Reconsidering Faithfulness in Regular, Self-Explainable and Domain Invariant GNNs

As Graph Neural Networks (GNNs) become more pervasive, it becomes paramount to build reliable tools for explaining their predictions. A core desideratum is that explanations are \textit{faithful}, \ie that they portray an accurate picture of the GNN's reasoning process. However, a number of different faithfulness metrics exist, begging the question of what is faithfulness exactly and how to achieve it. We make three key contributions. We begin by showing that \textit{existing metrics are not interchangeable} -- \ie explanations attaining high faithfulness according to one metric may be unfaithful according to others -- and can systematically ignore important properties of explanations. We proceed to show that, surprisingly, \textit{optimizing for faithfulness is not always a sensible design goal}. Specifically, we prove that for injective regular GNN architectures, perfectly faithful explanations are completely uninformative. This does not apply to modular GNNs, such as self-explainable and domain-invariant architectures, prompting us to study the relationship between architectural choices and faithfulness. Finally, we show that \textit{faithfulness is tightly linked to out-of-distribution generalization}, in that simply ensuring that a GNN can correctly recognize the domain-invariant subgraph, as prescribed by the literature, does not guarantee that it is invariant unless this subgraph is also faithful.The code is publicly available on GitHub