Coleman et al. showed that reordering the nodes in every layer such that the neighbors of each node are laid out closer in memory improves query time performance by about 40%. The idea is that reordering provides a cache-efficient search mechanism that reduces the search overhead due to random accesses in HNSW.

They also showed that using the hierarchy is not strictly necessary in certain settings. They replaced the hierarchy with "a process where we randomly sample 50 nodes and use the closest option as the initialization." They observed no statistically significant difference between the hierarchical search procedure and this random sampling process in terms of recall or query time over 10k items.

I can work on integrating these features.