Interpolation representation of feedforward neural networks

Mathematical essence and structures of feedforward neural networks are researched in detail in this paper. First of all, interpolation mechanism of Feedforward neural networks is exposed, so we can more clearly understand why a feedforward network is of approximation. For example, a well-known conclusion for arbitrarily a continuous function, there exists a three-layer forward neural network such that the network can approximate the function to within any given precision. It, in fact, is regarded as a natural result of interpolation representation. Then the learning algorithms of feedforward neural networks are discussed by some new ideas.