Latitudinal and longitudinal neural network structures for function approximations

This paper proposes a novel neural network structure for approximating arbitrary functions. The convergence property of this kind of structure is given. Another aim of this paper is devoted to constructing neural networks to approximate arbitrary continuous functions by local piecewise quadratic functions. It is shown that such constructive neural networks can be applied to approximate any continuous function with sufficiently small error. Compared with existing works, this paper provides the strategy to use much fewer neurons to achieve the desired precision, and approximate the given function with more favorable smoothness by using a piecewise nonlinear function. The relationship between the two neural network structures mentioned above is discussed