addition

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 $c_{\text{probe}}$ 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…

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