← All parts of this equation

Equation 3 · Part 10 · How to Actually Compare Frontier AI Models Without Building a Misleading Leaderboard

=

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

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

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

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the surrounding passage

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