$$I(m)$$

Equation 15 · Evolutionary AI

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

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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…

Meanings in this article

• $I$: a dimensionless rate between 0 and 1: the fraction of probes that elicit the trait.

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Equation 16 · Evolutionary AI

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

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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…

Meanings in this article

• $I$: a dimensionless rate between 0 and 1: the fraction of probes that elicit the trait.

Equation guide → · Article →

Equation 40 · Evolutionary AI

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

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

The borrowing above is not decorative. Dan Sperber’s “epidemiology of representations” argued that a mental representation spreading through a population is better modeled as a chain of alternating public productions and private re-representations than as a single replicating code: “a human population is inhabited by a much wider population of mental representations,” connected by “complex causal chains where mental representations and public productions alternate” [ 13 ] . That is a close description of what this article’s transfer rate measures: a rate of spread through contact, not a rate of copying through a shared germline. The mapped part of the analogy is real and does useful work: a…

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Equation 62 · Evolutionary AI

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

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

Then do the one thing neither real-world case above allows: decommission the teacher . Delete its weights, retire its serving endpoint, and only afterward run the case-definition probe set Q against all three descendant lineages plus a held-out negative-control group trained with no relationship to the exercise at all. Compute I(m) for every model, $I_0$ from the negative controls, and $T_V$ , $T_H$ from the two exposed lineages; compute $\mu_V$ and $\mu_H$ from the surface form of every trait-positive response, and, if a curation step separates the teacher’s raw outputs from what the horizontal lineage actually trained on, compute s across that step. Because the trait was seeded rather than found,…

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