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Equation 7 · Part 1 · The Hardest Unsolved Problems in Frontier AI Model Comparisons

Symbol b

bb
bb

What this part means

b is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

b is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

where θi\theta_i is some unobservable underlying ability vector for model i , gbg_b is the mapping from ability to expected score that is specific to benchmark b and not shared across benchmarks, δi,b\delta_{i,b} is a contamination or leakage term specific to that model-benchmark pair, and εi,b\varepsilon_{i,b} is sampling and decoding noise. Because gbg_b differs across benchmarks by construction — a multiple-choice knowledge test and a pairwise human-preference…

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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 article section

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