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On learning and energy-entropy dependence in recurrent and nonrecurrent signed networks

Abstract

Learning of patterns by neural networks obeying general rules of sensory transduction and of converting membrane potentials to spiking frequencies is considered. Any finite number of cellsA can sample a pattern playing on any finite number of cells ∇ without causing irrevocable sampling bias ifA = ℬ orA ∩ ℬ =

. Total energy transfer from inputs ofA to outputs of ℬ depends on the entropy of the input distribution. Pattern completion on recall trials can occur without destroying perfect memory even ifA = ℬ by choosing the signal thresholds sufficiently large. The mathematical results are global limit and oscillation theorems for a class of nonlinear functional-differential systems.

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The preparation of this work was supported in part by the National Science Foundation (GP 9003), the Office of Naval Research (N00014-67-A-024-OQ16), and the A.P. Sloan Foundation.

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Grossberg, S. On learning and energy-entropy dependence in recurrent and nonrecurrent signed networks. J Stat Phys 1, 319–350 (1969). https://doi.org/10.1007/BF01007484

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  • DOI: https://doi.org/10.1007/BF01007484

Key words

  • learning
  • stimulus sampling
  • nonlinear difference-differential equations
  • global limits and oscillations
  • flows on signed networks
  • functional-differential systems
  • energy-entropy dependence
  • pattern completion
  • recurrent and nonrecurrent anatomy
  • sensory transduction rules
  • ratio limit theorems