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Equation 3 · Part 7 · Two Different Bets on How to Align a Frontier Model

superscript

pk=1−(1−p)k,p_k = 1 - (1-p)^k,
superscript

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

There is a simple reason a single successful transfer matters more than its raw success rate suggests. If one crafted probe defeats a given safety-trained policy with probability p , and successive attempts against it were independent, the probability that at least one of k attempts succeeds is pk=1−(1−p)kp_k = 1 - (1-p)^k. which climbs quickly even when p is small per attempt. Two caveats matter as much as the formula. Attempts against one fixed, deployed model are usually correlated rather than independent, so real gains from repeated probing fall below this bound; and a universal, transferable suffix is close to the case the formula flatters most, because it is a single artefact effective across…

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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.

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Sources cited in the article section

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