This paper examines a number of stochastic computational elements employed in artificial neural networks, several of which are introduced for the first time, together with an analysis of their operation. We briefly include multiplication, squaring, addition, subtraction, and division circuits in both unipolar and bipolar formats, the principles of which are well-known, at least for unipolar signals. We have introduced several modifications to improve the speed of the division operation. The primary contribution of this paper, however, is in introducing several state machine-based computational elements for performing sigmoid nonlinearity mappings, linear gain, and exponentiation functions. We also describe an efficient method for the generation of, and conversion between, stochastic and deterministic binary signals. The validity of the present approach is demonstrated in a companion paper through a sample application, the recognition of noisy optical characters using soft competitive learning. Network generalization capabilities of the stochastic network maintain a squared error within 10 percent of that of a floating-point implementation for a wide range of noise levels. While the accuracy of stochastic computation may not compare favorably with more conventional binary radix-based computation, the low circuit area, power, and speed characteristics may, in certain situations, make them attractive for VLSI implementation of artificial neural networks.

For pt. I see ibid., p.891-905. An investigation has been made into the use of stochastic arithmetic to implement an artificial neural network solution to a typical pattern recognition application. Optical character recognition is performed on very noisy characters in the E-13B MICR font. The artificial neural network is composed of two layers, the first layer being a set of soft competitive learning subnetworks and the second a set of fully connected linear output neurons. The observed number of clock cycles in the stochastic case represents an order of magnitude improvement over the floating-point implementation assuming clock frequency parity. Network generalization capabilities were also compared based on the network squared error as a function of the amount of noise added to the input patterns. The stochastic network maintains a squared error within 10 percent of that of the floating-point implementation for a wide range of noise levels.