How do machines think? │ The History of Mathematics with Luc de Brabandère

Luc de Brabandère:

Today, everybody's talking about artificial intelligence, in the field of the car industry.

In the health industry you hear things about artificial intelligence. And this is supposed to produce things, incredible things nobody ever thought of before. But how is this possible?

Machines are programmed by humans after all.

Hello, I'm Luc de Brabandère, I'm teaching the philosophy of science in various universities,

and today I'm with Mérouane Debbah. Mérouane is director of the Huawei lab in Paris completely dedicated to algorithms and mathematics.

Mérouane has been studying applied mathematics for many, many years, so it's interesting to know in the end: ‘What do we mean by artificial intelligence?’

Mérouane Debbah:

To explain this, let me give you a very simple example. Suppose you want to kick a ball at a given distance D, say 450 metres. In this case, you have two options. The first option that you have at your disposal is what we call the Newton equations. In this case, you solve those equations and you're able to find the angle with which you can kick a ball at a given distance, here 450 metres.

It turns out that, in many cases, especially in telecommunication networks, it's extremely difficult to get those Newton equations which explain the behaviour of the network. The other option which is considered today by the machine learning community is around the topic of big data.

What you do in this case is that you kick the ball many times, and you start registering in a table the distance versus the angle with which you kicked the ball. By having tht huge data and numbers, next time you're asked to kick the ball at a given distance, say basically 450 metres, then you will start looking in that table if that distance is already there.

This has already been known about in our community for many years. It's called data mining.

There's no intelligence, but still you need to come up with some very sophisticated algorithms which enable you to do a fast search.

In the specific case I'm talking about, you will need basically now to search 1 metre, 2 metres, 3 metres, but you will clusterise your data and know immediately that 450 metres is in the class 400 - 500.

Now if the distance is not there, and this is where we talk about intelligence, you will start doing some kind of linear combinations of the distance which were already existing in your database to find what are the new linear combinations you need to do in the angle domain to find the angle with which you can kick the ball.

This linear regression that you're doing basically is at the heart of many machine learning algorithms. It requires some sophisticated mathematical tools and basically enables you to find the angle with which you can kick the ball. In the terminology of machine learning, or AI, we call this a black box that you train with the data, where the input basically is the distance that you need to find, and the output is the angle basically that is given to you.

Now this technique seems quite outstanding in the sense that you're able, with AI techniques, to recover Newton equations. However, you have to have in mind that there's a couple of caveats with that method.

The first caveat, of course, is when you start training basically your system, it might be sunny, but you're then asked to kick the ball when it's rainy. We have here basically a discrepancy which requires retraining every time the conditions change, so this has a cost.

The second caveat of this method is also what we call the input-output parameters which are not necessarily known. In the example that I gave, there's not a mapping or a unique mapping between distance and angle. There's also what we call the velocity which is important and the initial velocity with which you kick. And this is not something that is immediately known when you start tackling the problem.

The third caveat of this method is of course the generalisation problem. Imagine you start learning or kicking the ball basically on Earth and you're asked after to kick the ball on the Moon. It's extremely complicated to extrapolate from the existing data to be able to know what the governing laws are that will be required on the Moon.

This option or this point of view of replacing models with big data has had a huge impact on our discipline. Typically, in voice recognition, for many years people have spent time trying to model the larynx and trying to find the way voice was emitted. It turns out that this wasn't successful.

The first successes appeared when we decided to stop modelling but see voice recognition as what we call a classification problem. We register many, many data voices, and next time there's a new pattern of voice appearing, we do some kind of correlation to be able to infer what the sound was which was emitted.

The techniques of AI are not new, and they date back to a big conference in 1956 where top mathematicians gave their view, such as Shannon and Turing. It went into a couple of winters after 1956, and since the year 2000 we've been seeing basically a big outbreak of AI techniques in our community.

And this is for three main reasons: the first reason is basically the huge amount of data and storage capability that we have today and that enables us basically to have the capability of crunching the data; the second main reason is the computing capability that is available today and which enables us of course to also crunch the data; the third reason is basically the machinery of the algorithmic techniques that we have available today, which enables us to do inference.

Today, many mathematicians are working on new mathematical techniques that can provide trustworthy and explainable AI algorithms which are at the same time efficient and implementable.

Watch the full series on the YouTube channel ‘What makes it tick?’