From Local to Global: Spectral-Inspired Graph Neural Networks

• URL: http://arxiv.org/abs/2209.12054v1
• Date: Sat, 24 Sep 2022 17:19:00 GMT
• Title: From Local to Global: Spectral-Inspired Graph Neural Networks
• Authors: Ningyuan Huang, Soledad Villar, Carey E. Priebe, Da Zheng, Chengyue Huang, Lin Yang, Vladimir Braverman
• Abstract summary: Graph Neural Networks (GNNs) are powerful deep learning methods for Non-Euclidean data. MPNNs are message-passing algorithms that aggregate and combine signals in a local graph neighborhood. MPNNs can suffer from issues like over-smoothing or over-squashing.
• Score: 28.858773653743075
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Graph Neural Networks (GNNs) are powerful deep learning methods for Non-Euclidean data. Popular GNNs are message-passing algorithms (MPNNs) that aggregate and combine signals in a local graph neighborhood. However, shallow MPNNs tend to miss long-range signals and perform poorly on some heterophilous graphs, while deep MPNNs can suffer from issues like over-smoothing or over-squashing. To mitigate such issues, existing works typically borrow normalization techniques from training neural networks on Euclidean data or modify the graph structures. Yet these approaches are not well-understood theoretically and could increase the overall computational complexity. In this work, we draw inspirations from spectral graph embedding and propose $\texttt{PowerEmbed}$ -- a simple layer-wise normalization technique to boost MPNNs. We show $\texttt{PowerEmbed}$ can provably express the top-$k$ leading eigenvectors of the graph operator, which prevents over-smoothing and is agnostic to the graph topology; meanwhile, it produces a list of representations ranging from local features to global signals, which avoids over-squashing. We apply $\texttt{PowerEmbed}$ in a wide range of simulated and real graphs and demonstrate its competitive performance, particularly for heterophilous graphs.

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