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LPMAI\mathcal{L}^{AI}_{PM}

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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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