On Graph Neural Networks versus Graph-Augmented MLPs

• URL: http://arxiv.org/abs/2010.15116v2
• Date: Wed, 2 Dec 2020 16:46:23 GMT
• Title: On Graph Neural Networks versus Graph-Augmented MLPs
• Authors: Lei Chen, Zhengdao Chen, Joan Bruna
• Abstract summary: Graph-Augmented Multi-Layer Perceptrons (GA-MLPs) first augments node features with certain multi-hop operators on the graph. We prove a separation in expressive power between GA-MLPs and GNNs that grows exponentially in depth.
• Score: 51.23890789522705
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 graphs, 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.

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