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Hello and welcome back to the course
on Deep Learning.

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Now that we've seen neural networks
in action, it's time for us to find out

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how they learn.

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So let's dive straight into it.

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There are two fundamentally different

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approaches to getting a program
to do what you want it to do.

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One is hard coded coding
where you actually tell

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the program specific rules
and what outcomes you want,

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and you just guide it
throughout the whole way, and you account

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for all the possible options
that the program has to deal with.

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On the other hand, you have neural
networks where you create a facility

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for the program to be able to understand
what it needs to do on its own,

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to basically create this neural network
where you provided inputs.

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You tell it what you want as outputs,
and then you let it figure everything

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out on its own.

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Two fundamentally different approaches.

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And that is something to keep in mind
as we go through these tutorials.

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Our goal is to create this network
which then learns on its own.

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We are going to avoid it
trying to put in the rules.

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And a good example
that I can give you right now is,

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this will come further in the course,
but it's just a very visual example.

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For instance, how do you distinguish
between a dog and a cat?

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For on the left side, on the approach
that's, depicted on the left, you would,

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program things in like,
the cats ears have to be like this.

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Look out for, whiskers.

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Look out for this type of nose.

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Look out for this type of shape. of, face.

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Look out for these colors.

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You kind of.

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You describe all of these things,
and you'd have conditions

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like if if the ears are pointy,
then cat, if the ears,

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sloping down, then possibly dog and so on.

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On the other hand, for a neural network,
you'd just code the neural networks,

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you code the architecture,
and then you point the neural network

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at a folder of all these cats and dogs

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with images of cats and dogs,
which are already categorized.

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And you tell it, okay, I've got you.

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I've got some images of cats and dogs.

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Go and learn what a cat is.

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Go and learn what a dog is.

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And the neural network will on its own
understand

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everything it needs to understand

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and then further down, once it's trained
up, when you give it

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a new image of a cat or a dog,
it'll be able to understand what it was.

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So they're there. They are.

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Those are the two fundamentally
different approaches.

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And today we're going to slowly start

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getting into
how that second approach works.

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All right. So let's get straight to it.

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Here we have a very basic neural network
with a one layer.

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It's this is called a single layer
feedforward neural network.

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And it is also called a perceptron.

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Now before we proceed one thing that we do
need to adjust is that output value.

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Right now you can see that it's just a
why we need to put a y hat in there.

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And the reason for that
is usually y stands for the actual value.

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And that's what we're going to be using.

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So y is going to be the actual value
which we see in reality

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output value is the predicted value
by the algorithm,

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by the neural network
y hat is the, output value.

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Basically that's the denomination
for the output value.

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And the perceptron was first invented
in 1957 by Frank Rosenblatt.

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And his whole idea was to create
something that can actually learn,

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and, adjust itself.

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And this is what we're going
to be looking at now.

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So, we've got a perceptron.

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Let's see how a perceptron learns.

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So let's say we have some input values,
that have been supplied

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to the perceptron, and,
or basically to our neural network.

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Then,

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the activation function is applied,
we have an output,

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and now we're going
to plot the output on a, chart.

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So there it is, our output y hat.

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Now, what we need

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to do is in order to be able to learn,
we need to compare the output value

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to the actual value that we want
the neural network to get right.

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And that is, the value y.

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And so if we plot it here, you'll see that
there's a bit of a difference.

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Now we're going to calculate
a function called the cost

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function is calculated
as one half of the difference

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of the squared difference
between the actual value and output value.

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Now there there are many ways
you can come up with a cost function.

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There are many different cost functions
that you can use.

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this is probably the most commonly
used cost function.

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And why it is specifically this function
that we use.

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We'll find out further down when we're
talking about a gradient descent.

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But for now we're just going to, agree
that this is the cost function.

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And basically
what the cost function is telling us is,

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what is the error that you have
in your prediction?

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And, our goal is to minimize
the cost function because the,

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the lower the cost function, the closer
the y hat is to y.

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Okay.

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So as long as we agree on that,
let's proceed.

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So basically from here, what happens is, 
there's our cost function.

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And from here what happens is now
we're going to, once we've compared,

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now we're going to feed this information
back into, the neural network.

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So there we go.

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There's, the information
going back into the neural network,

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and it goes to the weights,
and the weights get updated.

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Basically,
the only thing that we have control of

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in this very simple neural network
are the weights w1, w2 all the way to W1.

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And, 
our goal is to minimize the cost function.

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So all we can do is update the weights.

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So we update the weights.

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tweak them a little bit and how exactly
we'll find out for the down.

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But for now we, we agree that we update
the weights and then we continue.

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So but here I've put up this,
screenshots of the data

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just to make some one point very clear
that right now, throughout this whole

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experiment, everything we're doing right
now, we're dealing with just the one row.

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So we're dealing with we have a data
set of one row where we have,

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for instance, we're dealing with,
how long you study like, the variable

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that we're predicting is what, what,
results you're going to get on an exam.

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And the dependent independent variables
that we have is how many hours

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did you study for
how many hours did you sleep,

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and what did you get on the quiz
in the mid semester.

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So in in the middle of the semester
it a quiz.

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What percentage did you get there.

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So based on those variables
we're trying to predict what score

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you'll get for the exam.

