Okay, hello, good evening.

We last time started to, we finished actually the reinforcement learning and then we will

start to discuss the connections to physics and to science.

So let me just give you an introduction how you might draw the connection between neural

networks, artificial neural networks and physics.

So as you can see here, at least initially when you think of an artificial neuron, you

think of it maybe as something that can be off or on, especially if you have the sigmoid,

a nonlinear activation function.

And likewise a real neuron could be silent or it could produce electrical impulses.

And so you can easily make a connection between this and a bit, which can be zero or one.

And if you want to look for a bit in physics, you would take a spin, a spin one half that

can be up or down.

And so neural networks have a strong connection to the physics of spin systems.

And indeed if you let them have stochastic transitions and you write down cost functions

in terms of energy functionals, then you can make this connection mathematically precise.

And there have been many different ways of making this connection.

One particular I mentioned here on the slide was started by Mr. Hopfield in the beginning

of the 80s.

But this is not what we will discuss.

We will not discuss so-called Hopfield models.

Instead what we will discuss is called a Boltzmann machine.

And as I go along, I will explain to you what a Boltzmann machine really is.

But first I want to explain to you what is the goal of a Boltzmann machine.

And that's a rather general goal in machine learning, namely to model probability distributions.

Now, of course, if I give you a probability distribution like a Gaussian distribution,

you could try to say construct a neural network that outputs in its output neurons the shape

of this distribution, namely a Gaussian for example.

But that's not what we are talking about.

We're talking about a situation where you don't want to represent the distribution function,

but you want to sample, you want to produce samples according to a distribution function.

And you don't want to produce samples according to a distribution function that is known to

you like analytically.

But maybe you want to produce samples according to a distribution function that you only have

observed empirically.

So what could this mean?

In practice, it could mean that I give you many different pictures and you want to be

able eventually by having looked at all these pictures to produce pictures that are sort

of similar to the pictures that you have seen before.

So that will be the goal of what we say.

So in one sentence, to use a neural network of some type to generate previously unseen

examples, but according to a probability distribution that you have sampled before in terms of training

data.

We already mentioned one version of this when we had a look at recurrent neural networks,

LSTM networks.

And we had this case where you would train it to predict the probabilities of the next

character in a large text.

And then you can use these probabilities to actually generate the next character in the

text and in this way you can generate whole text.

So in a sense, then you are generating a text according to a probability distribution, namely

of characters, that you have trained before.