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Equation 6 · Part 4 · Retrieval Is an Evidence System, Not a Memory

Symbol z

p(y∣x)≈∑z∈Zk(x)pη(z∣x)∏i=1∣y∣pθ(yi∣x,z,y1: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)
zz

What this part means

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

Its job in the formula

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

The passage around this formula

…for the top k passages returned by a retriever with parameters η\eta : p(y∣x)≈∑z∈Zk(x)pη(z∣x)∏i=1∣y∣pθ(yi∣x,z,y1: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). 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 weighted account of what those spans support. Everything outside Zk(x)\mathcal{Z}_k(x) has probability zero of influencing the answer, and the system has no representation of what it excluded. REALM made the same commitment on the training…

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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

These citations provide research context; check each source for the exact claim it supports.