We propose the extension of the classical framework of Cellular Nonlinear Networks (CNN) to in- corporate adaptivity of the cells. Adaptivity means that coupling template coeffi cients can evolve over time accord- ing to some specified rule. Here, the rule is described in terms of a differential equation for each template coeffi - cient. It is proposed that this dynamics can be obtained from the gradient flow of an objective function imposed on the network. The extension is exemplified for a signal pro- cessing application, namely the principal subspace analysis (PSA). The application illustrates a top-down approach to self-organization from a global objective to local process - ing and adaptation rules.
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