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The neural network with two weights is constructed and its approximation ability to any continuous functions is proved. For this neural network, the activation function is not confined to the odd functions. We prove that it can limitlessly approach any continuous function from limited close subset of Rm to Rn and any continuous function, which has limit at infinite place, from limitless close subset of Rm to Rn. This extends the nonlinear approximation ability of traditional BP neural network and RBF neural network.

The Estimate for Approximation Error of Neural Network with Two Weights