A study on neural networks

Abstract

The Hopfield neural network is a mathematical model in which each neuron performs a threshold logic function. an important property of the model is that a neural network always converges to a stable state when operating in a serial mode. This property is the basis of potential applications of neural networks such as associative memory devices, computational models, etc. This article reviews some of the known properties of the model and presents some new results regarding its possible applications. the principal contributions which are developed in this article are: Showing that a very large class of mappings are not feasible by neural nets, in particular mappings which contain spheres, e.g., Hamming codes. Showing that the neural network model can be designed to perform a local search algorithm for the Directed Min Cut problem. Exploring the term “capacity of the neural network model” and criticizing some results known in the literature. Showing the limitations of the model for its use as a pattern recognizer by proving that all images with a single black point can be recognized by the network iff the network is fully connected. Copyright © 1988 Wiley Periodicals, Inc., A Wiley Company