Equation 32 · Part 1 · How a Model Actually Gets Small Enough to Run on a Phone

Symbol s

s

s

What this part means

the scale.

Its job in the formula

s is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Full expressionSymbol sArticle meaning

Where the article explains it

The standard affine mapping takes a real value x , a scale s and a zero-point z , and produces an integer $x_q$ = $\mathrm{clip}$ $\left(\left\lfloor \frac{x}{s} \right\rceil + z,\ q_{\min},\ q_{\max}\right)$ , $\qquad$ $\hat{x}$ = s $\left(x_q - z\right)$ where $\lfloor$ $\cdot$ $\rceil$ is round-to-nearest and $\hat{x}$ is the dequantised approximation actually used in arithmetic.

The passage around this formula

so halving the number of bits, which roughly doubles s at fixed range, roughly quadruples the expected squared error per weight. That is why INT8 is usually described as close to free and INT4 is not: the error a network has to absorb does not grow gently as bits are removed, it grows quadratically in the step size, and every bit below eight is removed from an already-narrow budget.

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

[7] Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference ↗

These citations provide research context; check each source for the exact claim it supports.