Well... the authors of this paper propose using "anisotropic vector quantization" functions that take into account the density of points in the embedding space

Well... the authors of this paper propose using "anisotropic vector quantization" functions that take into account the density of points in the embedding space -- instead of more conventional locality sensitive hashing functions that ignore such density. I like to think of it as "clustering" in the space of vector quantization functions, then using those functions to quantize the data for fast nn search. The analogy with classical algorithms would be to apply something like DBSCAN or Spectral clustering to cluster points, then find a way to use the clusters to speed up nn search. In practice no one would do this; I'm mentioning it here only because I think it's a helpful analogy.