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Erschienen in:
2016 | OriginalPaper | Buchkapitel
Asymmetric Synaptic Connections in Z(2) Gauge Neural Network
verfasst von : Atsutomo Murai, Tetsuo Matsui
Erschienen in: Neural Information Processing
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Abstract
We consider Z(2) gauge neural network which involves neuron variables \(S_i (=\pm 1)\) and synaptic connection (gauge) variables \(J_{ij} (=\pm 1)\). Its energy consists of the Hopfield term \(-c_1S_iJ_{ij}S_j\) and the reverberation term \(-c_2J_{ij}J_{jk}J_{ki}\) for signal propagation on a closed loop. The model of symmetric couplings \(J_{ij}=J_{ji}\) has been studied; its phase diagram in the \(c_2-c_1\) plane exhibits Higgs, Coulomb and confinement phases, each of which is characterized by the ability of learning and/or recalling patterns. In this paper, we consider the model of asymmetric coupling (\(J_{ij}\) and \(J_{ji}\) are independent), and examine the effect of asymmetry on a partially connected random network.