Hopfield networks as discrete dynamical systems

A geometrical approach based on dynamical systems theory is presented for the analysis of Hopfield networks. Basic definitions from dynamical systems theory are presented and illustrated with a simple example. The eigenspaces of the weight matrix, the geometry of the energy manifold, and the diffeomorphisms induced by the sphere are presented as tools for the study of network dynamics. Some simple results are given. A number of topics for further research are proposed.<
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