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Random projection can reduce the dimension of data while capturing itsstructure and is a fundamental tool for machine learning, signal processing,and information retrieval, which deal with a large amount of data today.RandNLA (Randomized Numerical Linear Algebra) leverages random projection toreduce the computational complexity of low-rank decomposition of tensors andsolve least-square problems. While the computation of the random projection isa simple matrix multiplication, its asymptotic computational complexity istypically larger than other operations in a RandNLA algorithm. Therefore,various studies propose methods for reducing its computational complexity. Wepropose a fast mixed-precision random projection method on NVIDIA GPUs usingTensor Cores for single-precision tensors. We exploit the fact that the randommatrix requires less precision, and develop a highly optimized matrixmultiplication between FP32 and FP16 matrices -- SHGEMM (Single andHalf-precision GEMM) -- on Tensor Cores, where the random matrix is stored inFP16. Our method can compute Randomized SVD 1.28 times faster and Randomprojection high order SVD 1.75 times faster than baseline single-precisionimplementations while maintaining accuracy.

Mixed-Precision Random Projection for RandNLA on Tensor Cores