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Equation 1 · Part 9 · How Do We Know a Compressed Model Still Works?

Starting index or lower bound: i=1

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

What this part means

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

Its job in the formula

i=1 appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

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

Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.

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