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Equation 6 · Part 4 · AI Feeds on the Distance Between an Intention and an Outcome

Symbol hat p

Htr=−∑c∈Ctrp^(c∣t,r)log⁡2p^(c∣t,r).H_{tr}=-\sum_{c\in\mathcal{C}_{tr}}\hat p(c\mid t,r)\log_2 \hat p(c\mid t,r).
p^\hat p

What this part means

hat p is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

hat p is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

The first factor is Shannon entropy: Htr=−∑c∈Ctrp^(c∣t,r)log⁡2p^(c∣t,r)H_{tr}=-\sum_{c\in\mathcal{C}_{tr}}\hat p(c\mid t,r)\log_2 \hat p(c\mid t,r). Its unit is bits. A request that commits competent readers to one completion class has HtrH_{tr}=0 bits. A request that leaves two equally plausible classes alive has one bit. This does not imply that either task takes one unit of labor. It says only how much uncertainty about the reasonable completion story remains after the initial request is read. The estimator should carry a resampling interval across annotators and adjudication choices; a point estimate without its classification fragility would make the most subjective part of the design look falsely exact.

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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See this notation across published equations →

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