mlsanityData to 7 Oct 2026

BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation

arXiv 2106.10994 ↗First posted 21 Jun 2021cs.LG cs.AIcited by 195

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Abstract (arXiv)

Many representative graph neural networks, e.g., GPR-GNN and ChebNet, approximate graph convolutions with graph spectral filters. However, existing work either applies predefined filter weights or learns them without necessary constraints, which may lead to oversimplified or ill-posed filters. To overcome these issues, we propose BernNet, a novel graph neural network with theoretical support that provides a simple but effective scheme for designing and learning arbitrary graph spectral filters. In particular, for any filter over the normalized Laplacian spectrum of a graph, our BernNet estimates it by an order-K Bernstein polynomial approximation and designs its spectral property by setting the coefficients of the Bernstein basis. Moreover, we can learn the coefficients (and the corresponding filter weights) based on observed graphs and their associated signals and thus achieve the BernNet specialized for the data. Our experiments demonstrate that BernNet can learn arbitrary spectral filters, including complicated band-rejection and comb filters, and it achieves superior performance in real-world graph modeling tasks. Code is available at https://github.com/ivam-he/BernNet.

Key facts. Cited by 195 papers in the map (data through 7 Oct 2026). Builds on 27 of its 43 references that are in the map. First posted on arXiv 21 Jun 2021.

Builds on

27 of 43 references.

References · 27

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  2. 2017Graph Attention Networkscited by 8,854
  3. 2019A Comprehensive Survey on Graph Neural Networkscited by 2,906
  4. 2019Fast Graph Representation Learning with PyTorch Geometriccited by 2,414
  5. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,085
  6. 2019Simplifying Graph Convolutional Networkscited by 1,470
  7. 2018Graph Convolutional Neural Networks for Web-Scale Recommender Systemscited by 1,133
  8. 2018Predict then Propagate: Graph Neural Networks meet Personalized PageRankcited by 987
  9. 2016Revisiting Semi-Supervised Learning with Graph Embeddingscited by 970
  10. 2018Representation Learning on Graphs with Jumping Knowledge Networkscited by 875
  11. 2020Geom-GCN: Geometric Graph Convolutional Networkscited by 821
  12. 2015Image-based Recommendations on Styles and Substitutescited by 702
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  1. 2020Adaptive Universal Generalized PageRank Graph Neural Networkcited by 592
  2. 2019Multi-scale Attributed Node Embeddingcited by 543
  3. 2019Diffusion Improves Graph Learningcited by 414
  4. 2019Multi-Label Image Recognition with Graph Convolutional Networkscited by 320
  5. 2018Session-based Recommendation with Graph Neural Networkscited by 312
  6. 2020Towards Deeper Graph Neural Networkscited by 296
  7. 2019Semantic Graph Convolutional Networks for 3D Human Pose Regressioncited by 204
  8. 2017CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filterscited by 203
  9. 2019Graph Neural Networks with convolutional ARMA filterscited by 185
  10. 2018Traffic Graph Convolutional Recurrent Neural Network: A Deep Learning Framework for Network-Scale Traffic Learning and Forecastingcited by 145
  11. 2019Graph Wavelet Neural Networkcited by 131
  12. 2021Interpreting and Unifying Graph Neural Networks with An Optimization Frameworkcited by 131
  13. 2018DeepInf: Social Influence Prediction with Deep Learningcited by 128
  14. 2020Graph Convolutional Networks using Heat Kernel for Semi-supervised Learningcited by 50
  15. 2021AdaGNN: Graph Neural Networks with Adaptive Frequency Response Filtercited by 43

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 6; 2022: 22; 2023: 47; 2024: 52; 2025: 41; 2026: 27.

195 papers.

