关于神经网络的能量函数

能量函数在神经网络的研究中有着非常重要的作用，人们普遍认为：只要能量函数沿着网络的解是下降的，能量函数的导数为零的点是网络的平衡态，能量函数有下界，则网络是稳定的且网络的平衡态是能量函数的极小点，文中取反例说明上述条件下不能保证网络的稳定性，并取例说明即使网络稳定也不能保证网络的平衡态与能量函数的极小点，证明了在网络具有上述条件的能量函数的情况下网络稳定的充分必要条件是网络的解有界，讨论了网络的平

ON THE ENERGY FUNCTIONS OF NEURAL NETWORKS

Energy functions are used widely in the study of neural networks. It is known that if a neural network has a decreasing energy function bounded below and the equilibrium points of the network are identical with the zero points of the derivative of the energy function, then the network is stable and the equilibrium points are the local minimum points of the energy function. Examples are given in this paper to show that these results are actually not correct. It is proved under the above conditions for the energy functions that a neural network is stable if and only if all the solutions of the network are bounded. Relationships between the equilibrium points of neural networks and the local minimum points of energy functions are discussed. As applications, the stability of Hopfield neural network is proved rigorously and a neural network is given for finding out all eigenvectors of real symmetric matrix corresponding to the largest eigenvalue.