Asymmetric Synaptic Connections in Z(2) Gauge Neural Network

摘要

We consider Z(2) gauge neural network which involves neuron variables S_i(＝ ±1) and synaptic connection (gauge) variables J_(ij)(＝ ±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.