and is well known to impair the performance of homophilic Graph Neural Networks (GNNs). Prior work has attempted to adapt GNNs to heterophilic graphs through non-local neighbor extension or architecture refinement. However, the fundamental reasons behind misclassifications remain poorly understood. In this work, we take a novel perspective by examining recurring inductive subgraphs, empirically and theoretically showing that they act as spurious shortcuts that mislead GNNs and reinforce non-causal correlations in heterophilic graphs. To address this, we adopt a causal inference perspective to analyze and correct the biased learning behavior induced by shortcut inductive subgraphs. We propose a debiased causal graph that explicitly blocks confounding and spillover paths responsible for these shortcuts. Guided by this causal graph, we introduce Causal Disentangled GNN (CD-GNN), a principled framework that disentangles spurious inductive subgraphs from true causal subgraphs by explicitly blocking non-causal paths. By focusing on genuine causal signals, CD-GNN substantially improves the robustness and accuracy of node classification in heterophilic graphs. Extensive experiments on real-world datasets not only validate our theoretical findings but also demonstrate that our proposed CD-GNN outperforms state-of-the-art heterophily-aware baselines.

Xiangmeng Wang, Qian Li, Haiyang Xia +3

Curtin University Perth, Australia · The Education University of Hong Kong New Territories, Hong Kong

Disentangled Representation Learning Graph Neural Networks Causal Representation Learning Graph Heterophily

Apr 20, 2026

Subgraph Concept Networks: Concept Levels in Graph Classification

The reasoning process of Graph Neural Networks is complex and considered opaque, limiting trust in their predictions. To alleviate this issue, prior work has proposed concept-based explanations, extracted from clusters in the model's node embeddings. However, a limitation of concept-based explanations is that they only explain the node embedding space and are obscured by pooling in graph classification. To mitigate this issue and provide a deeper level of understanding, we propose the Subgraph Concept Network. The Subgraph Concept Network is the first graph neural network architecture that distils subgraph and graph-level concepts. It achieves this by performing soft clustering on node concept embeddings to derive subgraph and graph-level concepts. Our results show that the Subgraph Concept Network allows to obtain competitive model accuracy, while discovering meaningful concepts at different levels of the network.

Lucie Charlotte Magister, Alexander Norcliffe, Iulia Duta +1

University of Cambridge Cambridge, UK

Graph Neural Networks Hierarchical Representation Learning Concept-Based Explanations Graph Classification GNN Explainability

Apr 20, 2026

Multi-View Hierarchical Graph Neural Network for Sketch-Based 3D Shape Retrieval

Sketch-based 3D shape retrieval (SBSR) aims to retrieve 3D shapes that are consistent with the category of the input hand-drawn sketch. The core challenge of this task lies in two aspects: existing methods typically employ simplified aggregation strategies for independently encoded 3D multi-view features, which ignore the geometric relationships between views and multi-level details, resulting in weak 3D representation. Simultaneously, traditional SBSR methods are constrained by visible category limitations, leading to poor performance in zero-shot scenarios. To address these challenges, we propose Multi-View Hierarchical Graph Neural Network (MV-HGNN), a novel framework for SBSR. Specifically, we construct a view-level graph and capture adjacent geometric dependencies and cross-view message passing via local graph convolution and global attention. A view selector is further introduced to perform hierarchical graph coarsening, enabling a progressively larger receptive field for graph convolution and mitigating the interference of redundant views, which leads to more discriminate discriminative hierarchical 3D representation. To enable category agnostic alignment and mitigate overfitting to seen classes, we leverage CLIP text embeddings as semantic prototypes and project both sketch and 3D features into a shared semantic space. We use a two-stage training strategy for category-level retrieval and a one-stage strategy for zero-shot retrieval under the same model architecture. Under both category-level and zero-shot settings, extensive experiments on two public benchmarks demonstrate that MV-HGNN outperforms state-of-the-art methods.

Hang Cheng, Muyan He, Mingyu Fan +3

Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen, Guangdong, China · Control and Simulation Center, Harbin Institute of Technology, Harbin, Heilongjiang

Graph Neural Networks Hierarchical Representation Learning Multi-View Learning

Apr 19, 2026

Contraction and Hourglass Persistence for Learning on Graphs, Simplices, and Cells

Persistent homology (PH) encodes global information, such as cycles, and is thus increasingly integrated into graph neural networks (GNNs). PH methods in GNNs typically traverse an increasing sequence of subgraphs. In this work, we first expose limitations of this inclusion procedure. To remedy these shortcomings, we analyze contractions as a principled topological operation, in particular, for graph representation learning. We study the persistence of contraction sequences, which we call Contraction Homology (CH). We establish that forward PH and CH differ in expressivity. We then introduce Hourglass Persistence, a class of topological descriptors that interleave a sequence of inclusions and contractions to boost expressivity, learnability, and stability. We also study related families parametrized by two paradigms. We also discuss how our framework extends to simplicial and cellular networks. We further design efficient algorithms that are pluggable into end-to-end differentiable GNN pipelines, enabling consistent empirical improvements over many PH methods across standard real-world graph datasets. Code is available at this https URL.

