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Equation 7 · Part 4 · Naive, Graph, and Agentic: A Systems Comparison of RAG Architectures

Symbol z

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),
zz

What this part means

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

Its job in the formula

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

The passage around this formula

…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…

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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

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