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Equation 9 · Part 1 · The Safeguards Behind a Claude Refusal, and What They're Actually Trading Off

Symbol s

s(x)s(x)
ss

What this part means

s is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

s is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

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 τ\tau . Two error rates follow directly from that single rule:

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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