Position: Spectral GNNs Are Neither Spectral Nor Superior for Node Classification
Spectral Graph Neural Networks (Spectral GNNs) for node classification promise frequency-domain filtering on graphs, yet rest on flawed foundations. Recent work shows that graph Laplacian eigenvectors do not in general have the key properties of a true Fourier basis, but leaves the empirical success of Spectral GNNs unexplained. We identify two theoretical glitches: (1) commonly used "graph Fourier bases" are not classical Fourier bases for graph signals; (2) (n-1)-degree polynomials (n = number of nodes) can exactly interpolate any spectral response via a Vandermonde system, so the usual "polynomial approximation" narrative is not theoretically justified. The effectiveness of GCN is comm...
| Authors | Qin Jiang, Chengjia Wang, Michael Lones et al. |
|---|---|
| Primary category | cs.LG |
| Published | 19 March 2026 |
| Last updated at source | 26 March 2026 |
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