Search for Optimal Systolic Arrays: A Comprehensive Automated Exploration Framework and Lessons Learned

Abstract: Systolic arrays have been widely used for accelerating HPC and deep learning applications. There is a plethora of previous works on the performance tuning of systolic arrays, but usually based on a number of oversimplified assumptions (e.g., only considering divisors for loop tiling, pruning based on off-chip data communication) to reduce the design space. In this paper, we present a comprehensive design space exploration tool named Odyssey for systolic array optimization. Odyssey does not rely on artificial assumptions to limit the design space, and yet it is highly efficient and scalable with a hybrid optimization technique. For example, for a 1024x1024x1024 matrix multiplication, it finds designs that reach 90% of the optimal performance in 5 seconds with a single CPU thread. Moreover, using Odyssey, we unveil and quantify the suboptimality introduced by multiple commonly used oversimplifications in prior studies for systolic array design space exploration. For example, Odyssey results show that limiting to divisors for loop tiling leads to a 39% performance loss, and pruning based on off-chip data movement results in a 45% performance loss. We applied Odyssey to explore the architecture trade-offs for matrix multiplication and convolutional neural network, providing inspiration into possible optimizations for these two applications.