Calculus and Artificial Intelligence

Rupika Nimbalkar
appengine.ai
Published in
3 min readJun 24, 2021

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Understanding calculus and working with Machine learning and AI.

Calculus is a branch of mathematics that analyzes every small little thing and that’s why it plays a very important role when it comes to AI. Calculus is all about conceptualizing things and formally presenting them. With the help of calculus, we study the rate of change of quantities like area, volume, and length of the object.

Calculus is a complex field of mathematics divided into two parts for better and accurate analysis. It is divided into differential Calculus [ derivative] and Integral calculus [integration]. To understand it properly let’s put it in simple ways.

Differential Calculus

Differential calculus is all about fragmenting or breaking it to understand the changes and study them. It is expressed as

Integral Calculus

Integral calculus is all about getting together or joining the fragments or broken parts to understand what has changed in it and study it. It is expressed as

But now the question arises, what these complex mathematical theories have to do with AI?

Here we are dealing with tiny particles or even say that it is just about maxima and minimum. and here in AI, we are dealing with cost function and loss of the function. To find the cost of the function first we need to find the minimum. While doing that we need to change all the parameters which are costly and time-consuming, and so Gradient descent techniques quite help full. So it becomes extremely important for AI-related platforms like appengine.ai to understand and use them in the proper way to deliver better products.

Gradient Descent

As we know gradient descent techniques are used to study how the output changes when input changed. let us consider a stone coming down a mountain. While doing so it follows a certain path and as it comes to the bottom its slope becomes less it is called gradient descent.

Let us consider the function

Here the derivative is used to find the slope at point x. We shall first see its first derivative

Here the derivative gives us the slope of point x. It shows how a small change in input x will change the output y.

And now when these one input increase to multiple inputs or the input is more than one we use partial derivative that is,

And the group of these particle derivatives is gradient which we use to find the maxima and minima for some functions.it is a vector that has all the particle derivatives. It deduces derivatives to scalar functions of many variables.

In the next blog, we shall be looking into The Jacob and Hessian concept for better understanding calculus and how machine learning and AI algorithms work.

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