Abstract
We investigate fusing several unreliable computational units that perform the same task. We model an unreliable computational outcome as an additive perturbation to its error-free result in terms of its fidelity and cost. We analyze reliability of replication-based strategies that distribute cost across several unreliable units and fuse their outcomes. When the cost is a convex function of fidelity, the optimal replication-based strategy in terms of incurred cost while achieving a target mean-square error level may fuse several unreliable computational units. For concave and linear costs, a single more reliable unit incurs lower cost compared to fusion of several lower cost and less reliable units while achieving the same mean-square error level. We show how our results give insight into problems from theoretical neuroscience and circuits.
Highlights
We consider the problem of fusing outcomes of several unreliable computational units in order to form a reliable outcome from the individual contributions
We prove that using only a single and more reliable computational unit is more cost-efficient than the fusion of several lower cost but less reliable computational units when a desired level of mean-square error (MSE) is larger than a certain threshold, i.e., larger MSE can be tolerated
OVERVIEW In Section II, we propose a model for an unreliable computational unit that produces a noisy version of the error-free computation, and introduce replication-based strategies that distribute cost across several unreliable computational units and combine their outcomes to produce a final estimate of the error-free computation
Summary
We consider the problem of fusing outcomes of several unreliable computational units in order to form a reliable outcome from the individual contributions. A. OVERVIEW In Section II, we propose a model for an unreliable computational unit that produces a noisy version of the error-free computation, and introduce replication-based strategies that distribute cost across several unreliable computational units and combine their outcomes to produce a final estimate of the error-free computation. We model reliability of any computational unit through a fidelity parameter that controls the deviation from the error-free computation in mean-square error sense, and focus on investigating the optimal strategy for generic cost functions. We later use the results of this section to analyze and compare the cost-reliability tradeoff achieved by replication-based strategies in terms of minimizing the total incurred cost while achieving the same MSE level. We use τ to denote the MSE level achieved by a replicationbased strategy
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