Well, actually, most things I will tell are already 30 years old, I guess.

So it's not so much change.

The problem is every time I talk about these things is I feel really old because I have

survived this first wave of neural networks in the 1990s.

So I still have a few papers on that even from that time in the late 90s.

And then for about 10 years you were in a scientific conference not even allowed to

mention the word neural network.

And in the last years it somehow came back.

And still, again, the second wave is as hysterical as the first one was.

So I think one has to be a bit careful.

And when it's, particularly I think more mathematicians to do something and to get some understanding

and translate it into mathematics.

And this is, well, the idea kind of for this talk.

So for the non-Germans, Langenscheid is always the standard book for translating to other

languages.

So either to other languages or to other complicated things.

So what I want to do is kind of this translation between math and deep learning.

And what scares a lot of mathematicians are things like this.

When people talk about deep learning, they actually do some mathematics.

But what you see is always strange pictures like this.

So a lot of nodes, arrows, or even in fancy colors.

And you actually don't really know what is going on.

So what I try to do is to take the basic things in deep learning or neural networks and relate

them to things that we do for many, many years so that it becomes a bit more apparent what

is going on.

And at some points there are some special things that I will mention.

I have this anonymous quote from a friend of mine, which I think scares.

It again goes on with this caring of mathematicians because when you hear all these nice stories

in deep learning and other areas, it cannot apparently relate it to things that you're

used to.

But actually, in many cases, these are just different names for things that you learn

in numerical analysis or in other classes, actually.

So I hope to convince you there is a lot of relation.

There are things that are actually not so complicated when you go to that.

So first, let me start on explaining a bit what are these crazy pictures there.

So from a mathematical point of view, what these neural network things do, and actually

they do since 50 years or so when first mathematical models of the human brain came out.

They tried to mimic what is going on in a network of neurons.

That's obviously also where the name comes from.

And roughly speaking, what you think about this thing as a neuron and the other things

as the axons going from one to the other.

And what is going on is you propagate signals from one neuron to others.

You kind of add them here.

And if the sum of the incoming signals is strong enough, the neuron will fire and will

propagate a signal to the other neurons it's connected to.

And this is what's going on.

So mathematically, this means you kind of have a system in different layers.

So this is the first index I will use.

You have some input.

Call it x.