Integer quantization

The scale $s$ is how much real value one integer step stands for. The zero-point $z$ is the integer that stands for exactly 0.0. It must be exact, or every zero in the tensor (including padding) would come back slightly off.

The mixed brackets $\lfloor \cdot \rceil$ mean round to the nearest integer. $\operatorname{clamp}$ clips the result into the range the integer type can hold, from $q_{\min}$ to $q_{\max}$ (for example $-128$ to $127$ for 8-bit). To convert back, $\hat{x} = s(q - z)$. In general $\hat{x} \ne x$, and keeping that error small is the whole design problem.