  While instance-level explanation of GNN is a well-studied problem with plenty
of approaches being developed, providing a global explanation for the behaviour
of a GNN is much less explored, despite its potential in interpretability and
debugging. Existing solutions either simply list local explanations for a given
class, or generate a synthetic prototypical graph with maximal score for a
given class, completely missing any combinatorial aspect that the GNN could
have learned. In this work, we propose GLGExplainer (Global Logic-based GNN
Explainer), the first Global Explainer capable of generating explanations as
arbitrary Boolean combinations of learned graphical concepts. GLGExplainer is a
fully differentiable architecture that takes local explanations as inputs and
combines them into a logic formula over graphical concepts, represented as
clusters of local explanations. Contrary to existing solutions, GLGExplainer
provides accurate and human-interpretable global explanations that are
perfectly aligned with ground-truth explanations (on synthetic data) or match
existing domain knowledge (on real-world data). Extracted formulas are faithful
to the model predictions, to the point of providing insights into some
occasionally incorrect rules learned by the model, making GLGExplainer a
promising diagnostic tool for learned GNNs.
