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This entry links every published equation using this exact notation. Its meaning may change between equations.

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Used in 177 equations

Approval(a)={automatic,p(a) S(a)≤Bhuman required,p(a) S(a)>B\text{Approval}(a) = \begin{cases} \text{automatic}, & p(a)\, S(a) \le B \\ \text{human required}, & p(a)\, S(a) > B \end{cases}

AI Agent Architecture in 2035: Four Scenarios, Their Signals, and What Would Falsify Them · Equation 5

This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.

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LPMAI(θ)=− E(x, yA, yB, p) ∼ DAI[p log⁡σ(rθ(x,yA)−rθ(x,yB))+(1−p) log⁡σ(rθ(x,yB)−rθ(x,yA))],\mathcal{L}^{AI}_{PM}(\theta) = -\,\mathbb{E}_{(x,\,y_A,\,y_B,\,p)\,\sim\, D_{AI}}\Big[p\,\log \sigma\big(r_\theta(x,y_A)-r_\theta(x,y_B)\big) + (1-p)\,\log \sigma\big(r_\theta(x,y_B)-r_\theta(x,y_A)\big)\Big],

How Constitutional AI Actually Constrains a Model's Behavior · Equation 11

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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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),

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

This equation gives an approximation: it relates the quantities while allowing an approximation.

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