← Mathematical compendium

Published equation contexts

Pat least one=1−(1−α)kP_{\text{at least one}} = 1 - (1-\alpha)^k

Why this formula appears here

Put simply: if a search evaluates k candidate directions against a validation check, and each candidate independently has a small probability α\alpha of appearing to pass that check purely by chance — because it happens to correlate with the labeled examples used to test it — then the probability that the search turns up at least one apparent “finding” is Pat least one=1−(1−α)kP_{\text{at least one}} = 1 - (1-\alpha)^k. a quantity that climbs toward near-certainty long before k reaches even a small fraction of the directions a real residual stream offers. A single successful-looking direction, reported without the number of candidates it was selected from, is close to uninterpretable on its own.

Read the full article-specific guide →

Read the representative guide

Pat least oneP_{\text{at least one}}

Symbol P_at least one

PaP_at least one is part of the quantity the equation computes from the expression on the right.

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

Learn the mathematics behind it

Published contexts (1)

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

Pat least one=1−(1−α)k,P_{\text{at least one}} = 1 - (1-\alpha)^k,

Equation 3 · AI Research

Ten Ways Mechanistic Interpretability Research Can Mislead You

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

Put simply: if a search evaluates k candidate directions against a validation check, and each candidate independently has a small probability α\alpha of appearing to pass that check purely by chance — because it happens to correlate with the labeled examples used to test it — then the probability that the search turns up at least one apparent “finding” is Pat least one=1−(1−α)kP_{\text{at least one}} = 1 - (1-\alpha)^k. a quantity that climbs toward near-certainty long before k reaches even a small fraction of the directions a real residual stream offers. A single successful-looking direction, reported without the number of candidates it was selected from, is close to uninterpretable on its own.

Meanings in this article

Equation guide → · Article →