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Equation 4 · Part 5 · The Safeguards Behind a Claude Refusal, and What They're Actually Trading Off

=

cˉ=cprobe+pesc⋅cexchange.\bar{c} = c_{\text{probe}} + p_{\text{esc}} \cdot c_{\text{exchange}}.
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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

That first version cost real computation: 23.7% more inference compute than running the model alone, and a 0.38 percentage-point increase in refusals on ordinary, harmless traffic [ 4 ] . Anthropic’s January 2026 follow-up redesigned the system around a two-stage cascade rather than a single classifier pass: a lightweight probe reads the language model’s own internal activations and screens every exchange cheaply, escalating only the fraction it flags to a slower, more capable classifier that reviews the input and output together [ 1 ] . If cprobec_{\text{probe}} is the near-free cost of the first pass and cexchangec_{\text{exchange}} the much larger cost of the second, and pescp_{\text{esc}} is the fraction…

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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 surrounding passage

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