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Equation 3 · Part 4 · Two Different Bets on How to Align a Frontier Model

=

pk=1−(1−p)k,p_k = 1 - (1-p)^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

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 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.

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Sources cited in the article section

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