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Delta-Sigma Domain Signal Processing Applied to Artificial Neurons
Takao Waho, Akihisa Koyama and Hitoshi Hayashi
First- and second-order delta-sigma (ΔΣ) modulated bitstreams are applied to implement the multiply-and-accumulate (MAC) operation and the rectified linear unit (ReLU) activation function. Our simulation shows that the numerical accuracy is improved by using ΔΣ-modulated bitstreams compared to the bitstreams used in stochastic computing (SC). This improvement is due to the noise shaping properties inherent in ΔΣ modulation. Specifically, we found that for both MAC and ReLU, the root mean square error (RMSE) can be reduced in proportion to the inverse of 𝑁3/2 and 𝑁5/2 by employing first- and second-order ΔΣ modulation as the bitstream length 𝑁 increases. This demonstrates the superiority of the ΔΣ modulation over the conventional SC in terms of achieving higher numerical accuracy with shorter bitstream lengths.
Keywords: delta-sigma modulation, stochastic computing, artificial neuron, noise-shaping, multiply-and-accumulate, activation function, signal processing