Equation 31 · Part 4 · How a Model Actually Gets Small Enough to Run on a Phone
Symbol s^2
What this part means
the square of s; the scale.
Its job in the formula
occurs above the fraction bar. The numerator is divided by the entire denominator below it.
Full expression→Symbol s^2→Article 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 = , = s where is round-to-nearest and 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 . 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…
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.
Open the illustrated exponents: repeated multiplication and powers guide →
See this notation across published equations →
Sources cited in the article section
These citations provide research context; check each source for the exact claim it supports.