  How to leverage cross-document interactions to improve ranking performance is
an important topic in information retrieval (IR) research. However, this topic
has not been well-studied in the learning-to-rank setting and most of the
existing work still treats each document independently while scoring. The
recent development of deep learning shows strength in modeling complex
relationships across sequences and sets. It thus motivates us to study how to
leverage cross-document interactions for learning-to-rank in the deep learning
framework. In this paper, we formally define the permutation-equivariance
requirement for a scoring function that captures cross-document interactions.
We then propose a self-attention based document interaction network and show
that it satisfies the permutation-equivariant requirement, and can generate
scores for document sets of varying sizes. Our proposed methods can
automatically learn to capture document interactions without any auxiliary
information, and can scale across large document sets. We conduct experiments
on three ranking datasets: the benchmark Web30k, a Gmail search, and a Google
Drive Quick Access dataset. Experimental results show that our proposed methods
are both more effective and efficient than baselines.
