Fascinating rhythms by chaotic Hopfield networks

This papers aims at experimentally confirming in very small Hopfield networks that chaos becomes the spontaneous dynamics of a network, when the number of inputs to be learned and stored in its dynamical attractors is superior to the size of this network. The spontaneous dynamics of the network are shown to increase in complexity by increasing the size of the learning set. The type of chaos exploited to code these inputs is related with the frustrated chaos described in previous papers. When, following a brute-force but robust learning of the inputs, the network is presented with a series of unlearned ambiguous input, experimental results show how chaotic regimes become the natural response of the network, reflecting in its frustrated dynamics the inherent ambiguity of the input. A live demonstration can be shown where the rhythms associated with the dynamics can be heard. This experimental work might give additional support to the Skarda and Freeman strong intuition that chaos should play an important role in the storage and the search capacities of our brains.