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

Qin Jiang; Chengjia Wang; Michael Lones; Dongdong Chen; Wei Pang

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arXiv · 2603.19091

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

Qin Jiang·Chengjia Wang·Michael Lones·Dongdong Chen·Wei Pang

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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 spectral: it arises from implementation issues that reduce them to powerful MPNNs. When implemented consistently with the claimed spectral algorithms, performance becomes weak. This position paper argues that: for node classification, Spectral GNNs neither meaningfully capture the graph spectrum nor reliably improve performance; competitive results are better explained by their equivalence to MPNNs, sometimes aided by implementations inconsistent with their intended design.

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Qin Jiang, Chengjia Wang, Michael Lones, Dongdong Chen, Wei Pang. 2026-03-26. Position: Spectral GNNs Are Neither Spectral Nor Superior for Node Classification. https://arxiv.org/abs/2603.19091

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