Hard-limiting nonlinear functions in artificial neural networks

The authors show how the optimum hard-limiter can be found. They also show what the optimum operating point of this type of nonlinear function should be, by illustrating the performance of this optimum hard-limiter when it is used with a simple neural network in content-addressable memories. It is demonstrated that there is a narrow band of values for the normal operation of the hard-limiting function, beyond which the network would not be able to accurately recall any of the stored patterns. Mathematical analysis of the theoretical bounds of this parameter showed that this band will narrow if one expects the network to work with noisier data. The network is expected to suffer no deterioration in the quality of recall with small deviations in the threshold when the noise ratio in the test patterns is low. However, the margin of safe operation will narrow when the noise ratio of the test patterns is high. Other types of nonlinear functions with offsets have been shown to improve the performance of this type of neural network in accurately recovering the original patterns