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Equation 7 · Part 8 · Naive, Graph, and Agentic: A Systems Comparison of RAG Architectures

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p(y∣x)≈∑z∈Zk(x)pη(z∣x) pθ(y∣x,z),p(y \mid x) \approx \sum_{z \in \mathcal{Z}_k(x)} p_\eta(z \mid x)\, p_\theta(y \mid x, z),
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What this part means

Approximately equal to; the equality is not exact.

Its job in the formula

Approximately equal to; the equality is not exact.

The passage around this formula

Start with the architecture that gives the pattern its name. A query is encoded, a retriever returns its top- k passages against a fixed index, and a generator conditions on those passages to produce one answer. No step revisits an earlier one. Lewis and colleagues’ original formulation makes the mechanism explicit: writing x for the query, y for the output, and z for a retrieved passage drawn from a top- k set Zk(x)\mathcal{Z}_k(x) , the model marginalises over that set, p(y∣x)≈∑z∈Zk(x)pη(z∣x) pθ(y∣x,z)p(y \mid x) \approx \sum_{z \in \mathcal{Z}_k(x)} p_\eta(z \mid x)\, p_\theta(y \mid x, z). with retriever parameters η\eta and generator parameters θ\theta [ 1 ] . One retrieval call, one generation pass, and the entire system’s dependence on the corpus runs through that single set Zk(x)\mathcal{Z}_k(x)…

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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

These citations provide research context; check each source for the exact claim it supports.