LoRAStencil: Low-Rank Adaptation of Stencil Computation on Tensor Cores

Stencil computations play a pivotal role in numerous scientific and industrial applications, yet their efficient execution on specialized hardware accelerators like Tensor Core Units (TCUs) remains a challenge. This paper introduces LoRAStencil¹, a novel stencil computing system designed to mitigate memory access redundancies on TCUs through low-rank adaptation. We first identify a nuanced form of this redundancy, dimension residue, specific to TCUs. Then LoRAStencil leverages orchestrated mathematical transformations to decompose stencil weight matrices into smaller rank-1 matrices, facilitating efficient data gathering along residual dimensions. It comprises three key components: memory-efficient Residual Dimension Gathering to facilitate more data reuse, compute-saving Pyramidal Matrix Adaptation to exploit the inherent low-rank characteristics, and performance-boosting Butterfly Vector Swapping to circumvent all data shuffles. Comprehensive evaluations demonstrate that LoRAStencil address dimension residues effectively, which outperforms state-of-the-arts with up to a 2.16x speedup, offering promising advancements for efficient tensorized stencil computation on TCUs by Low-Rank Adaptation.