$$\mathcal{M}=\{m_1,\dots,m_N\}$$

Equation 4 · Evolutionary AI

A Chatbot Confessed to Being Built by a Company That Never Trained It

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Sort a population of models $\mathcal{M}$=\{$m_1$,$\dots$,$m_N$\} into the three exposure classes just defined, $\mathcal{M}_V$ , $\mathcal{M}_H$ , and $\mathcal{M}_\varnothing$ . For each model m , define its trait incidence as I(m)=$\frac{1}{k}$$\sum_{q\in Q}$$\mathbb{1}$[$r_m(q)$$\in$$\mathcal{T}$] , where Q is the held-out probe set of size k and $r_m(q)$ is m ’s response to probe q . I(m) is a dimensionless rate between 0 and 1: the fraction of probes that elicit the trait. Average I(m) within each class to get $\bar I_V$ , $\bar I_H$ , and $I_0$=$\bar I_\varnothing$ . $I_0$ is the article’s single most important number, because it is the rate at which the trait shows up in models that never touched the source at all — the…

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