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Hello and welcome back to the course
on Deep Learning.

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Today we're talking about max pooling.

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And we've got some very exciting slides
coming up ahead.

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And even a special surprise
at the very end of the tutorial.

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So let's get started.

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The first question is what is pooling
and why do we need it?

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Well, to answer that question,
let's have a look at these images.

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On these three images we've got a cheetah.

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In fact, it is the same exact cheetah
on the first image.

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The image is positioned properly and
the cheetah is looking straight at you.

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On the second image it's a bit rotated
and the third image is a bit squashed.

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And the thing here is that we want
the neural network to be able

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to recognize the cheetah
in every single one of these images.

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In fact, this is just one cheetah.

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What if we have lots of different
cheetahs?

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Here's a cheetah, here's a cheetah,
here's another cheetah.

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Here's a cheetah, here's a cheetah,
and here's a cheetah.

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And we want the neural network
to recognize all of these cheetahs

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as cheaters.

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And how can it do that if they're all
looking in different directions?

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They're all in different parts
of the image.

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They're like their faces are positioned
in different parts of the image.

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Somebody on the right hand side,
somebody in the left corner,

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somebody is in the middle.

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They're all a bit different.

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The texture's a little bit different.

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The lighting is a bit different.

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There's lots of little differences.

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And so if the neural network looks for
exactly a certain feature, for instance,

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a distinctive feature of the cheetah is

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the tears that are, on its face
going from the eyes or the,

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the shadows that look like tears,

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the texture or the pattern
that is going from its eyes down.

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It's, on the size of its nose.

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It looks like tears.

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That's a distinctive feature
of this, cheetah.

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But if it's looking for that feature,
which it learned from, certain cheetahs,

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in an exact location or an exact shape

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or form or texture,
it'll never find these other cheetahs.

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So we have to make sure
that our neural network,

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has a property called spatial invariance,
meaning that it doesn't care

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where the, features are located.

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Not not so much as in
which part of the image,

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because we we've kind of taken
that into consideration

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with our map,
with our, with our convolution layer.

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But it doesn't have to care
if the features are a bit tilted,

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if the features are a bit different
in texture,

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if the features are a bit closer,
if features are a bit further

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apart relative to, relative to each other.

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So if the feature itself is a bit
distorted, we our neural network

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has to have some level of flexibility
to be able to still find that feature.

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And that is what pooling is all about.

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So let's have a look at how pooling works.

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Here's our feature map.

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So we've already done our convolution
and we've completed that part.

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And now we're working
with the convolution layer.

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Now we're going to apply pooling.
So how does it work.

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We're going to be applying max pooling.

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there's several different types

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of pooling complies
mean pooling max pooling some pooling.

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And we'll comment on those towards
the end of this tutorial.

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But for now
we're just applying max pooling.

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So we take a box of two
by two pixels like that.

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And again
it doesn't have to be two by two.

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You can choose any size of box.

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And again we'll comment on that
towards our tutorial.

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And you place it in the top left
hand corner

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and you find the maximum value
in that box.

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And then you record only that value
and you disregard the other three.

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So in your box you have four values.

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You just disregard three.

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You only keep one the maximum,
which is one. In this case.

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Then you move your box to the right
by a stride.

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You select the stride once again.

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So here we select a stride of two
and you that's what you normally select.

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You can select a straight of one.
You can select.

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So there are overlapping boxes.

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You can select any kind of stride
that you like even three if you want.

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But we're selecting a stride of two here
and that's what is commonly used.

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And then you repeat the repeat
the process.

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You record the maximum here.

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If you crossover and it doesn't matter,
you just keep continue

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doing what you're doing.

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So, you still record the max over here.

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Zero.

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here the maximum is four.

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Here the maximum is two here.

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The maximum is one, zero
one as a row, two and then one.

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So as you can see, a few things happened.

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First of all, we still were able
to preserve the features.

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Right.

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the maximum numbers they represent
because we know how the convolution

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layer works.

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We know that the maximum or the bit
large numbers in your feature map,

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they represent where you actually found
the closest similarity to a feature.