Mattie Ji, Indradyumna Roy, Vikas Garg

University of Pennsylvania · Aalto University · Indian Institute of Technology Bombay +1

Graph Neural Networks Graph Representation Learning Persistent Homology Topological Representation Learning Topological Data Analysis

Apr 17, 2026

Graph self-supervised learning based on frequency corruption

Graph self-supervised learning can reduce the need for labeled graph data and has been widely used in recommendation, social networks, and other web applications. However, existing methods often underuse high-frequency signals and may overfit to specific local patterns, which limits representation quality and generalization. We propose Frequency-Corrupt Based Graph Self-Supervised Learning (FC-GSSL), a method that builds corrupted graphs biased toward high-frequency information by corrupting nodes and edges according to their low-frequency contributions. These corrupted graphs are used as inputs to an autoencoder, while low-frequency and general features are reconstructed as supervision targets, forcing the model to fuse information from multiple frequency bands. We further design multiple sampling strategies and generate diverse corrupted graphs from the intersections and unions of the sampling results. By aligning node representations from these views, the model can discover useful frequency combinations, reduce reliance on specific high-frequency components, and improve robustness. Experiments on 14 datasets across node classification, graph prediction, and transfer learning show that FC-GSSL consistently improves performance and generalization.

Haojie Li, Mengjiao Zhang, Guanfeng Liu +3

School of Data Science, Qingdao University of Science and Technology Qingdao, China · School of Information Science and Technology, Qingdao University of Science and Technology Qingdao, China · School of Computing, Macquarie University Sydney, Australia

Graph Neural Networks Graph Representation Learning Graph SSL Frequency-Domain Feature Learning Graph Contrastive Learning

Apr 17, 2026

NK-GAD: Neighbor Knowledge-Enhanced Unsupervised Graph Anomaly Detection

Graph anomaly detection aims to identify irregular patterns in graph-structured data. Most unsupervised GNN-based methods rely on the homophily assumption that connected nodes share similar attributes. However, real-world graphs often exhibit attribute-level heterophily, where connected nodes have dissimilar attributes. Our analysis of attribute-level heterophily graphs reveals two phenomena indicating that current approaches are not practical for unsupervised graph anomaly detection: 1) attribute similarities between connected nodes show nearly identical distributions across different connected node pair types, and 2) anomalies cause consistent variation trends between the graph with and without anomalous edges in the low- and high-frequency components of the spectral energy distributions, while the mid-part exhibits more erratic variations. Based on these observations, we propose NK-GAD, a neighbor knowledge-enhanced unsupervised graph anomaly detection framework. NK-GAD integrates a joint encoder capturing both similar and dissimilar neighbor features, a neighbor reconstruction module modeling normal distributions, a center aggregation module refining node features, and dual decoders for reconstructing attributes and structures. Experiments on seven datasets show NK-GAD achieves an average 3.29% AUC improvement.

Zehao Wang, Lanjun Wang

College of Intelligence and Computing, Tianjin University, Tianjin, China · School of New Media and Communication, Tianjin University, Tianjin, China

Graph Neural Networks Reconstruction-Based Anomaly Detection Unsupervised Anomaly Detection Graph Heterophily Anomaly Detection

Apr 17, 2026

A Structure-Preserving Graph Neural Solver for Parametric Hyperbolic Conservation Laws

Hyperbolic conservation laws govern a wide range of transport-driven dynamics featuring shocks, contact discontinuities, and complex wave interactions, posing distinct challenges for deep-learning-based surrogate modeling. While classical numerical methods provide robust and physically admissible solutions, their computational cost restricts applicability in many-query tasks such as parametric studies and design optimization. Conversely, existing neural surrogates offer rapid inference but often fail to respect intrinsic PDE structures, leading to non-physical artifacts, rollout instability, and poor generalization. We present an interpretable, structure-preserving graph neural solver that bridges classical numerical principles with graph neural networks (GNNs). The network is designed as a learned reconstruction-and-flux operator rather than a black-box state updater, thereby inherently preserving key properties such as local conservation and upwinding. Inspired by Arbitrary high-order DERivatives schemes, we further recast message-passing GNNs as high-order space-time predictors, enabling conservative and stable neural updates with large time steps. Evaluation is performed on challenging supersonic flow benchmarks spanning broad parametric variations in geometry, initial/boundary conditions, and flow regimes. The neural solver achieves superior long-horizon rollout stability and accuracy compared with strong surrogate baselines, outperforms low-order discretizations, and delivers orders-of-magnitude runtime speedups over high-resolution simulations.

