Hopfield-Tank模型的收敛性证明

PROOF OF THE CONVERGENCE IN HOPFIELD-TANK MODEL

本文研究了Hopfield－Tank能量函数在Hopfield网络中的收敛性以及优化率方面的问题．虽然离散的Hopfield网络模型与连续的Hopfield网络模型都有严格的收敛性证明，但是HopfieldTank模型一直没有人给出严格的收敛性证明．本文指出连续的Hopfield网络模型与Hopfield－Tank模型是有区别的，所以需要另外给出Hopfield-Tank模型的收敛性证明．因此本文给出了Hopfield－Tank模型的收敛性证明，这一证明使Hopfield网络的优化计算理论更加完善．文中还讨论了网络参数1／τ对极小点的影响以及合适的取值范围．

In this paper, the energy function of Hopfield--Tank is studied in convergence andoptimum rate in Hopfield neural network. Hopfield presented the discrete neural network modal in1982,and the continuous neural network modal in 1984, applying the conception of energy functioninto the research of neural network, and made the lay foundation for the optimization computationaltheory of neural network. In 1985,Hopfield and Tank first used the neural network by softwaresimulation to gain the success of TSP, which drew attention of many researchers, afterward neuralnetwork computation paved a new way for combination optimization. Though many neural networkoptimization algorithms were presented in the following years,there is no doubt that the most basicand important neural network algorithm is Hopfield and Tank algorithm, others are all based on it.So it has important significance to research the theory foundation of Hopfield--Tank algorithm.Although the convergence proof of discrete and continuous Hopfield network have been given byHopfield, the convergence proof of Hopfield-Tank model has not been given up to now. The differencebetween continuous Hopfield network and Hopfield-Tank model is firstly proposed in this paper.Then a convergence proof of Hopfield-Tank model is given. It will make the optimal computationtheory of Hopfield network more complete. In addition. The effect of network parameter 1/τ onminimum point and appropriate value interval is discussed in detail.