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But by then pooling these features,

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we are first of all
getting rid of 75% of the information

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that, is not the feature
which is which is not,

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the important things
that we're looking out for,

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because we are disregarding
three pixels out of four.

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so we're only keeping 25%.

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And then also because

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we are taking the maximum of the,

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pixels that way
or the values that we have,

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we are therefore accounting
for any distortion.

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So for instance,
two images in which, for example,

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the cheetah's, tears on the eyes are

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in one image, they're a bit to the left,
or a bit rotated to the left.

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And another one, they're a bit
and they're how they're supposed to be or

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how we, like, if we take one as the bases
and another one, they're a bit

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rotate to the left, the the pooled feature
will be exactly the same.

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So you can see here, if we are talking
about the cheetah's tears,

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then let's say this is the four
and this is where it was here.

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Then if it was a bit rotated.

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So for instance
the four ended up over here.

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Then when we're doing the pooling

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we're still going
to get the same pooled feature map.

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And that's kind of the
the principle behind it.

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It's a very, rough explanation.

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Again, intuitive explanation,
but that's the point of pooling

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that we're still being able
to preserve the features.

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And moreover, accounts for,
their possible

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spatial or textural
or other kind of distortions.

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And in addition to all of that,
we are reducing the size.

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So there's another benefit.

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So we've got
we're preserving the features.

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We're introducing spatial invariance.

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We're reducing the size by 75%,

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which is huge, which is really going
to help us in terms of processing.

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And moreover,
another benefit of pooling is

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we are reducing the number of parameters.

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So we're reducing again by 75%.

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We're reducing the number of parameters

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that are going to go into our final layers
of the neural network.

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And therefore we're preventing
overfitting.

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It is a very important benefit of pooling
that we're removing information.

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And that is a good thing.

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That is a good thing because that way,

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our model won't be able to overfit

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onto that information because especially
because that information is not real.

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And remember, like at the very start
we were talking about even for humans,

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us as humans, it's important
to see exactly the features

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rather than all this other noise
that is coming into our eyes.

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Well, same thing for neural networks.

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They by disregarding the unnecessary,

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not important information we're helping
with preventing of overfitting.

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So there we go.
That is what pooling is about.

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And the question here is, of course,
why why max pooling.

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Right. There's
lots of different types of pooling.

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And you know why why a stride of two?

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Why a size of two by two pixels.

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Lots of all these things.

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And on that note,
I'd like to introduce you to this,

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a lovely research paper
called Evaluation of Pooling Operations

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in Convolutional Architectures
for Object Recognition

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by Dominic Scherrer
from University of Bonn.

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There's the link.

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And the beauty about this paper
is that it's very,

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very simple, very straightforward.

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So if you've never read a research paper

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before which you'd like to give it a go,
this is a great place to start.

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It's very short,
only ten pages, very easy to read.

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And plus the extra benefit is that now
that we've discussed convolution

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and pooling,
you will be totally comfortable

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with everything
that they're talking about in this paper.

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And you, this is a great way
to actually reinforce you knowledge.

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So I highly recommend
checking this paper out.

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I will take 20 minutes to read it.

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And you can even skip part two,
which is called related work

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if it feels a bit farfetched
or alienating, just don't read that part.

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Go straight to from part
one to part three.

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And the one thing that you do need to know
about this paper.

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They talk about a concept
called subsampling,

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while subsampling
is basically average pooling.

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So remember how here we were taking,
we were taking the maximum.

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So you know
square we're taking the maximum value.

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There's a concept called mean pooling
or some pooling.

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Some pooling is you just sum
these values up.

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Average pooling or mean pooling.

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You take the average value
out of all of these.

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And subsampling is kind of like
a generalization of mean pooling.

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It's 
it's a more kind of generalized approach

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to taking the average of,
of these values.

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And you can read a bit more about it
in the paper.

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But otherwise, just think of it as average
pooling when you're reading that paper.

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And so that's where you can get
some additional information on this topic.

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And now kind of let's recap
where have we got into it.

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So there's our input image.

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Then we applied the convolution operation
and we got the convolution layer.

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And now to each of those feature maps

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that we get
we've applied the pooling layer.

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So we've got, we've done these 
two steps convolution and pooling.

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And now we're going to do something
very fun, something exciting.

