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Current Graph Neural Networks (GNN) architectures generally rely on twoimportant components: node features embedding through message passing, andaggregation with a specialized form of pooling. The structural (or topological)information is implicitly taken into account in these two steps. We propose inthis work a novel point of view, which places distances to some learnable graphtemplates at the core of the graph representation. This distance embedding isconstructed thanks to an optimal transport distance: the FusedGromov-Wasserstein (FGW) distance, which encodes simultaneously feature andstructure dissimilarities by solving a soft graph-matching problem. Wepostulate that the vector of FGW distances to a set of template graphs has astrong discriminative power, which is then fed to a non-linear classifier forfinal predictions. Distance embedding can be seen as a new layer, and canleverage on existing message passing techniques to promote sensible featurerepresentations. Interestingly enough, in our work the optimal set of templategraphs is also learnt in an end-to-end fashion by differentiating through thislayer. After describing the corresponding learning procedure, we empiricallyvalidate our claim on several synthetic and real life graph classificationdatasets, where our method is competitive or surpasses kernel and GNNstate-of-the-art approaches. We complete our experiments by an ablation studyand a sensitivity analysis to parameters.

Template based Graph Neural Network with Optimal Transport Distances