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Equation 7 · Part 1 · Naive, Graph, and Agentic: A Systems Comparison of RAG Architectures

Symbol p

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),
pp

What this part means

p is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

p is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the surrounding passage

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