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Equation 12 · Part 2 · The Hardest Unsolved Problems in Open-Weight AI

Symbol c

sobs=(1−c) strue+c.s_{\text{obs}} = (1 - c)\, s_{\text{true}} + c.
cc

What this part means

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

Its job in the formula

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

The passage around this formula

…makes clear why this is a measurement problem and not merely an inconvenience. Let sobss_{\text{obs}} be an observed benchmark score, strues_{\text{true}} the underlying capability the benchmark intends to measure, and c the fraction of test instances the model has effectively memorized, whether verbatim or through a rephrased variant. If a memorized instance is answered correctly with certainty, then approximately sobs=(1−c) strue+cs_{\text{obs}} = (1 - c)\, s_{\text{true}} + c. Every published leaderboard number implicitly assumes c ≈\approx 0 . The…

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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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