Graph Representation Learning

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Overview

Graph representation learning studies how to turn relational data into useful representations while preserving information about connectivity, node and edge attributes, and sometimes time or geometry. Common approaches include message-passing graph neural networks, spectral and positional encodings, graph Transformers, and self-supervised methods such as contrastive learning and masked prediction. These representations support tasks including node classification, link prediction, graph comparison, clustering, and molecular or social prediction; newer work also explores higher-order structure and foundation models that transfer across graphs. A central challenge is balancing expressive, scalable models with reliable generalization across graph sizes, domains, feature types, and structural shifts, while establishing when graph structure helps beyond simpler baselines.

Latest papers

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305 papers33 papers in the last four weeks, up 3% on the four weeks before. 0.2% of all new papers.

May 12, 2026

Graph-Based Financial Fraud Detection with Calibrated Risk Scoring and Structural Regularization

Financial transaction fraud prevention faces challenges such as complex relationship structures, concealed behavioral patterns, and dynamically changing data distribution. Discrimination models relying solely on independent sample features are insufficient to fully characterize the risks of group collaboration and chain transfers within transaction networks. This paper proposes a graph neural network representation learning and risk discrimination framework for financial transaction fraud prevention. It integrates transaction records and identity information into node attributes and constructs a transaction graph based on shared attributes and interaction consistency to explicitly model inter-transaction relationships. In model design, a multi-layer message passing mechanism is employed to aggregate neighborhood information, learn node embedding representations containing structural context semantics, and output transaction-level fraud probability and risk scores through a lightweight risk discrimination head. A weighted supervision objective is introduced to mitigate training bias caused by class imbalance, and structural consistency regularization constraints are combined to suppress the impact of noisy edges on representation drift, thereby improving the stability and usability of risk characterization. Experiments are conducted on a publicly available financial transaction dataset, comparing various methods in the same direction and comprehensively evaluating them under a unified evaluation protocol. The results show that the proposed method outperforms other methods in risk ranking and probability calibration quality, validating the effectiveness of graph structure modeling and representation learning collaboration in financial transaction fraud prevention.

Yunfei Nie, Jiawei Wang, Ruobing Yan +3

Brandeis University, Waltham, USA · University of California, Los Angeles, USA · Georgetown University, Washington, D.C., USA +2

Graph Neural NetworksGraph Representation LearningFinancial Fraud Detection
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May 12, 2026

Modeling Heterophily in Multiplex Graphs: An Adaptive Approach for Node Classification

Existing multiplex graph models often assume homophily, where connected nodes tend to belong to the same class or share similar attributes. Consequently, these models may struggle with graphs exhibiting heterophily, where connected nodes typically belong to different classes and have dissimilar attributes. While recent methods have been developed to learn reliable node representations from unidimensional graphs with heterophily, they do not fully address the complexities of multiplex graphs. In a multiplex graph, nodes are linked through multiple types of edges (referred to as dimensions), which can simultaneously exhibit homophilic and heterophilic interactions. To address this gap, we propose \methodname, a novel method for node classification in multiplex graphs that adapts to both homophilic and heterophilic dimensions. \methodname introduces dimension-specific compatibility matrices to model varying degrees of homophily and heterophily across dimensions. A key innovation is its use of a product of trainable low-pass and high-pass filters, approximated via Chebyshev polynomials, to capture both smooth and abrupt changes in the graph signal. By composing these filters and optimizing label predictions using a proximal-gradient method, \methodname dynamically adjusts to the heterophilic characteristics of each dimension. Extensive experiments on synthetic and real-world datasets provide evidence that \methodname captures the complex interplay of homophilic and heterophilic interactions in multiplex graphs, and tends to yield improved node classification performance compared to state-of-the-art methods.

Kamel Abdous, Nairouz Mrabah, Mohamed Bouguessa

Department of Computer Science, University of Quebec at Montreal, Montreal, QC, Canada

Graph Representation LearningSpectral MethodsNode ClassificationGraph Heterophily
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May 12, 2026

A Unified Perspective for Learning Graph Representations Across Multi-Level Abstractions

Graph Self-Supervised Learning (GSSL) has emerged as a powerful paradigm for generating high-quality representations for graph-structured data. While multi-scale graph contrastive learning has received increasing attention, many existing methods still predominantly focus on a single graph abstraction level. To address this limitation, we propose a unified contrastive framework that can target node-level, proximity-level, cluster-level, and graph-level information and integrate them through a linear combination of similarity scores on positive pairs and dissimilarity scores (i.e., similarity scores on negative pairs). Furthermore, current approaches typically assign uniform penalty strengths to all examples, which reduces optimization flexibility and leads to ambiguous convergence status. To overcome this, we introduce a novel parameter-free fine-grained self-weighting mechanism that adaptively assigns weights to individual similarity and dissimilarity scores. The proposed mechanism emphasizes the scores that deviate significantly from their target values. Our approach not only enhances optimization flexibility but also eliminates the computational overhead of hyperparameter tuning in conventional multi-task GSSL methods. Comprehensive experiments on real-world datasets show that our methods consistently outperform state-of-the-art approaches across downstream tasks, including classification, clustering, and link prediction, in both single-level and multi-level scenarios.

