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Equation 26 · Part 5 · How a Model Actually Gets Small Enough to Run on a Phone

fraction

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

What this part means

Divide the expression above the line by the one below it.

Its job in the formula

The expression above the fraction bar is divided by the complete expression below it. The denominator must not be zero.

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.