发表机构
University of California, Berkeley; NVIDIA Corp.; University of Colorado Denver; Lawrence Berkeley National Lab; Microsoft Corp.（加州大学伯克利分校; 英伟达公司; 科罗拉多大学丹佛分校; 劳伦斯伯克利国家实验室; 微软公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
为应对ML加速器低精度矩阵乘法带来的精度问题，我们提出一个基准来评级BLAS实现的精度，从A到C级，并设计不可作弊测试，以指导厂商和用户验证精度并评估对LU、QR等分解的影响。
AI 中文摘要
受加速机器学习（ML）的驱动，许多计算机厂商和芯片制造商正在构建矩阵乘法的加速器，这些加速器通过以ML所需的较低精度运行来节省时间和能源。这反过来又促使许多努力利用这些加速器，以许多其他线性代数应用所需的高精度提供更快的矩阵乘法实现。鉴于逼近高精度的算法设计空间庞大，且存在显著的性能/精度权衡，我们提供了一个基准来“评级”矩阵乘法实现（或更一般地，BLAS）的精度，范围从达到经典浮点误差界的“A”级，到达到较弱但仍有用且Strassen类算法满足的界的“C”级。我们还提出了“不可作弊”的测试，供厂商或用户运行以验证其承诺的精度，并描述了这些不同等级如何影响诸如LU、QR和Cholesky分解等应用的精度。我们的测试代码已在此http URL公开，供开发者和用户使用，同时我们也计划公开发布所有测试结果。
英文摘要
Motivated by accelerating machine learning (ML), many computer vendors and chip manufacturers are building accelerators for matrix multiplication, which save time and energy by operating in the lower precisions needed for ML. This has in turn motivated many efforts to use these accelerators to provide faster matrix multiplication implementations with the higher precision required by many other linear algebra applications. Motivated by the large design space of algorithms for approximating higher precision, with significant performance/accuracy tradeoffs, we provide a benchmark to "grade the accuracy" of a matrix multiplication implementation (or the BLAS more generally), ranging from an "A" for attaining the classic floating point error bound, to a "C" for attaining a weaker but still useful bound, that is satisfied by Strassen-like algorithms. We also propose "ungameable" tests that vendors or users can run to verify their promised accuracy, and describe how these different grades impact the accuracy of applications like LU, QR, and Cholesky decomposition. Our test code is publicly available at github.com/Reference-LAPACK/grading-the-BLAS for developers and users, and we also plan to publicly release all our test results.
