基于Pi演算的人工神经网络模型

ANN model based on Pi calculus

人工神经网络是一种重要的人工智能实现方法，但是目前人工神经网络缺乏通用的数学模型，用来模拟各种结构的神经网络．然而形式化方法对于建模和验证系统是一种有效的方法，所以对人工神经网络的形式化描述和验证是一个重要的研究方向．Pi演算是一种移动进程代数，可用于对并发和动态变化的系统进行建模，因此Pi演算和人工神经网络的基础都是并发计算．在这个基础上，首先通过Pi演算建模人工神经网络，证明了它们之间的等价性，然后设计了基于Pi演算的人工神经网络分类器．最后，讨论了这个模型的优越性．

Artificial neural network （ANN） is an important method of artificial intelligence, but ANN lacks an all-purpose mathematical model, which can simulate all kinds of neuron architecture. At present, formal method is an effective method for modeling and verifying system. Therefore it is an important research direction to describe and verify ANN by formal method. The Pi calculus is a kind of mobile process algebra that can be used to model concurrent and dynamic system. Therefore, both Pi calculus and ANN are on the basis of concurrent computation. This paper firstly introduces a method to use Pi calculus for modeling ANN and illustrating equivalence between them. Then on the basis of this, an artificial neural network classifier based on Pi calculus, which takes the same basic principles of concurrent computation as neural networks, is discussed in this paper. Finally, its superiority is also discussed.