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Equation 12 · Part 4 · The Hardest Unsolved Problems in Open-Weight AI

=

sobs=(1−c) strue+c.s_{\text{obs}} = (1 - c)\, s_{\text{true}} + c.
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What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

A simple decomposition 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 methods above show that assumption is not something the field can currently verify for a given open-weight release, only something it can occasionally catch violated in…

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the article section

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