Matrix Multiplication Using Only Addition

Daniel Cussen, Jeffrey D. Ullman
Fgemm SPA
arXiv:2307.01415 [cs.DS], (4 Jul 2023)


   title={Matrix Multiplication Using Only Addition},

   author={Daniel Cussen and Jeffrey D. Ullman},






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Matrix multiplication consumes a large fraction of the time taken in many machine-learning algorithms. Thus, accelerator chips that perform matrix multiplication faster than conventional processors or even GPU’s are of increasing interest. In this paper, we demonstrate a method of performing matrix multiplication without a scalar multiplier circuit. In many cases of practical interest, only a single addition and a single on-chip copy operation are needed to replace a multiplication. It thus becomes possible to design a matrix-multiplier chip that, because it does not need time, space- and energy-consuming multiplier circuits, can hold many more processors, and thus provide a net speedup.
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