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We're going to, experiment with this.

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So this is a screenshot
I took from a, tool

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created by Adam Harley from,

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well, back when he was at Ryerson
University of Computer Science,

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and now he's at Carnegie Mellon,
I think, doing his PhD and great tool.

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So let's open up.

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Let's have a look so you can find it.

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You can't actually find it through Google.

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You have to know the URL.

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It's it's it's just hard to find this on
Google because there's no text here.

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See we're
just this URL x dot Ryerson okay.

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And then this stuff on then
and basically this

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is exactly what we're doing
but visualized.

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So here you need to draw a number.

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So let's say I draw number four.

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And this tool
will put the number four here.

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That's your image in our first step.

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Then this is the convolution step right.

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And this is the pooling step.

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And also pooling by the way
is also called downsampling.

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So pooling and downsampling
are the same things.

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So you can see it's applied convolution.

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Then it's applied pooling.

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And you can see how it exactly works.

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So you can see what kind of convolutions
that it has applied or

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what kind of filters
it applied, what they look like.

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You can see what features
it's looking out for.

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and then it's applying pooling.

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So it's reducing the size.

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And you can see here
that this is important right.

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So you can see, that
this is the convolved image

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and this is the pooled image.

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And you can still see the same features.

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It's just lesson information,
but same features, right?

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The features are preserved.

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That's the important part.

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and moreover, if you know, if all four
was a bit to the kind of like rotated

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a bit to the side, it would still be able
to pick up very similar pooled layers.

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And then after that it's got more layers.

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We haven't talked about that yet.

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So then it's got another 
convolutional, convolution

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layer here, which, we actually won't have.

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and then it has another pool layer,
but it's basically just repeating that

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same process.

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And then after that,

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this is what we're going to be talking
further down in the course,

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is got the fully connected layers
and so on.

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But you can
definitely play around with that.

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So if I delete that,
you like if I draw a seven

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you will see that, it actually tells you
the guesses.

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It guesses that this is a seven.

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And the second guess
the second likelihood is a three.

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So you can draw it some some challenging
things and see if it can pick them up.

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So let's say
if I draw something that looks like a zero

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but it's not a finished zero,
will it pick it up

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now this this time didn't pick it up.

250
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Looks like a nine to it to the image.

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What if I kind of like finished like that?

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So now it thinks it's a zero or a nine

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and you can see over there
what's lighting up the zero or the nine.

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But we'll talk about that part
for the dog.

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Let's do one more.

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Let's say like like eight.

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I think it's a pretty hard for this now.

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Picked up an eight.

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So you can see that goes into an eight
and then like after that

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it stops being recognizable.

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The subs making sense to us humans, right?

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These, features that it's working with.

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But at the same time, it is correctly
recognizing that it's an eight.

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Yeah. So definitely play around with that.

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You can draw a smiley
face, see what happens then.

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Looks like a three to this, to this tool

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because the tool is obviously trained up
only on digits from 0 to 9.

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So it has to recognize something.

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There are of those.

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And it recognizes a three.

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It's like in life when you when you see
something like a a type of fruit

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that you've never seen before,
like a, custard apple or something.

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And you think that it's,
like it's, it's a pear

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because you've never actually seen
one before.

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You don't know what to classify it as.

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Same thing here.

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So it hasn't actually trained
on the smiley faces.

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And that's
why it's thinks it's a tree. It's a three.

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So there you go. It's
a very powerful, powerful tool.

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It'll be helpful
for you to play around with.

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It actually when you put your mouse
over a pixel, it pixels, it shows you,

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where the, 
feature detector was to pick up that pixel

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so you can see where those, 
this pixel is coming from.

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And, also
so you can see how the filter was

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kind of like going through the image,
exactly how we talked about in the course.

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And here you can see,

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you can see the, the pooling,
you can see that the pooling is done with,

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the pooling is done with a,

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little square size of two by two.

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And you can see that
it's, it's a stride of two as well.

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Just as we discussed in,
today's tutorial.

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So there you go.

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Have a play around with that.

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And I hope you enjoyed today's, session.

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I look forward to seeing you next time.

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And until then, enjoy deep learning.