Mohamed Mahmoud Amar, Nairouz Mrabah, Mohamed Bouguessa +1

Department of Computer Science, University of Quebec at Montreal, Montreal, QC, Canada

Graph Representation LearningGraph SSLAdaptive Loss WeightingGraph Contrastive Learning
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May 12, 2026

From Message-Passing to Linearized Graph Sequence Models

Message-passing based approaches form the default backbone of most learning architectures on graph-structured data. However, the rapid progress of modern deep learning architectures in other domains, particularly sequence modeling, raises the question of how graph learning can benefit from these advances. We introduce Linearized Graph Sequence Models, a framework that recasts message-passing graph computation from the perspective of sequence modeling to simplify architectural choices. Our approach systematically separates the computational processing depth from the information propagation depth, allowing core graph architectural decisions to be treated as sequence modeling choices. Specifically, we analyze, both empirically and theoretically, what sequence properties make methods effective for learning and preserving the graph inductive bias. In particular, we validate our findings, demonstrating improved performance on long-range information tasks in graphs. Our findings provide a principled way to integrate modern sequence modeling advances into message-passing based graph learning. Beyond this, our work demonstrates how the separation of processing and information depth can recast central architectural questions as input modeling choices.

Joël Mathys, Basil Rohner, Saku Peltonen +1

1ETH Zurich, Switzerland

Long-Range Graph LearningGraph Representation LearningMessage Passing Neural NetworksSequence Modeling
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May 12, 2026

CAD-feature enhanced machine learning for manufacturing effort estimation on sheet metal bending parts

Graph-based machine learning has emerged as a promising approach for manufacturability analysis by learning directly from CAD models represented as Boundary Representations (B-reps), exploiting both surface geometry and topological connectivity. However, purely geometric representations often lack the process-specific semantics required for accurate manufacturability prediction: many manufacturing factors, such as surface roles or bend intent, are not explicitly encoded in shape alone and are difficult for data-driven models to infer reliably. We propose a hybrid approach that addresses this challenge by enriching B-rep attributed adjacency graphs with manufacturing features recognized through a rule-based module. Applied to sheet metal bending, recognized features, such as bend characteristics, flange lengths, and surface roles are integrated as node attributes, concentrating the learning signal on process-relevant geometric patterns. Experiments on both a large-scale synthetic manufacturability benchmark and a real-world industrial dataset with measured bending times, one of the first such validations on genuine production data, demonstrate that combining domain knowledge with graph-based learning improves prediction accuracy across both tasks. The results demonstrate that hybrid modeling offers a feasible and effective path toward deployable tools for manufacturability assessment and effort estimation in industrial CAD environments.

Matteo Ballegeer, Toon Van Camp, Willem Jaspers +6

ManufacturingGraph Representation Learning
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May 12, 2026

A Unified Graph Language Model for Multi-Domain Multi-Task Graph Alignment Instruction Tuning

Leveraging Graph Neural Networks (GNNs) as graph encoders and aligning the resulting representations with Large Language Models (LLMs) through alignment instruction tuning has become a mainstream paradigm for constructing Graph Language Models (GLMs), combining the generalization ability of LLMs with the structural modeling capacity of GNNs. However, existing GLMs that adopt GNNs as graph encoders largely overlook the problem of aligning GNN-encoded representations across domains and tasks with the LLM token space to obtain unified graph tokens, thereby limiting their ability to generalize across diverse graph data. To bridge this gap, we aim to incorporate a multi-domain, multi-task GNN encoder into GLMs and align its representations with LLMs to enable multi-domain, multi-task graph alignment instruction tuning. This alignment problem remains underexplored and poses two key challenges: 1) learning GNN-encoded representations that are simultaneously generalizable across domains and tasks and well aligned with textual semantics is difficult, due to substantial variations in graph structures, feature distributions, and supervision signals, together with the lack of textual-semantic alignment guidance in task-specific GNN training; 2) diverse graph data and task-specific instructions can exhibit different degrees of compatibility with the LLM token space during instruction tuning, leading to varying alignment difficulty and rendering a fixed alignment strategy suboptimal. To tackle these challenges, we propose UniGraphLM, a Unified Graph Language Model that incorporates a multi-domain, multi-task GNN encoder to learn generalizable graph representations aligned with textual semantics, and then adaptively aligns these representations with the LLM.

Haibo Chen, Xin Wang, Jiaheng Chao +2

Tsinghua University

LLM AlignmentGraph Representation LearningLanguage ModelingInstruction Tuning
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May 12, 2026

Learning Feature Encoder with Synthetic Anomalies for Weakly Supervised Graph Anomaly Detection

Weakly supervised graph anomaly detection aims to unveil unusual graph instances, e.g., nodes, whose behaviors significantly differ from normal ones, given only a limited number of annotated anomalies and abundant unlabeled samples. A major challenge is to learn a meaningful latent feature representation that reduces intra-class variance among normal data while remaining highly sensitive to anomalies. Although recent works have applied self-supervised feature learning for graph anomaly detection, their strategies are not specifically tailored to its unique requirements, motivating our exploration of a more domain-specific approach. In this paper, we introduce a weakly supervised graph anomaly detection method that leverages a feature learning strategy tailored for graph anomalies. Our approach is built upon a multi-task learning scheme that extracts robust feature representations through synthesized anomalies. We generate synthetic anomalies by perturbing the normal graph in various ways and assign a dedicated detection head to each anomaly type, ensuring that learned features are sensitive to potential deviations from normal patterns. Although synthetic anomalies may not perfectly replicate real-world patterns, they provide valuable auxiliary data for effective feature learnin, much like features learned from ImageNet classification transfer to downstream vision tasks. Additionally, we adopt a two-phase learning strategy: an initial warm-up phase using only synthetic samples, followed by a full-training phase integrating both tasks, to balance the influence of synthetic and real data. Extensive experiments on public datasets demonstrate the superior performance of our method over its competitors. Code is available at https://github.com/yj-zhou/SAWGAD.

