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Equation 3 · Part 7 · Ten Ways Mechanistic Interpretability Research Can Mislead You

superscript

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

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

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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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

Open the illustrated exponents: repeated multiplication and powers guide →

Sources cited in the article section

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