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Equation 6 · Part 2 · The Hardest Unsolved Problems in Small and On-Device AI

Symbol t

Δmax⁡=max⁡t(AcctFP−AcctQ).\Delta_{\max} = \max_{t}\left(\mathrm{Acc}_t^{FP} - \mathrm{Acc}_t^{Q}\right).
tt

What this part means

t is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

t is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

while what governs whether any individual deployment is safe to ship is closer to the worst-case regression Δmax⁡=max⁡t(AcctFP−AcctQ)\Delta_{\max} = \max_{t}\left(\mathrm{Acc}_t^{FP} - \mathrm{Acc}_t^{Q}\right). A quantization scheme can post a Δˉ\bar{\Delta} close to zero while Δmax⁡\Delta_{\max} is large, provided the loss concentrates on one or a few tasks that are a small share of the suite. Nothing about Δˉ\bar{\Delta} being small implies Δmax⁡\Delta_{\max} is small; the two only converge if degradation is spread evenly, and the studies below find that it is not.

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the article section

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