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Now that you understand how exactly a convolution layer works including the bias term and activation

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function we can now consider the architecture of a convolution or neural network and why it's that way.

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So as a little bit of a history lesson modern CNN is essentially all originated from the same model.

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The Lean In this is named after Yan LA -- one of the original Deep Learning pioneers along with Jeffrey

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Hinton and Joshua NGO.

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What we're going to do in this lecture is just start with what the architecture is and then go through

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it piece by piece so that you understand why it is the way it is.

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Okay so let's look at a typical CNN.

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A typical CNN has two stages.

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The first stage is a series of convolution of layers.

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Importantly these convolution of layers are usually followed by pooling layers which is another type

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of layer we'll discuss shortly.

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The second stage is a series of dense layers also called a fully connected layers.

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These are just a regular feet for a neural network.

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As you saw in the previous section.

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If you recall I said in the previous section that neural networks have this hierarchical structure.

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Each layer is always looking at features that were found in the previous layer so you can even think

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of the first stage as just another feature transformer.

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It's a feature transformer that specifically works on images and finds IMAGE FEATURES.

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Then once it's found those image features it passes those into a neuron that work and then the neural

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network does what it does best nonlinear classification or regression

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so let's have a closer look at the convolution of stage.

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Now I just added a new layer without really explaining it.

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The pooling layer.

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Why would we want to do that at a high level.

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Pooling as a down sampling operation what is down sampling.

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That's when you make a smaller image out of a bigger image.

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So imagine your images one hundred by one.

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After pooling.

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If the pool size is two then you would get a 50 by 50.

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That's down sampling by 2.

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Let's go over mechanically how this works and then we'll explain why it works and why we would want

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to include it in our neural network

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so there are two kinds of pooling Max pulling an average pooling choosing which one to use is as you

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probably guessed a hyper pragmatic choice.

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Let's talk about Max pooling first since I think this one's a bit more common.

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The best way to see how it works is by example.

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So if we start with an image let's say it's a four by four and contains these numbers one two three

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four five six seven eight sixteen fifteen fourteen thirteen twelve eleven ten nine so just the numbers

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one the sixteen but organized non sequentially what Max pulling will do is take each two by two square

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of which there are four and just return the maximum value in each of those squares so the max of 1 2

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5 6 is 6 the max of 3 4 7 and 8 is 8 the max of sixteen fifteen twelve eleven is sixteen and the max

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of fourteen thirteen Ten Nine is fourteen so the output image is six eight sixteen fourteen

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as you might have guessed average pulling a similar but instead of taking the max we take the average

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so for the same input image we have the following the average of one two five and six is three point

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five the average of three four seven and eight is 5.5 the average of sixteen 15 2011 is thirteen point

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five and the average of thirteen fourteen Ten Nine is eleven point five.

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So the output image is three point five five point five thirteen point five eleven point five

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now that you know how pooling works.

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Let's talk about why we should use it the first advantage of pooling is practical.

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If we down sample the image the image shrinks and therefore we have less data to process less multiplications

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to do and of course that will speed things up but the second and more important advantage has to do

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with image processing itself recall this idea of translational and variance This is the idea that I

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don't care where in an image the feature occurred.

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I just care that it occurred for example.

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Both you and I can recognize this as in a we also recognize this as an A.

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It doesn't matter where I put the A on the screen so translational and variance is important from a

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biological point of view and how we as humans learn.

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We don't have to learn how to recognize A's at each point in our field of vision.

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Once we know what something looks like we can recognize it.

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No matter if it's up down left or right.

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So what is Max pulling doing.

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Well consider a small two by two box.

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Remember that convolution it tells us whether or not a feature has been found.

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It's a pattern finder.

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So imagine that in this two by two box I have these flags pattern found not found not found and not

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found.

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So it's a high number and a small number and a small number and a small number.

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The pattern being found.

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Returns a higher number.

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So when I take the max it says the pattern has been found.

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That's good because it tells me that the pattern has been found without carrying where it was found.

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Average pooling is the same idea but I think Max pooling is a little more intuitive in this regard.

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As a side note keep in mind that in this lecture I've assumed that we're using a pool size of two and

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that at each pooling layer we select boxes which are two spaces apart now pulling layers have some flexibility

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in this regard.

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First it's not necessary for the pool size to be the same in both directions.

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For example you could look at a two by three box or a three by two box although generally that's unconventional.

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Second is that it's possible for the boxes to overlap the hyper parameter that controls this is called

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the stride.

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It tells us how many spaces to move the pulling box for each output previously we looked at the situation

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where we had a pool size of two by two and a stride was also two.

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This is a pretty common scenario.

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If you add a string of one then or two by two box would overlap.

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This is not really too common.

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So while you have these options which I want to make you aware of they are usually not changed too often.

