Using Quantized Integer in LU Factorization with Partial Pivoting (Poster)

Quantization is a common technique to speed the deep learning inference. It is using integers with a shared scalar to represent a set of equally spaced numbers. The quantized integer method has shown great success in compressing the deep learning models, reducing the computation cost without losing too much accuracy. New application specific hardware and specialized CPU extension instructions like Intel AVX-512 VNNI are providing capabilities for us to do integer MADD (multiply and add) efficiently. In this poster, we would like to show our preliminary results of using quantization integers for LU factorization with partial pivoting. Using Int32, the backward error can outperform single precision. However, quantized integer has the similar issue of limited range as FP16 that it would not work directly for large matrices because of big numbers would occur in factored U. We will show some possible solutions to it and how we would like to apply this quantized integer technique to other numerical linear algebra applications.