a-Tucker: Input-Adaptive and Matricization-Free Tucker Decomposition for Dense Tensors on CPUs and GPUs

Tucker decomposition is one of the most popular models for analyzing and compressing large-scale tensorial data. Existing Tucker decomposition algorithms usually rely on a single solver to compute the factor matrices and core tensor, and are not flexible enough to adapt with the diversities of the input data and the hardware. Moreover, to exploit highly efficient GEMM kernels, most Tucker decomposition implementations make use of explicit matricizations, which could introduce extra costs in terms of data conversion and memory usage. In this paper, we present a-Tucker, a new framework for input-adaptive and matricization-free Tucker decomposition of dense tensors. A mode-wise flexible Tucker decomposition algorithm is proposed to enable the switch of different solvers for the factor matrices and core tensor, and a machine-learning adaptive solver selector is applied to automatically cope with the variations of both the input data and the hardware. To further improve the performance and enhance the memory efficiency, we implement a-Tucker in a fully matricization-free manner without any conversion between tensors and matrices. Experiments with a variety of synthetic and real-world tensors show that a-Tucker can substantially outperform existing works on both CPUs and GPUs.