  Optimal selection of a subset of items from a given set is a hard problem
that requires combinatorial optimization. In this paper, we propose a subset
selection algorithm that is trainable with gradient-based methods yet achieves
near-optimal performance via submodular optimization. We focus on the task of
identifying a relevant set of sentences for claim verification in the context
of the FEVER task. Conventional methods for this task look at sentences on
their individual merit and thus do not optimize the informativeness of
sentences as a set. We show that our proposed method which builds on the idea
of unfolding a greedy algorithm into a computational graph allows both
interpretability and gradient-based training. The proposed differentiable
greedy network (DGN) outperforms discrete optimization algorithms as well as
other baseline methods in terms of precision and recall.
