On Relationship of Multilayer Perceptrons and Piecewise Polynomial Approximators

The relationship between a multilayer perceptron (MLP) regressor and a piecewise polynomial approximator is investigated in this work. We propose an MLP construction method, including the choice of activation, the specification of neuron numbers and filter weights. Through the construction, a one-to-one correspondence between an MLP and a piecewise polynomial is established. Especially, we point out that the form of nonlinear activation is related to the polynomial order. Since the approximation capability of piecewise polynomials is well understood, our study sheds new light on the universal approximation capability of an MLP.