Equation 6 · Part 17 · Retrieval Is an Evidence System, Not a Memory

Starting index or lower bound: i=1

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)

i=1

What this part means

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

Its job in the formula

i=1 appears in the bound of this product. The bound states where the repeated operation starts, ends, or which values it includes.

Full expressionStarting index or lower bound: i=1Article meaning

The passage around this formula

The retrieval literature said the opposite. Lewis and colleagues introduced RAG explicitly as a combination of parametric and non-parametric memory, 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 its output distribution is a…

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Learn the underlying idea

Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.

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Sources cited in the surrounding passage

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