Equation 31 · Part 8 · How a Model Actually Gets Small Enough to Run on a Phone
superscript
superscript
What this part means
A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.
Its job in the formula
A raised mark can be a power or an index. Its position and the surrounding notation determine which.
Full expression→superscript→Article meaning
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 →
Sources cited in the article section
These citations provide research context; check each source for the exact claim it supports.