Equation 3 · Part 2 · The Hardest Unsolved Problems in Frontier AI Model Comparisons

Symbol g_b

\hat{s}_{i,b} = g_b(\theta_i) + \delta_{i,b} + \varepsilon_{i,b},

g_b

What this part means

the mapping from ability to expected score that is specific to benchmark b and not shared across benchmarks.

Its job in the formula

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

Full expressionSymbol g_bArticle meaning

Where the article explains it

where $\theta_i$ is some unobservable underlying ability vector for model i , $g_b$ is the mapping from ability to expected score that is specific to benchmark b and not shared across benchmarks, $\delta_{i,b}$ is a contamination or leakage term specific to that model-benchmark pair, and $\varepsilon_{i,b}$ is sampling and decoding noise.

The passage around this formula

…the problem is structural. A published score for model i on benchmark b can be decomposed, at least conceptually, as $\hat{s}_{i,b} = g_b(\theta_i) + \delta_{i,b} + \varepsilon_{i,b}$ . where $\theta_i$ is some unobservable underlying ability vector for model i , $g_b$ is the mapping from ability to expected score that is specific to benchmark b and not shared across benchmarks, $\delta_{i,b}$ is a contamination or leakage term specific to that model-benchmark pair, and $\varepsilon_{i,b}$ is sampling and decoding noise. Because $g_b$ differs across benchmarks by…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

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