arXiv AI By Evangelos Georganas, Alexander Heinecke, Pradeep Dubey

Space Filling Curves is All You Need: Communication-Avoiding Matrix Multiplication Made Simple

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The paper proposes a new matrix multiplication approach called SFC-CA GEMM that uses space‑filling curves to partition work in a platform‑ and shape‑oblivious way, achieving communication‑avoiding properties. It demonstrates provable asymptotic communication optimality for both square and rectangular matrices and outperforms vendor libraries on multiple x86 and Arm platforms, with speedups up to 5.5× for specific shapes and 1.8× in weighted harmonic mean throughput. The method is applied to real‑world tasks, improving large‑language‑model inference by up to 1.85× and distributed‑memory GEMM by up to 2.3× over state‑of‑the‑art frameworks.

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arXiv Machine Learning
Sep 23

Accelerating the Mitigation of LLM Inference Nondeterminism Across GPU Architectures

The paper addresses the problem of non‑deterministic outputs from large language models (LLMs) when run on different GPU architectures, caused by floating‑point non‑associativity and hardware‑dependent kernel choices. It proposes a set of fixed‑configuration fused‑upcast GEMM kernels that load 16‑bit weights, upcast to FP32, and perform IEEE‑754 compliant reductions in a problem‑shape‑dependent order, ensuring identical linear‑layer outputs across NVIDIA Ampere, Ada, and Hopper GPUs. The new approach achieves 1.17–3.1× faster end‑to‑end performance than existing solutions and halves weight‑memory traffic while maintaining cross‑architecture reproducibility.

By Liam Cooper, Shinnung Jeong, Hyeran Jeon, Jeffrey Young, Hyesoon Kim