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Technically speaking a function is a relation between input and output. It is like a machine which converts your input to some other output and that output is related somehow to that input. Function is written as (y=f(x)) in mathematics, where F represents that relationships and x represent input and y represent output.

We have only three things in function one is input, output and relationship (y=f(x))

It is also represent as below

A function can also be thought as collection of some input is some fashion which give's you some output. Let's take on example Jon father is 25 times older than Jon. Then if Jon's age 15 what is his fathers age. This can be represented as a function.

FATHER'S AGE = 25 + JON AGE

JONS AGE = 15

FATHERS AGE = 25+15=40

Like wise a function is a relationship between two variables.

PYTHON CODE for Jons example

JON = 15

FATHER = 25+JON

PRINT(FATHER)

Graph is a visual representation of function on paper where y coordinates, represent dependent variable and x coordinates represent independent variable. For our Jons example graph will be represented as

As Jon's grew older jons father grew 25 years ahead.

Graph drawing in python using MATHPLOTLIB for Jon's sage example is given below import mathplotlib.

Deep learning highly uses linear equation in learning representation of input and provides it output. Linear equation is basically a function which relates input to output linearly with some intercepts. If some input is directly related to its output , Jon's father age is clear example of linear equation.

FATHER'S = JON'S+25

Here above father is linear associated with jon's age plus 25, here 25 is intercept. Any equation of this type

y=ax+b

**UNIVERSAL APPROXIMATION THEOREM** state that anything in this world can be defined and expressed by function. You can approximate anything in this world through function. This theorem is stated long back ago but none of the technology at that times supports it's full strength. But after invention of deep learning by Geoffrey Hinton and his team. This theorem is totally satisfied. Deep learning performs this theorem. It is stated that when linear equation is passed through some activation than take its derivative will provide you such weight which can act as a function. The input representation means a function can represent anything in this world. Lets say you have dog image and dog as a label in text. here above dog image is a input and label is a output to that image we pass this image in linear function than pass its through activation and its derivation. After taking derivatives and adding those gradient to original function will give you function which correlate that input image of dog to output text dog. Its little bit confusing but you will get it as you go.

We have discussed different mathematical concept which are required to learn deep learning (AI). We have discussed Function, Graph, Linear Equation and highly important universal approximation theorem. In next blog we will discuss more about derivatives and how much framework provide as library to form derivatives.

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