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Apart from search, ANN could be use for recommendations, classification, and other information retrieval problems.
Currently, ES and Solr, both based on Lucene, can't really manage vector representations, as they are mainly based on inverted indexes to n-grams.
ANN potential applications extend to audio, bioinformatics, video, among any modality that can be represented as a vector. All you need is an encoder! How nice.
Faiss is definitely powerful. I have been running experiments using 80 million vectors that map to legal documents, and vectorizing protein-folds (using Alphafold). While it is an interesting technology, at this moment is more a lib or tool than a full-featured product like ES or Solr.
ATM, updating a Faiss index is a non trivial process, with many of the workflow tools you would see in ES missing.
I recently been found with pgvector (postgres + vector support) https://github.com/ankane/pgvector. Perhaps less performant, but easier to work with for teams. With support of migrations, ORM, sharing, and all the postgres goodies.
nmslib (https://github.com/nmslib/nmslib) supports sparse vectors for some of its spaces. It has fewer indexing methods than faiss, though.
https://github.com/nmslib/nmslib/blob/master/manual/spaces.m...