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And in an exam the 93%.

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That's the actual value. So that's why.

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So, so we feed these three values

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into our neural network again
for the second time now,

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and then we're going
to be comparing the result to Y.

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So let's see how this works.

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We feed these values
into the neural network.

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Everything gets adjusted and weights
get adjust.

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So as you can see this is again
we're going to feed the values again.

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The point here is
that we're feeding in these same values.

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So we only have one row.

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We're trying to we're training on one row.

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This is because this is just a very simple
basic example.

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Then we'll see what happens
when there's more rows.

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So again we feed these rows
in our cost functions get adjusted.

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As you can see everything happens along
those lines again.

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So as you can see,
every time our y hat is changing

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because we've tweaked the weights,
all I had is changing.

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Our cost function is changing.
Let's have a look again.

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So we feed those in Y hat is changing.

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Cost function is changing.

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We get information
back, feed back to the weights

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so that the weights get adjusted. Again.

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We feed in the same values.

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Every time everything gets adjusted
goes back to the weights and one more time

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feed in. Okay

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and another time.

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So we've adjust the weight, adjusted
the weights we feed in the information.

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And there we go.

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So, now this time the y hat is equal
to y equals functional zero.

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Usually we won't get cost
function equal to zero.

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But this is a very simple example.

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So hopefully all that made sense
every time we feed in exactly

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that same row.

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Because just in this case
we're just dealing with that one row

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into our neural network, where then, 
the weights get, the values get

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well supplied by the weights,
the activation function is applied.

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We get y hat, Y hat is compared to y.

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Then we see how the cost function
has changed.

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Feed back, feed that information

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back into the neural network
and then just adjust the weights again.

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and then we repeat the same process again
with the same exact row.

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we're trying to minimize
that cost function.

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So up until now we've been dealing with
just that one row.

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Let's see what happens
when you have multiple rows.

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So here's the full data set.

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We have eight rows of,
how many hours you slept.

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Or maybe these are, different students
in a day taking the same exam.

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How many other hours they studied,
how many hours they slept before the exam?

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What to get on the quiz
and their final result on the test.

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And as you can see here on the left,
I've got eight of these perceptrons.

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Actually,
they are all the same perceptron.

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So this is also important to understand.

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I just multiplied it or like duplicated
eight times just so that we can

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conceptual understand.

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But the important thing
here, it's the same neural network.

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We're going to be feeding these
into one same neural network.

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So let's go. Let's get started.

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So one epoch,

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as you all here
had learned, mentioning one epoch is

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when we go through our whole data set
and we train our,

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neural network on, on all of these, rows.

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So let's go, let's get started.

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So there's our first row,
and there's y hat for the first row.

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There's the second
row, there's y hat for the second row.

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So again it's being fed
into the same neural network every time.

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I've just copied them several times.

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So we can visually see how
this is happening.

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Then again is it's happening again.

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That's third row. Fourth row.

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There's our y hat for the fourth row
and so on basically.

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Then we get the same values
for the remaining four rows as well.

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So every time we just feed in a row into 
our neural network, we get a value.

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then we compare to the actual values.

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So they are the actual values.

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So for every single row
we have an actual value.

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And now based on all of these differences

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between y hat
and y, we can calculate the cost function

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which is the sum of all of those

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squared differences between y hat and y.

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And all of that is halved.

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And there's our cost function.

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And basically now what we do
after we have the full cost function,

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we go back and we update the weights,
we update w1, w2, w3.

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And the important thing to remember here
is that all of these,

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perceptrons, all of these neural networks
is actually one neural network.

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So there's not eight of them,
there's just one.

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And when we update the weights
we're going to update the weights

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in that one neural network.

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So basically the weights are going
to be the same for all of the rows.

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So it's not the case
that every row has its own weights.

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Now all the rows share the weights.

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And so that's why we 
looked at the cost function,

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which is the sum of the 
squared differences.

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And then we updated the weights.

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And now from here
that was just one iteration.

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Next we're going to

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run this whole thing again.

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We're going to, feed every single row
into the neural network,

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find out our cost function
and do this whole process again.

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So just as we saw previously,
where we had just one row

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and we were doing everything again
and again, again, again, same thing here.

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But now we're going to be doing it
for rows or 800 rows or a thousand rows,

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however many rows
you have in your data set.

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you do this process
and then you calculate the cost function.

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And the goal here is to minimize

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the cost function, 
and to get as soon as you found

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the minimum of the cost function,
that is your final neural network.

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That means your weights have been adjusted
and you have,

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found the optimal,

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weights for

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this, data set that you, you're
training on and you're ready

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to proceed to the testing phase
or to the application phase.

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And this whole process is called back
propagation.

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So some additional reading that you might
want to do for the cost function.

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And I know we just talked about one
and there are many different ones.

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A good article is located
on Cross-Validated.

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it's called a list of cost

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functions used in neural networks
alongside applications.

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So the URL is there,
but you can just Google

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for that exact search term
or a search phrase.

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And you will that this one will be
the first one that pops up.

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It's actually got some good
examples and application

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or use cases for different cost function.

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So if you're interested
to learn more about cost functions

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check out this article.

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And on that note,
I hope you enjoyed today's tutorial.

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I look forward to seeing you next time.

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Until then, enjoy deep learning.