Yingjie Zhou, Yuqin Xie, Fanxing Liu +3

Sichuan University, Chengdu 610065, China · University of Connecticut, Storrs, CT 06269, USA · University of Electronic Science and Technology of China, Chengdu 611731, China +1

Graph Representation LearningAnomaly Detection
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May 12, 2026

Knowledge Graphs Meet Graph Neural Networks: A Comprehensive Survey

Graph Neural Networks (GNNs) have emerged as a powerful paradigm in Knowledge Graphs (KGs) due to their intrinsic ability to model graph-structured data. However, there remains a lack of a systematic review about GNN-based methodologies across the entire knowledge graph technologies pipeline. To address this gap, we first propose a novel two-level taxonomy framework for GNN-based knowledge graph technologies: the KG technologies pipeline and GNN-based perspective. Specifically, the knowledge graph technologies pipeline covers knowledge graph construction, knowledge graph embedding, knowledge reasoning and knowledge graph applications. Meanwhile, the GNN-based perspective provides a new categorization of knowledge graph technologies with GNN models, such as GCN, GAT, and HGNN. Then, we analyze the advantages of GNN technology based on the characteristics of different tasks in the knowledge graph lifecycle. Furthermore, we detailed review various GNN-based models for knowledge graph following the proposed taxonomy, and summarize strengths and limitations. Finally, we discuss unresolved challenges and outline promising directions for future research.

Chengcheng Sun, Jiayun Tian, Cheng Zhai +5

School of Safety Engineering, China University of Mining and Technology, China · School of Computer Science and Technology, China University of Mining and Technology, China · State Key Laboratory of Coal Mine Disaster Prevention and Control, China University of Mining and Technology, China +1

KG ConstructionGraph Neural NetworksGraph Representation LearningKG EmbeddingKnowledge Graphs
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May 11, 2026

CORE: Cyclic Orthotope Relation Embedding for Knowledge Graph Completion

Knowledge graph completion (KGC) aims to automatically infer missing facts in multi-relational data by mapping entities and relations into continuous representation spaces. Recent region-based embedding models have shown great promise in capturing complex logical patterns by representing relations as geometric regions. However, these models inevitably suffer from absolute boundary constraints during optimization. Conversely, without such constraints, relation regions expand indefinitely. To address the limitation, we propose CORE (Cyclic Orthotope Relation Embedding), a novel KGC model that embeds entities and relations onto a boundary-less torus manifold.CORE represents relations as cyclic orthotopes on the torus manifold, allowing regions to seamlessly wrap around spatial boundaries to ensure smooth gradient conduction. Furthermore, an adaptive width regularization is introduced to prevent unconditional region expansion. Theoretical analysis proves that CORE can capture various complex relation patterns such as subsumption and intersection. Extensive experiments on four benchmark datasets demonstrate that CORE achieves highly competitive performance, significantly improving link prediction accuracy in dense semantic environments.

Yingqi Zeng, Luying Wang, Huiling Zhu

Graph Representation LearningKG EmbeddingGraph EmbeddingKG Completion
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May 11, 2026

Rank Is Not Capacity: Spectral Occupancy for Latent Graph Models

Graph representation learning has become a standard approach for analyzing networked data, with latent embeddings widely used for link prediction, community detection, and related tasks. Yet a basic design choice, the latent dimension, is still treated as a brittle hyperparameter, fixed before training and tuned by held-out performance. Learned factors are also identifiable only up to rotation and rescaling, so the nominal rank rarely coincides with the quantity that governs model behavior. We propose Spectral Prefix Extraction and Capacity-Targeted Representation Analysis (Spectra), which replaces rank as the unit of analysis with the spectrum of a learned positive semidefinite kernel, trace-normalized so that spectra are comparable across fits. The normalized eigenvalues form a distribution on the simplex, and their Shannon effective rank acts both as a summary of learned capacity and as a controllable training-time coordinate: a single scalar shapes this realized dimension during training, and bisection targets any desired value within the rank cap. To theoretically support that, we show local regularity and monotonicity of the realized-dimension profile. Across collaboration, social, biological, and infrastructure networks, Spectra traces performance--capacity frontiers that make the trade-off between predictive accuracy and realized dimension visible. It performs competitively with strong link-prediction baselines, yields aligned lower-capacity views of the same fitted model through spectral prefixes, and provides a principled handle on capacity in the overparameterized regime. Capacity thus becomes a property of the fitted model rather than a hyperparameter of the training.

Nikolaos Nakis, Panagiotis Promponas, Konstantinos Tsirkas +4

Human Nature Lab, Yale University · Department of Electrical and Computer Engineering, Yale University · Department of Statistics and Data Science, Yale University +1

Representation GeometryIntrinsic DimensionalityGraph Representation Learning
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May 11, 2026

It's All Connected: Topology-Aware Structural Graph Encoding Improves Performance on Polymer Prediction

Graph Neural Networks (GNNs) have achieved strong results in molecular property prediction, but polymers present distinct challenges: labeled datasets are scarce and small (typically in the order of hundreds of polymers) due to the need for expensive experimentation, and complex polymer chain distributions influence polymer properties. Established practice in polymer prediction represents polymers solely by graphs of their repeat units, discarding the chain-scale morphology that governs key properties such as the glass transition temperature (TgT_g). In this work, we propose a principled graph construction that addresses this gap. Given a polymer's molecular mass distribution (MMD), we sample representative chains from the Schulz-Zimm distribution and construct representative sets of large graphs encoding chain-scale topology directly, with atoms and bonds featurized using rich chemical descriptors. We further pretrain GNN encoders via masked graph modeling on 100,000 unlabeled PSMILES strings before fine-tuning on labeled data. On a dataset of 381 polymers (180 homopolymers and 201 copolymers), we show that graph construction and self-supervised pretraining are jointly necessary: without pretraining, the large graph method matches the repeat-unit baseline (28.40 K vs. 28.36 K RMSE); with pretraining, it achieves 24.76 K +/- 3.30 K, a 5.1% reduction in mean error over the pretrained repeat-unit baseline (26.08 K +/- 4.20 K, p < 0.001, 30 runs). An ablation removing chemical features degrades performance to 36.65 K, confirming both components are essential. Results are architecture-agnostic, holding for both GINE and GATv2 encoders.

