Some problems of mathematical theory of neural nets

The formal mathematical theory of neural nets is considered. A novel approach to neural net research is proposed, based on the representation of a trained neural net as a set of five mathematical objects: two Boolean rings and three functions, determined on these rings. This approach made it possible to obtain some new results on the capacity of the Hopfield-Hebb net. Using this approach, some results on the capacity of specific uniform neural nets have been proved