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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 xed 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.