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Equation 6 · Part 5 · Retrieval Is an Evidence System, Not a Memory

Symbol Z_k

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)
Zk\mathcal{Z}_k

What this part means

ZkZ_k 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

ZkZ_k 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

…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 Zk(x)\mathcal{Z}_k(x) 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…

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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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