  Existing Graph Neural Networks (GNNs) compute the message exchange between
nodes by either aggregating uniformly (convolving) the features of all the
neighboring nodes, or by applying a non-uniform score (attending) to the
features. Recent works have shown the strengths and weaknesses of the resulting
GNN architectures, respectively, GCNs and GATs. In this work, we aim at
exploiting the strengths of both approaches to their full extent. To this end,
we first introduce the graph convolutional attention layer (CAT), which relies
on convolutions to compute the attention scores. Unfortunately, as in the case
of GCNs and GATs, we show that there exists no clear winner between the three
(neither theoretically nor in practice) as their performance directly depends
on the nature of the data (i.e., of the graph and features). This result brings
us to the main contribution of our work, the learnable graph convolutional
attention network (L-CAT): a GNN architecture that automatically interpolates
between GCN, GAT and CAT in each layer, by adding only two scalar parameters.
Our results demonstrate that L-CAT is able to efficiently combine different GNN
layers along the network, outperforming competing methods in a wide range of
datasets, and resulting in a more robust model that reduces the need of
cross-validating.
