A Power Transform

TL;DR

This paper introduces a novel power transform that unifies various functions in mathematics and machine learning, enhancing normalization, loss functions, and neural network activations.

Contribution

The paper presents a new power transform that acts as a unifying framework for diverse functions in statistics and neural networks.

Findings

Unifies multiple loss and kernel functions under a single framework.

Provides a new approach for normalization and activation functions.

Enhances understanding of the mathematical relationships among various functions.

Abstract

Power transforms, such as the Box-Cox transform and Tukey's ladder of powers, are a fundamental tool in mathematics and statistics. These transforms are primarily used for normalizing and standardizing datasets, effectively by raising values to a power. In this work I present a novel power transform, and I show that it serves as a unifying framework for wide family of loss functions, kernel functions, probability distributions, bump functions, and neural network activation functions.