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Unlike the conventional fully connected feedforward multilayer neural networks for approximating functions on continuous input spaces, this paper investigates simplified neural networks (which use a common linear function in the hidden layer) for approximating functions on discrete input spaces. By developing the corresponding learning algorithms and testing with different data sets, it is shown that, comparing conventional multilayer neural networks for approximating functions on discrete input spaces, the proposed simplified neural network architecture and algorithms can achieve similar or better approximation accuracy especially when dealing with high dimensional-low sample cases, but with a much simpler architecture and less parameters.