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  1. 2023One for All: Towards Training One Graph Model for All Classification Taskscited by 239
  2. 2023Language is All a Graph Needscited by 219
  3. 2022Rethinking Graph Neural Networks for Anomaly Detectioncited by 185
  4. 2022Sign and Basis Invariant Networks for Spectral Graph Representation Learningcited by 176
  5. 2022How Powerful are Spectral Graph Neural Networkscited by 169
  6. 2022Revisiting Heterophily For Graph Neural Networkscited by 169
  7. 2023Specformer: Spectral Graph Neural Networks Meet Transformerscited by 102
  8. 2022Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisitedcited by 87
  9. 2023Graph Prompt Learning: A Comprehensive Survey and Beyondcited by 61
  10. 2022Understanding convolution on graphs via energiescited by 58
  11. 2023GADBench: Revisiting and Benchmarking Supervised Graph Anomaly Detectioncited by 57
  12. 2022GREAD: Graph Neural Reaction-Diffusion Networkscited by 54
38 more
  1. 2022Graph Filters for Signal Processing and Machine Learning on Graphscited by 53
  2. 2024ARC: A Generalist Graph Anomaly Detector with In-Context Learningcited by 46
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  4. 2023Demystifying Structural Disparity in Graph Neural Networks: Can One Size Fit All?cited by 41
  5. 2023Graph Neural Networks with Learnable and Optimal Polynomial Basescited by 36
  6. 2023Beyond Homophily: Reconstructing Structure for Graph-agnostic Clusteringcited by 29
  7. 2023PC-Conv: Unifying Homophily and Heterophily with Two-fold Filteringcited by 28
  8. 2022EvenNet: Ignoring Odd-Hop Neighbors Improves Robustness of Graph Neural Networkscited by 26
  9. 2023A Survey on Spectral Graph Neural Networkscited by 26
  10. 2023Finding the Missing-half: Graph Complementary Learning for Homophily-prone and Heterophily-prone Graphscited by 25
  11. 2021A New Perspective on the Effects of Spectrum in Graph Neural Networkscited by 24
  12. 2024How Universal Polynomial Bases Enhance Spectral Graph Neural Networks: Heterophily, Over-smoothing, and Over-squashingcited by 24
  13. 2024Optimizing OOD Detection in Molecular Graphs: A Novel Approach with Diffusion Modelscited by 21
  14. 2024Partitioning Message Passing for Graph Fraud Detectioncited by 21
  15. 2023HoloNets: Spectral Convolutions do extend to Directed Graphscited by 20
  16. 2022Improving Graph Neural Networks with Learnable Propagation Operatorscited by 19
  17. 2022Complete the Missing Half: Augmenting Aggregation Filtering with Diversification for Graph Convolutional Neural Networkscited by 19
  18. 2023Rayleigh Quotient Graph Neural Networks for Graph-level Anomaly Detectioncited by 19
  19. 2023Breaking the Entanglement of Homophily and Heterophily in Semi-supervised Node Classificationcited by 19
  20. 2021Bridging the Gap between Spatial and Spectral Domains: A Unified Framework for Graph Neural Networkscited by 18
  21. 2022Node-oriented Spectral Filtering for Graph Neural Networkscited by 17
  22. 2023Robust Mid-Pass Filtering Graph Convolutional Networkscited by 17
  23. 2024Spatio-Spectral Graph Neural Networkscited by 17
  24. 2024Node-wise Filtering in Graph Neural Networks: A Mixture of Experts Approachcited by 17
  25. 2023Graph Distillation with Eigenbasis Matchingcited by 16
  26. 2024FedSSP: Federated Graph Learning with Spectral Knowledge and Personalized Preferencecited by 16
  27. 2022How Expressive are Transformers in Spectral Domain for Graphs?cited by 15
  28. 2022Exploiting Neighbor Effect: Conv-Agnostic GNNs Framework for Graphs with Heterophilycited by 15
  29. 2023LSGNN: Towards General Graph Neural Network in Node Classification by Local Similaritycited by 15
  30. 2023Higher-order Graph Convolutional Network with Flower-Petals Laplacians on Simplicial Complexescited by 15
  31. 2024Learn from Global Correlations: Enhancing Evolutionary Algorithm via Spectral GNNcited by 15
  32. 2022Homophily modulates double descent generalization in graph convolution networkscited by 13
  33. 2023How Curvature Enhance the Adaptation Power of Framelet GCNscited by 13
  34. 2024A Survey on Learning from Graphs with Heterophily: Recent Advances and Future Directionscited by 13
  35. 2024Large Language Model Meets Graph Neural Network in Knowledge Distillationcited by 13
  36. 2024UniGAD: Unifying Multi-level Graph Anomaly Detectioncited by 13
  37. 2024Gegenbauer Graph Neural Networks for Time-varying Signal Reconstructioncited by 12
  38. 2021Adaptive Gaussian Processes on Graphs via Spectral Graph Waveletscited by 11

50 most cited of 195 All 195 (JSON)