Spectral Graph Convolution

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Spectral graph convolution studies how to transform node features using the frequency structure of a graph, often defined by its Laplacian. Common approaches use polynomial filters such as Chebyshev, Jacobi, or Hermite expansions to avoid costly eigendecomposition, alongside adaptive Laplacians, multi-scale bases, and filters for temporal or higher-order graph signals. These methods are used in settings including node classification, anomaly detection, time-series forecasting, and scientific modeling, with practical attention to scalability, robustness, and preserving high-frequency information. A central tension is whether spectral components provide reliable advantages over message-passing networks: theoretical claims and benchmark gains depend on the filter, implementation, training conditions, and task.

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22 papers3 papers in the last four weeks, level with the four weeks before. 0.0% of all new papers.

Spectral Limits of Polynomial Graph Filters on the Long-Range Ising Model Benchmark
Oct 15, 2026Amin Najafgholizadeh, Mohsen AfsharchiGNN Expressivity Graph Signal Processing
University of Zanjan.
ChronoSheaf: Joint Spatio-Temporal Spectral Filtering on Cellular Sheaves
Oct 15, 2026Abeer Mostafa, Zahra AhmadiSheaf Neural Networks Spatiotemporal Forecasting
Peter L. Reichertz Institute for Medical Informatics, Hannover Medical School, Germany · Lower Saxony Center for Artificial Intelligence and Causal Methods in Medicine (CAIMed), Hannover, Germany
Inverse Cross-spectral Neural Networks for Multivariate Time Series
Oct 5, 2026Lorenzo Marinucci, Leonardo Di Nino, Gabriele D'Acunto +2Graph Neural Networks Spectral Graph Convolution
Statistical Sciences Dept., Sapienza University of Rome, Italy · DIET Dept., Sapienza University of Rome, Italy
TwinS-GCN: Spectral conjugate for Spectral Graph Convolutional Networks
Sep 26, 2026Chun Hei Michael Chan, Flavia Petruso, Dimitri Van De VilleGraph Neural Networks Spectral Graph Convolution
Neuro-X Institute and Department of Electrical Engineering ´Ecole polytechnique f´ed´erale de Lausanne (EPFL) Geneva, 1202, Switzerland
Spectral Graph Neural Networks with Hermite Polynomials: A Comprehensive Study
Sep 24, 2026Shuang WuGraph Neural Networks Spectral Graph Convolution
UCLA
LiftGCN: Efficient Energy-Preserving Graph Learning via Joukowski Spectral Lifting for Finite Element Stress Prediction
Sep 14, 2026Chen Zeng, Qiao WangGraph Neural Networks Spectral Graph Convolution
School of Information Science and Engineering, Southeast University · School of Economics and Management, Southeast University
Feature Transformation Enhanced Jacobi Polynomial Graph Filtering for Graph Anomaly Detection
Aug 27, 2026Xiang Wang, Zhijun Cheng, Zhenyu MengAnomaly Detection Graph Neural Networks
School of Artificial Intelligence and Transportation Engineering, Fujian University of Technology, Fuzhou, China · Institute of Artificial Intelligence, Fujian University of Technology, Fuzhou, China
Nonlinear Laplacians Improve Signed-Directed Graph Learning
Aug 1, 2026Ali Parviz, Yuichi YoshidaGraph Neural Networks Spectral Graph Convolution
Mila - Quebec AI Institute · New Jersey Institute of Technology · National Institute of Informatics (NII) +1
Dynamic Spectral Filtering for Temporal Graph Learning: Learning Evolving Propagation Operators
Jul 30, 2026Yan KongTemporal GNNs Temporal Link Prediction
Nanjing University of Information Science and Technology, China
Beyond Sparse Supervision: Diffusion-Guided Learning for Few-Shot Graph Fraud Detection
Jun 26, 2026Liming Liu, Chao Hu, Mingfei Lu +3Graph Neural Networks Graph SSL
Central South University, Changsha, China · University of Technology Sydney, Australian Artificial Intelligence Institute, Sydney, Australia
Convex--Concave Quadratic Spectral Filtering for Graph Neural Networks
Jun 23, 2026Ranhui Yan, Jia Cai, Mengzhu Chen +1Graph Neural Networks Graph Robustness
School of Computing and Artificial Intelligence, Guangzhou Xinhua University, Guangzhou, Guangdong, China · School of Statistics and Data Science, Guangdong University of Finance and Economics,2026 Guangzhou, Guangdong, China
A Graph Foundation Model with Spectral Parsing and Prototype-Guided Spatial Propagation
Jun 2, 2026Ankang Yang, Jitao Zhao, Dongxiao He +3Graph Neural Networks Cross-Domain Generalization
School of Computer Science and Technology Tianjin University Tianjin, China · School of Artificial Intelligence Hebei University of Technology Tianjin, China · Department of Health Technology and Informatics Department of Data Science and Artificial Intelligence The Hong Kong Polytechnic University Kowloon, Hong Kong
Outage Detection in Self-Healing Smart Grids Using Reinforcement Learning with Spectral Graph Neural Networks
May 26, 2026Lihui Liu, Mucun Sun, Caisheng WangRL Control Graph Neural Networks
Wayne State University, Detroit, MI, USA
Beyond Oversquashing: Understanding Signal Propagation in GNNs Via Observables
May 13, 2026Eden Nagar, Ya-Wei Eileen Lin, Ron LevieGraph Neural Networks Over-Squashing in GNNs
Technion - Israel Institute of Technology, Faculty of Mathematics · Technical University of Munich, School of Computation, Information and Technology · Munich Center for Machine Learning
Hierarchical Multi-Scale Graph Neural Networks: Scalable Heterophilous Learning with Oversmoothing and Oversquashing Mitigation
May 8, 2026Md Sazzad Hossen, Avimanyu SahooGraph Heterophily Over-Squashing
University of Alabama in Huntsville, Huntsville, AL, USA.
Full-Spectrum Graph Neural Networks: Expressive and Scalable
May 7, 2026Xiaohan Wang, Deyu Bo, Longlong Li +1Graph Neural Networks GNN Expressivity
Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore.
Generalization Bounds for Spectral GNNs via Fourier Domain Analysis
Apr 1, 2026Vahan A. Martirosyan, Daniele Malitesta, Hugues Talbot +2Generalization Bounds Neural Network Generalization
Université Paris-Saclay, CentraleSupélec, Inria, France · LTCI, Télécom Paris, Institut Polytechnique de Paris, France
Position: Spectral GNNs Are Neither Spectral Nor Superior for Node Classification
Mar 19, 2026Qin Jiang, Chengjia Wang, Michael Lones +2Spectral Graph Convolution Node Classification
Department of Computer Science, University of Heriot-Watt, Edinburgh, UK
L2G-Net: Local to Global Spectral Graph Neural Networks via Cauchy Factorizations
Feb 21, 2026Samuel Fernández-Menduiña, Eduardo Pavez, Antonio OrtegaSpectral Graph Convolution Graph Signal Processing
University of Southern California.
Geometry-Induced Diffusion on Graphs: A Learnable Weighted Laplacian for Spectral GNNs
Feb 20, 2026Mia Zosso, Ali Hariri, Victor Kawasaki-Borruat +2Long-Range Graph Learning Graph Representation Learning
École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland · École Normale Supérieure – PSL, Paris, France
Spectral Convolution on Orbifolds for Geometric Deep Learning
Feb 16, 2026Tim Mangliers, Bernhard Mössner, Benjamin HimpelGeometric Representation Learning Spectral Graph Convolution
Department of Computer Science Reutlingen University, Germany
Structured Spectral Graph Representation Learning for Multi-label Abnormality Analysis from 3D CT Scans
Oct 12, 2025Theo Di Piazza, Carole Lazarus, Olivier Nempont +1Graph Neural Networks Graph Representation Learning
INSA Lyon, University of Lyon, CNRS, INSERM, CREATIS UMR 5220, U1294, Villeurbanne, France · Hospices Civil de Lyon, Lyon, France · Philips Clinical Informatics, Innovation Paris, France

