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Revisiting Graph Neural Networks: All We Have is Low-Pass Filters

arXiv 1905.09550 ↗First posted 23 May 2019stat.ML cs.IT cs.LGcited by 260

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Abstract (arXiv)

Graph neural networks have become one of the most important techniques to solve machine learning problems on graph-structured data. Recent work on vertex classification proposed deep and distributed learning models to achieve high performance and scalability. However, we find that the feature vectors of benchmark datasets are already quite informative for the classification task, and the graph structure only provides a means to denoise the data. In this paper, we develop a theoretical framework based on graph signal processing for analyzing graph neural networks. Our results indicate that graph neural networks only perform low-pass filtering on feature vectors and do not have the non-linear manifold learning property. We further investigate their resilience to feature noise and propose some insights on GCN-based graph neural network design.

Key facts. Cited by 260 papers in the map (data through 7 Oct 2026). First posted on arXiv 23 May 2019.

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Citing papers per year: 2021: 44; 2022: 54; 2023: 49; 2024: 49; 2025: 47; 2026: 17.

260 papers.

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  1. 2021Understanding over-squashing and bottlenecks on graphs via curvaturecited by 471
  2. 2021Beyond Low-frequency Information in Graph Convolutional Networkscited by 361
  3. 2021Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methodscited by 309
  4. 2021GRAND: Graph Neural Diffusioncited by 258
  5. 2023A Survey on Oversmoothing in Graph Neural Networkscited by 246
  6. 2022Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNscited by 208
  7. 2022Rethinking Graph Neural Networks for Anomaly Detectioncited by 185
  8. 2021Anomaly Detection on Attributed Networks via Contrastive Self-Supervised Learningcited by 175
  9. 2022Revisiting Heterophily For Graph Neural Networkscited by 169
  10. 2023On Over-Squashing in Message Passing Neural Networks: The Impact of Width, Depth, and Topologycited by 163
  11. 2022Anti-Oversmoothing in Deep Vision Transformers via the Fourier Domain Analysis: From Theory to Practicecited by 136
  12. 2021Interpreting and Unifying Graph Neural Networks with An Optimization Frameworkcited by 131
38 more
  1. 2022Graph-Coupled Oscillator Networkscited by 123
  2. 2021Dirichlet Energy Constrained Learning for Deep Graph Neural Networkscited by 97
  3. 2021Breaking the Limit of Graph Neural Networks by Improving the Assortativity of Graphs with Local Mixing Patternscited by 95
  4. 2021EDITS: Modeling and Mitigating Data Bias for Graph Neural Networkscited by 92
  5. 2023On the Expressive Power of Geometric Graph Neural Networkscited by 89
  6. 2023Edge Directionality Improves Learning on Heterophilic Graphscited by 88
  7. 2021Beltrami Flow and Neural Diffusion on Graphscited by 84
  8. 2021Is Heterophily A Real Nightmare For Graph Neural Networks To Do Node Classification?cited by 82
  9. 2021New Benchmarks for Learning on Non-Homophilous Graphscited by 81
  10. 2023DRew: Dynamically Rewired Message Passing with Delaycited by 81
  11. 2021Subgroup Generalization and Fairness of Graph Neural Networkscited by 69
  12. 2021Elastic Graph Neural Networkscited by 67
  13. 2022Understanding convolution on graphs via energiescited by 58
  14. 2021Cold Brew: Distilling Graph Node Representations with Incomplete or Missing Neighborhoodscited by 57
  15. 2022Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminatingcited by 57
  16. 2023Unsupervised Learning for Solving the Travelling Salesman Problemcited by 57
  17. 2023Locality-Aware Graph-Rewiring in GNNscited by 55
  18. 2022GREAD: Graph Neural Reaction-Diffusion Networkscited by 54
  19. 2022Graph Filters for Signal Processing and Machine Learning on Graphscited by 53
  20. 2022Gradient Gating for Deep Multi-Rate Learning on Graphscited by 49
  21. 2021AdaGNN: Graph Neural Networks with Adaptive Frequency Response Filtercited by 43
  22. 2022Revisiting Graph Contrastive Learning from the Perspective of Graph Spectrumcited by 43
  23. 2025On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph Learningcited by 42
  24. 2021Sampling methods for efficient training of graph convolutional networks: A surveycited by 40
  25. 2021p-Laplacian Based Graph Neural Networkscited by 39
  26. 2023Taming Local Effects in Graph-based Spatiotemporal Forecastingcited by 37
  27. 2021Bag of Tricks for Training Deeper Graph Neural Networks: A Comprehensive Benchmark Studycited by 36
  28. 2024Revisiting Multimodal Emotion Recognition in Conversation from the Perspective of Graph Spectrumcited by 33
  29. 2022ACMP: Allen-Cahn Message Passing with Attractive and Repulsive Forces for Graph Neural Networkscited by 31
  30. 2023Class-Imbalanced Graph Learning without Class Rebalancingcited by 29
  31. 2024The Heterophilic Graph Learning Handbook: Benchmarks, Models, Theoretical Analysis, Applications and Challengescited by 29
  32. 2022EvenNet: Ignoring Odd-Hop Neighbors Improves Robustness of Graph Neural Networkscited by 26
  33. 2022Model Degradation Hinders Deep Graph Neural Networkscited by 26
  34. 2023Learning Probabilistic Symmetrization for Architecture Agnostic Equivariancecited by 25
  35. 2024Question Calibration and Multi-Hop Modeling for Temporal Question Answeringcited by 25
  36. 2021Meta-Aggregator: Learning to Aggregate for 1-bit Graph Neural Networkscited by 24
  37. 2021A New Perspective on the Effects of Spectrum in Graph Neural Networkscited by 24
  38. 2024Spectral Graph Pruning Against Over-Squashing and Over-Smoothingcited by 23

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