On Graph Neural Networks versus Graph-Augmented MLPs

Lei Chen, Zhengdao Chen, Joan Bruna

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.

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics

One-sentence Summary: We establish a separation in expressive power and flexibility of learning between GNNs and Graph-Augmented MLPs.

Code: [ leichen2018/GNN_vs_GAMLP](https://github.com/leichen2018/GNN_vs_GAMLP)