Hopfield networks and symmetry groups

Autor: David William Pearson
Rok vydání: 1995
Předmět:
Zdroj: Neurocomputing. 8:305-314
ISSN: 0925-2312
DOI: 10.1016/0925-2312(94)00075-4
Popis: Recurrent neural network state-space trajectories can be considered as local one-parameter transformation groups. If such a group transforms the solution of a certain equation to another solution of the same equation then the group is referred to as a symmetry group of the equation. In this article we illustrate how a synaptic weight matrix of a recurrent neural network of Hopfield type can be calculated so that the resulting trajectory becomes a local one-parameter transformation group for a given equation. One particular application of this technique is where the equation to be solved comes from forcing a nonlinear output function of a dynamical system to be zero by applying a suitable control signal.
Databáze: OpenAIRE
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