分层递归精度加速MXU上的对称线性求解
Hierarchical Recursive Precision for Accelerating Symmetric Linear Solves on MXUs
AI总结：
提出一种基于Cholesky分解的嵌套递归混合精度求解器，通过在大规模非对角块使用FP16低精度、对角块保持高精度，在NVIDIA Tensor Cores和AMD Matrix Cores上实现高达5.07倍加速和100倍精度提升。
摘要：
基于Cholesky分解的对称正定系统求解器是许多科学应用（如气候建模）的基础。我们提出了一种可移植的、嵌套递归混合精度求解器，专为矩阵处理单元（MXU）设计，包括NVIDIA Tensor Cores（H200）和AMD Matrix Cores（MI300X），该求解器将低精度FP16算术分配给大型非对角块，同时在对角块上保持高精度以确保数值稳定性。该求解器用Julia实现，提供了高级、硬件无关的接口。我们展示了相对于对角精度供应商基线高达5.07倍的加速，在H200上比纯半精度精度提高100倍，以比高精度更快的速度提供比低精度更高的精度。在MI300X上也观察到了积极的性能趋势，展示了跨GPU的广泛适用性。
英文摘要：
Symmetric positive-definite system solvers based on Cholesky factorization are fundamental to many scientific applications, such as climate modeling. We present a portable, nested recursive mixed-precision solver designed for Matrix Processing Units (MXUs), including NVIDIA Tensor Cores (H200) and AMD Matrix Cores (MI300X), that assigns low-precision FP16 arithmetic to large off-diagonal blocks, while preserving high precision on diagonal blocks to ensure numerical stability. The solver is implemented in Julia, providing a high-level, hardware-agnostic interface. We demonstrate up to a 5.07x speedup relative to the diagonal-precision vendor baseline, with 100x better accuracy than pure half precision on H200, providing higher accuracy than low-precision at higher speed than high-precision. Positive performance trends are also observed on MI300X, demonstrating broad applicability across GPUs.
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