As Graph Neural Networks (GNNs) become more pervasive, it becomes paramount to build robust tools for computing explanations of their predictions. A key desideratum is that these explanations are faithful, i.e., that they portray an accurate picture of the GNN's reasoning process. A number of different faithfulness metrics exist, begging the question of what faithfulness is exactly, and what its properties are. We begin by showing that existing metrics are not interchangeable -- i.e., explanations attaining high faithfulness according to one metric may be unfaithful according to others -- and can be systematically insensitive to important properties of the explanation, and suggest how to address these issues. We proceed to show that, surprisingly, optimizing for faithfulness is not always a sensible design goal. Specifically, we show that for injective regular GNN architectures, perfectly faithful explanations are completely uninformative. The situation is different for modular GNNs, such as self-explainable and domain-invariant architectures, where optimizing faithfulness does not compromise informativeness, and is also unexpectedly tied to out-of-distribution generalization.

翻译：随着图神经网络（GNN）的日益普及，构建用于解释其预测的稳健工具变得至关重要。一个核心需求是这些解释应具有忠实性，即它们能准确反映GNN的推理过程。目前存在多种不同的忠实性度量指标，这引发了关于忠实性本质及其特性的疑问。我们首先证明现有度量指标并非可互换的——即根据某一指标获得高忠实性的解释可能在其他指标下并不忠实——并且可能系统性地忽略解释的重要特性，进而提出解决这些问题的途径。进一步研究发现，优化忠实性并不总是合理的设计目标。具体而言，我们证明对于内射正则GNN架构，完全忠实的解释完全不具信息量。而对于模块化GNN（如自解释架构和领域不变架构），优化忠实性不会损害信息量，并且意外地与分布外泛化能力相关联。