Improving Expressive Power of Spectral Graph Neural Networks with Eigenvalue Correction

arXiv:2401.15603v2 Announce Type: replace
Abstract: In recent years, spectral graph neural networks, characterized by polynomial filters, have garnered increasing attention and have achieved remarkable performance in tasks such as node classification. These models typically assume that eigenvalues for the normalized Laplacian matrix are distinct from each other, thus expecting a polynomial filter to have a high fitting ability. However, this paper empirically observes that normalized Laplacian matrices frequently possess repeated eigenvalues. Moreover, we theoretically establish that the number of distinguishable …

abstract arxiv attention classification cs.lg cs.si eigenvalue filters graph graph neural networks matrix networks neural networks node performance polynomial power tasks type