Hebbian Learning In Chaotic Neural Networks

We propose Hebb-like learning rules to store a static pattern as a dynamical attractor in a neural network with chaotic dynamics. We show that these kind of rules reduces the attractor dimension while learning, until a fixed point is reached. We choose to stop learning when the system is on a strange attractor or limit cycle. We associate this attractor with the pattern learned: the presentation of the pattern on the chaotic network leads to the reduction of the dynamics on the attractor after learning. This reproduces with a very simple network the results observed by Freeman in the olfactory bulb of the rabbit. Introduction We are concerned with the coding of patterns by dynamical attractors (limit cycles, strange attractors). Instead of building the dynamics of the network knowing the patterns to be stored 1 , we begin with a network having a chaotic dynamics, and we modify the connection weights in order for the network to converge to some complex attractor when a pattern is i..