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Equation 8 · Part 2 · What Actually Happens Between a Query and an Answer in RAG

Symbol r

RRF(d)=∑r∈R1k+r(d)\mathrm{RRF}(d) = \sum_{r \in R} \frac{1}{k + r(d)}
rr

What this part means

r occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Its job in the formula

r occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

The passage around this formula

Reciprocal rank fusion avoids the currency problem by discarding scores altogether and combining rank positions instead. For a document d and a set of ranked result lists R , with r(d) the rank of d in a given list and a smoothing constant k : RRF(d)=∑r∈R1k+r(d)\mathrm{RRF}(d) = \sum_{r \in R} \frac{1}{k + r(d)}. Cormack, Clarke, and Buettcher introduced the method and reported that it consistently outperformed both the individual ranked lists and a Condorcet-style fusion baseline, with the specific virtue that it…

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A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the surrounding passage

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