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Equation 8 · Part 3 · From BM25 to Agentic Retrieval: A History of Retrieval-Augmented Generation

Symbol q_i

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)},
qiq_i

What this part means

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

Its job in the formula

qiq_i 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

…after its position in a numbered sequence of variants the group had tried. Written in its now-standard form, a document D scores against a query Q as 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)}. where f(qiq_i, D) is the frequency of query term qiq_i in D , |D| is the document’s length, avgdl\mathrm{avgdl} is the average document length in the collection, and k1k_1 and b are tuned constants controlling term-frequency saturation and length normalization respectively. The saturation term is the substantive advance over a raw term-frequency-times-IDF…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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