Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisited

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. 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.