H. Ibrahim Erdogan, Punith Raviswamy, Nikita Agrawal +5

University of Bayreuth, Germany · Faculty of Engineering Science, University of Bayreuth, Germany · Faculty of Mathematics, Physics & Computer Science, University of Bayreuth, Germany +5

Graph Representation LearningMaterials Property PredictionPolymer Property PredictionMolecular Property PredictionMolecular Representation Learning
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May 11, 2026

Relations Are Channels: Knowledge Graph Embedding via Kraus Decompositions

Knowledge graph embedding (KGE) models typically represent each relation as an operator on entity embeddings. In this work, we identify three structural axioms that any principled relation operator must satisfy, linearity, trace preservation, and complete positivity, and show that they characterize a Kraus channel structure via the Kraus representation theorem. The completeness constraint defining this family is equivalent to these axioms, providing a principled foundation rather than an externally imposed condition. Under this formulation, most existing operator-based KGE models are recoverable as special cases with Kraus rank κ=1κ= 1 under specific embedding choices. We further generalize this characterization to arbitrary metric geometries by introducing \mbox{w-Kraus} channels, which satisfy completeness by construction within their respective spaces. Building on this theory, we propose KrausKGE, a principled KGE model that naturally handles 11-to-NN and NN-to-NN relations, supports kk-hop reasoning without requiring explicit path encoders, and eliminates the need for norm constraints on entity embeddings. Additionally, our framework yields the first theoretically grounded per-relation complexity measure in the KGE literature, with a provable lower bound in terms of the empirical relation matrix rank. Empirical evaluation demonstrates that KrausKGE consistently outperforms strong baselines on NN-to-NN relations, with performance gains that increase monotonically with relation fan-out, in alignment with theoretical predictions.

Sayan Kumar Chaki

Inria, Laboratoire Hubert Curien, Université Jean Monnet

Graph Representation LearningKG EmbeddingKG Completion
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May 11, 2026

Learning Graph Foundation Models on Riemannian Graph-of-Graphs

Graph foundation models (GFMs), pretrained on massive graph data, have transformed graph machine learning by supporting general-purpose reasoning across diverse graph tasks and domains. Existing GFMs pretrained with fixed-hop subgraph sampling impose a fixed receptive field, causing scale mismatch on diverse tasks, which often require heterogeneous and unknown structural contexts beyond a fixed sampling scale. We propose R-GFM, a Riemannian Graph-of-Graphs (GoG) based foundation model, that treats structural scale as a first-class citizen in modeling. R-GFM constructs a multi-scale GoG over-sampled subgraphs at different hop distances and learns geometry-adaptive representations from Riemannian manifolds. Theoretical analysis shows that R-GFM reduces structural domain generalization error compared to fixed-scale GFMs. Experiments on various datasets demonstrate that R-GFM achieves state-of-the-art performance, with up to a 49% relative improvement on downstream tasks. Our code is available at https://github.com/USTC-DataDarknessLab/R-GFM.

Haokun Liu, Zezhong Ding, Xike Xie

School of Biomedical Engineering, University of Science and Technology of China (USTC), Suzhou, Jiangsu, China · Data Darkness Lab, Suzhou Institute for Advanced Research, USTC, Suzhou, Jiangsu, China · School of Artificial Intelligence and Data Science, USTC, Hefei, Anhui, China

Graph Representation LearningDomain GeneralizationGeometric Representation LearningGraph Foundation Models
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May 11, 2026

Learning the Interaction Prior for Protein-Protein Interaction Prediction: A Model-Agnostic Approach

Protein-protein interactions (PPIs) are fundamental to cellular function and disease mechanisms. Current learning-based PPI predictors focus on learning powerful protein representations but neglect designing specialized classification heads. They mainly rely on generic aggregating methods like concatenation or dot products, which lack biological insight. Motivated by the biological "L3 rule", where multiple length-3 paths between a pair of proteins indicate their interaction likelihood, our study addresses this gap by designing a biologically informed PPI classifier. In this paper, we provide empirical evidence that popular PPI datasets strongly support the L3 rule. We propose an L3-path-regularized graph prompt learning method called L3-PPI, which can generate a prompt graph with virtual L3 paths based on protein representations and controls the number of paths. L3-PPI reformulates the classification of protein embedding pairs into a graph-level classification task over the generated prompt graph. This lightweight module seamlessly integrates with PPI predictors as a plug-and-play component, injecting the interaction prior of complementarity to enhance performance. Extensive experiments show that L3-PPI achieves superior performance enhancements over advanced competitors.

Ziqi Gao, Chenyi Zi, Zijing Liu +3

Tsinghua University · The Hong Kong University of Science and Technology (Guangzhou) · IDEA Research +1

Prompt LearningGraph Representation LearningGraph Prompt LearningProtein-Protein Interaction Prediction
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May 10, 2026

CTQWformer: A CTQW-based Transformer for Graph Classification

Graph Neural Networks (GNN) and Transformer-based architectures have achieved remarkable progress in graph learning, yet they still struggle to capture both global structural dependencies and model the dynamic information propagation. In this paper, we propose CTQWformer, a hybrid graph learning framework that integrates continuous-time quantum walks (CTQW) with GNN. CTQWformer employs a trainable Hamiltonian that fuses graph topology and node features, enabling physically grounded modeling of quantum walk dynamics that captures rich and intricate graph structure information. The extracted CTQW-based representations are incorporated into two complementary modules:(i) a Graph Transformer module that embeds final-time propagation probabilities as structural biases in the self-attention mechanism, and (ii) a Graph Recurrent Module that captures temporal evolution patterns with bidirectional recurrent networks. Extensive experiments on benchmark graph classification datasets demonstrate that CTQWformer outperforms graph kernel and GNN-based methods, demonstrating the potential of integrating quantum dynamics into trainable deep learning frameworks for graph representation learning. To the best of our knowledge, CTQWformer is the first hybrid CTQW-based Transformer, integrating CTQW-derived structural bias with temporal evolution modeling to advance graph learning.