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So what you see in this lecture is what we do most often we use the pool size of two in each direction

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and we have a string of two so that we don't have any overlapping boxes.

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So now that you know what pooling does and why it works let's discuss why the convolution part of the

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CNN is organized the way it is.

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Why should we have a sequential pattern consisting of a convoy layer followed by a pooling layer followed

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by a convoy layer followed by another pooling layer and so forth.

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If you recall I told you earlier that one cool thing researchers discovered is that CNN are able to

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learn features hierarchically so the initial layers end up learning basic strokes.

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The next layer ends up learning individual facial features such as nose eyes and lips.

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The next layer ends up learning whole faces

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the key points to keep in mind is that after each pulling the image shrinks but the filter sizes generally

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stay around the same comment filter sizes are 3 by 3 5 by 5 and 7 by 7.

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Generally speaking they are much smaller than the input image but what happens as the image shrinks

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as it passes through each layer.

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Well let's suppose we start with a 32 by 32 image and we have four convolution and pulling layers.

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Let's assume we do convolution and same mode so it doesn't change the size of the image and let's assume

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all our convolution filters are size 3 by 3.

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Although this doesn't come into play just yet.

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In this case after the first convolution and pulling the image shrinks down to 16 by 16.

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After the second convolution and pull in the image shrinks down to a by 8.

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After the third convolution and pulling the image shrinks down a four by four.

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And finally after a fourth convolution and pulling the image shrinks down to two by two what happens

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after this is still a mystery.

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So let's just leave that for now and focus on the image shrinking

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as you can see if you take a three by three filter and place it over a 32 by 32 image it occupies only

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a very small portion of the image.

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In other words is looking for very tiny patterns to match like for example simple edges and strokes.

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Then the image becomes size 16 by 16.

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Now all of a sudden in the three by three filter takes up four times as much space in the image it takes

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up twice as much space in each direction and two times to his four.

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In any case it occupies a much larger portion of the image relative to the first filter.

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So now it's looking for patterns which take up more space on the image patterns like nose eyes and lips.

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Next we get to an eight by eight image a three by three filter occupies almost a quarter of the image

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after that convolution and pulling.

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We get a four by four image now a three by three filter takes up most of the image.

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So what have we learned.

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We've learned that in a convolution on their own that work convolution and pooling results in two things

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which are corollaries of each other first that the image input shrinks.

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Second since filters generally stay the same size the filter looks for larger and larger patterns in

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image.

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This is what leads to the CNN learning hierarchical features of the input.

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It first learns things that are relatively small compared to the total size of the image.

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Then it learns to find bigger patterns and bigger patterns and so forth.

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The last concepts regarding the convolution of layers we have to think about is are we not losing information

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at every layer.

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If we shrink the image and the answer is yes that's true.

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We are losing spatial information because the image keeps shrinking.

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We're saying we don't care where in the image the feature was found just that it was found somewhere

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in the image.

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So we're losing information about where it was.

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But there's another component of the convolution process we haven't considered yet which is the number

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of feature maps.

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Again we have a general pattern to follow which is that while the size of the image generally decreases

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the number of feature maps generally increases.

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In other words I don't care where the feature is found.

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I just care that it was found but I do care about different possible features.

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I could find.

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So while you're losing spatial information you're gaining information in terms of what features were

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found in the image

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one last note on this convolution and pulling pattern.

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One of the hardest things to grasp for new students and deep learning is that we have so many choices.

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We call these hyper parameters previously for a minute.

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We looked at the learning rate the number of hidden layers and the number of hidden units.

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But now with CNN is we have a ton of more choices with convolution.

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We have to choose the filter size.

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We have to choose the number of feature maps we have to choose the pool size and so forth.

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But luckily I think this is one instance where there is a general pattern that most people follow.

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So you're not going in completely blind so stick with these guidelines and you can be sure that you're

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at least doing things per accepted convention that is choosing small filters relative to the image like

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three by three five by five or seven by seven.

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Another guideline is to repeat the pattern convolution followed by pooling.

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Another guideline is to increase the number of feature maps at each convolution.

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So you might start with 32 and then 64 then 128 and maybe 128 again.

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The best way to learn about how other people are doing it is to read lots of papers and check out which

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hyper parameters they selected.

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Generally you'll find that this is the pattern followed by most convolution or networks

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next.

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I want to mention something a little funny but in fact pooling is sometimes not what we are going to

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end up using in our CNN.

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Researchers have found that we can do something similar but which is more efficient and sometimes works

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just as well.

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In particular recall that for pooling we have this concept of stride that tells us how far apart each

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box should be when we take the max.

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In fact convolution has a stride option as well so in this animation you can see how convolution works

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with Stride.

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Remember convolution just means multiply an ad with a sliding window when we have convolution with a

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stripe parameter.

