  In this work we propose Pathfinder Discovery Networks (PDNs), a method for
jointly learning a message passing graph over a multiplex network with a
downstream semi-supervised model. PDNs inductively learn an aggregated weight
for each edge, optimized to produce the best outcome for the downstream
learning task. PDNs are a generalization of attention mechanisms on graphs
which allow flexible construction of similarity functions between nodes, edge
convolutions, and cheap multiscale mixing layers. We show that PDNs overcome
weaknesses of existing methods for graph attention (e.g. Graph Attention
Networks), such as the diminishing weight problem. Our experimental results
demonstrate competitive predictive performance on academic node classification
tasks. Additional results from a challenging suite of node classification
experiments show how PDNs can learn a wider class of functions than existing
baselines. We analyze the relative computational complexity of PDNs, and show
that PDN runtime is not considerably higher than static-graph models. Finally,
we discuss how PDNs can be used to construct an easily interpretable attention
mechanism that allows users to understand information propagation in the graph.
