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

arXiv: https://arxiv.org/abs/2010.07871 · HTML: https://mlsanity.com/paper/2010.07871/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Oct 2020.

## Built on by (most cited first, 1 of 1)

- [CoFie: Learning Compact Neural Surface Representations with Coordinate Fields](https://mlsanity.com/paper/2406.03417/) (2024)

## Abstract (arXiv)

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.