Symbol D
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where f(, D) is the frequency of query term in D , |D| is the document’s length, is the average document length in the collection, and 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 score: a term’s contribution grows quickly at first and then flattens, so a document that happens to repeat a query word fifty times does not dominate one that uses it three times in the right place. Decades later, this same function remains the default first-stage ranking method built into widely used open-source search engines, which is a strong…
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Equation 12 · AI Agents & Systems
From BM25 to Agentic Retrieval: A History of Retrieval-Augmented Generation
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
where f(, D) is the frequency of query term in D , |D| is the document’s length, is the average document length in the collection, and 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 score: a term’s contribution grows quickly at first and then flattens, so a document that happens to repeat a query word fifty times does not dominate one that uses it three times in the right place. Decades later, this same function remains the default first-stage ranking method built into widely used open-source search engines, which is a strong…
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