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Equation 21 · Part 2 · From BM25 to Agentic Retrieval: A History of Retrieval-Augmented Generation

Symbol y

p(y∣x)≈∑z∈top-k(pη(⋅∣x))pη(z∣x) pθ(y∣x,z),p(y \mid x) \approx \sum_{z \in \mathrm{top}\text{-}k\left(p_\eta(\cdot \mid x)\right)} p_\eta(z \mid x) \, p_\theta(y \mid x, z),
yy

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The passage around this formula

…end to end through a single differentiable objective, treating the retrieved passage as a latent variable to be marginalized over rather than a fixed input handed to a frozen reader [ 8 ] . Writing x for the input, y for the output, z for a retrieved passage, and η\eta and θ\theta for the retriever’s and generator’s parameters respectively, the RAG-Sequence variant approximates p(y∣x)≈∑z∈top-k(pη(⋅∣x))pη(z∣x) pθ(y∣x,z)p(y \mid x) \approx \sum_{z \in \mathrm{top}\text{-}k\left(p_\eta(\cdot \mid x)\right)} p_\eta(z \mid x) \, p_\theta(y \mid x, z). holding a single retrieved passage fixed across the whole generated sequence, while the RAG-Token variant allows…

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