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Sparse matricized tensor times Khatri-Rao product (MTTKRP) is one of the most computationally expensive kernels in sparse tensor computations. This work focuses on optimizing the MTTKRP operation on GPUs, addressing both performance and storage requirements. We begin by identifying the performance bottlenecks in directly extending the state-ofthe-art CSF (compressed sparse fiber) format from CPUs to GPUs. A significant challenge with GPUs compared to multicore CPUs is that of utilizing the much greater degree of parallelism in a load-balanced fashion for irregular computations like sparse MTTKRP. To address this issue, we develop a new storage-efficient representation for tensors that enables highperformance, load-balanced execution of MTTKRP on GPUs. A GPU implementation of sparse MTTKRP using the new sparse tensor representation is shown to outperform all currently known parallel sparse CPU and GPU MTTKRP implementations.

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This work presents a systematic exploration on the promise and special challenges of deep learning for sparse matrix format selection---a problem of determining the best storage format for a matrix to maximize the performance of Sparse Matrix Vector Multiplication (SpMV). It describes how to effectively bridge the gap between deep learning and the special needs of the pillar HPC problem through a set of techniques on matrix representations, deep learning structure, and cross-architecture model migrations. The new solution cuts format selection errors by two thirds, and improves SpMV performance by 1.73X on average over the state of the art.

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