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The stride tells us how far apart each window should be.

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And of course our intuition tells us that if we use a strike of two then the output image length will

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be half of what the input was.

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In other words we get the same reduction in size by using a striking convolution instead of convolution

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followed by pooling

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the intuition behind why this works is that if you consider what an image looks like an image is just

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large patches of stuff.

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What I mean by that is each pixel is likely to have a similar value to its neighboring pixels.

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For example suppose I'm looking at a red car.

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I find a red pixel.

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Now ask yourself is the pixel above that also red.

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Yes.

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Is the pixel below that also probably red.

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Yes.

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The same can be said of the pixel to the left and to the right.

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That's just the nature of images pixels near each other are often very highly correlated.

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You won't have this random jumping around of pixel values because something like that wouldn't look

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like an image at all.

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That would probably just be noise and so using a stride of two simply means having your filter skipping

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every other pixel.

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It's saying we don't care what those skipped pixels are because they probably are very close to the

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pixels we were already looking at.

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So to summarize the convolution part of our convolution on their own that work now looks like this.

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We can have a series of static convolutions all with approximately the same filter size with increasing

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feature maps at each layer.

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Or we can have a series of convolutions followed by pooling again all with approximately the same filter

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size and with increasing numbers of feature maps at each layer

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the last part of this lecture will focus on the second half of the CNN which is the feed for neural

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network part.

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Now there's not much to discuss here except that we have to consider the shape of an image is not appropriate

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for a dense field for no network.

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Remember that when an image comes out of a convolution it's going to be three dimensional height by

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width by number of feature maps but a field for a neural network takes in a feature vector a one dimensional

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object.

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Luckily we've already discussed how this works.

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We can turn a 3D object into a one B object using the view function in PI torch

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one alternative to the flan layer which I really like is the global Max pooling layer.

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This is a little different from the regular kind of pooling we discussed earlier consider the question.

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What if we have different sized images.

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The largest source of images is the internet.

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Generally speaking images we find on the Internet are not all the same size so it makes sense to wonder

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is it possible to build a convolution or known network that is capable of handling different image sizes.

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And the answer is yes.

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Using a global Max pooling layer

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Let's consider first why a simple flat in layer would not work.

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Suppose again we have an input image of size 32 by 32 and for convolutions assume again we use convolution

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and same mode.

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And we have a stride of two.

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So after the first convolution We get a 16 by 16.

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After the second convolution We get an eight by eight.

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After the third convolution We get a four by four.

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And after the fourth convolution We get a two by two.

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But now let's say we have an input image of size 64 by 64.

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In this case the output after four convolutions would be four by four.

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Let's say for simplicity's sake the number of output feature maps is one hundred then for the 32 by

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32 image.

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Doing a flat in operation would yield an output of size two by two by one hundred two times two times

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100 which is four hundred four sixty four by sixty for image.

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Doing a flat in operation would yield an output size four times four times 100 which is sixteen hundred.

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And of course a feat for a neural network is not capable of handling vectors of different sizes.

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Now let's consider how global mass pooling works.

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The idea is simple if our input image is h by W. by C then the output is one by one by C or equivalently

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just a vector of size C.

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In other words it takes a max over the entire image along the spatial dimensions over each feature map.

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Since we have C feature maps we end up with what is essentially a one dimensional vector of size C since

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the 1 dimensions are redundant.

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This follows the same general idea of pooling where we're saying I don't care where in the image the

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feature was found just that it was found somewhere.

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Global mass pooling is the extreme of this saying that the feature can be found anywhere in the entire

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image across the entire height and width since the output is always a vector of size C it does not depend

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on the size of the image meaning that it allows the network to handle images of any size.

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As a side note we also have global average Pooley which is just the global version of regular average

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pulling.

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The only exception to this is if your images are too small in which case you'll just get an error when

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you try to run your code.

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For example if your image starts out as a two by two then it's not possible to reduce the dimensions

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by half four times.

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You'll notice this happens if you do something like add too many convolutions to your neural network.

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All right so let's summarize the basic architecture of a modern convolution all knowing that we're the

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first stage is a series of stride convolutions or optionally convolution followed by pooling and repeating

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that pattern in the interface between convolution layers and dense layers.

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We have a flatten.

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We also optionally have a global Max pooling that reduces the image to just the max for each feature

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map.

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Finally once we flattened our data into a one dimensional vector we have a regular feed for a neural

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network made up of a series of dense layers as usual and as you learned in the previous section the

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activation and number of nodes for the final layer depends on the type of task being done.

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So if you're doing scalar regression then you'll only have one output node with no activation function.

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If you're doing binary classification you could have one output node with a sigmoid.

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However for k equals two or more classes you can have K output nodes with a soft Max activation.