Papers › Graph Neural Networks with Learnable and Optimal Polynomial Bases
Graph Neural Networks with Learnable and Optimal Polynomial Bases
Yuhe Guo, Zhewei Wei
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.
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Code
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Tasks
Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| Node Classification | Film (60%/20%/20% random splits) | FavardGNN | 1:1 Accuracy | 43.05 ± 0.53 | #3 of 37 | Archive leaderboard | report |
| Node Classification | Film (60%/20%/20% random splits) | OptBasisGNN | 1:1 Accuracy | 42.39 ± 0.52 | #4 of 37 | Archive leaderboard | report |
| Node Classification | pokec | OptBasisGNN | Accuracy | 82.83±0.04 | #5 of 7 | Archive leaderboard | report |
| Node Classification on Non-Homophilic (Heterophilic) Graphs | genius | OptBasisGNN | 1:1 Accuracy | 90.83±0.11 | #9 of 26 | Archive leaderboard | report |
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