The Lower Bound on the Number of Hidden Neurons in Multi-Valued Multi-Threshold Neural Networks

Estimating the number of hidden neurons required for the implementation of an arbitrary function is a fundamental problem of neural networks. This paper presents the lower bound on the number of hidden neurons in three-layer multi-valued multi-threshold neural networks for implementation of an arbitrary q-valued function defined on a set of N-point with n-dimension (N¿qⁿ). This result can be applied to design constructive learning algorithms with training set of N numbers. For the special case of N=qⁿ, we obtain the lower bound on the number of hidden neurons for implementation of all the q-valued functions. Our results are tighter than the results that have been existed.