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Hybrid full-text search and vector search with SQLite. As part of Alex’s work on his sqlite-vec SQLite extension - adding fast vector lookups to SQLite - he’s been investigating hybrid search, where search results from both vector similarity and traditional full-text search are combined together.

The most promising approach looks to be Reciprocal Rank Fusion, which combines the top ranked items from both approaches. Here’s Alex’s SQL query:

-- the sqlite-vec KNN vector search results
with vec_matches as (
  select
    article_id,
    row_number() over (order by distance) as rank_number,
    distance
  from vec_articles
  where
    headline_embedding match lembed(:query)
    and k = :k
),
-- the FTS5 search results
fts_matches as (
  select
    rowid,
    row_number() over (order by rank) as rank_number,
    rank as score
  from fts_articles
  where headline match :query
  limit :k
),
-- combine FTS5 + vector search results with RRF
final as (
  select
    articles.id,
    articles.headline,
    vec_matches.rank_number as vec_rank,
    fts_matches.rank_number as fts_rank,
    -- RRF algorithm
    (
      coalesce(1.0 / (:rrf_k + fts_matches.rank_number), 0.0) * :weight_fts +
      coalesce(1.0 / (:rrf_k + vec_matches.rank_number), 0.0) * :weight_vec
    ) as combined_rank,
    vec_matches.distance as vec_distance,
    fts_matches.score as fts_score
  from fts_matches
  full outer join vec_matches on vec_matches.article_id = fts_matches.rowid
  join articles on articles.rowid = coalesce(fts_matches.rowid, vec_matches.article_id)
  order by combined_rank desc
)
select * from final;

I’ve been puzzled in the past over how to best do that because the distance scores from vector similarity and the relevance scores from FTS are meaningless in comparison to each other. RRF doesn’t even attempt to compare them - it uses them purely for row_number() ranking within each set and combines the results based on that.

Posted 4th October 2024 at 4:22 pm

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