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Gauged neural network: Phase structure, learning, and associative memory

Author

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  • Kemuriyama, Motohiro
  • Matsui, Tetsuo
  • Sakakibara, Kazuhiko

Abstract

A gauge model of neural network is introduced, which resembles the Z(2) Higgs lattice gauge theory of high-energy physics. It contains a neuron variable Sx=±1 on each site x of a 3D lattice and a synaptic-connection variable Jxμ=±1 on each link (x,x+μ^)(μ=1,2,3). The model is regarded as a generalization of the Hopfield model of associative memory to a model of learning by converting the synaptic weight between x and x+μ^ to a dynamical Z(2) gauge variable Jxμ. The local Z(2) gauge symmetry is inherited from the Hopfield model and assures us the locality of time evolutions of Sx and Jxμ and a generalized Hebbian learning rule. At finite “temperatures”, numerical simulations show that the model exhibits the Higgs, confinement, and Coulomb phases. We simulate dynamical processes of learning a pattern of Sx and recalling it, and classify the parameter space according to the performance. At some parameter regions, stable column-layer structures in signal propagations are spontaneously generated. Mutual interactions between Sx and Jxμ induce partial memory loss as expected.

Suggested Citation

  • Kemuriyama, Motohiro & Matsui, Tetsuo & Sakakibara, Kazuhiko, 2005. "Gauged neural network: Phase structure, learning, and associative memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 356(2), pages 525-553.
    • Handle: RePEc:eee:phsmap:v:356:y:2005:i:2:p:525-553
    DOI: 10.1016/j.physa.2005.05.083
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