Equation 4 · Part 2 · The Safeguards Behind a Claude Refusal, and What They're Actually Trading Off

Symbol c_probe

\bar{c} = c_{\text{probe}} + p_{\text{esc}} \cdot c_{\text{exchange}}.

c_{\text{probe}}

What this part means

the near-free cost of the first pass and $c_{\text{exchange}}$ the much larger cost of the second.

Its job in the formula

$c_p$ robe is one of the signed contributions combined to compute the quantity on the left.

Full expressionSymbol c_probeArticle meaning

Where the article explains it

If $c_{\text{probe}}$ is the near-free cost of the first pass and $c_{\text{exchange}}$ the much larger cost of the second, and $p_{\text{esc}}$ is the fraction of traffic the probe escalates, the expected added cost per request is $\bar{c} = c_{\text{probe}} + p_{\text{esc}} \cdot c_{\text{exchange}}$ .

The passage around this formula

…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 $c_{\text{probe}}$ is the near-free cost of the first pass and $c_{\text{exchange}}$ the much larger cost of the second, and $p_{\text{esc}}$ is the fraction of traffic the probe escalates, the expected added cost per request is $\bar{c} = c_{\text{probe}} + p_{\text{esc}} \cdot c_{\text{exchange}}$ . Because $p_{\text{esc}}$ is small on ordinary traffic,…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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