On Graph Neural Networks versus Graph-Augmented MLPs
It addresses the theoretical understanding of graph learning models for researchers, revealing limitations of simplified alternatives to GNNs.
This work compares Graph Neural Networks (GNNs) and Graph-Augmented MLPs (GA-MLPs) in expressive power, showing that GA-MLPs can distinguish almost all non-isomorphic graphs like the Weisfeiler-Lehman test, but have an exponential separation from GNNs in depth and cannot count attributed walks.
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.