← All parts of this equation

Equation 5 · Part 4 · The Main Technical Approaches to AI Alignment, Compared

Symbol x

PAI(yA≻yB∣x,C)=σ(rψ(x,yA,C)−rψ(x,yB,C)),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),
xx

What this part means

x 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

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

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…

Read this part in the article →

Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

Open the illustrated variables: a letter stands for a value guide →

See this notation across published equations →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.