  Graph neural networks (GNNs) have emerged as a powerful model to capture
critical graph patterns. Instead of treating them as black boxes in an
end-to-end fashion, attempts are arising to explain the model behavior.
Existing works mainly focus on local interpretation to reveal the
discriminative pattern for each individual instance, which however cannot
directly reflect the high-level model behavior across instances. To gain global
insights, we aim to answer an important question that is not yet well studied:
how to provide a global interpretation for the graph learning procedure? We
formulate this problem as globally interpretable graph learning, which targets
on distilling high-level and human-intelligible patterns that dominate the
learning procedure, such that training on this pattern can recover a similar
model. As a start, we propose a novel model fidelity metric, tailored for
evaluating the fidelity of the resulting model trained on interpretations. Our
preliminary analysis shows that interpretative patterns generated by existing
global methods fail to recover the model training procedure. Thus, we further
propose our solution, Graph Distribution Matching (GDM), which synthesizes
interpretive graphs by matching the distribution of the original and
interpretive graphs in the GNN's feature space as its training proceeds, thus
capturing the most informative patterns the model learns during training.
Extensive experiments on graph classification datasets demonstrate multiple
advantages of the proposed method, including high model fidelity, predictive
accuracy and time efficiency, as well as the ability to reveal class-relevant
structure.
