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E(x, yw, yl) ∼ DH∪DAI\mathbb{E}_{(x,\,y_w,\,y_l)\,\sim\, D_H \cup D_{AI}}

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LPM(θ)=− E(x, yw, yl) ∼ DH∪DAI[log⁡σ(rθ(x,yw)−rθ(x,yl))].\mathcal{L}_{PM}(\theta) = -\,\mathbb{E}_{(x,\,y_w,\,y_l)\,\sim\, D_H \cup D_{AI}}\Big[\log \sigma\big(r_\theta(x,y_w) - r_\theta(x,y_l)\big)\Big].

How Constitutional AI Actually Constrains a Model's Behavior · Equation 6

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

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