基于复数权神经元的布尔函数稳健学习算法

Robust Learning Algorithm for Boolean Function Based on Neurons with Complex-Valued Weights

复数权神经元由于引入了多阈值逻辑而具有更强的性能.文中根据其数学模型,结合二进感知器神经元稳健设计概念,提出了该神经元的稳健性数学定义,并根据定义,得到了简单逻辑和异或逻辑的单个神经元稳健实现方案.然后根据该方案提出了任意复杂布尔函数稳健实现算法,同时证明了该算法的正确性.最后通过具体实例演示该算法实现布尔函数的过程和方法,结果表明了基于该神经元的稳健学习算法实现布尔函数优点和灵活性,说明了其强大的逻辑处理能力.

Neurons with complex-valued weights have a stronger performance due to the multi-threshold logic.In the paper,the robustness for this kind of neurons is presented in accordance with its mathematical model and the binary perceptron＇s definitions of robustness.The robust design for basic digital logics of multiple variables or XOR logic is proposed after that and the robust algorithm for any Boolean functions base on the neurons is given,also the correctness of the algorithm is proved.The final use of specific examples not only shows that the algorithm can realize an arbitrary Boolean function.It also shows that the neurons used to achieve the flexibility and advantage of realizing any digital logic function,illustrates its powerful logical processing capabilities.