A spectral perspective on GCNs

1 Jan 2021  ·  Nathan Grinsztajn, Philippe Preux, Edouard Oyallon ·

In this work, we study the behavior of standard GCNs under spectral manipulations. We relate the numerical performances of a GCN through bandpass filtering: we empirically show that most of the necessary and used information for nodes classification is contained in the low-frequency domain, through various ablation experiments. In particular, it is possible to recover accuracies competitive with the state of the art with simple MLPs and only a few low frequencies. We further derive a simple procedure to adjust the trade-off between smoothing and high-frequency propagation for deeper GCNs, without diagonalizing the Laplacian. We conduct our experiments on standard and challenging benchmarks.

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