Behavior of two, three and four site states self-interacting neural networks

Abstract

The role of interaction terms in the models of neural networks is critically analyzed. It is demonstrated that the addition of self-interaction in the Hopfield model improves the performance of the network. The network evolves more quickly to an attractor state and is able to identify the correct image from more corrupt versions. The restriction of a critical storage capacity also disappears. The quality of retrieval does deteriorate with the increase in the number of stored pictures. The deterioration is gradual. One can define a working storage capacity. The working storage capacity is found to be significantly higher than the critical storage capacity of a corresponding network without self-interaction terms. The model is extended to generalized neurons capable of existing in multiple site states. The basis vectors giving the site states of neurons influence the working of the network through scalar products. Optimum performance is attained when scalar products satisfy a linear constraint relation. The constraint relation permits the use of Potts and Ising spin states for basis vectors. Non-Potts spin states are allowed in networks of generalized neurons with 4 or more site states. The retrieval characteristics of networks of generalized neurons having 2, 3, and 4 site states are investigated through computer simulations. The working storage capacity, the average error in retrieval, permissible initial corruption and their dependence on the size of the network are determined.