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Equation 12 · Part 5 · The Hardest Unsolved Problems in Open-Weight AI

addition

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

What this part means

Add the term after the plus sign to the term or group before it.

Its job in the formula

Add the term after the plus sign to the term or group before it.

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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