$$p(y \mid x) \approx \sum_{z \in \mathcal{Z}_k(x)} p_\eta(z \mid x)\, p_\theta(y \mid x, z)$$

Equation 7 · AI Agents & Systems

Naive, Graph, and Agentic: A Systems Comparison of RAG Architectures

This equation gives an approximation: it relates the quantities while allowing an approximation.

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 $\mathcal{Z}_k(x)$ , the model marginalises over that set, $p(y \mid x) \approx \sum_{z \in \mathcal{Z}_k(x)} p_\eta(z \mid x)\, p_\theta(y \mid x, z)$. with retriever parameters $\eta$ and generator parameters $\theta$ [ 1 ] . One retrieval call, one generation pass, and the entire system’s dependence on the corpus runs through that single set $\mathcal{Z}_k(x)$…

Meanings in this article

• $x$: the writing.

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