Application Performance Modeling via Tensor Completion

TL;DR

This paper introduces a tensor completion approach using low-rank tensor decomposition to accurately model and predict application performance across high-dimensional parameter spaces, improving efficiency and extrapolation.

Contribution

It presents a novel application of CP tensor decomposition with tensor completion for performance modeling, outperforming existing piecewise and supervised learning models.

Findings

CP tensor decomposition accurately approximates performance tensors.

Tensor completion enables effective extrapolation in unobserved regions.

Method outperforms alternative models in prediction accuracy and memory efficiency.

Abstract

Performance tuning, software/hardware co-design, and job scheduling are among the many tasks that rely on models to predict application performance. We propose and evaluate low-rank tensor decomposition for modeling application performance. We discretize the input and configuration domains of an application using regular grids. Application execution times mapped within grid-cells are averaged and represented by tensor elements. We show that low-rank canonical-polyadic (CP) tensor decomposition is effective in approximating these tensors. We further show that this decomposition enables accurate extrapolation of unobserved regions of an application's parameter space. We then employ tensor completion to optimize a CP decomposition given a sparse set of observed execution times. We consider alternative piecewise/grid-based models and supervised learning models for six applications and demonstrate that CP decomposition optimized using tensor completion offers higher prediction accuracy and memory-efficiency for high-dimensional performance modeling.