  This paper outlines a conceptual framework for understanding recent
developments in information retrieval and natural language processing that
attempts to integrate dense and sparse retrieval methods. I propose a
representational approach that breaks the core text retrieval problem into a
logical scoring model and a physical retrieval model. The scoring model is
defined in terms of encoders, which map queries and documents into a
representational space, and a comparison function that computes query-document
scores. The physical retrieval model defines how a system produces the top-$k$
scoring documents from an arbitrarily large corpus with respect to a query. The
scoring model can be further analyzed along two dimensions: dense vs. sparse
representations and supervised (learned) vs. unsupervised approaches. I show
that many recently proposed retrieval methods, including multi-stage ranking
designs, can be seen as different parameterizations in this framework, and that
a unified view suggests a number of open research questions, providing a
roadmap for future work. As a bonus, this conceptual framework establishes
connections to sentence similarity tasks in natural language processing and
information access "technologies" prior to the dawn of computing.
