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

2025-12-03

AI Summary

GPU GEMM kernels traditionally rely on time-consuming runtime autotuning to determine optimal launch parameters. Method: This paper proposes an analytical modeling approach that explicitly and jointly models the GPU memory hierarchy, code generation logic, and data layout constraints—enabling prediction of near-optimal kernel configurations solely from matrix dimensions, hardware architectural features, and tiling strategies. Implemented as a lightweight Triton-based GEMM framework, it eliminates runtime tuning entirely. Results: Across multiple GPU generations and GEMM problem sizes, the method achieves ≥95% of the performance attained by state-of-the-art autotuners, while reducing tuning overhead to zero. Its core contribution is the first interpretable, tuning-free analytical model for GEMM parameter prediction—significantly improving deployment efficiency and cross-architecture generalizability.

Technology Category

Machine Learning: Matrix & Tensor MethodsNatural Language Processing: Interpretability, Analysis, and Evaluation of NLP ModelsSearch and Optimization: Learning to Search

Application Category

User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendationGraph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphsSemantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• Develops a fast analytical model for GPU GEMM kernel parameter selection
• Predicts near-optimal configurations without runtime autotuning
• Achieves high performance as a practical replacement for empirical tuning

Innovation

• Analytical model predicts GPU GEMM kernels without autotuning
• Lightweight framework implemented entirely within Triton
• Achieves near-optimal performance with zero tuning time