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Equation 7 · Part 8 · Reliable AI Agents Are Control Systems, Not Chatbots

=

p(y∣x)=∑z∈Zk(x)pη(z∣x) pθ(y∣x,z),p(y \mid x) = \sum_{z \in \mathcal{Z}_k(x)} p_\eta(z \mid x)\,p_\theta(y \mid x,z),
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

Retrieval-augmented generation is routinely marketed as “giving the model your data.” The original RAG formulation was more precise: combine parametric memory in a sequence model with non-parametric memory in an external index. A simplified sequence-level expression is p(y∣x)=∑z∈Zk(x)pη(z∣x) pθ(y∣x,z)p(y \mid x) = \sum_{z \in \mathcal{Z}_k(x)} p_\eta(z \mid x)\,p_\theta(y \mid x,z). where the retriever assigns probability to documents z and the generator conditions on a selected set Zk(x)\mathcal{Z}_k(x) [ 6 ] . The decomposition matters because retrieval and generation fail differently.

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the surrounding passage

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