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Published equation contexts

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

Why this formula appears here

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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ii

Symbol i

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

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nn

Symbol n

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

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i=1i=1

Starting index or lower bound: i=1

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.

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nn

Ending index or upper bound: n

This label says where the repeated addition, multiplication, or accumulation stops. It sets the last term or end of the range.

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Published contexts (1)

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

Equation 1 · Edge AI & Electronics

How Do We Know a Compressed Model Still Works?

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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…

Meanings in this article

  • SS: the same.
  • aia_i: accuracy, or another per-task quality measure, on task i.
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