Upcoming Event: CSEM Student Forum

Developing a Memory Efficient Dense MTTKRP for Many-Core CPUs and GPUs

Gabriel Kosmacher, CSEM Student, Oden Institute

Abstract

The matricized-tensor times Khatri-Rao product (MTTKRP) is the bottleneck kernel for canonical polyadic (CP) tensor decompositions. Current methods to compute the MTTKRP for dense tensors rely on explicitly forming a Khatri-Rao matrix Z, whose memory footprint grows like O(R(nmk)), where R is some specified CP rank. Given Z, the product can be computed with optimized matrix-multiply routines.  In contrast, we utilize an element based definition of the MTTKRP, whose memory footprint grows like O(R(n+m+k)), and develop performance portable algorithms to efficiently compute the product.   We will discuss the optimization techniques employed in developing element based MTTKRPs that take advantage of the idiosyncrasies of modern high-performance hardware and provide fine grained performance models for the algorithms on ideal multi-level cache machines. Numerical results will be provided on tensors relevant to scientific computing to show the efficacy of our optimized element based algorithm.

Biography

Gabriel was born and raised in Chicago, Illinois before earning his bachelor of science in Mathematics & Computer Science at the University of Illinois at Urbana-Champaign. Gabriel started the CSEM program in Fall 2023, and his current research interest include fast algorithms for differential and integral equations and parallel algorithms for scientific computing. Outside of school, Gabriel likes to bake bread and pastries, read (mostly fiction), and do any array of baseball related activities.