  Protein function prediction may be framed as predicting subgraphs (with
certain closure properties) of a directed acyclic graph describing the
hierarchy of protein functions. Graph neural networks (GNNs), with their
built-in inductive bias for relational data, are hence naturally suited for
this task. However, in contrast with most GNN applications, the graph is not
related to the input, but to the label space. Accordingly, we propose
Tail-GNNs, neural networks which naturally compose with the output space of any
neural network for multi-task prediction, to provide relationally-reinforced
labels. For protein function prediction, we combine a Tail-GNN with a dilated
convolutional network which learns representations of the protein sequence,
making significant improvement in F_1 score and demonstrating the ability of
Tail-GNNs to learn useful representations of labels and exploit them in
real-world problem solving.
