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Gauged Neural Network: Phase Structure, Learning, and Associative Memory | | Motohiro Kemuriyama
; Tetsuo Matsui
; Kazuhiko Sakakibara
; | | Date: |
6 Mar 2002 | | Journal: | Physica A356 (2005) 525-553 | | Subject: | Disordered Systems and Neural Networks | cond-mat.dis-nn hep-lat q-bio | | 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 S_x =pm 1 on each site x of a 3D lattice and a synaptic-connection variable J_{xmu}=pm 1 on each link connecting x and x+mu(mu=1,2,3). It may be viewed as a generalization of the Hopfield model of associative memory to a model of learning by converting J_{xmu} to another dynamical variable. J_{xmu} plays the role of path-dependent phase factor(gauge variable) in gauge theory. The local Z(2) gauge symmetry is inherited from the Hopfield model in which two configurations (J_{ij},S_j) and (-J_{ij},-S_j) for a pair (i,j) have the same energy. The latter configuration is obtained from the former by applying a Z(2) local gauge transformation at j. The gauge symmetry assures us the locality of time evolutions of S_x and J_{xmu} and a generalized Hebbian learning rule. At finite "temperatures", the model exhibits three phases; Higgs, confinement, and Coulomb phases. In Higgs phase, both abilities of learning patterns and recalling them are high. This nature has a close resemblance to the quantum memory of a toric code studied by Kitaev et al., in which the memory works accurately in Higgs phase of a corrsponding 3D Z(2) pure lattice gauge theory. In Coulomb phase, learning is possible, but recalling is disabled. The confinement phase was not considered in the Hopfield model, where both abilities are disabled. At some parameter regions, stable column-layer structures of SJS are spontaneously generated. We simulate dynamical processes of learning a pattern of S_x and recalling it, and classify each region of parameter space according to the performance in learning and recalling. Mutual interactions between S_x and J_{xmu} induce memory loss as expected. | | Source: | arXiv, cond-mat/0203136 | | Services: | Forum | Review | PDF | Favorites | |
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