Reciprocal Rank Fusion

Where we left off

Lesson 7 fused dense and sparse scores, which meant normalizing two incomparable scales and then tuning a weight against a labeled set, the same fragile pattern flagged for any hyperparameter tuned against a small eval set. Reciprocal Rank Fusion (RRF) sidesteps both problems at once: it never looks at scores, only at rank, which document came first, second, third in each retriever's own ranking.

The code, piece by piece

def reciprocal_rank_fusion(rankings: list[list[str]], k: int = 60) -> list[str]:
    rrf_scores = {}
    for ranking in rankings:
        for rank, name in enumerate(ranking, start=1):
            rrf_scores[name] = rrf_scores.get(name, 0.0) + 1 / (k + rank)
    return sorted(rrf_scores, key=lambda name: rrf_scores[name], reverse=True)

For every ranking (dense, sparse, or more if there were more), each document gets 1 / (k + its rank in that ranking). Rank 1 contributes the most, rank 6 the least, and a document that doesn't appear in a ranking at all (dropped below the cutoff, in a fuller system) simply contributes zero from that side. Sum a document's contributions across every ranking, sort by the total, done. No score from dense is ever compared to a score from sparse, because neither score is used at all, only where each document landed.

k (the constant, unrelated to top-k retrieval's k) softens how much rank 1 dominates over rank 2; a large k makes the difference between ranks small, a small k makes it sharp. 60 is the standard default from the original RRF paper, and this course leaves it there until Lesson 11 examines it directly.