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Asymmetric Boltzmann machines.

B Apolloni1, A Bertoni, P Campadelli

  • 1Dipartimento di Scienze dell' Informazione, Università di Milano, Italy.

Biological Cybernetics
|January 1, 1991
PubMed
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This study explores asymmetric stochastic networks, revealing that their stochastic augmentation acts as a search for global minima. Minimizing these networks is linked to NP-complete problems, impacting optimization and learning algorithms.

Area of Science:

  • Theoretical Computer Science
  • Machine Learning
  • Statistical Physics

Background:

  • Asymmetric stochastic networks present challenges in optimization and learning.
  • Understanding their behavior requires integrating combinatorial optimization and learning algorithms.

Purpose of the Study:

  • To investigate asymmetric stochastic networks using combinatorial optimization and relative entropy minimization.
  • To analyze the properties of Lyapunov functions in deterministic and stochastic network evolution.
  • To develop and test learning algorithms for these networks.

Main Methods:

  • Analysis of Lyapunov functions under deterministic parallel evolution.
  • Stochastic augmentation of networks to search for global minima.
  • Investigation of entropic learning in non-equilibrium, time-dependent formalisms.

Related Experiment Videos

  • Development of a Hebbian learning rule based on time averages.
  • Testing the general algorithm on a feed-forward architecture.

    • Main Results:

    • Non-trivial classes of asymmetric networks admit a Lyapunov function L.
    • Stochastic augmentation of these networks performs a stochastic search for global minima of L.
    • Minimizing L for totally antisymmetric parallel networks is NP-complete.
    • A Hebbian rule based on time averages emerges from the entropic learning study.
    • The general algorithm shows efficacy on a feed-forward network.

    Conclusions:

    • Asymmetric stochastic networks can be analyzed through the lens of optimization and learning.
    • The complexity of minimizing Lyapunov functions highlights computational challenges.
    • Entropic learning provides a viable approach for developing adaptive algorithms for these networks.