Constructing Multilayer Perceptrons as Piecewise Low-Order Polynomial Approximators: A Signal Processing Approach

TL;DR

This paper presents a method to construct multilayer perceptrons as piecewise low-order polynomial approximators using a signal processing approach, providing insights into their universal approximation capabilities.

Contribution

It introduces a novel construction method linking MLPs to piecewise low-order polynomials, enhancing understanding of their approximation power.

Findings

Establishes a one-to-one correspondence between MLPs and piecewise polynomials.

Provides a comparison between polynomial and MLP approximations.

Offers insights into the universal approximation capability of MLPs.

Abstract

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.