Title of article :
Gauged neural network: Phase structure, learning, and associative memory
Author/Authors :
Motohiro Kemuriyama، نويسنده , , Tetsuo Matsui، نويسنده , , Kazuhiko Sakakibara، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2005
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 . 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 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.
Journal title :
Physica A Statistical Mechanics and its Applications
Journal title :
Physica A Statistical Mechanics and its Applications