Brief Announcement: Minimizing Communication for Parallel Symmetric Tensor Times Same Vector Computation
In this article, we focus on the parallel communication cost of multiplying the same vector along two modes of a 3-dimensional symmetric tensor. This is a key computation in the higher-order power method for determining eigenpairs of a 3-dimensional symmetric tensor and in gradient-based methods for computing a symmetric CP decomposition. We establish communication lower bounds that determine how much data movement is required to perform the specified computation in parallel. We demonstrate that the communication lower bounds are tight by presenting an optimal algorithm where the data distribution is a natural extension of the triangle block partition scheme for symmetric matrices to 3-dimensional symmetric tensors.
Authors
- Hussam Al Daas (ORCID: https://orcid.org/0000-0001-9355-4042)
- Laura Grigori (ORCID: https://orcid.org/0000-0002-5880-1076)
- Grey Ballard (ORCID: https://orcid.org/0000-0003-1557-8027)
- Suraj Kumar (ORCID: https://orcid.org/0009-0001-1449-0165)
- Kathryn Rouse (ORCID: https://orcid.org/0009-0001-4045-0423)
- Mathieu Vérité (ORCID: https://orcid.org/0000-0003-0581-2772)
Institutions
- Rutherford Appleton Laboratory (GB)
- Wake Forest University (US)
- École Polytechnique Fédérale de Lausanne (CH)
Publication Details
- Published
- 2025-07-16
- DOI
- https://doi.org/10.1145/3694906.3743332
- Citations
- 1
- Primary Topic
- Tensor decomposition and applications
- Type
- article
- Field-Weighted Citation Impact
- 1.53
Funders
- National Science Foundation
- U.S. Department of Energy
- UK Research and Innovation
- European Commission
- Office of Science
- Science and Technology Facilities Council
- Advanced Scientific Computing Research