On Polynomial Approximation of Activation Function

TL;DR

This paper introduces a polynomial approximation method for activation functions that incorporates gradient information into the least squares framework to achieve low-degree polynomial approximations.

Contribution

It extends traditional least squares by including gradient information, enabling more accurate polynomial approximations of activation functions.

Findings

Effective polynomial approximations achieved for activation functions.

Inclusion of gradient information improves approximation accuracy.

Method applicable to various activation functions.

Abstract

In this work, we propose an interesting method that aims to approximate an activation function over some domain by polynomials of the presupposing low degree. The main idea behind this method can be seen as an extension of the ordinary least square method and includes the gradient of activation function into the cost function to minimize.