Equation 3 · Ten Ways Mechanistic Interpretability Research Can Mislead You
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
Symbol P_at least one
t least one is part of the quantity the equation computes from the expression on the right.
Symbol k
k is one of the signed contributions combined to compute the quantity on the left.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →subtraction
Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.
subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
superscript
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.
See an illustrated explanation →How to interpret it
Read it with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
Put simply: if a search evaluates k candidate directions against a validation check, and each candidate independently has a small probability 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 . 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.
Sources cited in the article section
These citations give research context. Read each source to check which claims it supports.
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