Okay, so let's get started.

Hello everyone, welcome back.

So last time we looked into convolutional neural networks and I want to start with a

quick recap.

So if you have an image processing program like Photoshop or GIMP, then you know that

you can apply filters to an image.

So as to enhance the edges or to blur the image.

And last time I told you that basically a convolutional network exactly does the same

except that the filter can be learned.

And so you would provide an image that you feed into your neural network and then layer

by layer different filters would be applied and it could look like the situation shown

here where you imagine that you scan across the pixels of an image and you always collect

information from all the neighboring pixels, apply a filter that is you just multiply,

you weight the values, the pixel values and then you combine them into the result that

is written into the pixel of the outgoing image.

So that's the idea behind a convolutional neural network.

It's called convolutional because mathematically the operation we are applying is just a convolution

here in a discrete space defined by the grid of pixels and it is extremely useful simply

because the amount of information you have to store in these filters is much much smaller

than if you were to process the same size of images using a fully connected neural network.

So if you have n pixels in an image, then for a fully connected neural network that

maps an n pixel image to another n pixel image, you would have n squared weights,

n squared connections and you would have to store all these weights and train them.

Whereas for a convolutional neural network actually the number of parameters does not

even scale with n, it is just given by the number of pixels that your filter encompasses

and maybe that's a 5 by 5 filter, so you would have 25 values of the trainable weights to

store.

And so that not only means that the memory consumption is much less, but it also means

that training is much more efficient because in a sense what the neural network learns

from features that it observes, say in the lower left hand corner of the image, it will

also later be able to apply to the upper right hand corner of the image.

So in a sense a single training image already provides training information as if you had

many many small patches and apply your neural network to those.

So it's really efficient.

So let's jump directly to this example of how a usual convolutional neural network would

look like in practice.

It's actually a combination of a convolutional neural network consisting of several stages

plus subsequent stages of a standard, default, fully connected neural network that do the

final stages of processing.

So in the example that I show here we have the input image, let's say it is a monochrome

image, so it has only one channel in that sense, one color channel, and then it can

be mapped by these convolutional filters into an image that maybe in this case has several

channels and so if these channels are input channels they would possibly correspond to

a color image like red, green, blue, but further up in the stages they can represent anything

and it's actually not you who decides what these channels mean, but it's the neural network

via the training process that makes choices as to what these channels mean.

And if you're lucky you can later try to analyze what is going on.

And then we also learned last time that not only in image processing but also for this

kind of neural network it's smart to play around with the resolution.

So for example you can decrease the resolution by always averaging over small patches of