Stochastic Number Research Articles

Approximating stochastic numbers to reduce latency

Abstract Approximate Computing (AC) and Stochastic Computing (SC) have been studied as new computing paradigms to achieve energy-efficient designs for error-tolerant applications. The hardware cost of SC generally can be small compared to that of AC, but SC has not been applied to a wide range of applications as AC because SC needs very long cycles to use long random bit strings called Stochastic Numbers (SNs) when we need to maintain the desired precision. To mitigate this disadvantage of SC, we propose a new idea to approximate numbers represented by SNs; our idea is to use multiple SNs to represent one number. Indeed our method can shorten the length of SNs drastically while keeping the precision level compared to conventional SNs. We study two specific cases where we use two and three shorter bit-strings to represent a single conventional SN, which we call a dual-rail and a triple-rail SNs, respectively. We also discuss a general case when we use many SNs corresponding to a single conventional SNs. We also compare triple-rail, dual-rail and conventional SNs in terms of hardware overhead and calculation errors in this paper. From the comparison, we can conclude that our idea can be used to shorten the necessary cycles for SC.

Accurate and compact stochastic computations by exploiting correlation

Recent studies have shown, contrary to what was previously believed, that by exploiting correlation in stochastic computing (SC) designs, more accurate SC circuits with low area cost can be realized. However, if these basic SC circuits or blocks are cascaded in series to form a large complex system, correlation between stochastic numbers (SNs) from one block to the next would be lost; thus, inaccuracies are introduced. In this study, we propose correlating circuits to be used in building complex correlated SC systems. One of the circuits is the correlator that restores lost correlations between two SNs due to previous processing. In addition, a correlated SN generator is introduced to generate SN correlated to a specific SN. Experimental results show that our methods have improved the accuracy of stochastic computation and preserved the stochastic computing correlation without the need for conversion from SC to the conventional binary-encoded computing, and vice versa. Consequently, lower latency and lower area cost are achieved.

The Promise and Challenge of Stochastic Computing

Stochastic computing (SC) is an unconventional method of computation that treats data as probabilities. Typically, each bit of an ${N}$ -bit stochastic number (SN) ${X}$ is randomly chosen to be 1 with some probability $p_{X}$ , and ${X}$ is generated and processed by conventional logic circuits. For instance, a single AND gate performs multiplication. The value X of an SN is measured by the density of 1 s in it, an information-coding scheme also found in biological neural systems. SC has uses in massively parallel systems and is very tolerant of soft errors. Its drawbacks include low accuracy, slow processing, and complex design needs. Its ability to efficiently perform tasks like communication decoding and neural network inference has rekindled interest in the field. Many challenges remain to be overcome, however, before SC becomes widespread. In this paper, we discuss the evolution of SC, mostly focusing on recent developments. We highlight the main challenges and discuss potential methods of overcoming them.