Rabab Alomairy

Hatem Ltaief, Rabab Alomairy, Qinglei Cao et al.

We exploit the widening margin in tensor-core performance between [FP64/FP32/FP16/INT8,FP64/FP32/FP16/FP8/INT8] on NVIDIA [Ampere,Hopper] GPUs to boost the performance of output accuracy-preserving mixed-precision computation of Genome-Wide Association Studies (GWAS) of 305K patients from the UK BioBank, the largest-ever GWAS cohort studied for genetic epistasis using a multivariate approach. Tile-centric adaptive-precision linear algebraic techniques motivated by reducing data motion gain enhanced significance with low-precision GPU arithmetic. At the core of Kernel Ridge Regression (KRR) techniques for GWAS lie compute-bound cubic-complexity matrix operations that inhibit scaling to aspirational dimensions of the population, genotypes, and phenotypes. We accelerate KRR matrix generation by redesigning the computation for Euclidean distances to engage INT8 tensor cores while exploiting symmetry.We accelerate solution of the regularized KRR systems by deploying a new four-precision Cholesky-based solver, which, at 1.805 mixed-precision ExaOp/s on a nearly full Alps system, outperforms the state-of-the-art CPU-only REGENIE GWAS software by five orders of magnitude.

Vicki Carrica, Rabab Alomairy, Evelyne Ringoot et al.

Symmetric linear solves are fundamental to a wide range of scientific and engineering applications, from climate modeling and structural analysis to machine learning and optimization. These workloads often rely on Cholesky (POTRF) decomposition and its supporting operations, triangular solves (TRSM) and symmetric rank-k updates (SYRK), which together form the computational core for solving symmetric positive-definite systems. To accelerate these kernels, we present a portable, mixed-precision solver designed for Matrix Processing Units (MXUs), including NVIDIA Tensor Cores (H200) and AMD Matrix Cores (MI300X). Our algorithm builds on a nested recursive formulation in which Cholesky exposes parallelism through recursive decomposition of its TRSM and SYRK sub-problems. This structure yields a hierarchical recursion that maximizes GEMM throughput while enabling fine-grained control over numerical precision. We introduce a custom recursive data structure 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, leveraging array programming, multiple dispatch, and dynamic type inference to enable seamless expression of mixed-precision computation. This design provides a high-level, hardware-agnostic interface while efficiently interfacing with low-level vendor libraries for backend portability. On H200, our recursive FP64 SYRK achieves a 14x speedup over cuBLAS, while mixed-precision delivers up to 27x speedup in SYRK and 5x in TRSM over full-precision baselines. This results in a 5x overall speedup for Cholesky versus cuSOLVER FP64, with 100x better accuracy than pure FP16 while retaining 88% of its peak speedup. Comparable performance and accuracy trends are observed on MI300X, demonstrating broad applicability across GPUs.