Jiamin Jiang, Shanglin Lv, Jingrun Chen

School of Artificial Intelligence and Data Science and Suzhou Institute for Advanced Research, University of Science and Technology of China, and Suzhou Big Data & AI Research and Engineering Center, China · School of Mathematical Sciences, University of Science and Technology of China, China · School of Mathematical Sciences and Suzhou Institute for Advanced Research, University of Science and Technology of China, and Suzhou Big Data & AI Research and Engineering Center, China

Graph Neural Networks Neural PDE Solvers PDE Solving PDE Surrogate Modeling

Apr 16, 2026

Beyond the Laplacian: Doubly Stochastic Matrices for Graph Neural Networks

Graph Neural Networks (GNNs) conventionally rely on standard Laplacian or adjacency matrices for structural message passing. In this work, we substitute the traditional Laplacian with a Doubly Stochastic graph Matrix (DSM), derived from the inverse of the modified Laplacian, to naturally encode continuous multi-hop proximity and strict local centrality. To overcome the intractable

O(n^3)

complexity of exact matrix inversion, we first utilize a truncated Neumann series to scalably approximate the DSM, which serves as the foundation for our proposed DsmNet. Furthermore, because algebraic truncation inherently causes probability mass leakage, we introduce DsmNet-compensate. This variant features a mathematically rigorous Residual Mass Compensation mechanism that analytically re-injects the truncated tail mass into self-loops, strictly restoring row-stochasticity and structural dominance. Extensive theoretical and empirical analyses demonstrate that our decoupled architectures operate efficiently in

O(K|E|)

time and effectively mitigate over-smoothing by bounding Dirichlet energy decay, providing robust empirical validation on homophilic benchmarks. Finally, we establish the theoretical boundaries of the DSM on heterophilic topologies and demonstrate its versatility as a continuous structural encoding for Graph Transformers.

Zhaobo Hu, Vincent Gauthier, Mehdi Naima

SAMOVAR, Télécom SudParis · Institut Polytechnique de Paris · CNRS – LIP6 +1

Graph Neural Networks Graph Diffusion

Apr 16, 2026

CPGRec+: A Balance-oriented Framework for Personalized Video Game Recommendations

The rapid expansion of gaming industry requires advanced recommender systems tailored to its dynamic landscape. Existing Graph Neural Network (GNN)-based methods primarily prioritize accuracy over diversity, overlooking their inherent trade-off. To address this, we previously proposed CPGRec, a balance-oriented gaming recommender system. However, CPGRec fails to account for critical disparities in player-game interactions, which carry varying significance in reflecting players' personal preferences and may exacerbate over-smoothness issues inherent in GNN-based models. Moreover, existing approaches underutilize the reasoning capabilities and extensive knowledge of large language models (LLMs) in addressing these limitations. To bridge this gap, we propose two new modules. First, Preference-informed Edge Reweighting (PER) module assigns signed edge weights to qualitatively distinguish significant player interests and disinterests while then quantitatively measuring preference strength to mitigate over-smoothing in graph convolutions. Second, Preference-informed Representation Generation (PRG) module leverages LLMs to generate contextualized descriptions of games and players by reasoning personal preferences from comparing global and personal interests, thereby refining representations of players and games. Experiments on \textcolor{black}{two Steam datasets} demonstrate CPGRec+'s superior accuracy and diversity over state-of-the-art models. The code is accessible at https://github.com/HsipingLi/CPGRec-Plus.

Xiping Li, Aier Yang, Jianghong Ma +4

Harbin Institute of Technology, China · School of Computer Science, Wuhan University, China

Graph Neural Networks Recommender Systems User Preference Modeling

Apr 15, 2026

Leveraging LLM-GNN Integration for Open-World Question Answering over Knowledge Graphs

Open-world Question Answering (OW-QA) over knowledge graphs (KGs) aims to answer questions over incomplete or evolving KGs. Traditional KGQA assumes a closed world where answers must exist in the KG, limiting real-world applicability. In contrast, open-world QA requires inferring missing knowledge based on graph structure and context. Large language models (LLMs) excel at language understanding but lack structured reasoning. Graph neural networks (GNNs) model graph topology but struggle with semantic interpretation. Existing systems integrate LLMs with GNNs or graph retrievers. Some support open-world QA but rely on structural embeddings without semantic grounding. Most assume observed paths or complete graphs, making them unreliable under missing links or multi-hop reasoning. We present GLOW, a hybrid system that combines a pre-trained GNN and an LLM for open-world KGQA. The GNN predicts top-k candidate answers from the graph structure. These, along with relevant KG facts, are serialized into a structured prompt (e.g., triples and candidates) to guide the LLM's reasoning. This enables joint reasoning over symbolic and semantic signals, without relying on retrieval or fine-tuning. To evaluate generalization, we introduce GLOW-BENCH, a 1,000-question benchmark over incomplete KGs across diverse domains. GLOW outperforms existing LLM-GNN systems on standard benchmarks and GLOW-BENCH, achieving up to 53.3% and an average 38% improvement. GitHub code and data are available.

Hussein Abdallah, Ibrahim Abdelaziz, Panos Kalnis +1

Concordia University · IBM · KAUST

Knowledge Graph Question Answering LLM Reasoning with Graphs Graph Neural Networks