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Equation 8 · Part 11 · From BM25 to Agentic Retrieval: A History of Retrieval-Augmented Generation

subtraction

score(D,Q)=∑qi∈QIDF(qi)⋅f(qi,D)⋅(k1+1)f(qi,D)+k1⋅(1−b+b⋅∣D∣avgdl),\mathrm{score}(D, Q) = \sum_{q_i \in Q} \mathrm{IDF}(q_i) \cdot \frac{f(q_i, D) \cdot (k_1 + 1)}{f(q_i, D) + k_1 \cdot \left(1 - b + b \cdot \dfrac{|D|}{\mathrm{avgdl}}\right)},
subtraction

What this part means

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

Its job in the formula

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

The passage around this formula

The Text REtrieval Conference, run annually by the U.S. National Institute of Standards and Technology from 1992 onward, gave information retrieval something the field had mostly lacked: a shared, blind evaluation on a common document set, repeated every year with published results. Robertson, Walker, and colleagues at City University London entered TREC-3 in 1994 with the Okapi system, reporting a term-weighting approach within a probabilistic relevance framework and applying it, among other extensions, to phrase weighting and to query expansion using terms drawn from an initial pilot search [ 2 ] . Over that and the following TREC rounds, the Okapi team’s tuning of term-frequency…

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Learn the underlying idea

Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

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Sources cited in the surrounding passage

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