Constructing Multilayer Perceptrons as Piecewise Low-Order Polynomial Approximators: A Signal Processing Approach
This work provides theoretical insight into MLP approximation properties, which is foundational for neural network theory but incremental in nature.
The authors tackled the problem of understanding the universal approximation capability of multilayer perceptrons (MLPs) by constructing an MLP as a piecewise low-order polynomial approximator using a signal processing approach, establishing a one-to-one correspondence between the two approximations.
The construction of a multilayer perceptron (MLP) as a piecewise low-order polynomial approximator using a signal processing approach is presented in this work. The constructed MLP contains one input, one intermediate and one output layers. Its construction includes the specification of neuron numbers and all filter weights. Through the construction, a one-to-one correspondence between the approximation of an MLP and that of a piecewise low-order polynomial is established. Comparison between piecewise polynomial and MLP approximations is made. Since the approximation capability of piecewise low-order polynomials is well understood, our findings shed light on the universal approximation capability of an MLP.