Efficient k-NN filtering with Neural Search

Versions (relevant - OpenSearch/Dashboard/Server OS/Browser):
2.11

Describe the issue:

I am using neural search and would like to also use the filtering function on metadata of documents. After reading the documentation here in step 4, it mentions that “To perform vector search on your index, use the neural query clause either in the [k-NN plugin API] or [Query DSL] queries. You can refine the results by using a k-NN search filter.”

When looking at the lucene algorithm for example, it shows the algorithm when KNN search is used. However, when neural search is used, if the data returned after the filter is used, P is > k, what are the steps that follow? Would like to understand how the algorithm deals with a set of data that is greater than K.

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