Equation 31 · Part 1 · How a Model Actually Gets Small Enough to Run on a Phone
Symbol E
What this part means
The expected value operator: the probability-weighted average of the quantity inside its brackets.
Its job in the formula
E is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Full expression→Symbol E→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
Probability assigns a number from 0 to 1 to an event under a stated model. Zero means impossible within that model; one means certain.
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Sources cited in the article section
These citations provide research context; check each source for the exact claim it supports.