Adrien Grand commented on LUCENE-9004:

Pretty cool! I don't know HNSW so I can't comment on that part but it made me 
wonder about a couple things:
* +1 to per-segment structure and rebuild graphs when merging.
* You hacked doc-value formats for this POC, but I guess your end idea would 
have a dedicated file-format (in the Lucene API sense) to support this, e.g. 
VectorFileFormat, like we have PostingsFormat or PointsFormat?
* You added a TODO about supporting ints and floats, I worry this would 
complicate things too much. Supporting float only has a great advantage which 
is that you can compute distances with doubles and never have to worry about 
overflows or underflows. This would be much more challenging if we supported 
doubles. Regarding ints, codecs could optimize for the case when all dimensions 
don't have a fractional part (bfloat16 is another type that we might want to 
optimize for).
*  You said there is "no Query implementation", but I suspect getting one will 
be challenging with the current Query API which requires ordered iterators of 
doc IDs and accept arbitrary filters. So if you were to intersect with a 
selective filter, you wouldn't be able to know up-front how many 
nearest-neighbors you'd need to filter. Something like LongDistanceFeatureQuery 
or LatLonPointDistanceFeatureQuery which further filters documents as more 
documents get collected would be nice, but this sounds very challenging with 
high numbers of dimensions?

> Approximate nearest vector search
> ---------------------------------
>                 Key: LUCENE-9004
>                 URL: https://issues.apache.org/jira/browse/LUCENE-9004
>             Project: Lucene - Core
>          Issue Type: New Feature
>            Reporter: Michael Sokolov
>            Priority: Major
> "Semantic" search based on machine-learned vector "embeddings" representing 
> terms, queries and documents is becoming a must-have feature for a modern 
> search engine. SOLR-12890 is exploring various approaches to this, including 
> providing vector-based scoring functions. This is a spinoff issue from that.
> The idea here is to explore approximate nearest-neighbor search. Researchers 
> have found an approach based on navigating a graph that partially encodes the 
> nearest neighbor relation at multiple scales can provide accuracy > 95% (as 
> compared to exact nearest neighbor calculations) at a reasonable cost. This 
> issue will explore implementing HNSW (hierarchical navigable small-world) 
> graphs for the purpose of approximate nearest vector search (often referred 
> to as KNN or k-nearest-neighbor search).
> At a high level the way this algorithm works is this. First assume you have a 
> graph that has a partial encoding of the nearest neighbor relation, with some 
> short and some long-distance links. If this graph is built in the right way 
> (has the hierarchical navigable small world property), then you can 
> efficiently traverse it to find nearest neighbors (approximately) in log N 
> time where N is the number of nodes in the graph. I believe this idea was 
> pioneered in  [1]. The great insight in that paper is that if you use the 
> graph search algorithm to find the K nearest neighbors of a new document 
> while indexing, and then link those neighbors (undirectedly, ie both ways) to 
> the new document, then the graph that emerges will have the desired 
> properties.
> The implementation I propose for Lucene is as follows. We need two new data 
> structures to encode the vectors and the graph. We can encode vectors using a 
> light wrapper around {{BinaryDocValues}} (we also want to encode the vector 
> dimension and have efficient conversion from bytes to floats). For the graph 
> we can use {{SortedNumericDocValues}} where the values we encode are the 
> docids of the related documents. Encoding the interdocument relations using 
> docids directly will make it relatively fast to traverse the graph since we 
> won't need to lookup through an id-field indirection. This choice limits us 
> to building a graph-per-segment since it would be impractical to maintain a 
> global graph for the whole index in the face of segment merges. However 
> graph-per-segment is a very natural at search time - we can traverse each 
> segments' graph independently and merge results as we do today for term-based 
> search.
> At index time, however, merging graphs is somewhat challenging. While 
> indexing we build a graph incrementally, performing searches to construct 
> links among neighbors. When merging segments we must construct a new graph 
> containing elements of all the merged segments. Ideally we would somehow 
> preserve the work done when building the initial graphs, but at least as a 
> start I'd propose we construct a new graph from scratch when merging. The 
> process is going to be  limited, at least initially, to graphs that can fit 
> in RAM since we require random access to the entire graph while constructing 
> it: In order to add links bidirectionally we must continually update existing 
> documents.
> I think we want to express this API to users as a single joint 
> {{KnnGraphField}} abstraction that joins together the vectors and the graph 
> as a single joint field type. Mostly it just looks like a vector-valued 
> field, but has this graph attached to it.
> I'll push a branch with my POC and would love to hear comments. It has many 
> nocommits, basic design is not really set, there is no Query implementation 
> and no integration iwth IndexSearcher, but it does work by some measure using 
> a standalone test class. I've tested with uniform random vectors and on my 
> laptop indexed 10K documents in around 10 seconds and searched them at 95% 
> recall (compared with exact nearest-neighbor baseline) at around 250 QPS. I 
> haven't made any attempt to use multithreaded search for this, but it is 
> amenable to per-segment concurrency.
> [1] 
> https://www.semanticscholar.org/paper/Efficient-and-robust-approximate-nearest-neighbor-Malkov-Yashunin/699a2e3b653c69aff5cf7a9923793b974f8ca164

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