← All parts of this equation

Equation 3 · Part 4 · How AI Security Defenses Actually Work

=

Phit(k)=1−(1−p)k.P_{\mathrm{hit}}(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

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…

Read this part in the article →

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 surrounding passage

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