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Spectral Limits of Polynomial Graph Filters on the Long-Range Ising Model Benchmark

Amin Najafgholizadeh, Mohsen Afsharchi

University of Zanjan.

GNN Expressivity Graph Signal Processing Spectral Graph Convolution

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The Long-Range Ising Model benchmark (LRIM) guarantees long-range dependence by construction: each label is the node's spin times the spin field convolved with a power-law coupling, so any model's distance from the target is measurable. We prove that a readout whose filter is a polynomial in the adjacency, the linear core of isotropic message passing and spectral graph networks, leaves an error floor that no degree lowers, because the target varies along a level set of the spectrum on which every such filter is constant. Computed exactly, the floor and the best filter of each degree predict two spectral networks adapted from published architectures to within a tenth of a decade. A filter escapes the floor only if it weighs separately the offsets the adjacency lumps together, and must still resolve the coupling across the whole lattice. A strided filter of about fifty coefficients does both: fitted to the training labels, its test error is 52 times below the best published network's. A dilated convolutional network beats the best published result at 256 nodes, matches it at 1,024, and gives the first in-domain results at the three larger sizes, while a Fourier neural operator with its standard modes falls further behind as the lattice grows. At its standard budget the dilated network stays two to four orders of magnitude short of a larger strided filter fitted to the labels. The analysis carries over to the benchmark's second coupling.