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Equation 26 · Part 8 · How a Model Actually Gets Small Enough to Run on a Phone

Numerator: max(|x|)

s=max⁡(∣x∣)2 b−1−1s = \frac{\max(|x|)}{2^{\,b-1} - 1}
max⁡(∣x∣)\max(|x|)

What this part means

The complete quantity above the fraction bar.

Its job in the formula

max(|x|) occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

For weights, a common simplification is symmetric quantization around zero, with z=0 and the scale set directly by the largest magnitude present: s=max⁡(∣x∣)2 b−1−1s = \frac{\max(|x|)}{2^{\,b-1} - 1}. 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 fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

Open the illustrated fractions: division written vertically guide →

Sources cited in the article section

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