quantize(w: array, /, group_size: int = 64, bits: int = 4, *, stream: None | Stream | Device = None) Tuple[array, array, array]#

Quantize the matrix w using bits bits per element.

Note, every group_size elements in a row of w are quantized together. Hence, number of columns of w should be divisible by group_size. In particular, the rows of w are divided into groups of size group_size which are quantized together.


quantize currently only supports 2D inputs with dimensions which are multiples of 32

Formally, for a group of \(g\) consecutive elements \(w_1\) to \(w_g\) in a row of w we compute the quantized representation of each element \(\hat{w_i}\) as follows

\[\begin{split}\begin{aligned} \alpha &= \max_i w_i \\ \beta &= \min_i w_i \\ s &= \frac{\alpha - \beta}{2^b - 1} \\ \hat{w_i} &= \textrm{round}\left( \frac{w_i - \beta}{s}\right). \end{aligned}\end{split}\]

After the above computation, \(\hat{w_i}\) fits in \(b\) bits and is packed in an unsigned 32-bit integer from the lower to upper bits. For instance, for 4-bit quantization we fit 8 elements in an unsigned 32 bit integer where the 1st element occupies the 4 least significant bits, the 2nd bits 4-7 etc.

In order to be able to dequantize the elements of w we also need to save \(s\) and \(\beta\) which are the returned scales and biases respectively.

  • w (array) – Matrix to be quantized

  • group_size (int, optional) – The size of the group in w that shares a scale and bias. (default: 64)

  • bits (int, optional) – The number of bits occupied by each element of w in the returned quantized matrix. (default: 4)


A tuple containing

  • w_q (array): The quantized version of w

  • scales (array): The scale to multiply each element with, namely \(s\)

  • biases (array): The biases to add to each element, namely \(\beta\)

Return type: