Accelerating Sparse MTTKRP for Small Tensor Decomposition on GPU $\mathcal{X}_{(d)}$

Sparse Matricized Tensor Times Khatri-Rao Product (spMTTKRP) is the bottleneck kernel of sparse tensor decomposition. In tensor decomposition, spMTTKRP is per-formed iteratively along all the modes of an input tensor. In this work, we propose a mode-specific tensor layout on GPU that uses multiple tensor copies, where each copy is optimized for a specific mode. The proposed tensor layout increases the data locality of external memory accesses and eliminates the intermediate values communicated between the GPU thread blocks and the GPU global memory. We also propose a tensor partitioning scheme to optimally distribute the total computations among GPU streaming multiprocessors based on the sparsity and the dimensions of the input tensor. Our approach achieves a geometric mean speedup of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$2.4\times, 7.9\times$</tex>, and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$8.9\times$</tex> in total execution time compared with the state-of-the-art GPU baselines.