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Equation 1 · Part 8 · How Do We Know a Compressed Model Still Works?

superscript

S=∑i=1nwi aiS = \sum_{i=1}^{n} w_i \, a_i
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What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

An aggregate benchmark score is a weighted average over items or tasks: S=∑i=1nwi aiS = \sum_{i=1}^{n} w_i \, a_i. where aia_i is accuracy, or another per-task quality measure, on task i , and wiw_i is that task’s share of the total, with the weights summing to one. The arithmetic makes the trap explicit: S can be almost unchanged by compression even when some single aia_i collapses, provided wiw_i for that task is small relative to the rest, or provided a rise elsewhere offsets the fall. A single published number, ninety-eight point six percent of baseline, or a small perplexity increase, cannot by construction distinguish “compression cost nothing” from “compression cost a great deal on one task nobody weighted…

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

Open the illustrated exponents: repeated multiplication and powers guide →

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