Graph Neural Networks (GNNs) are a popular class of machine learning models. Inspired by the learning to explain (L2X) paradigm, we propose L2XGNN, a framework for explainable GNNs which provides faithful explanations by design. L2XGNN learns a mechanism for selecting explanatory subgraphs (motifs) which are exclusively used in the GNNs message-passing operations. L2XGNN is able to select, for each input graph, a subgraph with specific properties such as being sparse and connected. Imposing such constraints on the motifs often leads to more interpretable and effective explanations. Experiments on several datasets suggest that L2XGNN achieves the same classification accuracy as baseline methods using the entire input graph while ensuring that only the provided explanations are used to make predictions. Moreover, we show that L2XGNN is able to identify motifs responsible for the graph's properties it is intended to predict.

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