Analyzing the Performance Portability of Tensor Decomposition

TL;DR

This paper evaluates the performance portability of tensor decomposition algorithms, identifying bottlenecks, optimizing implementations with Kokkos, and comparing against vendor libraries across CPU and GPU systems.

Contribution

It provides a detailed analysis of performance bottlenecks in tensor decomposition, demonstrates optimization techniques with Kokkos, and assesses portability across hardware platforms.

Findings

Identified matrix computation $ abla^{(n)}$ as the main bottleneck.

Achieved up to 2.25x speedup on CPU and 1.70x on GPU with tuning.

Kokkos offers performance comparable to vendor libraries for key tensor operations.

Abstract

We employ pressure point analysis and roofline modeling to identify performance bottlenecks and determine an upper bound on the performance of the Canonical Polyadic Alternating Poisson Regression Multiplicative Update (CP-APR MU) algorithm in the SparTen software library. Our analyses reveal that a particular matrix computation, $\Phi^{(n)}$, is the critical performance bottleneck in the SparTen CP-APR MU implementation. Moreover, we find that atomic operations are not a critical bottleneck while higher cache reuse can provide a non-trivial performance improvement. We also utilize grid search on the Kokkos library parallel policy parameters to achieve 2.25x average speedup over the SparTen default for $\Phi^{(n)}$ computation on CPU and 1.70x on GPU. We conclude our investigations by comparing Kokkos implementations of the STREAM benchmark and the matricized tensor times Khatri-Rao product (MTTKRP) benchmark from the Parallel Sparse Tensor Algorithm (PASTA) benchmark suite to implementations using vendor libraries. We show that with a single implementation Kokkos achieves performance comparable to hand-tuned code for fundamental operations that make up tensor decomposition kernels on a wide range of CPU and GPU systems. Overall, we conclude that Kokkos demonstrates good performance portability for simple data-intensive operations but requires tuning for algorithms with more complex dependencies and data access patterns.