  Answer sentence selection (AS2) in open-domain question answering finds
answer for a question by ranking candidate sentences extracted from web
documents. Recent work exploits answer context, i.e., sentences around a
candidate, by incorporating them as additional input string to the Transformer
models to improve the correctness scoring. In this paper, we propose to improve
the candidate scoring by explicitly incorporating the dependencies between
question-context and answer-context into the final representation of a
candidate. Specifically, we use Optimal Transport to compute the question-based
dependencies among sentences in the passage where the answer is extracted from.
We then represent these dependencies as edges in a graph and use Graph
Convolutional Network to derive the representation of a candidate, a node in
the graph. Our proposed model achieves significant improvements on popular AS2
benchmarks, i.e., WikiQA and WDRASS, obtaining new state-of-the-art on all
benchmarks.
