Implement vector search in Hibernate Search, giving users the ability to index vectors produced using AI (e.g. Large Language Models) and to search for documents whose vector is closest to a given vector (k-nearest-neighbors).

1. Ability to index vectors of floats, with a @VectorField(?) annotation.

   1. Must handle at least List<Float> + float[] (this will likely require adding default bridges to org.hibernate.search.mapper.pojo.bridge.mapping.impl.BridgeResolver.Builder#addDefaults; registering a default bridge for List<Float> might be challenging, feel free to ping Yoann about that)

   2. Must accept a (static) parameter to specify the number of dimensions.

   3. Must ignore container extractors by default (we need to pass the full List to the backend, not a sequence of floats).

2. Ability to include a k-nearest-neighbors (KNN) predicate in search queries, to find the “k” documents with a given field holding the most similar vectors when compared to a given vector.

   1. May accept a parameter to specify the similarity function (Lucene apparently offers several?)

We can accept the following limitations:

• The feature is limited to the Lucene backend for a start.

• The feature is incubating/experimental for a start.

• We don’t provide any integration with AI libraries: we only deal with vectors and it’s up to users to transform text/images/sound into vectors.

• During indexing, vectors must be single-valued.

• During indexing, vectors cannot be in a nested document.

• KNN search is incompatible with paging.

• If we must (but preferably let’s avoid this limitation): KNN search is incompatible with other predicates.