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Equation 19 · Part 3 · A Chatbot Confessed to Being Built by a Company That Never Trained It

=

I0=Iˉ∅I_0=\bar I_\varnothing
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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

Sort a population of models M\mathcal{M}=\{m1m_1,…\dots,mNm_N\} into the three exposure classes just defined, MV\mathcal{M}_V , MH\mathcal{M}_H , and M∅\mathcal{M}_\varnothing . For each model m , define its trait incidence as I(m)=1k\frac{1}{k}∑q∈Q\sum_{q\in Q}1\mathbb{1}[rm(q)r_m(q)∈\inT\mathcal{T}] , where Q is the held-out probe set of size k and rm(q)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 IˉV\bar I_V , IˉH\bar I_H , and I0I_0=Iˉ∅\bar I_\varnothing . I0I_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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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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The article lists its research sources here.