Model neural networks
Thomas B. Kepler · 1989
After a brief introduction to the techniques and philosophy of neural network modeling by spin glass inspired system, we investigate several properties of these discrete models for autoassociative memory. Memories are represented as patterns of neural activity; their traces are stored in a distributed manner in the matrix of synaptic coupling strengths. Recall is dynamic, an initial state containing partial information about one of the memories evolves toward that memory. Activity in each neuron creates fields at every other neuron, the sum total of which determines its activity. By averaging over the space of interaction matrices with memory constraints enforced by the choice of measure, we show that there exist universality classes defined by families of field distributions and the associated network capacities. We demonstrate the dominant role played by the field distribution in determining the size of the domains of attraction and present, in two independent ways, an expression for this size. We present a class of convergent learning algorithms which improve upon known algorithms for producing such interaction matrices. We demonstrate that spurious states, or unexperienced memories, may be practically suppressed by the inducement of n-cycles and chaos. We investigate aspects of chaos in these systems, and then leave discrete modeling to implement the analysis of chaotic behavior on a continuous valued network realized in electronic hardware. In each section we combine analytical calculation and computer simulations.