mlsanityData to 7 Oct 2026

Graph Neural Networks with Learnable and Optimal Polynomial Bases

arXiv 2302.12432 ↗First posted 24 Feb 2023cs.LG cs.AIcited by 36

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Abstract (arXiv)

Polynomial filters, a kind of Graph Neural Networks, typically use a predetermined polynomial basis and learn the coefficients from the training data. It has been observed that the effectiveness of the model is highly dependent on the property of the polynomial basis. Consequently, two natural and fundamental questions arise: Can we learn a suitable polynomial basis from the training data? Can we determine the optimal polynomial basis for a given graph and node features? In this paper, we propose two spectral GNN models that provide positive answers to the questions posed above. First, inspired by Favard's Theorem, we propose the FavardGNN model, which learns a polynomial basis from the space of all possible orthonormal bases. Second, we examine the supposedly unsolvable definition of optimal polynomial basis from Wang & Zhang (2022) and propose a simple model, OptBasisGNN, which computes the optimal basis for a given graph structure and graph signal. Extensive experiments are conducted to demonstrate the effectiveness of our proposed models. Our code is available at https://github.com/yuziGuo/FarOptBasis.

Key facts. Cited by 36 papers in the map (data through 7 Oct 2026). Builds on 23 of its 45 references that are in the map. First posted on arXiv 24 Feb 2023.

Builds on

23 of 45 references.

References · 23

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  3. 2019Optuna: A Next-generation Hyperparameter Optimization Frameworkcited by 2,455
  4. 2020Open Graph Benchmark: Datasets for Machine Learning on Graphscited by 2,148
  5. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,085
  6. 2019Simplifying Graph Convolutional Networkscited by 1,470
  7. 2018Predict then Propagate: Graph Neural Networks meet Personalized PageRankcited by 987
  8. 2016Revisiting Semi-Supervised Learning with Graph Embeddingscited by 970
  9. 2020Simple and Deep Graph Convolutional Networkscited by 857
  10. 2020Adaptive Universal Generalized PageRank Graph Neural Networkcited by 592
  11. 2019MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixingcited by 442
  12. 2021Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methodscited by 309
11 more
  1. 2020SIGN: Scalable Inception Graph Neural Networkscited by 283
  2. 2021BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximationcited by 195
  3. 2019Graph Neural Networks with convolutional ARMA filterscited by 185
  4. 2022How Powerful are Spectral Graph Neural Networkscited by 169
  5. 2020Scalable Graph Neural Networks via Bidirectional Propagationcited by 87
  6. 2022Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisitedcited by 87
  7. 2021Optimization of Graph Neural Networks: Implicit Acceleration by Skip Connections and More Depthcited by 55
  8. 2022Graph Filters for Signal Processing and Machine Learning on Graphscited by 53
  9. 2021Node Dependent Local Smoothing for Scalable Graph Learningcited by 45
  10. 2020EdgeNets:Edge Varying Graph Neural Networkscited by 36
  11. 2019Improving Graph Attention Networks with Large Margin-based Constraintscited by 34

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 4; 2024: 14; 2025: 9; 2026: 9.

36 papers.

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  1. 2024fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functionscited by 60
  2. 2024How Universal Polynomial Bases Enhance Spectral Graph Neural Networks: Heterophily, Over-smoothing, and Over-squashingcited by 24
  3. 2023Breaking the Entanglement of Homophily and Heterophily in Semi-supervised Node Classificationcited by 19
  4. 2024Spatio-Spectral Graph Neural Networkscited by 17
  5. 2024PolyFormer: Scalable Node-wise Filters via Polynomial Graph Transformercited by 10
  6. 2023Spectral Heterogeneous Graph Convolutions via Positive Noncommutative Polynomialscited by 8
  7. 2024A Comprehensive Benchmark on Spectral GNNs: The Impact on Efficiency, Memory, and Effectivenesscited by 6
  8. 2023Clarify Confused Nodes via Separated Learningcited by 5
  9. 2024Improving Expressive Power of Spectral Graph Neural Networks with Eigenvalue Correctioncited by 5
  10. 2024Optimizing Polynomial Graph Filters: A Novel Adaptive Krylov Subspace Approachcited by 5
  11. 2024ERGNN: Spectral Graph Neural Network With Explicitly-Optimized Rational Graph Filterscited by 5
  12. 2025Homophily Heterogeneity Matters in Graph Federated Learning: A Spectrum Sharing and Complementing Perspectivecited by 4
24 more
  1. 2024Rethinking Spectral Graph Neural Networks with Spatially Adaptive Filteringcited by 3
  2. 2024Simplified PCNet with Robustnesscited by 3
  3. 2024Spectral GNN via Two-dimensional (2-D) Graph Convolutioncited by 3
  4. 2024Equivariant Machine Learning on Graphs with Nonlinear Spectral Filterscited by 2
  5. 2024Scalable Graph Compressed Convolutionscited by 2
  6. 2025Toward Effective Digraph Representation Learning: A Magnetic Adaptive Propagation based Approachcited by 2
  7. 2025Addressing Noise and Stochasticity in Fraud Detection for Service Networkscited by 2
  8. 2025Partition-wise Graph Filtering: A Unified Perspective Through the Lens of Graph Coarseningcited by 2
  9. 2025Hyperbolic-PDE GNN: Spectral Graph Neural Networks in the Perspective of A System of Hyperbolic Partial Differential Equationscited by 2
  10. 2024Polynomial Selection in Spectral Graph Neural Networks: An Error-Sum of Function Slices Approachcited by 1
  11. 2025Piecewise Constant Spectral Graph Neural Networkcited by 1
  12. 2026Heterogeneity-Aware Knowledge Sharing for Graph Federated Learningcited by 1
  13. 2023An Effective Universal Polynomial Basis for Spectral Graph Neural Networkscited by 0
  14. 2025Toward Data-centric Directed Graph Learning: An Entropy-driven Approachcited by 0
  15. 2025Convexified Message-Passing Graph Neural Networkscited by 0
  16. 2025On the Impact of Downstream Tasks on Sampling and Reconstructing Noisy Graph Signalscited by 0
  17. 2026Learning from Historical Activations in Graph Neural Networkscited by 0
  18. 2026Position: Spectral GNNs Are Neither Spectral Nor Superior for Node Classificationcited by 0
  19. 2026Full-Spectrum Graph Neural Networks: Expressive and Scalablecited by 0
  20. 2026Hierarchical Multi-Scale Graph Neural Networks: Scalable Heterophilous Learning with Oversmoothing and Oversquashing Mitigationcited by 0
  21. 2026Graph Navier Stokes Networkscited by 0
  22. 2026SMGFM: Spectral Multimodal Graph Pretraining for Multimodal-Attributed Graphscited by 0
  23. 2026Continuous-Time Quantum Walks based Graph Neural Networkcited by 0
  24. 2026Spectral Graph Neural Networks with Hermite Polynomials: A Comprehensive Studycited by 0