Feedback Neural Networks Metastable Research

The asymmetric feedback neural network are multi-body dynamics system, in this paper we study the position and stability of metastable states in the fully connected asymmetric neural network which designed by the generalized perceptron rule. In terms of the actual application, the neural network can be used for associative memory and pattern recognition, but the existence of a huge number of metastable states may cause them fail to achieve, so it is important to study the metastable states in neural networks.Previously, the study of metastable states was more concentrated in the symmetric neural network, on the one hand the dynamics properties can be obtained by the nonlinear dynamics method, on the other hand the macroscopic properties of equilibrium system can be done by statistical mechanics especially the mean-field approximation method. Especially the memory pattern is three the number and structure has been obtained accurately by the ground theory, while this method is not used when the memory pattern increased. Because of the symmetrical characteristic there will be more metastable states exist in the neural network, so increase the asymmetry was proposed to eliminate the metastable state, e.g. design asymmetric neural network. Moreover, the experimental data shows that the brain network was asymmetric, which provides the biological basis of asymmetric feedback neural network.At present, the asymmetric feedback neural network can be designed by perceptron rule and MCA rule. It’s more beneficial for the associative memory and pattern recognition, on one hand, in order to improve the stability of the memory patterns, the attraction domain of the attractors which corresponding the memory patterns can be controlled by specific learning rules directly, on the other hand the influence of metastable states within the system can be eliminated thoroughly. For asymmetric neural network the deficiency of energy function which described the global properties made the physical properties can’t be studied by statistical mechanics, so people focus on the dynamics property by numerical calculation. In this paper we study the metastable states in the system which designed by the perceptron rule. The Hamming distance between metastable states and ground states is calculated, which shows that the metastable states concentrate in the positions where approximately equidistant to all the ground states. In addition, the dependence of metastable states and the parameter κ was studied by compute the energy ratio of metastable states and ground states. Finally, we find that the energy ratio of asymmetric neural network is less than that of symmetric neural network, which means that the influence of metastable states can be decrease efficiently by the asymmetric neural network, thus demonstrating the superiority of the asymmetric neural network in practical applications.