  Tensor decomposition has been widely used in machine learning and high-volume
data analysis. However, large-scale tensor factorization often consumes huge
memory and computing cost. Meanwhile, modernized computing hardware such as
tensor processing units (TPU) and Tensor Core GPU has opened a new window of
hardware-efficient computing via mixed- or low-precision arithmetic
representations. In this paper, we exploit the low-precision representation of
tensor factorization, and propose a mixed-precision block stochastic gradient
descent (SGD) method to reduce the costs of CP tensor decomposition. Our method
achieves robust and fast convergence via a two-stage optimization, i.e.,
SignSGD followed by mixed-precision SGD. Detailed theoretical analysis is
provided to prove the convergence of the proposed mixed-precision algorithm.
Numerical experiments on both synthetic and realistic tensor data sets show the
superior efficiency of our mixed-precision algorithm compared to full-precision
CP decomposition. This work can remarkably reduce the memory, computing and
energy cost on resource-constraint edge computing devices. We demonstrate this
benefit via an FPGA prototype.
