tritonBLAS: Triton-based Analytical Approach for GEMM Kernel Parameter Selection

Abstract

We present tritonBLAS, a fast and deterministic analytical model that uses architectural parameters like the cache hierarchy, and relative code and data placement to generate performant GPU GEMM kernels. tritonBLAS explicitly models the relationship between architectural topology, matrix shapes, and algorithmic blocking behavior to predict near-optimal configurations without runtime autotuning. Based on this model, we developed and implemented a lightweight GEMM framework entirely within Triton. We evaluate the performance of tritonBLAS across a diverse set of GEMM problem sizes on modern GPUs. tritonBLAS achieves over 95% of the performance of autotuning solutions, while reducing autotuning time to zero. This makes tritonBLAS a practical drop-in replacement for empirical tuning in production HPC and ML workloads.