← Mathematical compendium

Published equation contexts

P(yA≻yB∣x)=σ(rϕ(x,yA)−rϕ(x,yB))P(y_A \succ y_B \mid x) = \sigma\big(r_\phi(x,y_A) - r_\phi(x,y_B)\big)

Why this formula appears here

The procedure fits a scalar reward model to pairwise comparisons using the Bradley–Terry choice model, P(yA≻yB∣x)=σ(rϕ(x,yA)−rϕ(x,yB))P(y_A \succ y_B \mid x) = \sigma\big(r_\phi(x,y_A) - r_\phi(x,y_B)\big). then optimizes the policy against that fitted reward under a penalty that keeps it near its starting point,

Read the full article-specific guide →

Read the representative guide

yAy_A

Symbol y_A

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

Read this term in its guide →
yBy_B

Symbol y_B

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

Read this term in its guide →

How to interpret it

Read it with the definitions, units, and assumptions supplied by the article.

Research cited beside this formula

Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

P(yA≻yB∣x)=σ(rϕ(x,yA)−rϕ(x,yB)),P(y_A \succ y_B \mid x) = \sigma\big(r_\phi(x,y_A) - r_\phi(x,y_B)\big),

Equation 1 · AI Safety

The Main Technical Approaches to AI Alignment, Compared

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

The procedure fits a scalar reward model to pairwise comparisons using the Bradley–Terry choice model, P(yA≻yB∣x)=σ(rϕ(x,yA)−rϕ(x,yB))P(y_A \succ y_B \mid x) = \sigma\big(r_\phi(x,y_A) - r_\phi(x,y_B)\big). then optimizes the policy against that fitted reward under a penalty that keeps it near its starting point,

Equation guide → · Article →