在GPU上扩展基于傅里叶的稀疏矩阵分析
Scaling Fourier-Based Sparse Matrix Analysis on GPUs
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中文总结 AI 辅助
针对大规模稀疏矩阵在GPU上难以进行傅里叶分析的问题，提出BS-FFT及两种压缩方法，大幅降低内存和计算时间，并成功处理大型图邻接矩阵。
中文摘要 AI 辅助
稀疏计算是科学计算、图神经网络（GNN）和机器学习等应用中的重要工作负载。虽然许多稀疏操作可以从现代GPU中受益，但稀疏模式对性能仍然很重要，因为它影响内存合并、块组织和负载平衡。先前的研究表明，频谱特征可以帮助分析稀疏矩阵的全局结构。快速傅里叶变换（FFT）常用于提取频谱特征，并且有高效的GPU FFT库可用。然而，稀疏矩阵，尤其是大型图的邻接矩阵，往往非常大且稀疏。现有的基于稠密矩阵的FFT实现难以扩展，使得这些矩阵的频谱模式难以获得。因此，我们提出了一种三管齐下的研究方法，包括无损的二元稀疏FFT（BS-FFT）和两种压缩方法：弹性BS-FFT（在采样频率网格上重用BS-FFT流水线）和基于密度图的空间压缩。实验表明，相对于稠密cuFFT，BS-FFT将GPU内存使用减少了2.9至11.6倍，并在40 GB A100上完成了所有15个GNN邻接矩阵，而稠密cuFFT只完成了6个。弹性BS-FFT和密度图压缩相对于BS-FFT将GPU计算时间减少了2.0至1466.4倍，在采样率从6.25%到0.0061%的范围内，频谱特征误差仅为0.16%至11.56%。
英文摘要
Sparse computations are important workloads in applications such as scientific computing, graph neural networks (GNNs), and machine learning. While many sparse operations can benefit from modern GPUs, the sparsity pattern remains important to performance because it affects memory coalescing, block organization, and load balancing. Previous studies show that spectral signatures can help analyze the global structure of sparse matrices. The fast Fourier transform (FFT) is commonly used to extract spectral signatures, and efficient GPU FFT libraries are available. However, sparse matrices, especially adjacency matrices for large graphs, tend to be very large and sparse. Existing dense-matrix-based FFT implementations are difficult to scale up, making the spectral patterns of these matrices difficult to obtain. We therefore propose a three-fold research approach comprising a lossless Binary-Sparse FFT (BS-FFT) and two compression methods: Elastic BS-FFT, which reuses the BS-FFT pipeline on a sampled frequency grid, and density-map-based spatial compression. Experiments show that BS-FFT reduces GPU memory use by 2.9--11.6 times relative to dense cuFFT and completes all 15 GNN adjacency matrices where dense cuFFT completes 6 on a 40 GB A100. Elastic BS-FFT and Density Map compression reduce GPU computation time by 2.0--1466.4 times relative to BS-FFT with spectral feature error of only 0.16% to 11.56% across the sampling rates from 6.25% to 0.0061%.
发表机构
- North Carolina State University（北卡罗来纳州立大学）
- Purdue University（普渡大学）
机构由 AI 辅助整理，请以论文原文为准。
