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Used in 121 equations

E[rθ(x,y)]−β E[DKL ⁣(πRL ∥ πSFT)]+γ E[log⁡πRL(x)],\mathbb{E}\big[r_\theta(x,y)\big] - \beta\,\mathbb{E}\big[D_{\mathrm{KL}}\!\left(\pi^{\mathrm{RL}} \,\|\, \pi^{\mathrm{SFT}}\right)\big] + \gamma\,\mathbb{E}\big[\log \pi^{\mathrm{RL}}(x)\big],

What RLHF Actually Optimises: Rated Agreeableness, and Where It Parts from Helpfulness · Equation 3

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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Δln⁡L  =  η Δln⁡Y⏟productivity  −  ∫II+ΔIs(x) dx⏟displacement  +  ∫NN+ΔNs(x) dx⏟reinstatement\Delta \ln L \;=\; \underbrace{\eta \, \Delta \ln Y}_{\text{productivity}} \;-\; \underbrace{\int_{I}^{I+\Delta I} s(x)\,dx}_{\text{displacement}} \;+\; \underbrace{\int_{N}^{N+\Delta N} s(x)\,dx}_{\text{reinstatement}}

What the Machine Breakers Actually Wanted · Equation 5

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

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P(correct)=P(Zk(x)∩S(x)≠∅)⋅P(grounded∣Zk(x)∩S(x)≠∅)P(\text{correct}) = P\left(\mathcal{Z}_k(x) \cap S(x) \neq \emptyset\right) \cdot P\left(\text{grounded} \mid \mathcal{Z}_k(x) \cap S(x) \neq \emptyset\right)

Retrieval Is an Evidence System, Not a Memory · Equation 20

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

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