Position: Spectral GNNs Are Neither Spectral Nor Superior for Node Classification

A recent study critiques Spectral Graph Neural Networks (Spectral GNNs), highlighting that they lack the foundational properties of true Fourier bases and questioning their effectiveness in node classification. The research identifies two main flaws: the commonly used graph Fourier bases do not function as classical Fourier bases, and the narrative surrounding polynomial approximation lacks theoretical justification.

This development is significant as it challenges the prevailing assumptions about the efficacy of Spectral GNNs, particularly their perceived advantages in low-pass filtering for node classification tasks. By exposing these theoretical glitches, the study calls into question the reliability of Spectral GNNs and their applications in real-world scenarios.

The findings contribute to ongoing debates in the field of Graph Neural Networks, particularly regarding the interpretability and performance of various architectures. The complexities of message passing in GNNs, as explored in related research, further complicate the understanding of how these models operate, suggesting a need for more rigorous theoretical frameworks to assess their capabilities.