mlsanityData to 7 Oct 2026

Graph Neural Networks with convolutional ARMA filters

arXiv 1901.01343 ↗First posted 5 Jan 2019cs.LG stat.MLcited by 185

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Abstract (arXiv)

Popular graph neural networks implement convolution operations on graphs based on polynomial spectral filters. In this paper, we propose a novel graph convolutional layer inspired by the auto-regressive moving average (ARMA) filter that, compared to polynomial ones, provides a more flexible frequency response, is more robust to noise, and better captures the global graph structure. We propose a graph neural network implementation of the ARMA filter with a recursive and distributed formulation, obtaining a convolutional layer that is efficient to train, localized in the node space, and can be transferred to new graphs at test time. We perform a spectral analysis to study the filtering effect of the proposed ARMA layer and report experiments on four downstream tasks: semi-supervised node classification, graph signal classification, graph classification, and graph regression. Results show that the proposed ARMA layer brings significant improvements over graph neural networks based on polynomial filters.

Key facts. Cited by 185 papers in the map (data through 7 Oct 2026). First posted on arXiv 5 Jan 2019.

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Citing papers per year: 2021: 37; 2022: 40; 2023: 29; 2024: 45; 2025: 22; 2026: 12.

185 papers.

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  1. 2021BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximationcited by 195
  2. 2022Discovering Invariant Rationales for Graph Neural Networkscited by 186
  3. 2022Sign and Basis Invariant Networks for Spectral Graph Representation Learningcited by 176
  4. 2022How Powerful are Spectral Graph Neural Networkscited by 169
  5. 2022Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisitedcited by 87
  6. 2022GraphWorld: Fake Graphs Bring Real Insights for GNNscited by 56
  7. 2021Transferability of Graph Neural Networks: an Extended Graphon Approachcited by 51
  8. 2021VQ-GNN: A Universal Framework to Scale up Graph Neural Networks using Vector Quantizationcited by 39
  9. 2023Graph Neural Networks with Learnable and Optimal Polynomial Basescited by 36
  10. 2022Unlearning Graph Classifiers with Limited Data Resourcescited by 31
  11. 2022Parallel and Distributed Graph Neural Networks: An In-Depth Concurrency Analysiscited by 29
  12. 2023PC-Conv: Unifying Homophily and Heterophily with Two-fold Filteringcited by 28
38 more
  1. 2021Topological Relational Learning on Graphscited by 27
  2. 2023Dynamic Scenario Representation Learning for Motion Forecasting with Heterogeneous Graph Convolutional Recurrent Networkscited by 27
  3. 2021Learning Conjoint Attentions for Graph Neural Netscited by 26
  4. 2022EvenNet: Ignoring Odd-Hop Neighbors Improves Robustness of Graph Neural Networkscited by 26
  5. 2023A Survey on Spectral Graph Neural Networkscited by 26
  6. 2022High-Level Synthesis Performance Prediction using GNNs: Benchmarking, Modeling, and Advancingcited by 25
  7. 2022NAS-Bench-Graph: Benchmarking Graph Neural Architecture Searchcited by 25
  8. 2021Learning Connectivity with Graph Convolutional Networks for Skeleton-based Action Recognitioncited by 20
  9. 2023HoloNets: Spectral Convolutions do extend to Directed Graphscited by 20
  10. 2021Power Flow Balancing with Decentralized Graph Neural Networkscited by 19
  11. 2022Understanding Non-linearity in Graph Neural Networks from the Bayesian-Inference Perspectivecited by 19
  12. 2021Beyond Low-Pass Filters: Adaptive Feature Propagation on Graphscited by 18
  13. 2021Bridging the Gap between Spatial and Spectral Domains: A Unified Framework for Graph Neural Networkscited by 18
  14. 2023Distill n' Explain: explaining graph neural networks using simple surrogatescited by 18
  15. 2022RoSGAS: Adaptive Social Bot Detection with Reinforced Self-Supervised GNN Architecture Searchcited by 17
  16. 2022TIDE: Time Derivative Diffusion for Deep Learning on Graphscited by 17
  17. 2022Node-oriented Spectral Filtering for Graph Neural Networkscited by 17
  18. 2024Node-wise Filtering in Graph Neural Networks: A Mixture of Experts Approachcited by 17
  19. 2021TraverseNet: Unifying Space and Time in Message Passing for Traffic Forecastingcited by 16
  20. 2021Joint Detection and Localization of Stealth False Data Injection Attacks in Smart Grids using Graph Neural Networkscited by 15
  21. 2022How Expressive are Transformers in Spectral Domain for Graphs?cited by 15
  22. 2024Collaborate to Adapt: Source-Free Graph Domain Adaptation via Bi-directional Adaptationcited by 15
  23. 2021AutoGL: A Library for Automated Graph Learningcited by 14
  24. 2022GMSS: Graph-Based Multi-Task Self-Supervised Learning for EEG Emotion Recognitioncited by 14
  25. 2022ES-GNN: Generalizing Graph Neural Networks Beyond Homophily with Edge Splittingcited by 13
  26. 2022Graph-adaptive Rectified Linear Unit for Graph Neural Networkscited by 12
  27. 2021Pre-Training on Dynamic Graph Neural Networkscited by 11
  28. 2021You too Brutus! Trapping Hateful Users in Social Media: Challenges, Solutions & Insightscited by 11
  29. 2022Neural Graph Databasescited by 11
  30. 2023Regular Splitting Graph Network for 3D Human Pose Estimationcited by 11
  31. 2024LightDiC: A Simple yet Effective Approach for Large-scale Digraph Representation Learningcited by 11
  32. 2021Pyramidal Reservoir Graph Neural Networkcited by 10
  33. 2021Predicting Basin Stability of Power Grids using Graph Neural Networkscited by 10
  34. 2021SkipNode: On Alleviating Performance Degradation for Deep Graph Convolutional Networkscited by 10
  35. 2023A clean-label graph backdoor attack method in node classification taskcited by 10
  36. 2022Restructuring Graph for Higher Homophily via Adaptive Spectral Clusteringcited by 9
  37. 2023On Manipulating Signals of User-Item Graph: A Jacobi Polynomial-based Graph Collaborative Filteringcited by 9
  38. 2023Graph Neural Networks with Diverse Spectral Filteringcited by 9

50 most cited of 185 All 185 (JSON)