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Automatic transformation of irreducible representations for efficient contraction of tensors with cyclic group symmetry

Gao, Yang and Helms, Phillip and Chan, Garnet Kin-Lic and Solomonik, Edgar (2020) Automatic transformation of irreducible representations for efficient contraction of tensors with cyclic group symmetry. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20200818-074353010

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Abstract

Tensor contractions are ubiquitous in computational chemistry and physics, where tensors generally represent states or operators and contractions are transformations. In this context, the states and operators often preserve physical conservation laws, which are manifested as group symmetries in the tensors. These group symmetries imply that each tensor has block sparsity and can be stored in a reduced form. For nontrivial contractions, the memory footprint and cost are lowered, respectively, by a linear and a quadratic factor in the number of symmetry sectors. State-of-the-art tensor contraction software libraries exploit this opportunity by iterating over blocks or using general block-sparse tensor representations. Both approaches entail overhead in performance and code complexity. With intuition aided by tensor diagrams, we present a technique, irreducible representation alignment, which enables efficient handling of Abelian group symmetries via only dense tensors, by using contraction-specific reduced forms. This technique yields a general algorithm for arbitrary group symmetric contractions, which we implement in Python and apply to a variety of representative contractions from quantum chemistry and tensor network methods. As a consequence of relying on only dense tensor contractions, we can easily make use of efficient batched matrix multiplication via Intel's MKL and distributed tensor contraction via the Cyclops library, achieving good efficiency and parallel scalability on up to 4096 Knights Landing cores of a supercomputer.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
https://arxiv.org/abs/2007.08056arXivDiscussion Paper
ORCID:
AuthorORCID
Gao, Yang0000-0003-2320-2839
Helms, Phillip0000-0002-6064-3193
Chan, Garnet Kin-Lic0000-0001-8009-6038
Solomonik, Edgar0000-0002-6480-9066
Additional Information:We thank Linjian Ma for providing the batched BLAS backend used in our calculations. ES was supported by the US NSF OAC SSI program, via awards No. 1931258 and No. 1931328. YG, PH, GKC were supported by the US NSF OAC SSI program, award No. 1931258. PH was also supported by a NSF Graduate Research Fellowship via grant DGE-1745301 and an ARCS Foundation Award. The work made use of the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by US National Science Foundation grant number ACI-1548562. We use XSEDE to employ Stampede2 at the Texas Advanced Computing Center (TACC) through allocation TG-CCR180006.
Funders:
Funding AgencyGrant Number
NSFOAC-1931258
NSFOAC-1931328
NSF Graduate Research FellowshipDGE-1745301
ARCS FoundationUNSPECIFIED
NSFACI-1548562
NSFTG-CCR180006
Record Number:CaltechAUTHORS:20200818-074353010
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200818-074353010
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:104989
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:18 Aug 2020 15:26
Last Modified:29 Oct 2020 21:53

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