On The Analysis of The Hopfield Network: A Geometric Approach

Artificial neural networks have been studied for many years in the hope of achieving human-like performance in the fields of speech and image recognition. A great landmark in this field is the Hopfield Network. It is simple to implement, simple to analyze. However, it suffers from the existence of the so-called spurious states which tend to inundate the space and reduce the value of this network. In this thesis we provide a complete analysis of the spurious states. This analysis involves the number of such states, their distribution in the space of states, an experimental study of their basins of attractions, and finally, most importantly, their equations. We also describe an algorithm that takes a Hopfield network and replaces it by an equivalent one but with less internal connections. The importance of this algorithm is obvious when it comes to the issues of implementation using VLSI. Finally, we comment on this network and discuss its usefulness as a Content