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Integer neural network has been already extensively applied, but the result of application is always due to its operators because of the lack of theoretical guidance. In our paper, we will introduce a theoretical result that an integer network can present a good performance on approximating continuous function. Firstly we will make a quantitative analysis on integer networks capability of approximating a function from function spaces or . Then two new formulas will be first given to calculate the approximation error. Correspondently, we will give two new formulas to calculate the number of neurons in a three-layer network which has certain significance to engineering practice to construct a reasonable network.

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