Equation 21 · Part 11 · From BM25 to Agentic Retrieval: A History of Retrieval-Augmented Generation
Starting index or lower bound: z in top-k(p_eta( × mid x))
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
z in top-k(ta( × mid x)) appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.
Full expression→Starting index or lower bound: z in top-k(p_eta( × mid x))→Article meaning
The passage around this formula
By the time Lewis and colleagues published in 2020, learned dense retrieval and large pretrained generators both already existed as separate lines of work. The paper’s specific technical contribution was neither — it was making the whole pipeline trainable end to end through a single differentiable objective, treating the retrieved passage as a latent variable to be marginalized over rather than a fixed input handed to a frozen reader [ 8 ] . Writing x for the input, y for the output, z for a retrieved passage, and and for the retriever’s and generator’s parameters respectively, the RAG-Sequence variant approximates . holding a single retrieved passage fixed…
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.
Open the illustrated sums and products: repeat an operation over an index guide →
Sources cited in the surrounding passage
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