title: Asymmetric Boltzmann machines.
abstract: We study asymmetric stochastic networks from two points of view: combinatorial optimization and learning algorithms based on relative entropy minimization. We show that there are non trivial classes of asymmetric networks which admit a Lyapunov function L under deterministic parallel evolution and prove that the stochastic augmentation of such networks amounts to a stochastic search for global minima of L. The problem of minimizing L for a totally antisymmetric parallel network is shown to be associated to an NP-complete decision problem. The study of entropic learning for general asymmetric networks, performed in the non equilibrium, time dependent formalism, leads to a Hebbian rule based on time averages over the past history of the system. The general algorithm for asymmetric networks is tested on a feed-forward architecture.
authors.affiliation: Dipartimento di Scienze dell' Informazione, Università di Milano, Italy.
authors.forename: B
authors.initials: B
authors.lastname: Apolloni
authors.forename: A
authors.initials: A
authors.lastname: Bertoni
authors.forename: P
authors.initials: P
authors.lastname: Campadelli
authors.forename: D
authors.initials: D
authors.lastname: de Falco
mesh_terms: D000465:Algorithms; D000818:Animals; D007858:Learning; D008433:Mathematics; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D012984:Software; D013269:Stochastic Processes; D013569:Synapses / Q000502:physiology*