A Mixed Precision, Multi-GPU Design for Large-scale Top-K Sparse Eigenproblems

TL;DR

This paper presents a multi-GPU, mixed-precision approach to efficiently solve large-scale Top-K sparse eigenproblems, significantly outperforming CPU and FPGA implementations in speed and accuracy.

Contribution

It introduces a scalable multi-GPU framework with mixed-precision arithmetic for large sparse eigenproblems, achieving state-of-the-art performance and accuracy improvements.

Findings

67x faster than CPU ARPACK implementation

50% reduction in execution time using mixed-precision

12x more accurate than single-precision floating-point

Abstract

Graph analytics techniques based on spectral methods process extremely large sparse matrices with millions or even billions of non-zero values. Behind these algorithms lies the Top-K sparse eigenproblem, the computation of the largest eigenvalues and their associated eigenvectors. In this work, we leverage GPUs to scale the Top-K sparse eigenproblem to bigger matrices than previously achieved while also providing state-of-the-art execution times. We can transparently partition the computation across multiple GPUs, process out-of-core matrices, and tune precision and execution time using mixed-precision floating-point arithmetic. Overall, we are 67 times faster than the highly optimized ARPACK library running on a 104-thread CPU and 1.9 times than a recent FPGA hardware design. We also determine how mixed-precision floating-point arithmetic improves execution time by 50% over double-precision, and is 12 times more accurate than single-precision floating-point arithmetic.