[2603.19091] Position: Spectral GNNs Are Neither Spectral Nor Superior for Node Classification

Computer Science > Machine Learning arXiv:2603.19091 (cs) [Submitted on 19 Mar 2026 (v1), last revised 26 Mar 2026 (this version, v2)] Title:Position: Spectral GNNs Are Neither Spectral Nor Superior for Node Classification Authors:Qin Jiang, Chengjia Wang, Michael Lones, Dongdong Chen, Wei Pang View a PDF of the paper titled Position: Spectral GNNs Are Neither Spectral Nor Superior for Node Classification, by Qin Jiang and 4 other authors View PDF HTML (experimental) Abstract: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 commonly attributed to spectral low-pass filtering, yet we prove that low- and high-pass behaviors arise solely from message-passing dynamics rather than Graph Fourier Transform-based spectral formulations. We then analyze two representative directed spectral models, MagNet and HoloNet. Their reported effectiveness is not...