← All parts of this equation

Equation 3 · Part 4 · Ten Ways Mechanistic Interpretability Research Can Mislead You

=

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

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

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 equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the article section

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