  Learned sparse representations form an effective and interpretable class of
embeddings for text retrieval. While exact top-k retrieval over such embeddings
faces efficiency challenges, a recent algorithm called Seismic has enabled
remarkably fast, highly-accurate approximate retrieval. Seismic statically
prunes inverted lists, organizes each list into geometrically-cohesive blocks,
and augments each block with a summary vector. At query time, each inverted
list associated with a query term is traversed one block at a time in an
arbitrary order, with the inner product between the query and summaries
determining if a block must be evaluated. When a block is deemed promising, its
documents are fully evaluated with a forward index. Seismic is one to two
orders of magnitude faster than state-of-the-art inverted index-based solutions
and significantly outperforms the winning graph-based submissions to the BigANN
2023 Challenge. In this work, we speed up Seismic further by introducing two
innovations to its query processing subroutine. First, we traverse blocks in
order of importance, rather than arbitrarily. Second, we take the list of
documents retrieved by Seismic and expand it to include the neighbors of each
document using an offline k-regular nearest neighbor graph; the expanded list
is then ranked to produce the final top-k set. Experiments on two public
datasets show that our extension, named SeismicWave, can reach almost-exact
accuracy levels and is up to 2.2x faster than Seismic.
