Bayesian Accuracy Analysis of Stochastic Circuits

Understanding accuracy and the tradeoffs it entails is key to evaluating the growing list of stochastic computing (SC) circuit designs. Due to shortcomings of current SC error theory, simulation has become the standard way to estimate a circuit's accuracy. However, simulation can demand large computational resources and lead to uncertain, misleading, or unexplainable results. A soundly based analytic approach is therefore preferable to simulation. In this work, we first show the input value distribution's large influence on circuit accuracy. Then we develop a Bayesian error analysis methodology which uses the input value distribution as a prior to inform better accuracy estimates. This error formulation introduces concepts new to SC such as estimator dominance and points to ways of improving simulation-based accuracy estimates. Orthogonal to the Bayesian ideas, we also show how to use bias-variance decomposition to simplify and aggregate the effects of SC's many error sources. We present techniques that use the beta distribution to model the stochastic number value distribution. Finally, we demonstrate the use of these ideas to improve the accuracy and analysis of an SC-based neural network.