Hybrid Search

Dense and sparse retrieval fail on different queries. A dense retriever misses an exact product code it has never seen; a lexical one misses a paraphrase. Running both and combining the two rankings recovers most of each one's failures, which is why almost every production system does that rather than picking a side.

Either fuse the scores, which requires them to be on a comparable scale and therefore normalised, or fuse the ranks, which does not. Reciprocal rank fusion is the common choice for exactly that reason — it needs no calibration between two systems whose scores mean different things. A convex combination can beat it when the scores are well calibrated, and that is the condition worth checking before assuming either.

Reciprocal rank fusion scores a document as Σ sub _s  1/(k + rank sub _s (d)) across systems s, with a damping constant k — 60 by convention — that limits how much the single top position dominates. Because it reads only ranks, a system whose scores are wildly miscalibrated still contributes on equal terms, which is the property score fusion has to be made to have and this one gets for free.