多层前向小世界神经网络及其函数逼近

借鉴复杂网络的研究成果, 探讨一种在结构上处于规则和随机连接型神经网络之间的网络模型—-多层前向小世界神经网络. 首先对多层前向规则神经网络中的连接依重连概率p进行重连, 构建新的网络模型, 对其特征参数的分析表明, 当0 < p < 1时, 该网络在聚类系数上不同于Watts-Strogatz 模型; 其次用六元组模型对网络进行描述; 最后, 将不同p值下的小世界神经网络用于函数逼近, 仿真结果表明, 当p = 0:1时, 网络具有最优的逼近性能, 收敛性能对比试验也表明, 此时网络在收敛性能、逼近速度等指标上要优于同规模的规则网络和随机网络.

Multilayer feedforward small-world neural networks and its function approximation

Based on the research results from complex networks, a new neural networks model, multilayer feedforward small-world neural networks, is proposed, whose structure is between the regular and random connection model. At first, a new networks model is built up on rewiring the links of multilayer feedforward regular neural networks according to the rewiring probability p, and the characteristic parameters of new model show that it is different from the Watts-Strogatz model on clustering coefficients when 0 < p < 1. Secondly, the networks model is described as a six-element composition. Finally, when using multilayer feedforward small-world neural networks for function approximation under different p, the simulation results show that the networks have the best approximate performance when p = 0:1, and the comparison of convergent performance also shows that the small-world neural networks is superior to the same scale regular networks and random networks to a certain extent in convergence and approximate speed at the same rewiring probability.