Overparameterized DNNs have more degrees of freedom and this makes them good candidates for information compression [[1]]. When you quantize a model, two things generally happen - the model gets smaller and runs with better efficiency. Hardware vendors explicitly allow for faster processing of 8-bit data (than 32-bit data) resulting in higher throughput. A smaller model has lower memory footprint and power consumption [[2]], crucial for deployment at the edge.
Mapping function
The mapping function is what you might guess - a function that maps values from floating-point to integer space. A commonly used mapping function is a linear transformation given by , where  is the input and  are quantization parameters.