稀疏矩阵计算的谱分析：见解与潜力
Spectral Analysis for Sparse Matrix Computation: Insights and Potential
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中文总结 AI 辅助
本研究首次探索稀疏矩阵计算与谱分析的联系，将稀疏矩阵视为二维信号，用谱特征优化机器学习的SpMV格式选择和剪枝LLM解码，获1.035至1.245倍核加速，为稀疏计算提供新分析视角与优化方法。
中文摘要 AI 辅助
稀疏计算是科学计算、图分析和机器学习的基础，但其性能高度依赖于多样的稀疏性与模式，因为缓存复用、内存合并和负载均衡关键取决于稀疏模式。本研究首次探索稀疏矩阵计算与谱分析的联系，将稀疏矩阵视为二维信号，通过快速傅里叶变换分析其频域表示。研究表明，谱特征能揭示传统空间统计未充分捕捉的全局结构特征，为理解稀疏计算性能提供补充信息。实验将谱特征用于基于机器学习的稀疏矩阵-向量乘（SpMV）格式选择，证明该谱分析比最先进的仅空间模型更有用；在剪枝大语言模型（LLM）解码中，添加谱特征可改进核选择，获得1.035至1.245倍的核加速。通过揭示谱特征与稀疏矩阵计算的原理性联系，本研究为稀疏计算引入了新颖的分析视角，提供了增强当前稀疏结构表征与优化的新方法。
英文摘要
Sparse computations are fundamental to scientific computing, graph analytics, and machine learning, yet their performance is highly sensitive to the diverse sparsity and patterns. This is because cache reuse, memory coalescing, and load balancing depend critically on the sparsity patterns. This work gives the first known exploration of the connections between sparse matrix computation and spectral analysis by treating sparse matrices as two-dimensional signals and analyzing their frequency-domain representations through Fast Fourier Transform. We show that spectral signatures uncover global structural characteristics that are not sufficiently captured by conventional spatial statistics and provide complementary information for understanding sparse computation performance. Experiments on incorporating spectral features into machine-learning-based SpMV format selection demonstrate the usefulness of such spectral analysis over a state-of-the-art spatial-only model. By uncovering the principled connections between spectral characteristics and sparse matrix computations, this work introduces a novel analytical perspective into sparse computation, and provides a new approach to enhancing the current sparse structure characterization and optimization. On pruned LLM decoding, adding spectral features improves kernel selection and yields 1.035--1.245$\times$ kernel speedups.
发表机构
- North Carolina State University（北卡罗来纳州立大学）
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