Symbol b
b is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
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Why this formula appears here
with b > 0 , so predicted success falls as human-equivalent task length grows. The reported time horizon at success level x is then the duration at which the fitted curve crosses that threshold, i.e. the t solving p(t) = x . Two things follow directly from this formulation that a single reported number obscures: the curve, not the crossing point, is the actual result, and a different chosen threshold x produces a different headline number from the identical underlying data.
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Read this expression with the definitions, units, and assumptions supplied by the article.
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Published contexts (1)
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Equation 3 · Foundation Models
What Claude's Capability Evaluations Actually Measure
This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.
with b > 0 , so predicted success falls as human-equivalent task length grows. The reported time horizon at success level x is then the duration at which the fitted curve crosses that threshold, i.e. the t solving p(t) = x . Two things follow directly from this formulation that a single reported number obscures: the curve, not the crossing point, is the actual result, and a different chosen threshold x produces a different headline number from the identical underlying data.
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