Asymmetric Boltzmann machines.

B Apolloni; A Bertoni; P Campadelli; D de Falco

doi:10.1007/bf00196453

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Asymmetric Boltzmann machines.

B Apolloni·A Bertoni·P Campadelli·D de Falco

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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.

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B Apolloni, A Bertoni, P Campadelli, D de Falco. 1991. Asymmetric Boltzmann machines.. https://doi.org/10.1007/bf00196453

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