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Equation 6 · Part 8 · The Hardest Unsolved Problems in Small and On-Device AI

superscript

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

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

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

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.

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Sources cited in the article section

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