cuTensor-Tubal: Efficient Primitives for Tubal-Rank Tensor Learning Operations on GPUs

Tensors are the cornerstone data structures in high-performance computing, big data analysis and machine learning. However, tensor computations are compute-intensive and the running time increases rapidly with the tensor size. Therefore, designing high-performance primitives on parallel architecture...

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Bibliographic Details
Published in:IEEE transactions on parallel and distributed systems Vol. 31; no. 3; pp. 595 - 610
Main Authors: Zhang, Tao, Liu, Xiao-Yang, Wang, Xiaodong, Walid, Anwar
Format: Journal Article
Language:English
Published: New York IEEE 01.03.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Computation
Computational modeling
Computer architecture
cuTensor-tubal library
Data analysis
Data processing
Data structures
Data transfer (computers)
Frequency domain analysis
GPU
Graphics processing units
Libraries
Linear algebra
Low-tubal-rank tensor decomposition
Machine learning
Mathematical analysis
Matrix decomposition
Parallel processing
Subroutine libraries (computers)
Subroutines
t-SVD
tensor completion
Tensors
Video compression
ISSN:1045-9219, 1558-2183
Online Access:Get full text
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Summary:Tensors are the cornerstone data structures in high-performance computing, big data analysis and machine learning. However, tensor computations are compute-intensive and the running time increases rapidly with the tensor size. Therefore, designing high-performance primitives on parallel architectures such as GPUs is critical for the efficiency of ever growing data processing demands. Existing GPU basic linear algebra subroutines (BLAS) libraries (e.g., NVIDIA cuBLAS) do not provide tensor primitives. Researchers have to implement and optimize their own tensor algorithms in a case-by-case manner, which is inefficient and error-prone. In this paper, we develop the cuTensor-tubal library of seven key primitives for the tubal-rank tensor model on GPUs: t-FFT, inverse t-FFT, t-product, t-SVD, t-QR, t-inverse, and t-normalization. cuTensor-tubal adopts a frequency domain computation scheme to expose the separability in the frequency domain, then maps the tube-wise and slice-wise parallelisms onto the single instruction multiple thread (SIMT) GPU architecture. To achieve good performance, we optimize the data transfer, memory accesses, and design the batched and streamed parallelization schemes for tensor operations with data-independent and data-dependent computation patterns, respectively. In the evaluations oft-product, t-SVD, t-QR, t-inverse and t-normalization, cuTensor-tubal achieves maximum 16.91x, 27.03x, 38.97x, 22.36x,15.43x speedups respectively over the CPU implementations running on dual 10-core Xeon CPUs. Two applications, namely, t-SVD-based video compression and low-tubal-rank tensor completion, are tested using our library and achieve maximum 9.80x and 269.26x speedups over multi-core CPU implementations.
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ISSN:1045-9219
1558-2183
DOI:10.1109/TPDS.2019.2940192