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Published equation contexts

Phit(k)=1−(1−p)kP_{\mathrm{hit}}(k) = 1 - (1-p)^{k}

Why this formula appears here

The shared structural fact underneath both techniques, and the reason they are described here as one machine rather than two, is what a search process buys once it is automated rather than performed by hand. A single human red-teamer trying prompt variations by hand might realistically test dozens of candidates against a target in a working day. An automated pipeline built on either GCG- or PAIR-style search can attempt thousands of candidates against a running target in the same interval, entirely unattended. If a given search strategy succeeds against a defended target with independent per-attempt probability p , the probability that at least one of k automated attempts succeeds is…

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PhitP_{\mathrm{hit}}

Symbol P_hit

PhP_hit is part of the quantity the equation computes from the expression on the right.

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Phit(k)=1−(1−p)k.P_{\mathrm{hit}}(k) = 1 - (1-p)^{k}.

Equation 3 · AI Security

How AI Security Defenses Actually Work

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

The shared structural fact underneath both techniques, and the reason they are described here as one machine rather than two, is what a search process buys once it is automated rather than performed by hand. A single human red-teamer trying prompt variations by hand might realistically test dozens of candidates against a target in a working day. An automated pipeline built on either GCG- or PAIR-style search can attempt thousands of candidates against a running target in the same interval, entirely unattended. If a given search strategy succeeds against a defended target with independent per-attempt probability p , the probability that at least one of k automated attempts succeeds is…

Meanings in this article

  • kk: pushed into the thousands, which a machine can do overnight and a human red-team cannot do at all.
  • pp: the independent per-attempt probability.
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