Towards HalfPrecision Computation for Complex Matrices: A Case Study for Mixed Precision Solvers on GPUs The use of lowprecision computations is popular in accelerating machine learning and artificial intelligence (AI) applications. Hardware architectures, such as highend graphics processing units (GPUs), now support native 16bit floatingpoint arithmetic (i.e., halfprecision). While half precision provides a natural 2xc3x974xc3x97 speedup against the performance of singledouble precisions, respectively, modern GPUs are equipped with hard ware accelerators that further boost the FP16 performance. These accelerators, known as tensor cores (TCs), have a theoretical peak performance that is 8xc3x9716xc3x97 faster than FP32FP64 performance, respectively. Such a high level of performance has encouraged researchers to harness the compute power of TCs outside AI applications. This paper presents a mixedprecision dense linear solver (Ax  b) for complex matrices using the GPUxe2x80x99s TC units. Unlike similar efforts that have discussed accelerating Ax  b in real FP16 arithmetic, this paper focuses on complex FP16 precisions. The developed solution uses a xe2x80x9chalfcomplexxe2x80x9d pre cision to accelerate the solution of Ax  b while maintaining complex FP32 precision accuracy. The proposed solver requires the development of a highperformance mixedprecision ma trix multiplication (CGEMMFP16) that accepts halfcomplex inputs, and uses the TCsxe2x80x99 fullprecision products and FP32 accumulations for the computation. We discuss two designs and their performance. Similar to the way fast GEMMs power the performance of LAPACK, the mixedprecision CGEMM FP16 can enable the development of mixedprecision LAPACK algorithms. We illustrate this by integrating both CGEMMFP16s into the development of mixedprecision LU factorizations of complex matrices. Finally, an iterative refinement solver is used to deliver complex FP32 accuracy using a preconditioned GMRES solver. Our experiments, conducted on V100 GPUs, show that the mixedprecision solver can be up to 2.5xc3x97 faster than a full singlecomplex precision solver.

FineGrained Exploitation of Mixed Precision for Faster CNN Training As deep convolutional neural networks (CNNs) have become increasingly popular and successful at an everwidening number of machine learning tasks specialized hardware has become increasingly available for training and deploying them. NVIDIAu0027s recent Volta architecture includes tensor cores which perform a fused operation reduced and mixed precision (16bit multiply, 32bit accumulate). Recent research indicates that, typically, very little is lost (in terms of training accuracy) when half precision is used in place of single precision, and performance gains can be made by doing arithmetic in reduced precision. In this work we demonstrate that making layerbylayer choices as to the arithmeticdata precision can lead to further performance improvement. In our study of 25,200 CNNs we demonstrate an average speedup (over purely half precision) of 1.27x and speedups as high as 3.64x by appropriately combining single and half precision arithmetic and data types on a layerbylayer basis.