Equation 21 · Part 3 · From BM25 to Agentic Retrieval: A History of Retrieval-Augmented Generation

Symbol x

p(y \mid x) \approx \sum_{z \in \mathrm{top}\text{-}k\left(p_\eta(\cdot \mid x)\right)} p_\eta(z \mid x) \, p_\theta(y \mid x, z),

x

What this part means

the writing.

Its job in the formula

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

Full expressionSymbol xArticle meaning

Where the article explains it

Writing x for the input, y for the output, z for a retrieved passage, and $\eta$ and $\theta$ for the retriever’s and generator’s parameters respectively, the RAG-Sequence variant approximates $p(y \mid x) \approx \sum_{z \in \mathrm{top}\text{-}k\left(p_\eta(\cdot \mid x)\right)} p_\eta(z \mid x) \, p_\theta(y \mid x, z)$ .

The passage around this formula

…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 $\eta$ and $\theta$ for the retriever’s and generator’s parameters respectively, the RAG-Sequence variant approximates $p(y \mid x) \approx \sum_{z \in \mathrm{top}\text{-}k\left(p_\eta(\cdot \mid x)\right)} p_\eta(z \mid x) \, p_\theta(y \mid x, z)$ . holding a single retrieved passage fixed across the whole generated sequence, while the RAG-Token…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

[8] Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks ↗

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