Papers › From Local to Global: Spectral-Inspired Graph Neural Networks

From Local to Global: Spectral-Inspired Graph Neural Networks

24 Sep 2022arXiv:2209.12054archive 2025-07-28

Ningyuan Huang, Soledad Villar, Carey E. Priebe, Da Zheng, Chengyue Huang, Lin Yang, Vladimir Braverman

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 PowerEmbed -- a simple layer-wise normalization technique to boost MPNNs. We show 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 PowerEmbed in a wide range of simulated and real graphs and demonstrate its competitive performance, particularly for heterophilous graphs.

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