Expressivity of Graph Neural Networks Through the Lens of Adversarial Robustness
This work addresses a foundational issue in graph machine learning by exposing limitations in GNN expressivity, which is incremental as it builds on existing measures but introduces adversarial robustness as a novel lens.
The study tackled the problem of assessing the expressive power of Graph Neural Networks (GNNs) beyond traditional Message Passing Neural Networks (MPNNs) by using adversarial robustness as a tool, revealing that more powerful GNNs fail to generalize to small structural perturbations and out-of-distribution graphs in subgraph counting tasks.
We perform the first adversarial robustness study into Graph Neural Networks (GNNs) that are provably more powerful than traditional Message Passing Neural Networks (MPNNs). In particular, we use adversarial robustness as a tool to uncover a significant gap between their theoretically possible and empirically achieved expressive power. To do so, we focus on the ability of GNNs to count specific subgraph patterns, which is an established measure of expressivity, and extend the concept of adversarial robustness to this task. Based on this, we develop efficient adversarial attacks for subgraph counting and show that more powerful GNNs fail to generalize even to small perturbations to the graph's structure. Expanding on this, we show that such architectures also fail to count substructures on out-of-distribution graphs.