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Equation 3 · Part 1 · The Hardest Unsolved Problems in Frontier AI Model Comparisons

Symbol hats_i,b

s^i,b=gb(θi)+δi,b+εi,b,\hat{s}_{i,b} = g_b(\theta_i) + \delta_{i,b} + \varepsilon_{i,b},
s^i,b\hat{s}_{i,b}

What this part means

hatsis_i,b is part of the quantity the equation computes from the expression on the right.

Its job in the formula

hatsis_i,b is part of the quantity the equation computes from the expression on the right.

The passage around this formula

…across benchmarks by construction — a multiple-choice knowledge test and a pairwise human-preference vote are not measuring the same projection of θi\theta_i — there is no aggregation operator that turns a vector of s^i,b\hat{s}_{i,b} values into a single number without an additional, unverified assumption about how the gbg_b functions relate to one another. HELM’s response is to refuse the aggregation and publish the matrix. Epoch’s response is to aggregate anyway, for a stated and narrower purpose. Neither is…

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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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