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Equation 6 · Part 2 · How Do We Know a Compressed Model Still Works?

subscript

aia_i
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

The passage around this formula

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 heavily.” Both produce the same S .

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

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