Stochastic computing has a long history as an alternative method of performing arithmetic on a computer. While it can be considered an unbiased estimator of real numbers, it has a variance and MSE on the order of $\Omega(\frac{1}{N})$. On the other hand, deterministic variants of stochastic computing remove the stochastic aspect, but cannot approximate arbitrary real numbers with arbitrary precision and are biased estimators. However, they have an asymptotically superior MSE on the order of $O(\frac{1}{N^2})$. Recent results in deep learning with stochastic rounding suggest that the bias in the rounding can degrade performance. We proposed an alternative framework, called dither computing, that combines aspects of stochastic computing and its deterministic variants and that can perform computing with similar efficiency, is unbiased, and with a variance and MSE also on the optimal order of $\Theta(\frac{1}{N^2})$. We also show that it can be beneficial in stochastic rounding applications as well. We provide implementation details and give experimental results to comparatively show the benefits of the proposed scheme.

中文翻译：

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抖动计算：确定性-随机混合计算框架

随机计算作为在计算机上执行算术的一种替代方法，具有悠久的历史。尽管可以认为它是实数的无偏估计量，但它的方差和MSE约为$ \ Omega（\ frac {1} {N}）$。另一方面，随机计算的确定性变量消除了随机方面，但不能以任意精度近似任意实数，并且是有偏估计量。但是，它们的渐近优MSE约为$ O（\ frac {1} {N ^ 2}）$。随机舍入的深度学习的最新结果表明，舍入中的偏差会降低性能。我们提出了另一种框架，称为抖动计算，该框架结合了随机计算及其确定性变量的各个方面，并且可以以相似的效率执行计算，并且没有偏见，并且具有方差和MSE的最优顺序也为$ \ Theta（\ frac {1} {N ^ 2}）$。我们还表明，它在随机取整应用中也可能是有益的。我们提供了实施细节，并给出了实验结果，以比较地表明该方案的好处。