Equation 20 · Part 5 · Retrieval Is an Evidence System, Not a Memory

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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)

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.

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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 second is a pure generation quantity: given that sufficient evidence was present, did the model use it faithfully? Es and colleagues built RAGAS to score exactly this separation — retrieval effectiveness, the faithfulness with…

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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

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