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Equation 12 · Part 6 · The Hardest Unsolved Problems in Open-Weight AI

subtraction

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

What this part means

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

Its job in the formula

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

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

Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

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Sources cited in the article section

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