Int8 Weight Quantisation

Quantise a weight tensor to 8-bit integers and back, with symmetric per-tensor quantisation.

A float32 weight takes 4 bytes. Stored as int8 it takes 1, so the model is four times smaller and integer arithmetic can run faster. Symmetric quantisation maps the range [-max|x|, max|x|] onto the integers [-127, 127] with one scale factor:

scale = max(|x|) / 127          (use 1.0 if every value is 0)
q     = clip(round(x / scale), -127, 127)   as int8
x_hat = q * scale

round here is np.round, which rounds halves to the nearest even integer.

Write two functions: quantize_int8(x) returns (q, scale), and dequantize(q, scale) returns the float approximation x_hat.

Function signature

def quantize_int8(x):
def dequantize(q, scale):

Example

Input

q, scale = quantize_int8(np.array([0.5, -1.27, 0.0, 1.0]))
dequantize(q, scale)

Output

q     = array([  50, -127,    0,  100], dtype=int8)
scale = 0.01
x_hat = array([ 0.5 , -1.27,  0.  ,  1.  ])

Reasoning

The largest magnitude is 1.27, so scale = 1.27 / 127 = 0.01. Dividing by the scale gives 50, -127, 0 and 100, which are already whole numbers. Here the round trip is exact. In general each value can be off by at most half a scale step.

Constraints and notes

• q must have dtype int8 and the same shape as x.
• scale is a plain float.
• The error of the round trip is at most scale / 2 for every element.