Cost-reliability tradeoffs in fusing unreliable computational units

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.