Mathematical formulation of cognitive and learning processes in neural networks

Recent results in modeling the processes of recognition of complex patterns and learning performed by an artificial neural network as a nonlinear mapping from a data vector space into a space of binary strings are presented. By the construction of a suitable nonlinear functional space for this mapping. an optimal solution in terms of a closed-form description of the neural net model can be obtained. A learning algorithm for this model, which is aimed at reducing the redundancy and complexity of the net by the extraction of a minimal set of prototypes from the training set, is described