Equation 20 · Part 4 · Retrieval Is an Evidence System, Not a Memory

Symbol S

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)

S

What this part means

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

Its job in the formula

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

Full expressionSymbol SArticle 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 apparatus that BEIR standardised [ 6 ] . The…

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A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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