Symbol in context

$\mathbb{E}_{x \sim \mathcal{D},\ y \sim \pi_\theta(\cdot \mid x)}$

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Used in 2 equations

J(\theta) = \mathbb{E}_{x \sim \mathcal{D},\ y \sim \pi_\theta(\cdot \mid x)}\left[r(x,y)\right] - \beta D_{\mathrm{KL}}\left(\pi_\theta(\cdot \mid x) \,\|\, \pi_{\mathrm{ref}}(\cdot \mid x)\right)

Claude, From First Principles: Training, Constitutional Methods, and What Actually Shapes a Response · 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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\mathcal{J}(\theta) = \mathbb{E}_{x \sim \mathcal{D},\ y \sim \pi_\theta(\cdot \mid x)}\left[ r(x, y) \right],

From n-Grams to Reasoning Models: A Technical History of the Language Model · Equation 8

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

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