Controlling Chaos using adaptive weights in an Oscillatory Neural Network

The complex Hopfield neural network (CHNN)[1,2], which is an extension of the Hopfield Neural Network from real number domain to complex number domain, exhibits both fixed point and oscillatory behavior. It may be used as an associative memory in which patterns are stored as stable oscillations. Perfect retrieval is observed when only a single pattern is stored. However, when multiple patterns are stored, the network often wanders from one stored pattern to another without settling on any single pattern. This chaotic behavior, characteristic of a large network of nonlinear oscillators, results in unacceptably low storage capacity. We found that using weights that adapt even during retrieval can alleviate this problem. Simulations show that using adaptive weights dramatically enhances network capacity. This goes against the fundamental tenet of connectionism according to which weights are supposed to encode the information contained in the network, and must be held constant once training/storage is completed. The work gives rise to a novel view of the weights as transient, intermediate variables – the information which is traditionally supposed to be held in the weights is now imagined to be held in a longer-term memory store. Implications of the current work to neurophysiology are briefly considered. KeywordsNeural network, Lyapunov exponent, Chaos.