Sparsity-Aware Roofline Models for Sparse Matrix-Matrix Multiplication

2026-04-07

AI Summary

This work addresses the limitations of the traditional Roofline model in accurately predicting the performance of sparse matrix-dense matrix multiplication (SpMM), as it neglects the impact of sparsity patterns on arithmetic intensity and memory access behavior. To overcome this, the authors propose a sparsity-aware Roofline modeling approach that incorporates CSR and CSB storage formats along with Intel MKL implementations. Evaluation is conducted on an AMD platform using the SuiteSparse dataset, with matrices categorized by sparsity pattern. Experimental results demonstrate that structured sparsity and blocking strategies significantly alter effective arithmetic intensity. The proposed model yields more accurate SpMM performance predictions, highlighting the inadequacy of a single universal Roofline model and underscoring the necessity of integrating data layout and sparsity characteristics for fine-grained performance analysis.

Abstract

Sparse matrix-dense matrix multiplication (SpMM) is a critical kernel in scientific computing, graph analytics, and machine learning, whose performance is often constrained by memory bandwidth. In this work, we investigate the applicability and limitations of roofline modeling for SpMM by explicitly accounting for the impact of matrix sparsity structure on arithmetic intensity and attainable performance. We evaluate three SpMM implementations: Compressed Sparse Row (CSR), Compressed Sparse Blocks (CSB), and Intel's Math Kernel Library (MKL). Each implementation was tested using large-scale matrices from the SuiteSparse collection and grouped by sparsity pattern, including block-structured, banded (diagonal), scale-free, and uniformly random matrices. We derive sparsity-aware roofline models that incorporate memory traffic, cache locality, and blocking behavior, and demonstrate that a single model is insufficient to accurately predict performance across diverse structures. Experiments were conducted on an AMD-based Perlmutter compute node with a varying number of columns in the dense matrix. In particular, blocking and structured sparsity significantly alter effective arithmetic intensity. The results show that accurate roofline-based performance analysis of SpMM requires sparsity-aware modeling, and that data layout and blocking strategies must be evaluated in the context of matrix structure rather than through a single unified model.

Problem

• SpMM
• Roofline model
• sparsity structure
• arithmetic intensity
• performance modeling

Innovation

• sparsity-aware
• Roofline model
• Sparse Matrix-Matrix Multiplication
• arithmetic intensity
• memory traffic