mlsanityData to 7 Oct 2026

A New Perspective on the Effects of Spectrum in Graph Neural Networks

arXiv 2112.07160 ↗First posted 14 Dec 2021cs.LG cs.AIcited by 24

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Abstract (arXiv)

Many improvements on GNNs can be deemed as operations on the spectrum of the underlying graph matrix, which motivates us to directly study the characteristics of the spectrum and their effects on GNN performance. By generalizing most existing GNN architectures, we show that the correlation issue caused by the unsmooth spectrum becomes the obstacle to leveraging more powerful graph filters as well as developing deep architectures, which therefore restricts GNNs' performance. Inspired by this, we propose the correlation-free architecture which naturally removes the correlation issue among different channels, making it possible to utilize more sophisticated filters within each channel. The final correlation-free architecture with more powerful filters consistently boosts the performance of learning graph representations. Code is available at https://github.com/qslim/gnn-spectrum.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). Builds on 44 of its 59 references that are in the map. First posted on arXiv 14 Dec 2021.

Builds on

44 of 59 references.

References · 44

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  2. 2017Graph Attention Networkscited by 8,854
  3. 2017Inductive Representation Learning on Large Graphscited by 6,284
  4. 2018How Powerful are Graph Neural Networks?cited by 4,355
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32 more
  1. 2018Representation Learning on Graphs with Jumping Knowledge Networkscited by 875
  2. 2020Simple and Deep Graph Convolutional Networkscited by 857
  3. 2018Hierarchical Graph Representation Learning with Differentiable Poolingcited by 786
  4. 2019DropEdge: Towards Deep Graph Convolutional Networks on Node Classificationcited by 679
  5. 2020Benchmarking Graph Neural Networkscited by 672
  6. 2020Adaptive Universal Generalized PageRank Graph Neural Networkcited by 592
  7. 2020Principal Neighbourhood Aggregation for Graph Netscited by 477
  8. 2021Rethinking Graph Transformers with Spectral Attentioncited by 468
  9. 2019Diffusion Improves Graph Learningcited by 414
  10. 2021Beyond Low-frequency Information in Graph Convolutional Networkscited by 361
  11. 2017Residual Gated Graph ConvNetscited by 341
  12. 2021Do Transformers Really Perform Bad for Graph Representation?cited by 318
  13. 2016Learning Convolutional Neural Networks for Graphscited by 314
  14. 2020Improving Graph Neural Network Expressivity via Subgraph Isomorphism Countingcited by 312
  15. 2017Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphscited by 307
  16. 2019PairNorm: Tackling Oversmoothing in GNNscited by 297
  17. 2020Towards Deeper Graph Neural Networkscited by 296
  18. 2015Diffusion-Convolutional Neural Networkscited by 268
  19. 2019Revisiting Graph Neural Networks: All We Have is Low-Pass Filterscited by 260
  20. 2020DeeperGCN: All You Need to Train Deeper GCNscited by 249
  21. 2017CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filterscited by 203
  22. 2021BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximationcited by 195
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  24. 2021Interpreting and Unifying Graph Neural Networks with An Optimization Frameworkcited by 131
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 8; 2024: 7; 2025: 6; 2026: 1.

24 papers.

Sort:

  1. 2023Specformer: Spectral Graph Neural Networks Meet Transformerscited by 102
  2. 2023Energy Transformercited by 69
  3. 2023A Survey on Spectral Graph Neural Networkscited by 26
  4. 2024AdaFGL: A New Paradigm for Federated Node Classification with Topology Heterogeneitycited by 25
  5. 2024Partitioning Message Passing for Graph Fraud Detectioncited by 21
  6. 2025No Metric to Rule Them All: Toward Principled Evaluations of Graph-Learning Datasetscited by 16
  7. 2022Learnable Spectral Wavelets on Dynamic Graphs to Capture Global Interactionscited by 10
  8. 2024Graph Fourier Neural Kernels (G-FuNK): Learning Solutions of Nonlinear Diffusive Parametric PDEs on Multiple Domainscited by 5
  9. 2023Multiresolution Graph Transformers and Wavelet Positional Encoding for Learning Hierarchical Structurescited by 4
  10. 2023Towards Better Graph Representation Learning with Parameterized Decomposition & Filteringcited by 4
  11. 2022Deep representation learning: Fundamentals, Perspectives, Applications, and Open Challengescited by 3
  12. 2023Beyond Graph Convolutional Network: An Interpretable Regularizer-centered Optimization Frameworkcited by 3
12 more
  1. 2024Spectral GNN via Two-dimensional (2-D) Graph Convolutioncited by 3
  2. 2024Graph Neural Networks Are More Than Filters: Revisiting and Benchmarking from A Spectral Perspectivecited by 3
  3. 2023Perfect Alignment May be Poisonous to Graph Contrastive Learningcited by 2
  4. 2024Through the Dual-Prism: A Spectral Perspective on Graph Data Augmentation for Graph Classificationcited by 2
  5. 2023Degree-based stratification of nodes in Graph Neural Networkscited by 1
  6. 2025Federated Prototype Graph Learningcited by 1
  7. 2025Towards Unbiased Federated Graph Learning: Label and Topology Perspectivescited by 1
  8. 2025Towards Unsupervised Open-Set Graph Domain Adaptation via Dual Reprogrammingcited by 1
  9. 2024Technical Report: The Graph Spectral Token -- Enhancing Graph Transformers with Spectral Informationcited by 0
  10. 2025Toward Data-centric Directed Graph Learning: An Entropy-driven Approachcited by 0
  11. 2025Learning from Heterophilic Graphs: A Spectral Theory Perspective on the Impact of Self-Loops and Parallel Edgescited by 0
  12. 2026Controlled Dynamics Attractor Transformercited by 0