This paper studies a permutation binary neural network characterized by local binary connections, global permutation connections, and the signum activation function. Depending on the permutation connections, the network can generate various periodic orbits of binary vectors. Especially, we focus on globally stable periodic orbits such that almost all initial points fall into the orbits. In order to explore the periodic orbits, we present a simple evolutionary algorithm. Applying the algorithm to typical examples of PBNNs, existence of a variety of periodic orbits is clarified. Presenting an FPGA based hardware prototype, typical periodic orbits are confirmed experimentally. The hardware will be developed into various engineering applications such that stable control signals of switching circuits and stable approximation signals of time-series.

翻译：本文研究一种具有局部二值连接、全局置换连接及符号激活函数的置换二值神经网络。根据置换连接方式的不同，该网络可生成多种二值向量的周期轨道。我们特别关注全局稳定的周期轨道，即几乎所有初始点均能落入该轨道。为探索此类周期轨道，本文提出一种简单的进化算法。将该算法应用于典型的置换二值神经网络实例，揭示了多种周期轨道的存在性。通过构建基于FPGA的硬件原型，实验验证了典型周期轨道。该硬件可进一步开发为多种工程应用，例如开关电路的稳定控制信号以及时间序列的稳定逼近信号。