- Keywords: Graph Neural Networks, expressive power, feature propagation, rooted graphs, attributed walks, community detection, depth separation
- Abstract: From the perspectives of expressive power and learning, 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 learnable node-wise functions. 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 Weisfeiler-Lehman (WL) test and GNNs. 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, whereas GNNs have higher flexibility in learning.
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- One-sentence Summary: We establish a separation in expressive power and flexibility of learning between GNNs and Graph-Augmented MLPs.