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In many pattern classification applications of artificial neural networks, the objects to be classified are represented by fixed sized 2-dimensional (or 1-dimensional) arrays of which the elements are the values of cells in a fixed sized 2-dimensional (or 1-dimensional) grid and the values of these elements are of the same type. For such problems, besides a general neural network structure, called an undistricted neural network, a districted neural network can be used to reduce the training complexity. A districted neural network consists of two levels of sub-neural networks, where each of the lower level sub-neural networks takes the elements in a region of the array as its inputs and outputs a temperate class label, while the higher level sub-neural network, uses the outputs of lower level sub-neural networks as inputs and derives the consensus label decision. We show, by using a simple model, that a districted neural network is more stable than an undistricted neural network. The conclusion is verified by experiments of using neural networks for face recognition.