Learning cycles brings chaos in Hopfield networks

This paper aims at studying the impact of an Hebbian learning algorithm on the recurrent neural network\´s underlying dynamics. Two different kinds of learning are compared in order to encode information in the attractors of the Hopfield neural net: the storing of static patterns and the storing of cyclic patterns. We show that if the storing of static patterns leads to a reduction of the potential dynamics following the learning phase, the learning of cyclic patterns tends to increase the dimension of the potential attractors instead. In fact, such learning may be used as an extra "route to chaos": the more cycles to be learned, the more the network shows as spontaneous dynamics a form of chaotic itinerancy among brief oscillatory periods. These results are in line with the observations made by Freeman in the olfactory bulb of the rabbit: cycles are used to store information and the chaotic dynamics appears as the background regime composed of those cyclic "memory bags". It confirms precedent papers in which it was observed that huge encoding capacity in term of cyclic attractors implies strong presence of chaos.