On the cognitive function of deterministic chaos in neural networks

In neurophysiology experimental evidence has recently been produced suggesting that the different features of the external stimuli, processed in parallel along different pathways on the spatial dimension, are integrated dynamically on the temporal dimension. For this task, the deterministic chaos, experimentally found in the oscillatory behavior of nerve cell arrays of the sensory cortex, plays an essential role that is not yet clear from the theoretical standpoint. The authors propose a first approach to this problem. By the study of H. Sompolinsky's theoretical model of a neural net, which implements chaotic behavior in a dynamical Hopfield net, the authors show some properties of a chaotic net with respect to more classical models, such as the Rosenblatt perceptron, Hopfield net, and Boltzmann machine. At the same time, they advance theoretical research that links all these approaches. They suggest a first step toward the construction of a learning procedure founded on chaotic dynamics.<>