Improved Modeling and Generalization Capabilities of Graph Neural Networks With Legendre Polynomials

LegendreNet is a novel graph neural network (GNNs) model that addresses stability issues present in traditional GNN models such as ChebNet, while also more effectively capturing higher-order dependencies within graphical data. Compared to traditional GNNs models such as GCN, LegendreNet is better equipped to handle large-scale graphical data, demonstrating superior performance on such datasets. Furthermore, Legendre polynomials, which are a set of completely orthogonal polynomials, are capable of approximating any function to arbitrary precision within a bounded interval. As such, when applied to graph neural networks, Legendre polynomials provide a more precise and stable means of fitting spectral filters to graphical data. This enables LegendreNet to more accurately capture graphical features when dealing with complex graphical data, and to exhibit greater robustness in adversarial attack scenarios. Compared to traditional GNNs methods, LegendreNet offers improved modeling and generalization capabilities, making it a more effective solution across various graphical data applications. Our experiments have demonstrated that our model outperforms state-of-the-art methods on large-scale graphical datasets. The code for LegendreNet is available at https://github.com/12chen20/LegendreNet.