Equation 5 · Part 2 · The Main Technical Approaches to AI Alignment, Compared

Symbol y_A

P_{\mathrm{AI}}(y_A \succ y_B \mid x, C) = \sigma\big(r_\psi(x,y_A,C) - r_\psi(x,y_B,C)\big),

y_A

What this part means

$y_A$ is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Its job in the formula

$y_A$ is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Full expressionSymbol y_AArticle meaning

The passage around this formula

Constitutional AI keeps RLHF’s reward-model-and-KL-penalty backbone intact and changes where the comparison labels come from. Bai and colleagues describe a two-phase method: a supervised phase in which the model critiques and revises its own responses against a written set of principles, and a reinforcement phase in which a model, rather than a human, judges which of two candidate responses better satisfies those principles — producing an AI-generated preference dataset that trains the reward model [ 6 ] . Formally, this changes only the source of the comparison label. The Bradley–Terry equation above is unchanged in form; what changes is that the probability being fitted is now [displayed…

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A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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