Equation 30 · 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

for a signed integer of b bits. An 8-bit integer has 2^8=256 representable levels; a 4-bit integer has 2^4=16 . That sixteen-fold reduction in available codes is the entire cost of quantization in one number. Treating the rounding error as approximately uniform over one quantization step s , its expected squared magnitude is the classical result

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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.