RRF and weighted fusion¶

Intuition¶

When you run multiple sub-queries (title vector + body vector, or dense + FTS), each list has its own ranking. Reciprocal Rank Fusion (RRF) merges by rank, not raw score, so heterogeneous scorers combine cleanly. Weighted fusion scales per-field scores before aggregation.

Math¶

For a set of rankings \(Q\) and rank constant \(k\), RRF score of document \(d\):

\[ \mathrm{score}_{\mathrm{RRF}}(d) = \sum_{q \in Q} \frac{1}{k + r_q(d)} \]

where \(r_q(d)\) is the 1-based rank of \(d\) in list \(q\) (absent documents contribute nothing for that \(q\)).

Weighted fusion (schematic): each sub-query score \(s_q(d)\) is multiplied by weight \(w_q\) then aggregated under a fusion metric.

Illustration¶

flowchart TB
  q1["Sub-query 1"]
  q2["Sub-query 2"]
  l1["Ranked list 1"]
  l2["Ranked list 2"]
  fuse["RRF or Weighted"]
  out["Top-N fused hits"]
  q1 --> l1 --> fuse
  q2 --> l2 --> fuse
  fuse --> out

Citations¶

Cormack, Clarke, Buettcher, Reciprocal Rank Fusion outperforms Condorcet and individual Rank Learning Methods (SIGIR 2009)
Upstream hybrid / rerank docs: zvec.org

ZVec.NET mapping¶

Concern	SDK
RRF type	`ZVecRrfReranker`
Rank constant \(k\)	`RankConstant` default 60 (`ZVecDefaults.Rerank.RankConstant`)
`TopN`	Final fused count (`0` = return all merged, per XML docs)
Weighted type	`ZVecWeightedReranker` — `Weights` dictionary keyed by field name
Weight validation	`ZVecWeightedReranker.ValidateWeights` — count must match sub-query count
API	Multi-query `Query([...], reranker: …)` — requires ≥ 2 sub-queries
Guide	Hybrid search and FTS

Group-by fusion paths remain blocked at the C API — see coverage.