Equation 20 · Part 8 · Retrieval Is an Evidence System, Not a Memory

subscript

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)

subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

Full expressionsubscriptArticle 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 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

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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