Approximation and fault-tolerance performances of multilayer feedforward small world neural network

Based on the idea of Watts-Strogatz (W-S) network model, a multilayer feedforward small world neural network, which relies heavily on the rewiring probability, is constructed by reconnecting the regular links. The network model is described mathematically, and the function approximation and network fault-tolerance simulations are employed to investigate the performances of small world neural network. The results show that the small world neural network is endowed with better approximation performance compared with the regular or random connecting network; and when the learning rate parameter of network gets between 0.1 to 0.3, it exerts less impact on the approximation performance of small world neural network. In addition, when the network weight failure is less than 30%, small world neural network with rewiring probability less than 0.8 and regular network have the same better performance on fault-tolerance. When failure rate is more than 40%, small world neural network with high rewiring probability and random connecting neural network have distinctly better performance on fault-tolerance than the regular neural network has.