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Equation 3 · Part 1 · Ten Ways Mechanistic Interpretability Research Can Mislead You

Symbol P_at least one

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

What this part means

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

Its job in the formula

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

The passage around this formula

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.

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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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Sources cited in the article section

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