Started.

So now we are in a recorded part again.

And nevertheless, I will start with this slide here.

And this slide is a summary of whatever

we have done in the afternoon.

So you see, over the cloud, you can do a simple summary.

But nevertheless, in detail, you have

to know a lot of details before you are able to really apply it.

And one of the essential parts here

was the learning with the forward and the backward paths,

which we had here in this picture summarized here.

And please, whatever you recognize from what we have seen

yesterday, you should be able to repaint this picture

on a blank piece of paper.

So as an exercise in the afternoon here,

take this concept that you see here on this paper here

and try to repaint it on a piece of paper only out of your mind,

not because you have this in front of your computer picture

here.

So this is so important.

So let's go over it once again.

And here you have not so many indices,

so it's easier to understand.

You have an input vector here.

This input vector is coming in here.

And on the input level, nothing is

changed with the input vector here,

which means the output on level 0 here

is the same as the netto input on level 0.

Why do I use the wording netto input and output now?

You could simply say here that's the input.

But what I want to have is that every cluster of neurons

which I have here, the input to a cluster of neurons

is called netto input.

And the output of a cluster of neurons is called output.

That the netto input of the input cluster here

is the input itself.

That's fine.

But nevertheless, the wording of the accumulated input,

which is going in here, I will call netto input.

And then the output of a cluster I call output.

And this is the level 0.

And then I do this matrix multiplication

with the next matrix here to come to the netto input

of the next level.

And then I have a vector again.

And element by element, I go through the nonlinearities

of this level here, which means I have a vector again.

And then I do a matrix multiplication

of the next matrix here.