Equation 6 · Part 3 · Retrieval Is an Evidence System, Not a Memory

Symbol x

p(y \mid x) \approx \sum_{z \in \mathcal{Z}_k(x)} p_\eta(z \mid x) \prod_{i=1}^{|y|} p_\theta\left(y_i \mid x, z, y_{1:i-1}\right)

x

What this part means

the writing.

Its job in the formula

x appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

Full expressionSymbol xArticle meaning

Where the article explains it

Writing x for the query, y for the output, and $\mathcal{Z}_k(x)$ for the top k passages returned by a retriever with parameters $\eta$ : $p(y \mid x) \approx \sum_{z \in \mathcal{Z}_k(x)} p_\eta(z \mid x) \prod_{i=1}^{|y|} p_\theta\left(y_i \mid x, z, y_{1:i-1}\right)$ .

The passage around this formula

…and the architectural point is that the second is a different kind of object, not an extension of the first [ 1 ] . Their formulation treats the retrieved passage as a latent variable to be marginalised over. Writing x for the query, y for the output, and $\mathcal{Z}_k(x)$ for the top k passages returned by a retriever with parameters $\eta$ : $p(y \mid x) \approx \sum_{z \in \mathcal{Z}_k(x)} p_\eta(z \mid x) \prod_{i=1}^{|y|} p_\theta\left(y_i \mid x, z, y_{1:i-1}\right)$ . Read the structure rather than the arithmetic. The generator is never conditioned on the corpus. It is conditioned on z — one span, or a handful — and…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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