Fast and Practical Strassen's Matrix Multiplication using FPGAs

Abstract: Matrix multiplication is a cornerstone operation in a wide array of scientific fields, including machine learning and computer graphics. The standard algorithm for matrix multiplication has a complexity of $\mathcal{O}(n^3)$ for $n\times n$ matrices. Strassen's algorithm improves this to $\mathcal{O}(n^{2.807})$, but its practicality is limited for small to medium matrix sizes due to the large number of additions it introduces. This paper presents a novel FPGA-based implementation of Strassen's algorithm that achieves superior speed over an optimized General Matrix Multiply (GeMM) implementation for matrices as small as $n=256$. Our design, tested extensively on two high-performance FPGA accelerators (Alveo U50 and U280) across various data types, matches or surpasses the performance of a highly optimized baseline across a range of matrix sizes.