Space Filling Curves is All You Need: Communication-Avoiding Matrix Multiplication Made Simple

ArXi:2601.16294v2 Announce Type: replace-cross General Matrix Multiplication (GEMM) is the cornerstone of HPC workloads and Deep Learning. State-of-the-art vendor libraries tune tensor layouts, parallelization schemes, and cache blocking to minimize data movement across the memory hierarchy and maximize throughput. Optimal settings for these parameters depend on the tar and matrix shapes, making exhaustive tuning infeasible. We revisit Space Filling Curves (SFC) to alleviate this cumbersome tuning.