On Reliable Computation With Formal Neurons.

Santosh S. Venkatesh, Demetri Psaltis

Abstract: The authors investigate the computing capabilities of formal McCulloch-Pitts neurons when errors are permitted in decisions. They assume that m decisions are to be made on a randomly specified m set of points in n space and that an error tolerance of epsilon m decision errors is allowed, with 0<or= epsilon <1/2. The authors are interested in how large an m can be selected such that the neuron makes reliable decisions within the prescribed error tolerance. Formal results for two protocols for error-tolerance-a random error protocol and an exhaustive error protocol-are obtained. The results demonstrate that a formal neuron has a computational capacity that is linear in n and that this rate of capacity growth persists even when errors are tolerated in the decisions.