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Equation 3 · Part 9 · How to Actually Compare Frontier AI Models Without Building a Misleading Leaderboard

Symbol varepsilon

s=g(θ,H,T,k,P,t)+ε,s = g(\theta, \mathcal{H}, T, k, \mathcal{P}, t) + \varepsilon,
ε\varepsilon

What this part means

the plus sampling noise.

Its job in the formula

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

Where the article explains it

a function of the weights θ\theta , the harness H\mathcal{H} , the sampling temperature T , the number of samples k and how they are aggregated, the prompt template P\mathcal{P} , the date t a snapshot was queried, plus sampling noise ε\varepsilon .

The passage around this formula

…of the weights θ\theta , the harness H\mathcal{H} , the sampling temperature T , the number of samples k and how they are aggregated, the prompt template P\mathcal{P} , the date t a snapshot was queried, plus sampling noise ε\varepsilon . A citation that fixes θ\theta and leaves the other five free has not specified a comparable quantity. OpenAI’s own simple-evals table makes the same point from a different angle: rows the lab ran itself under a disclosed zero-shot chain-of-thought protocol sit beside rows for…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.