One of the most common, but at the same time expensive operations in linear algebra, is multiplying two matrices $A$ and $B$. With the rapid development of machine learning and increases in data volume, performing fast matrix intensive multiplications has become a major hurdle. Two different approaches to overcoming this issue are, 1) to approximate the product; and 2) to perform the multiplication distributively. A \textit{$CR$-multiplication} is an approximation where columns and rows of $A$ and $B$ are respectively sampled with replacement. In the distributed setting, multiple workers perform matrix multiplication subtasks in parallel. Some of the workers may be stragglers, meaning they do not complete their task in time. We present a novel \textit{approximate weighted $CR$ coded matrix multiplication} scheme, that achieves improved performance for distributed matrix multiplication.

中文翻译：

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近似加权 $CR$ 编码矩阵乘法

线性代数中最常见但同时也是代价高昂的运算之一是将两个矩阵 $A$ 和 $B$ 相乘。随着机器学习的快速发展和数据量的增加，执行快速矩阵密集乘法已成为主要障碍。解决这个问题的两种不同方法是：1) 近似乘积；和 2) 分布式地执行乘法。\textit{$CR$-multiplication} 是一个近似值，其中 $A$ 和 $B$ 的列和行分别被替换采样。在分布式设置中，多个 worker 并行执行矩阵乘法子任务。一些工人可能是落后者，这意味着他们没有及时完成任务。我们提出了一种新颖的 \textit{近似加权 $CR$ 编码矩阵乘法} 方案，