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Equation 20 · Part 3 · Retrieval Is an Evidence System, Not a Memory

Symbol x

P(correct)=P(Zk(x)∩S(x)≠∅)⋅P(grounded∣Zk(x)∩S(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)
xx

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

Its job in the formula

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

The passage around this formula

…retrieval and generation are separable, an end-to-end score is nearly uninformative about which one broke. Decompose it. Let Zk(x)\mathcal{Z}_k(x) be the retrieved set and S(x) the set of spans that would suffice to answer x : P(correct)=P(Zk(x)∩S(x)≠∅)⋅P(grounded∣Zk(x)∩S(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 second is a pure generation quantity: given that…

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