Understand Exponential Function in Machine Learning – Machine Learning Tutorial

By | June 9, 2021

Exponential function is defined as:

\(y = a^x\) where \(a >0\) and \(a \neq 0\).

This kind of function is widely used in machine learning. In this tutorial, we will introduce some important features when using it.

Look at image below:

exponential function in machine learning

1. if \(a<1\), \(b < 1\) and \(a < b\).

if \(x > 0\), then \(a^x < b^x\)

Here is an example:

\((\frac{1}{2})^{x_0}>(\frac{1}{3})^{x_0}\)

if \(x < 0\), then \(a^x > b^x\)

\((\frac{1}{2})^{x_0}<(\frac{1}{3})^{x_0}\)

2. if \(a>1\), \(b >1\) and \(a < b\).

if \(x > 0\), then \(a^x < b^x\)

\(2^{x_0}<3^{x_0}\)

if \(x < 0\), then \(a^x > b^x\)

\(2^{x_0}>3^{x_0}\)

In machine learning, decay function may use these feature. Here is an example:

an example of decay function

If \(\lambda\) is given. Different \(\frac{L-i+t}{L}\) will get different value.

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