On algorithms for and computing with the tensor ring decomposition
Abstract
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Feb 24, 2020
- Source ID
- 10.1002/nla.2289
Entities
People
- Oscar Mickelin
- Sertac Karaman
Organizations
- Army Research Office
- Massachusetts Institute of Technology
- National Science Foundation
- United States Army Research Laboratory