Zhan Li, Wuqing Yu, Yusen Wu +1

school of Artificial Intelligence, Beijing Normal University, Beijing, China

Graph Representation LearningQuantum-Inspired MLGraph ClassificationGraph Transformer
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May 10, 2026

GravityGraphSAGE: Link Prediction in Directed Attributed Graphs

Link prediction (inferring missing or future connections between nodes in a graph) is a fundamental problem in network science with widespread applications in, e.g., biological systems, recommender systems, finance and cybersecurity. The ability to accurately predict links has significant real-world applications, such as detecting fraudulent financial transactions or identifying drug-target interactions in biomedicine. Despite a rich literature, link prediction is still challenging, especially for graphs enriched with information on edges (direction) and nodes (attributes). In fact, research on link prediction, especially the one based on Graph Deep Learning (GDL), has mostly focused on undirected graphs, without fully leveraging node attributes. Here, we fill this gap by proposing Gravity-GraphSAGE (GG-SAGE), a modified version of GraphSAGE, a GDL model for node embeddings, composed of a gravity-inspired decoder. This implementation is the first example in the literature of a GraphSAGE backbone adopted for directed link prediction. Using the benchmark datasets Cora, Citeseer, PubMed and 16 real-world graphs from the online Netzschleuder repository, we show that our proposed model outperforms state-of-the-art GDL link prediction techniques. Using further experimental evidence, we relate the quality of the output of our model with various characteristics of the graph, suggesting that our framework scales well when applied to data of increasing complexity.

Riccardo Porcedda, Francesca Chiaromonte, Fabrizio Lillo +1

Department of Excellence L’EMbeDS, Sant’Anna School of Advanced Studies, Pisa, Italy · Department of Statistics and Huck Institutes of the Life Sciences, The Pennsylvania State University, USA · Class of Science, Scuola Normale Superiore, Pisa, Italy +1

Graph Neural NetworksGraph Representation LearningLink PredictionGraph Embedding
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May 8, 2026

Graph Computation Meets Circuit Algebra: A Task-Aligned Analysis of Graph Neural Networks for Electronic Design Automation

EDA problems are graph-structured, but not all graph-structured problems call for the same GNN computation. We argue that successful GNN-for-EDA methods are those whose propagation, aggregation, and supervision align with the native algebra of the target task. Concretely: static timing analysis is a max-plus/min-plus recurrence on a topologically ordered DAG, structurally aligned with asynchronous DAG-GNNs; placement is governed by hypergraph wirelength and density penalties and is exploited by differentiable placers rather than by message-passing GNNs alone; routing congestion is a sparse demand-supply field over a layout grid; switching-activity propagation is a probabilistic recurrence on a directed netlist; IR drop is a linear system on the power-delivery network; and analog symmetry extraction is a discrete constraint-prediction problem on schematic graphs. Through these task-by-task alignments we (i) review the GNN architectural toolkit relevant to circuits, (ii) formalize how circuit graphs differ from generic graphs (directed, heterogeneous, multi-scale, with sequential and clock structure), (iii) characterize where current methods succeed and where the algebra-architecture mismatch limits them, and (iv) identify failure modes--stage leakage, proxy-to-signoff gap, calibration, and design-distribution shift--that we believe are likely to dominate the next phase of work. We position the paper as a GNN-for-EDA, task-aligned analysis rather than a comprehensive AI-for-chip-design survey. Continuous SE(3)-equivariant geometric GNNs are usually mismatched to Manhattan digital layout, and LLM-for-RTL, HLS, and RL/diffusion-based topology generation are outside our scope.

Hyunmog Kim

Independent Researcher.

Graph Neural NetworksGraph Representation LearningElectronic Design Automation
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May 8, 2026

GraphReAct: Reasoning and Acting for Multi-step Graph Inference

Reasoning-acting frameworks enhance large language models (LLMs) by interleaving reasoning with actions for dynamic information acquisition. However, extending this paradigm to graph learning remains underexplored. Graph data is inherently structured, with information distributed across nodes and edges and encoded through both topology and latent representations. As a result, effective reasoning over graphs requires not only retrieving informative evidence from the graph, but also progressively refining the accumulated context during multi-step inference. In this work, we propose GraphReAct, a graph reasoning-acting framework that enables step-by-step inference over graph-structured data. Specifically, we design a graph-based action space with two complementary retrieval actions: topological retrieval, which captures local structural dependencies, and semantic retrieval, which accesses non-local but relevant evidence in the representation space. These actions dynamically expand the reasoning context. To further support multi-step reasoning, we introduce another type of action, context refinement, which distills and reorganizes accumulated information into a compact representation. By interleaving reasoning with both retrieval and refinement actions, our framework enables a progressive transition from context expansion to compression. Extensive experiments on six benchmark datasets demonstrate that GraphReAct consistently outperforms state-of-the-art methods, validating the effectiveness of reasoning-acting for graph learning.

