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vecindex: add adaptive search to increase accuracy #136032

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Adaptive search modifies the search algorithm to increase the search breadth in denser sections of the vector space and to decrease it in sparser sections. At each level of the tree, the search algorithm compiles a list of candidate partitions to search the next level down. It computes a Z-score for the candidates’ distances from the query vector, which indicates the “spread” of those distances, relative to the average. A negative Z-score indicates that partitions are more densely packed, and more should be searched. A positive Z-score indicates the opposite, and that fewer partitions should be searched.

Epic: CRDB-42943

Release note: None

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Adaptive search modifies the search algorithm to increase the search breadth
in denser sections of the vector space and to decrease it in sparser sections.
At each level of the tree, the search algorithm compiles a list of candidate
partitions to search the next level down. It computes a Z-score for the
candidates’ distances from the query vector, which indicates the “spread” of
those distances, relative to the average. A negative Z-score indicates that
partitions are more densely packed, and more should be searched. A positive
Z-score indicates the opposite, and that fewer partitions should be searched.

Epic: CRDB-42943

Release note: None
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