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Equation 7 · Part 5 · Naive, Graph, and Agentic: A Systems Comparison of RAG Architectures

Symbol Z_k

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),
Zk\mathcal{Z}_k

What this part means

ZkZ_k 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

ZkZ_k 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

…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 subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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