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Equation 7 · Part 5 · Reliable AI Agents Are Control Systems, Not Chatbots

Symbol Z_k

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),
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

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

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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