2020/06/22 by Somashekaracharya G. Bhaskaracharya, Julien Demouth, Bhaskaracharya, Somashekaracharya G. +3 · 3 citations
Computer Science · Mathematics · #Advanced Neural Network Applications #FOS: Computer and information sciences #Parallel Computing and Optimization Techniques #Programming Languages (cs.PL) #Tensor decomposition and applications #cs.PL
paper · pdf · doi:10.48550/arxiv.2006.12645
openalex publication_date 2020/06/22 · arxiv created 2020/08/01 · arxiv updated 2020/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A commonly occurring computation idiom in neural networks is to perform some pointwise operations on the result of a matrix multiplication. Such a sequence of operations is typically represented as a computation graph in deep learning compilers. When compiling to a GPU target, these computations can be individually mapped to manually tuned implementations provided by libraries such as cuBLAS and cuDNN. These libraries also provide off-the-shelf support for targeting tensor cores in NVIDIA GPUs, which can lead to huge performance boosts through their specialized support for mixed-precision matrix math. Alternatively, tensor cores can be programmed directly using CUDA APIs or inline assembly instructions, which opens up the possibility of generating efficient CUDA kernels automatically for such computations. Automatic kernel generation is particularly crucial when it is beneficial to generate efficient code for an entire computation graph by fusing several operations into a single device function instead of invoking a separate kernel for each of them. Polyhedral compilation techniques provide a systematic approach for the analysis and transformation of a sequence of affine loop-nests. In this paper, we describe a polyhedral approach to generate efficient CUDA kernels for matrix multiplication using inline assembly instructions for programming tensor cores on NVIDIA Volta GPUs. Furthermore, we build on this approach to generate fused kernels for computation sequences involving matrix multiplication and pointwise operations such as bias addition, ReLU activation etc. Experimental evaluation of these techniques show that automatically generated kernels can provide significantly better performance than manually tuned library implementations, with speedups ranging up to 2.55X.