Designing spectral convolutional networks is a challenging problem in graph learning. ChebNet, one of the early attempts, approximates the spectral graph convolutions using Chebyshev polynomials. GCN simplifies ChebNet by utilizing only the first two Chebyshev polynomials while still outperforming it on real-world datasets. GPR-GNN and BernNet demonstrate that the Monomial and Bernstein bases also outperform the Chebyshev basis in terms of learning the spectral graph convolutions. Such conclusions are counter-intuitive in the field of approximation theory, where it is established that the Chebyshev polynomial achieves the optimum convergent rate for approximating a function.
In this paper, we revisit the problem of approximating the spectral graph convolutions with Chebyshev polynomials. We show that ChebNet's inferior performance is primarily due to illegal coefficients learnt by ChebNet approximating analytic filter functions, which leads to over-fitting. We then propose ChebNetII, a new GNN model based on Chebyshev interpolation, which enhances the original Chebyshev polynomial approximation while reducing the Runge phenomenon. We conducted an extensive experimental study to demonstrate that ChebNetII can learn arbitrary graph convolutions and achieve superior performance in both full- and semi-supervised node classification tasks. Most notably, we scale ChebNetII to a billion graph ogbn-papers100M, showing that spectral-based GNNs have superior performance. Our code is available at https://github.com/ivam-he/ChebNetII.
Spectral Multigraph Networks for Discovering and Fusing Relationships in Molecules
University of Guelph（圭尔夫大学）；Vector Institute for Artificial Intelligence（向量人工智能研究院）；Canadian Institute for Advanced Research（加拿大高等研究院）；SRI International（SRI国际研究院）
Pruning By Explaining Revisited: Optimizing Attribution Methods to Prune CNNs and Transformers
Fraunhofer Heinrich-Hertz-Institute（弗劳恩霍夫海因茨·赫兹研究所）；Technische Universität Berlin（柏林工业大学）；BIFOLD – Berlin Institute for the Foundations of Learning and Data（柏林学习与数据基础研究所（BIFOLD））
Graph Representation Learning Strategies for Omics Data: A Case Study on Parkinson's Disease
University of Luxembourg（卢森堡大学）；École polytechnique fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；University of Cambridge（剑桥大学）；Luxembourg Center for Systems Biomedicine（卢森堡系统生物医学中心）
Gegenbauer Graph Neural Networks for Time-varying Signal Reconstruction
University of Delaware（特拉华大学）；Télécom Paris（巴黎电信学院）；Institut Polytechnique de Paris（巴黎理工学院）；Université Paris-Saclay（巴黎萨克雷大学）；CentraleSupélec（中央高等电力学院）；Inria（法国国家信息与自动化研究院）
Predicting Drug Solubility Using Different Machine Learning Methods -- Linear Regression Model with Extracted Chemical Features vs Graph Convolutional Neural Network
Harvard University（哈佛大学）；University of California, Berkeley（加州大学伯克利分校）；Carlmont High School（卡尔蒙特高中）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
