  In this paper, we investigate the degree of explainability of graph neural
networks (GNNs). Existing explainers work by finding global/local subgraphs to
explain a prediction, but they are applied after a GNN has already been
trained. Here, we propose a meta-learning framework for improving the level of
explainability of a GNN directly at training time, by steering the optimization
procedure towards what we call `interpretable minima'. Our framework (called
MATE, MetA-Train to Explain) jointly trains a model to solve the original task,
e.g., node classification, and to provide easily processable outputs for
downstream algorithms that explain the model's decisions in a human-friendly
way. In particular, we meta-train the model's parameters to quickly minimize
the error of an instance-level GNNExplainer trained on-the-fly on randomly
sampled nodes. The final internal representation relies upon a set of features
that can be `better' understood by an explanation algorithm, e.g., another
instance of GNNExplainer. Our model-agnostic approach can improve the
explanations produced for different GNN architectures and use any
instance-based explainer to drive this process. Experiments on synthetic and
real-world datasets for node and graph classification show that we can produce
models that are consistently easier to explain by different algorithms.
Furthermore, this increase in explainability comes at no cost for the accuracy
of the model.
