  Neural networks -- especially those that use large, pre-trained language
models -- have improved search engines in various ways. Most prominently, they
can estimate the relevance of a passage or document to a user's query. In this
work, we depart from this direction by exploring whether neural networks can
effectively predict which of a document's passages are unlikely to be relevant
to any query submitted to the search engine. We refer to this query-agnostic
estimation of passage relevance as a passage's quality. We find that our novel
methods for estimating passage quality allow passage corpora to be pruned
considerably while maintaining statistically equivalent effectiveness; our best
methods can consistently prune >25% of passages in a corpora, across various
retrieval pipelines. Such substantial pruning reduces the operating costs of
neural search engines in terms of computing resources, power usage, and carbon
footprint -- both when processing queries (thanks to a smaller index size) and
when indexing (lightweight models can prune low-quality passages prior to the
costly dense or learned sparse encoding step). This work sets the stage for
developing more advanced neural "learning-what-to-index" methods.
