基于平均场理论逼近的神经网络

Neural Network Based on Mean-Field Theory Approximation

本文试图从信息论观点导出平均场理论逼近的神经网络及其退火算法，证明ＡＭＦＴＡ（ＡｌｇｏｒｉｔｈｍｓｏｆＭｅａｎ－ｆｉｅｌｄｔｈｅｏｒｙａｐｐｒｏｘｉｍａｔｉｏｎ）和ＡＢＭ（ＡｌｇｏｒｉｔｈｍｏｆＢｏｌｔｚｍａｎｎｍａｃｈｉｎｅ）在一定条件下的等价性，既保留传统Ｂｏｌｔｚｍａｎｎ机算法的优点又提高了网络趋于稳态的收敛速度。

This paper intends to derive the neural network based on mean-field theory approximation and its annealing algorithm from the information-theoretic view point,to prove equivalence between AMFTA and ABM under certain condition.both keeping advantage of ABM and speeding up rate of convergence for the neural network to approach to equilibrium state.