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We perform the first adversarial robustness study into Graph Neural Networks(GNNs) that are provably more powerful than traditional Message Passing NeuralNetworks (MPNNs). In particular, we use adversarial robustness as a tool touncover a significant gap between their theoretically possible and empiricallyachieved expressive power. To do so, we focus on the ability of GNNs to countspecific 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 thatmore powerful GNNs fail to generalize even to small perturbations to thegraph's structure. Expanding on this, we show that such architectures also failto count substructures on out-of-distribution graphs.

Expressivity of Graph Neural Networks Through the Lens of Adversarial Robustness