Xingtong Yu, Zhongwei Kuai, Chang Zhou +6

The Chinese University of Hong Kong · The University of Science and Technology of China · University of Electronic Science and Technology of China +3

Graph Representation LearningGraph-Based RetrievalGraph Reasoning
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May 8, 2026

Learning Multi-Relational Graph Representations for DNA Methylation-Based Biological Age Estimation

Aging clocks aim to estimate biological age, a measure of physiological state distinct from chronological age, from observable biomarkers, and are widely used for health assessment and disease analysis. DNA methylation is a particularly informative biomarker due to its stability and strong association with aging, and recent learning-based approaches have improved predictive performance. However, most existing methods treat CpG sites as independent features, overlooking the complex and heterogeneous biological relationships among them. We propose RelAge-GNN, a multi-relational graph neural network framework for DNA methylation-based age prediction. Our method constructs three complementary graphs capturing co-methylation patterns, genomic co-localization, and gene-level associations among CpG sites. Each graph is modeled by an independent GNN branch, and a learnable gating mechanism adaptively fuses the resulting representations. Experiments on large-scale datasets show that RelAge-GNN achieves competitive accuracy and stronger correlation with chronological age compared to state-of-the-art methods. Moreover, the model exhibits improved sensitivity in detecting age acceleration across diverse disease cohorts, highlighting its potential utility for disease characterization. Finally, through post hoc interpretability analyses, we quantify the contributions of different relational structures and CpG sites, providing biologically meaningful insights and suggesting potential directions for aging-related research. Our code is available at: https://anonymous.4open.science/r/RelAge-GNN-F1E3/.

Qing Qing, Xikun Zhang, Zhongyuan Zhang +7

Jilin University · RMIT University · The Chinese University of Hong Kong +1

Graph Neural NetworksGraph Representation Learning
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May 8, 2026

GAD in the Wild: Benchmarking Graph Anomaly Detection under Realistic Deployment Challenges

Graph Anomaly Detection (GAD) is a critical task in graph machine learning with vital applications in financial fraud detection and social platform governance. However, existing GAD benchmarks are often restricted to small-scale, curated graphs with relatively balanced anomaly ratios, leaving a substantial gap between academic evaluation and real-world deployment. To bridge this gap, we present a multi-dimensional benchmark that systematically evaluates GAD models under three deployment-relevant challenges: million-scale graphs, extreme anomaly scarcity, and missing node attributes. We derive a family of controlled benchmark variants from five diverse graphs, including two native industrial-scale datasets with over 3.7 million nodes. Our extensive evaluation of nine representative GAD models reveals three major limitations: (1) most GNN-based methods fail to scale to million-node graphs due to prohibitive memory requirements; (2) detection performance drops sharply under realistic anomaly ratios (e.g., 0.1%), often resulting in zero recall; and (3) reconstruction-based models are highly sensitive to attribute imputation strategies. Our findings suggest that strong performance in laboratory settings does not guarantee robustness in production environments. We release this benchmark and empirical evaluation as a diagnostic testbed to promote the development of robust and scalable GAD systems for large-scale, imperfect graphs encountered in practice. Code is available at https://anonymous.4open.science/r/Benchmark_GAD-E7A3.

Jingjing Zhou, Shiyu Huang, Qing Qing +7

Zhejiang Gongshang University · Jilin University · Adelaide University +2

Graph Neural NetworksGraph Representation LearningLearning with Missing DataAnomaly Detection
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May 8, 2026

AdaTKG: Adaptive Memory for Temporal Knowledge Graph Reasoning

Temporal knowledge graphs (TKGs) represent time-stamped relational facts and support a wide range of reasoning tasks over evolving events. However, existing methods produce entity representations that are static at the entity level, in that each representation is a function of learned parameters only and retains no trace of the interactions in which the entity has participated. In this paper, we depart from this static view and propose that each entity be modeled as an adaptive process whose representation is refined every time the entity participates in a fact. To this end, we propose AdaTKG, which maintains a per-entity memory that is updated with every observed interaction, with the memory accumulating online and predictions improving as more interactions arrive. Specifically, we instantiate the memory update as a learnable exponential moving average governed by a single shared scalar instead of using learnable parameters for each entity, enabling AdaTKG to handle entities unseen during training. Extensive experiments confirm consistent gains over TKG baselines, demonstrating the effectiveness of adaptive memory. Code is available at: https://github.com/seunghan96/AdaTKG

Seunghan Lee, Jun Seo, Jaehoon Lee +7

LG AI Research Seoul, South Korea

Graph Representation LearningTemporal KGs
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May 7, 2026

Inductive Power Grid Cascading Failure Analysis with GRU-Gated Graph Attention

Identifying vulnerable transmission lines in power grids before a cascading failure occurs is challenging: existing methods can learn inter-line failure correlations from cascade data, but they are trained and evaluated on a single grid, and transferring the learned knowledge to an unseen grid remains an open problem. We address this by training a single Gated Recurrent Unit (GRU)-gated Graph Attention Network on combined cascading failure data from limited training grids and applying it directly to any unseen grid without retraining. A GRU gate controls what information each node retains or discards at each cascade iteration. Empirical evaluation shows that the model transfers zero-shot to multiple new grids spanning inter-time and inter-domain settings. Using information extracted from the trained model, we consistently identify more vulnerable lines than established structural and electrical baselines.

Tianxin Zhou, Xiang Li, Haibing Lu

Department of Computer Science & Engineering, Santa Clara University, Santa Clara, USA · Dept. of Information Systems & Analytics, Santa Clara University, Santa Clara, USA

Graph Attention NetworksGraph Representation LearningPower Systems
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May 7, 2026

Edge-specific signal propagation on mature chromophore-region 3D mechanism graphs for fluorescent protein quantum-yield prediction

