Understanding the message passing in graph neural networks via power iteration clustering

• Published in: Neural networks 2021-08, Vol.140, p.130-135
• Main Authors: Li, Xue, Cheng, Yuanzhi
• Format: Article
• Language: English
• Subjects: Graph neural networks; Message passing; Power iteration; Subspace power iteration clustering
• ISSN: 0893-6080; 1879-2782
• DOI: 10.1016/j.neunet.2021.02.025

The mechanism of message passing in graph neural networks (GNNs) is still mysterious. Apart from convolutional neural networks, no theoretical origin for GNNs has been proposed. To our surprise, message passing can be best understood in terms of power iteration. By fully or partly removing activation functions and layer weights of GNNs, we propose subspace power iteration clustering (SPIC) models that iteratively learn with only one aggregator. Experiments show that our models extend GNNs and enhance their capability to process random featured networks. Moreover, we demonstrate the redundancy of some state-of-the-art GNNs in design and define a lower limit for model evaluation by a random aggregator of message passing. Our findings push the boundaries of the theoretical understanding of neural networks. •Identify a possible theoretical origin for GNNs apart from CNNs.•Extend GNNs and enhance their capability to process random featured networks.•Classify GNNs and demonstrate the redundancy of current models.•Define a lower limit for GNN performance evaluation.