TY - JOUR

T1 - Simplicial Computation: A Methodology to Compute Vector-vector Multiplications with Reduced Complexity

AU - Julian, Pedro

AU - Villemur, Martin

AU - Rodriguez, Nicolas Daniel

AU - Andreou, Andreas G.

PY - 2021

Y1 - 2021

N2 - In this paper we propose the use of the simplicial algorithm, originally proposed to implement piecewise-linear functions, to compute a digital vector-vector multiplication (VVM) without multiplication operations. We show that when quantization of inputs and parameters are considered, the simplicial method achieves the same accuracy with fewer representation bits for the parameters, assuming the same quantization for the inputs. Actually, in the particular case of a large number of inputs, the simplicial method needs half the number of parameter bits of a linear combination plus one. In addition, we show that the simplicial method requires less energy to compute under an equal number of parameter and input representation bits.

AB - In this paper we propose the use of the simplicial algorithm, originally proposed to implement piecewise-linear functions, to compute a digital vector-vector multiplication (VVM) without multiplication operations. We show that when quantization of inputs and parameters are considered, the simplicial method achieves the same accuracy with fewer representation bits for the parameters, assuming the same quantization for the inputs. Actually, in the particular case of a large number of inputs, the simplicial method needs half the number of parameter bits of a linear combination plus one. In addition, we show that the simplicial method requires less energy to compute under an equal number of parameter and input representation bits.

U2 - https://doi.org/10.1002/cta.3128

DO - https://doi.org/10.1002/cta.3128

M3 - Article

SP - 1

EP - 23

ER -