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Equation 9 · Part 12 · A Chatbot Confessed to Being Built by a Company That Never Trained It

Starting index or lower bound: qin Q

I(m)=1k∑q∈Q1[rm(q)∈T]I(m)=\frac{1}{k}\sum_{q\in Q}\mathbb{1}[r_m(q)\in\mathcal{T}]
q∈Qq\in Q

What this part means

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

Its job in the formula

qin Q appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

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

Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.

Open the illustrated sums and products: repeat an operation over an index guide →

The article lists its research sources here.