Hello.
Welcome back.
Let's say you want to design in Europe network to predict how much muscle as you gain given how many
hours you workout and how many hours you rest let's say you recorded the number of hours you worked
out the number of hours you rested on the muscles you gained in the last three workout sessions and
you want to use this data to train your neural network.
This table over here represents that data once your model is properly trained you will simply enter
the number of hours you want to work out tomorrow and a number of hours you want to rest tomorrow and
it will predict how much muscles You will gain.
Let's just say you are a Coda and a professional body builder and you want to use this to optimize your
body building.
This is called a supervised regression problem.
It is supervised because our examples.
It is supervised because we have examples and inputs.
I should say and it's a regression problem because we have predicting your muscle gain which is continuous
output.
If we were predicting your mood I said whether you happy or sad.
This will be called a classification problem not a regression problem
before we throw our data into the model we need to account for the differences in the unit of our data
both of our inputs are in ours but our output is in grams and the output values we are dealing with
here are more than ten times larger than the input.
This will be a problem.
The solution to this is to scale our data this way.
Our model only sees standardised units.
We are going to take advantage of the fact that all of our data is positive and simply divide by the
maximum value for each variable effectively scaling the result to be between 0 and 1 x over here represent
our input.
That is hours of work out and hours of rest.
And y represent the output which is muscle gain.
Now we can build our neural network.
We know 0 our new network must have 2 input and one output the because of the table we have because
these are the dimensions of our data.
We will call AWA because of the table which also gives us the date dimension.
So after we've normalized by multiplying 0 by dividing each each input type and output type by its maximum
value to normalize it to be between 0 and 1.
We are ready to put in our a word neural network and we know the dimension because of the input we have
two inputs one output input one input to one output and we have three examples these ones.
The rules here indicate to the examples Column 1 Column 2 input 1 input to output as simple as the
Yeah we are.
Now we can build on your network like I said and we know our network must have two inputs and one output
like I just said because these are the dimensions of our data.
We will call our output y hot because it is an estimate of y y how it is basically the new name we've
given to the predicted value and y is the expected value any layer between our input and output layer
is called the hidden layer.
Here we are going to use one hidden layer with three hidden units but if we wanted to build a deep neural
network we would just stack a bunch of layers together cycles in our neural network here represent neurones
and lines represent synopses synopsis.
Have a really simple job.
They take a value from the input multiplied by a specific weight and output the result.
Then move on.
Add together the output of all the synopsis and apply on activation function search and activation functions
allow neuro networks to model complex nonlinear patterns that simpler models may miss.
We should deal with various activation functions later on in the course.
Over here is the activation function and we shall apply to the output of our neuron Zi represent the
results from the neuron each couple to X here represent the results coming from each synapse.
The snaps result is computed by multiplying the inputs by a weight the weight is not indicated in this
slide over here.
Each input value or element in matrix X needs to be more applied by a corresponding weight and then
added together with all the other resort for each neuron.
This is a complex operation but if we take the three outputs we are looking for us a single row of a
matrix and place all our individual weight into a matrix of weight.
We can create the accept behavior we need by multiplying our input data matrix by our weight matrix
using matrix multiplication allows us to pass multiple input through at once by simply adding rose to
the matrix X which will spend a lot of time in this course talking about how to understand the dimensions
of these types of matrices and how to multiply them for now.
Notice that each entry in Matrix Z 2 is a sum of weighted input to each head and neuron Z 2 is of size
through by 3 one row for each example and one column for each head in unit Z 2.
This the matrix multiplication of input and the corresponding weight to the hidden layer to this obtained
by applying our activation function to Z to Z is computed by multiplying the result of a 2 by the weight
of the sign ups connecting the hidden layer to the output layer and finally y hut and finally Y is obtained
by applying our activation function to Z 3 these 4 equations make up what is known as 4 propagation.
We have only 4 equations over here for forward propagation because our neural network has only one hidden
layer later on in the course we shall see how to determine the number of equations for 4 propagation.
Given an arbitrarily large neural network and we are going to dive deeper into food propagation This
is just to give you a simple example using a case study for a bodybuilder.
So if you don't completely grasp for propagation now it is fine.
But I'm sure if you post the um the video and you just observe this slide you would just get it.
It's very straightforward and well presented here but you can always send me a message if um if you
have any confusion at all.
So after further propagation our neural network will undergo gradient descent.
Then back propagation in order to update the weight we shall conclude in this example here we shall
um give another example from scratch where we shall go through the process of forward propagation back
propagation of propagation gradient descent and then back propagation.
So um this is the end of this very lesson if you have any questions at all.
Um just send me a message and I shall see you the next lesson.
And like I said You can post the figure on this slide and just observe the notations that subscript
the um the superscript in everything but again you can skip this or you can just move on with it.
Of course we're going to we're going to create food propagation from scratch again.
This is just a taste of it.
I'll see you later.