# When low-pass filtering helps graph neural networks

Why low-pass filtering helps graph neural networks, and when removing high-frequency signals can lose useful information.

Canonical: https://blogs.aasmanbashyal.com.np/blogs/spectral

Published: May 10, 2025

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.

![Graph convolutional network architecture from Kipf and Welling \[3\]](https://aasmanbashyal.com.np/img/blog/semi_hidden_layer_gnn.webp)

Graph convolutional network architecture from Kipf and Welling \[3\]

## 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](https://doi.org/10.1109/TNNLS.2020.2978386), 2021.

\[2\] F. Wu et al., [Simplifying Graph Convolutional Networks](https://arxiv.org/abs/1902.07153), 2019.

\[3\] T. N. Kipf and M. Welling, [Semi-Supervised Classification with Graph Convolutional Networks](https://arxiv.org/abs/1609.02907), 2017.

\[4\] O. Platonov et al., [A critical look at the evaluation of GNNs under heterophily: Are we really making progress?](https://arxiv.org/abs/2302.11640), 2024.

\[5\] O. Wieder et al., [A compact review of molecular property prediction with graph neural networks](https://doi.org/10.1016/j.ddtec.2020.11.009), 2020.

\[6\] R. Li et al., [Adaptive Graph Convolutional Neural Networks](https://arxiv.org/abs/1801.03226), 2018.

\[7\] H. NT and T. Maehara, [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://arxiv.org/abs/1905.09550), 2019.