Comparing Stochastic and Deterministic Computing

Technology scaling has raised the specter of myriads of cheap, but unreliable and/or stochastic devices that must be creatively combined to create a reliable computing system. This has renewed the interest in computing that exploits stochasticity-embracing, not combating the device physics. If a stochastic representation is used to implement a programmable general-purpose architecture akin to CPUs, GPUs, or FPGAs, the preponderance of evidence indicates that most of the system energy will be expended in communication and storage as opposed to computation. This paper presents an analytical treatment of the benefits and drawbacks of adopting a stochastic approach by examining the cost of representing a value. We show both scaling laws and costs for low precision representations. We also analyze the cost of multiplication implemented using stochastic versus deterministic approaches, since multiplication is the prototypical inexpensive stochastic operation. We show that the deterministic approach compares favorably to the stochastic approach when holding precision and reliability constant.