Symbol P

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Every mechanism described above shares a single underlying structure, and naming it precisely is more useful than treating “safety” and “usefulness” as opposed virtues balanced by instinct. A classifier, or a trained refusal policy, reduces to a decision rule: given some score s(x) computed from a request — and, for output classifiers, a response — block if s(x) exceeds a threshold $\tau$ . Two error rates follow directly from that single rule: $\text{FPR}(\tau) = P(\text{block} \mid \text{benign}), \qquad \text{FNR}(\tau) = P(\text{allow} \mid \text{harmful})$. Over-refusal is the false positive rate: benign requests wrongly blocked. Under-refusal is the false negative rate: harmful requests wrongly allowed through. Because both are read off the same score against the same threshold, they…

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