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Equation 3 · Part 2 · How to Actually Compare Frontier AI Models Without Building a Misleading Leaderboard

Symbol g

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

What this part means

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

Its job in the formula

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

The passage around this formula

Formally, an observed score s is not a property of a model θ\theta alone. It is closer to s=g(θ,H,T,k,P,t)+εs = g(\theta, \mathcal{H}, T, k, \mathcal{P}, t) + \varepsilon. 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 . 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 competitors’ models labelled “unknown” prompt style, sourced from…

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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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Sources cited in the surrounding passage

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