Large-scale eigenvalue computations on sparse matrices are a key component of graph analytics techniques based on spectral methods. In such applications, an exhaustive computation of all eigenvalues and eigenvectors is impractical and unnecessary, as spectral methods can retrieve the relevant properties of enormous graphs using just the eigenvectors associated with the Top-K largest eigenvalues. In this work, we propose a hardware-optimized algorithm to approximate a solution to the Top-K eigenproblem on sparse matrices representing large graph topologies. We prototype our algorithm through a custom FPGA hardware design that exploits HBM, Systolic Architectures, and mixed-precision arithmetic. We achieve a speedup of 6.22x compared to the highly optimized ARPACK library running on an 80-thread CPU, while keeping high accuracy and 49x better power efficiency.
翻译:稀有基质上的大型电子元值计算是基于光谱方法的图解分析技术的关键组成部分。 在这种应用中,详尽计算所有电子元值和源值都是不切实际和不必要的,因为光谱方法可以仅使用与最大最大电子元值相关的离子体来检索巨型图形的相关属性。在这项工作中,我们提议了一种硬件优化算法,以近似于代表大图形表层的稀有基质顶部问题解决方案。我们通过自定义的FPGA硬件设计,利用HBM、Systolic 建筑和混合精密算算,将我们的算法原型原型化为6.22x,而高级优化的ARPACK图书馆运行在80英尺的CPU上,同时保持高精度和49x更高的功率。