Equation 20 · Part 2 · Retrieval Is an Evidence System, Not a Memory

Symbol Z_k

P(\text{correct}) = P\left(\mathcal{Z}_k(x) \cap S(x) \neq \emptyset\right) \cdot P\left(\text{grounded} \mid \mathcal{Z}_k(x) \cap S(x) \neq \emptyset\right)

\mathcal{Z}_k

What this part means

$Z_k$ is one factor in the product that computes the quantity on the left.

Its job in the formula

$Z_k$ is one factor in the product that computes the quantity on the left.

Full expressionSymbol Z_kArticle meaning

The passage around this formula

Because retrieval and generation are separable, an end-to-end score is nearly uninformative about which one broke. Decompose it. Let $\mathcal{Z}_k(x)$ be the retrieved set and S(x) the set of spans that would suffice to answer x : $P(\text{correct}) = P\left(\mathcal{Z}_k(x) \cap S(x) \neq \emptyset\right) \cdot P\left(\text{grounded} \mid \mathcal{Z}_k(x) \cap S(x) \neq \emptyset\right)$ . The first factor is a pure retrieval quantity: recall at k , measurable against relevance judgements with no generator involved, using the established information-retrieval…

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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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