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Equation 8 · Part 13 · From BM25 to Agentic Retrieval: A History of Retrieval-Augmented Generation

Starting index or lower bound: q_i in Q

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)},
qi∈Qq_i \in Q

What this part means

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

Its job in the formula

qiq_i in Q appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

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

Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.

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Sources cited in the surrounding passage

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