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-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.