When low-pass filtering helps graph neural networks

Many graph convolution models smooth neighboring node features. Simple Graph Convolution, for example, applies a fixed low-pass filter followed by a linear classifier [2]. This is useful when nearby nodes have similar labels. Spectral graph filters can also preserve or emphasize other frequencies, so low-pass filtering is a model choice, not a requirement of every spectral GNN [1].

Low-pass filtering and homophily

In a citation network, linked papers may share research areas [3]. This tendency for connected nodes to share labels is called homophily [4]. Smoothing can make their feature representations more similar and help a classifier use the graph structure.

SGC precomputes repeated feature propagation before fitting its classifier [2]. It uses node features and graph connectivity for propagation, with the labeled nodes supplying the training targets. It does not need a label for every node.

Capturing graph-level patterns

Graph-level tasks, including molecular property prediction [5], combine node representations into a prediction for the whole graph. Smoothing can help aggregate information, but low-frequency components do not automatically capture every useful global property. The filter, propagation depth, and graph readout affect what information survives [6, 7].

When high frequencies matter

High-frequency components describe differences across neighboring nodes. Those differences may be useful, so treating them all as noise can remove information needed for a task. Repeated smoothing can also make distinct nodes harder to distinguish [7].

Heterophily alone does not establish that a model will fail. Platonov and colleagues found that standard GNNs performed strongly on several heterophilous benchmarks, and that flaws in earlier datasets affected comparisons [4]. Evaluate filtering choices on the actual graph and task.

References

[1] Z. Wu et al., A Comprehensive Survey on Graph Neural Networks, 2021.

[2] F. Wu et al., Simplifying Graph Convolutional Networks, 2019.

[3] T. N. Kipf and M. Welling, Semi-Supervised Classification with Graph Convolutional Networks, 2017.

[4] O. Platonov et al., A critical look at the evaluation of GNNs under heterophily: Are we really making progress?, 2024.

[5] O. Wieder et al., A compact review of molecular property prediction with graph neural networks, 2020.

[6] R. Li et al., Adaptive Graph Convolutional Neural Networks, 2018.

[7] H. NT and T. Maehara, Revisiting Graph Neural Networks: All We Have is Low-Pass Filters, 2019.