Topological analysis of infinite learning automata. II. Training dynamics

Summary form only given. Infinite learning automata were used to model the dynamical behavior of neural networks, where the network state space is infinite and in particular a continuum. The dynamics are described by a semigroup S´ of continuous transformations of the state space S. Three aspects of the training dynamics were considered: (1) boundedness of the training time; (2) trainability and robustness; and (3) the analysis of orbits in the state space to detect the presence of sufficient conditions for (1) and (2). These points were studied by giving the function space S´ a topology that inherits many of the topological properties of S. Compactness is related to training time boundedness. Joint continuity of the transition function is related to trainability. When joint continuity exists, S´ is a topological semigroup and orbits in S are related to the monothetic subsemigroups of S´. When S is a compact metric space, tile action of these subsemigroups on the set of orbit cluster points is isomorphic to that of a compact monothetic group