Equation 4 · From BM25 to Agentic Retrieval: A History of Retrieval-Augmented Generation
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Symbol d_k
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subscript
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Before any of this involved learning, it involved geometry. Salton, Wong, and Yang proposed representing each document as a vector of weighted index terms and ranking documents by the similarity of their vectors to a query vector, arguing that a well-separated document space — one where unrelated documents sit far apart — should correspond to better retrieval performance than a densely packed one [ 1 ] . Their paper is worth reading in the original rather than through summary, because the term-weighting scheme it specifies is exactly the ancestor of what every later retriever, sparse or dense, still does: score a term by how often it occurs locally and how rare it is globally. They define…
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Before any of this involved learning, it involved geometry. Salton, Wong, and Yang proposed representing each document as a vector of weighted index terms and ranking documents by the similarity of their vectors to a query vector, arguing that a well-separated document space — one where unrelated documents sit far apart — should correspond to better retrieval performance than a densely packed one [ 1 ] . Their paper is worth reading in the original rather than through summary, because the term-weighting scheme it specifies is exactly the ancestor of what every later retriever, sparse or dense, still does: score a term by how often it occurs locally and how rare it is globally. They define the inverse document frequency of a term k , for a collection of n documents in which k appears in of them, as
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