On algorithms for and computing with the tensor ring decomposition
Name
1807.02513.pdf
Description
Accepted version
Size
649.62 KB
Format
Adobe PDF
Checksum (MD5)
a6cfb8fc85080eac894d5b7e83c0c5c6
Author(s)
Mickelin, Oscar
Karaman, Sertac
Date Issued
2020
Journal
Numerical Linear Algebra with Applications
Publisher
Wiley
Version
Author's final manuscript
Abstract
© 2020 John Wiley & Sons, Ltd. Tensor decompositions such as the canonical format and the tensor train format have been widely utilized to reduce storage costs and operational complexities for high-dimensional data, achieving linear scaling with the input dimension instead of exponential scaling. In this paper, we investigate even lower storage-cost representations in the tensor ring format, which is an extension of the tensor train format with variable end-ranks. Firstly, we introduce two algorithms for converting a tensor in full format to tensor ring format with low storage cost. Secondly, we detail a rounding operation for tensor rings and show how this requires new definitions of common linear algebra operations in the format to obtain storage-cost savings. Lastly, we introduce algorithms for transforming the graph structure of graph-based tensor formats, with orders of magnitude lower complexity than existing literature. The efficiency of all algorithms is demonstrated on a number of numerical examples, and in certain cases, we demonstrate significantly higher compression ratios when compared to previous approaches to using the tensor ring format.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1002/NLA.2289
