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

TL;DR

tritonBLAS is an analytical model that predicts near-optimal GPU GEMM kernel configurations using architectural parameters, eliminating the need for runtime autotuning and enabling efficient, practical deployment in HPC and ML applications.

Contribution

We introduce tritonBLAS, an analytical approach that models GPU architecture to select GEMM kernel parameters without autotuning, achieving high performance with zero autotuning overhead.

Findings

Achieves over 95% of autotuning performance

Reduces autotuning time to zero

Works across diverse GEMM problem sizes

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.