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From Local to Global: Spectral-Inspired Graph Neural Networks
Ningyuan Huang · Soledad Villar · Carey E Priebe · Da Zheng · Chengyue Huang · Lin Yang · Vladimir Braverman
Event URL: https://openreview.net/forum?id=DhICIwGint_ »
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.

Author Information

Ningyuan Huang (Johns Hopkins University)
Soledad Villar (Johns Hopkins University)
Carey E Priebe (Johns Hopkins University)
Da Zheng (Amazon)
Chengyue Huang (Renmin University of China)
Lin Yang (UCLA)
Vladimir Braverman (Rice University)

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