基于复数权值神经元的数字逻辑最稳健设计

复数权值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,结合二进神经元稳健性的概念,提出了基于该神经元的稳健性定义。并结合定义,实现了基于单个神经元的基本数字逻辑以及异或运算的最稳健设计方案,从而证明了该稳健神经元实现任意数字逻辑的有效性和可行性,说明了其强大的处理能力。

基于复数权神经元的多值整形器稳健设计

复数权神经元是由于引入多阈值逻辑而使得权值为复数的神经元,被认为具有更强的性能。该文根据该神经元数学模型,结合POST代数系统中多值逻辑取值及运算的概念,实现了基于单个复数权神经元的多值整形运算,设计的多值逻辑整形运算具有稳健性能,所得结果表明用复数权神经元实现多值逻辑的有效性和可行性,说明了其强大的信息处理能力。

二进神经网络的最稳健设计

本文基于对ｎ维超立方体的分割超平面应处在任两不同类相邻顶点连线的中点、且与连线正交的思想，设计了能够实现逻辑功能的具有次强和最强稳健能力的多层前向神经网络，给出了稳健神经元之间的连接权和偏置值的设计规则，并证明了运用这一规则能够设计出既能实现所希望的逻辑功能，又具有对输入数据的次强和最强稳健能力的前向网络，相应的网络规模分别为ｎ－ｋ－１和ｎ－ｎ－ｋ－１（ｋ≤２ｎ－１）．由于所构造的网络其连接权值只可能是＋１、－１、０，使得网络灵活而易于实现．最后进行了大量的仿真实验，结果表明，这样构造的网络能够获得次强和最强的对输入数据的容错能力．

The most robust design for digital logics of multiple variables based on neurons with complex-valued weights

Neurons with complex-valued weights have stronger capability because of their multi-valued threshold logic. Neurons with such features may be suitable for solution of different kinds of problems including associative memory,image recognition and digital logical mapping. In this paper,robustness or tolerance is introduced and newly defined for this kind of neuron ac-cording to both their mathematical model and the perceptron neuron's definition of robustness. Also,the most robust design for basic digital logics of multiple variables is proposed based on these robust neurons. Our proof procedure shows that,in robust design each weight only takes the value of i or -i,while the value of threshold is with respect to the number of variables. The results demonstrate the validity and simplicity of using robust neurons for realizing arbitrary digital logical functions.