On Graph Neural Networks versus Graph-Augmented MLPs [article]

Lei Chen, Zhengdao Chen, Joan Bruna
2020 arXiv   pre-print
From the perspective of expressive power, this work compares multi-layer Graph Neural Networks (GNNs) with a simplified alternative that we call Graph-Augmented Multi-Layer Perceptrons (GA-MLPs), which first augments node features with certain multi-hop operators on the graph and then applies an MLP in a node-wise fashion. From the perspective of graph isomorphism testing, we show both theoretically and numerically that GA-MLPs with suitable operators can distinguish almost all non-isomorphic
more » ... aphs, just like the Weifeiler-Lehman (WL) test. However, by viewing them as node-level functions and examining the equivalence classes they induce on rooted graphs, we prove a separation in expressive power between GA-MLPs and GNNs that grows exponentially in depth. In particular, unlike GNNs, GA-MLPs are unable to count the number of attributed walks. We also demonstrate via community detection experiments that GA-MLPs can be limited by their choice of operator family, as compared to GNNs with higher flexibility in learning.
arXiv:2010.15116v2 fatcat:zdiirbcuevhrvkei6kpakuaro4