Fluorescent protein quantum yield (QY) is governed by the mature chromophore and its three-dimensional microenvironment rather than sequence identity alone. Protein language models and emission-band averages capture global trends, but do not model how local physical signals act on specific chromophore regions. We present a chromophore-centred mechanism graph algorithm for QY prediction. Each PDB structure is converted into a typed 3D residue graph, registered to a mature-CRO state, partitioned into phenolate, bridge and imidazolinone regions, and transformed by channel-signal-region propagation. The representation contains 121 enrichment features; after removing identity shortcuts, 52 non-identity features are used for band-specific ExtraTrees regression. Because each feature encodes a contact channel, seed signal and target CRO region, interpretation is intrinsic rather than post hoc. On a 531-protein benchmark, the method achieved the best random-CV performance among model-based baselines (R = 0.772 +/- 0.008, MAE = 0.131 +/- 0.002), exceeding Band mean (R = 0.632), ESM-C (R = 0.734) and SaProt (R = 0.731), and ranked first in bright screening (Bright P@5 = 0.704). Under homology control, the advantage was clearest in the remote bucket (<50% similarity; R = 0.697 versus 0.633, 0.575 and 0.408), with the strongest overall bright/dark Top-K screening. Stable selected features recovered band-specific mechanisms: aromatic packing and clamp asymmetry in GFP-like proteins, charge/clamp balance in Red proteins, and flexibility-risk/bulky-contact features in Far-red proteins. Source code, feature tables and evaluation scripts are available from the first author upon request. Contact: [email protected]

Yuchen Xiong, Swee Keong Yeap, Steven Aw Yoong Kit

1China-ASEAN College of Marine Sciences, Xiamen University Malaysia, Sepang 43900, Selangor, Malaysia

Graph Representation LearningMolecular Property Prediction
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May 7, 2026

On the Safety of Graph Representation Learning

Graph representation learning (GRL) has evolved from topology-only graph embeddings to task-specific supervised GNNs, and more recently to reusable representations and graph foundation models (GFMs). However, existing evaluations mainly measure clean transfer, adaptation, and task coverage. It remains unclear whether GRL methods stay reliable when deployment stresses affect graph signals, graph contexts, label support, structural groups, or predictive evidence. We introduce GRL-Safety, a multi-axis safety evaluation benchmark for GRL. GRL-Safety evaluates twelve representative methods, spanning topology-only embedding methods, supervised GNNs, self-supervised graph models, and GFMs, on twenty-five graph datasets under standardized evaluation conditions while preserving method-native adaptation. The evaluation covers five safety axes: corruption robustness, OOD generalization, class imbalance, fairness, and interpretation, with per-axis and sub-condition reporting rather than a single aggregate score. Our analysis yields three cross-axis insights that can inspire future research. First, safety behavior is shaped by the interaction between representation design and the stressed graph factor, rather than by method family alone. Second, foundation-era methods show axis-specific strengths rather than broad safety dominance. Third, several deployment regimes remain difficult even for the best evaluated method, revealing capability gaps that require new robustness, adaptation, or training objectives beyond model selection. The benchmark, evaluation protocols, and code are available at: https://github.com/GXG-CS/GRL-Safety.

Xiaoguang Guo, Zehong Wang, Ziming Li +5

University of Connecticut · University of Notre Dame

Graph Representation LearningAlgorithmic FairnessOOD GeneralizationGraph Robustness
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May 7, 2026

Patch-Effect Graph Kernels for LLM Interpretability

Mechanistic interpretability aims to reverse-engineer transformer computations by identifying causal circuits through activation patching. However, scaling these interventions across diverse prompts and task families produces high-dimensional, unstructured datasets that are difficult to compare systematically. We propose a framework that reframes mechanistic analysis as a graph machine-learning problem by representing activation-patching profiles as patch-effect graphs over model components. We introduce three graph-construction methods: direct-influence via causal mediation, partial-correlation, and co-influence and apply graph kernels to analyze the resulting structures. Evaluating this approach on GPT-2 Small using Indirect Object Identification (IOI) and related tasks, we find that patch-effect graphs preserve discriminative structural signals. Specifically, localized edge-slot features provide higher classification accuracy than global graph-shape descriptors. A screened paired-patching validation suggests that CI and PC selected candidate edges correspond to stronger activation-influence effects than random or low-rank candidates. Crucially, by evaluating these representations against rigorous prompt-only and raw patch-effect controls, we make the evidential scope of the benchmark explicit: graph features compress structured patching signal, while raw tensors and surface cues define strong baselines that any circuit-level claim should address. Ultimately, our framework provides a compression and evaluation pipeline for comparing patching-derived structures under controlled baselines, separating robust slice-discriminative evidence from stronger task-general causal-circuit claims.

Ruben Fernandez-Boullon, David N. Olivieri

Department of Computer Science, University of Vigo, Ourense 32004, Spain

Graph Representation LearningMechanistic InterpretabilityCausal Interventions in Language ModelsActivation Patching
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May 7, 2026

Diversity Curves for Graph Representation Learning

Graph-level representations are crucial tools for characterising structural differences between graphs. However, comparing graphs with different cardinalities, even when sampled from the same underlying distribution, remains challenging. Unsupervised tasks in particular require interpretable, scalable, and reliable size-aware graph representations. Our work addresses these issues by tracking the structural diversity of a graph across coarsening levels. The resulting graph embeddings, which we denote diversity curves, are interpretable by construction, efficient, and directly comparable across coarsening hierarchies. Specifically, we track the spread of graphs, a novel isometry invariant that is inherently well-suited for encoding the metric diversity and geometry of graphs. We utilise edge contraction coarsening and prove that this improves expressivity, thus leading to more powerful graph-level representations than structural descriptors alone. Demonstrating their utility over a range of baseline methods in practice, we use diversity curves to (i) cluster and visualise simulated graphs across varying sizes, (ii) distinguish the geometry of single-cell graphs, (iii) compare the structure of molecular graph datasets, and (iv) characterise geometric shapes.

