Using Three Layer Neural Network to Compute Multi-valued Functions

Authors:
Nan Jiang;Yixian Yang;Xiaomin Ma;Zhaozhi Zhang
Affiliations:
College of Computer Science, Beijing University of Technology, Beijing 100022, China;Information Security Center, Beijing University of Posts and Telecommunications, Beijing 100876, China;Engineering and Physics Department, Oral Roberts University, Tulsa, OK 74171, USA;Institute of Systems Science, Academia Sinica, Beijing 100080, China
Venue:
ISNN '07 Proceedings of the 4th international symposium on Neural Networks: Advances in Neural Networks, Part III
Year:
2007

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Abstract

This paper concerns how to compute multi-valued functions using three-layer feedforward neural networks with one hidden layer. Firstly, we define strongly and weakly symmetric functions. Then we give a network to compute a specific strongly symmetric function. The number of the hidden neurons is given and the weights are 1 or -1. Algorithm 1 modifies the weights to real numbers to compute arbitrary strongly symmetric functions. Theorem 3 extends the results to compute any multi-valued functions. Finally, we compare the complexity of our network with that of binary one. Our network needs fewer neurons.