I. Introduction
Signals IN digital neural networks may be represented by the Bernoulli probabilities of binary random variables. These signals may be estimated by the frequency of 1s or pulses, i.e., by their pulse count distributions, taken over a sampling interval of multiple clock cycles. Signal values may be multiplied using simple logic gates and may be added or weight-averaged using (stochastic) multiplexers. Unlike the binary radix representations of conventional digital signals, the stochastic signals have unary representations, and their estimates are, therefore, relatively insensitive to imperfect pulse detection and noise. These are among the advantages of (nonlinear) stochastic signal processing (SSP), which is a method of reducing the power dissipation and the silicon area of digital circuit implementations of neural networks, while improving their error and fault tolerance and enabling variable-precision computations in fixed hardware.