Deterministic and probabilistic neural nets with loops

The paper presents the fundamentals of the theory of neural nets with loops based on functional matrices, which are a generalization of the state transition matrices for a net. Problems of analysis and synthesis; given a net, find its functional matrix and vice versa, are treated for probabilistic and deterministic nets. Questions about universal nets, oscillations, and stability are studied for deterministic nets. Reduction of probabilistic nets with loops is considered. It is shown that any probabilistic net with loops can be duplicated by a deterministic net with loops plus a probabilistic loop-free encoder. The motivation for the work is a search for formulation of the general theory of neural nets that could be tied to the theory of triadic intensional relations, as suggested by Warren S. McCulloch.