Symmetric int8 quantization

Problem

Quantization stores weights as small integers and one float scale for each group of values. Symmetric int8 quantization maps the value with the largest magnitude to 127 and maps 0 to 0. A per-tensor scale uses one number for the whole matrix. A per-row scale uses one number for each row, so a row with an outlier does not reduce the precision of the other rows.

Task

Write four functions.

1. quantize_symmetric(tensor) returns (quantized, scale) with one scale for the whole tensor.
2. dequantize_symmetric(quantized, scale) returns the float tensor.
3. quantize_per_channel(tensor) returns (quantized, scales) with one scale for each row of a 2D tensor.
4. dequantize_per_channel(quantized, scales) returns the float tensor.

For a group of values x (the whole tensor, or one row):

Use np.round. It rounds a value that is exactly halfway to the nearest even integer, so 2.5 becomes 2. The dequantized value is q \cdot \text{scale}.

When \max |x| = 0, the scale of that group is 1.0. All its quantized values are then 0.

Input and output

• quantize_symmetric returns a tuple (quantized, scale). quantized is an np.int8 array with the shape of tensor. scale is a Python float.
• quantize_per_channel returns a tuple (quantized, scales). quantized is an np.int8 array of shape (R, C). scales is a float array of shape (R,), also when R is 1.
• Both dequantize functions return a float64 array with the shape of quantized.

Constraints

• 1 <= R, C <= 256. All values are finite.
• Do not change the input arrays.
• Use numpy only.

Examples

pythonCopytensor = np.array([[0.5, -1.0, 0.25], [2.0, 0.1, -0.04]])
q, scale = quantize_symmetric(tensor)

textCopyq
[[ 32 -64  16]
 [127   6  -3]]
scale
0.015748031496062992
dequantize_symmetric(q, scale)
[[ 0.50393701 -1.00787402  0.2519685 ]
 [ 2.          0.09448819 -0.04724409]]

pythonCopyq, scales = quantize_per_channel(tensor)

textCopyq
[[  64 -127   32]
 [ 127    6   -3]]
scales
[0.00787402 0.01574803]
dequantize_per_channel(q, scales)
[[ 0.50393701 -1.          0.2519685 ]
 [ 2.          0.09448819 -0.04724409]]

pythonCopyquantize_per_channel(np.array([[0.0, 0.0], [1.0, -3.0]]))

textCopyq
[[   0    0]
 [  42 -127]]
scales
[1.         0.02362205]