Katharina Limbeck, Nadja Häusermann, Martin Carrasco +2

1Helmholtz Munich · 2Technical University of Munich · 5Université de Fribourg +2

Graph Representation LearningGraph Coarsening
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May 7, 2026

Measuring Structure in Graph Benchmark Datasets Using Graph Invariants

Progress in graph learning is hindered by benchmark practices that conflate the contributions of node features and graph structure, making it hard to tell whether a model actually learns from the graph, or whether it even needs to. We propose measuring this using graph invariants, i.e., permutation-invariant, task-agnostic structural descriptors. Our analysis on datasets substantiates three tacit assumptions in graph learning, namely that (i) a curated subset of invariants is more expressive than standard GNNs, (ii) benchmark datasets exhibit structural heterogeneity even when originating from the same domain, and (iii) simple models are often competitive with, and sometimes exceed, approaches based on transformers or message passing. We thus posit that graph invariants should become a standard tool for measuring graph learning task complexity and the relevance of graph structure.

Richard von Moos, Mathieu Alain, Bastian Rieck

University of Fribourg · University College London

Graph Neural NetworksGraph Representation Learning
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May 7, 2026

Graphlets as Building Blocks for Structural Vocabulary in Knowledge Graph Foundation Models

Foundation models excel at language, where sentences become tokens, and vision, where images become pixels, because both reduce to discrete symbols on a shared, fixed grid. Knowledge Graphs share the discreteness, but not the geometry. Their entities and relations are discrete symbols, yet their arrangement is relational and lacks a common, fixed grid. Knowledge Graphs (KGs) share the discreteness, but not the geometry. They form irregular, non-Euclidean topologies whose local neighborhoods differ from graph to graph. Therefore, Knowledge Graph Foundation Models (KGFMs) rely on identifying structural invariances to produce transferable representations. Without a universal token set, KGFMs are limited in their ability to transfer representations across unseen KGs. We close this gap by treating graphlets, small connected graphs, as structural tokens that recur in heterogeneous KGs. In this paper, We introduce a model-agnostic framework based on a vocabulary of graphlets that mines a KG between relations via pattern matching. In particular, we considered closed and open 2- and 3-path, and star graphlets, to obtain robust invariances. The framework is evaluated on 51 KGs from a wide range of domains, for zero-shot inductive and transductive link prediction. Experiments show that adding simple graphlets to the vocabulary yields models that outperform prior KGFMs.

Kossi Amouzouvi, Robert Wardenga, Jens Lehmann +1

ScaDS.AI Dresden/Leipzig, Technische Universität Dresden, Dresden, Germany · alphaspeech - c/o alpha NT GmbH, Dresden, Germany · Amazon, Technische Universität Dresden, Dresden, Germany +1

Graph Representation LearningGraph Foundation ModelsKG Completion
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May 6, 2026

Bridging Input Feature Spaces Towards Graph Foundation Models

Unlike vision and language domains, graph learning lacks a shared input space, as input features differ across graph datasets not only in semantics, but also in value ranges and dimensionality. This misalignment prevents graph models from generalizing across datasets, limiting their use as foundation models. In this work, we propose ALL-IN, a simple and theoretically grounded method that enables transferability across datasets with different input features. Our approach projects node features into a shared random space and constructs representations via covariance-based statistics, thus eliminating dependence on the original feature space. We show that the computed node-covariance operators and the resulting node representations are invariant in distribution to permutations of the input features. We further demonstrate that the expected operator exhibits invariance to general orthogonal transformations of the input features. Empirically, ALL-IN achieves strong performance across diverse node- and graph-level tasks on unseen datasets with new input features, without requiring architecture changes or retraining. These results point to a promising direction for input-agnostic, transferable graph models.

Moshe Eliasof, Krishna Sri Ipsit Mantri, Beatrice Bevilacqua +2

University of Cambridge · Ben-Gurion University of the Negev · Purdue University

Graph Representation LearningTransfer LearningGraph Foundation ModelsInvariant Representation LearningGraph Transfer Learning
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May 5, 2026

Graph Neural Network based Hierarchy-Aware Embeddings of Knowledge Graphs: Applications to Yeast Phenotype Prediction

We present a method for finding hierarchy-aware embeddings of knowledge graphs (KGs) using graph neural networks (GNNs) enriched with a semantic loss derived from underlying ontologies. This method yields embeddings that better reflect domain knowledge. To demonstrate their utility, we predict and interpret the effects of gene deletions in the yeast Saccharomyces cerevisiae and learn box embeddings for KGs in the absence of a prediction task. We further show how box embeddings can serve as the basis for evaluating KG revisions. Our yeast KG is constructed from community databases and ontology terms. Low-dimensional box embeddings combined with GNNs are used to predict cell growth for double gene knockouts. Over 10-fold cross validation, these predictions have a mean R2R^2scoreof~0.360, significantly higher than baseline comparisons, demonstrating that high-level qualitative knowledge is informative about experimental outcomes. Incorporating semantic loss terms in the training of the models improves their predictive performance (R2R^2=0.377) by aligning embeddings with ontology structure. This shows that class hierarchies from ontologies can be exploited for quantitative prediction. We also test the trained models on triple gene knockouts, showing they generalise to data beyond those seen in training. Additionally, by identifying co-occurring relations in the yeast KG important for the cell-growth predictions, we construct hypotheses about interacting traits in yeast. A biological experiment validates one such finding, revealing an association between inositol utilisation and osmotic stress resistance, highlighting the model's potential to guide biological discovery.

Filip Kronström, Alexander H. Gower, Daniel Brunnsåker +2

Department of Computer Science and Engineering, Chalmers University of Technology and University of Gothenburg, Sweden · Department of Life Sciences, Chalmers University of Technology, Sweden · Department of Industrial Biotechnology, KTH Royal Institute of Technology, Sweden +1

Graph Neural NetworksRepresentation LearningGraph Representation LearningHierarchical Representation LearningKG EmbeddingKnowledge Graphs+1
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