Neural Networks and the 2024 Nobel Prize in Physics - Sixty Symbols

The 2024 Nobel Prize in Physics seems to have blurred the lines a bit between physics and computer science, so we've made a video that blurs the lines between our two channels, 60 Symbols and Computerphile, and we're posting this video on both channels. Sorry if this causes any confusion, you can blame the people in Stockholm. So the 2024 Nobel Prize in Physics, it went jointly 50-50 to John Hopfield of Princeton University and a little bit more surprising, Geoff Hinton of the University of Toronto, for fundamental contributions to models of neural networks, which are the basic models that power artificial intelligence systems and deep learning and all of that. So it's gone to two people who have been responsible for really laying the foundations of machine learning, and one of whom, contrary to rumour, is most definitely a physicist, that's John Hopfield, and the other is most definitely, it's got to be said, a computer scientist. And this has got a lot of people up in arms, entirely unnecessarily, I would say. My take is that this is the Nobel Committee making a very strong statement that machine learning, artificial intelligence, owes a lot to physics and in particular statistical physics. I spent the first couple of years of my degree thinking I should have done computer science. So a Nobel Prize that bridges computer science and physics for me is an absolutely wonderful thing. But even better than that is that for the first time I get to be in a video with the inestimable Mike Pound over in computer science. Hi Mike. One thing that makes it slightly confusing is the physics-inspired part happened almost near the beginning, and then it's been slowly evolving into the computer science side of things nowadays in modern AI. So Mike and I, just to show you where these links are forged and how setting up these boundaries between disciplines is a bit silly, Mike and I currently jointly supervise a PhD researcher, which is funded, thank you University of Nottingham, via something called the Doctoral Training Centre in Artificial Intelligence, which is all about bringing the different disciplines together to explore these aspects. We don't have a Nobel Prize in computer science, so we spend a lot of time not necessarily getting credit where actually that was a computer scientist that did that thing. And actually that's true of most science. So maybe some breakthrough happens in chemistry, or some breakthrough happens in astronomy, but they were algorithms programmed on a computer by someone that can code. So there was an element of computer science happening in that field, even if you didn't realise it. And so I think it's nice that we're sharing the wealth a little bit. The actual citation is something along the lines of for foundational discoveries that have laid the ground for machine learning via artificial neural networks. Words to that effect. So John Hopfield, who is a very, very famous physicist, who early on in his career discovered polaritons, and then made lots of contributions in other areas of biophysics as well. He's been awarded this for what's called the Hopfield model. And this is a model of associative memory, of how one can define a system that operates as a memory and can retrieve known patterns from some imperfect realisation of them. So Hinton is an incredibly influential and pioneering computer scientist. He's done a lot of the early work on AI. The prize is what are called Boltzmann machines, which again are physical models, very similar to those of Hopfield, but that are designed to do what in machine learning is called unsupervised learning. It's to, in essence, learn from data and then be able to generate new examples compatible with the data they learned from. But the building blocks are the same. And even the name Boltzmann suggests that they are grounded on fundamental principles of statistical physics. There's been quite a lot of online chatter, debate, discussion, argument, a lot of sort of flame wars about, well, is this really physics? I think there's very little computer science that's purely computer science, right? The most pure computer science that I can think of is typically the mathematical side of things, right? Which means it's like maths, you know. And there's lots of applied computer science that is in other fields that we use all the time. So I don't think it's necessarily helpful to categorise some piece of work as one or the other, right? In this case, we have essentially some algorithms that have been developed with physics as a sort of inspiration, and they have led on to new developments, and then new developments, and then new developments, and so on and onwards until we find ourselves in 2024 able to create pictures of frogs on stilts or anything we like using generative AI. Okay, back to the controversy. The controversy is, well, are they really, is this really for physics? We haven't hunted down the latest particle in the particle zoo, the, I don't know, the ZZ9, plural Z alpha of particles. You know, is it really physics if we're not doing that? And I would say that this is, the core of the prize here is absolutely physics. And there's a wonderful article called Whatever Happened to Solid-State Physics that goes through Hopfield's history, well worth a read. What particularly drew me to Hopfield is that the reason he got into physics was very much, the reason I got into physics is through batteries, and coils, and building radios, and crystal sets, and there's a mindset, a physicist's mindset, and Hopfield had that in spades about, we take a complex system, in this case it was neural networks is what's going on in here, and what are the fundamental elements? And what are the connections between those fundamental elements that give rise to complex behaviour? Physicists tend to want to, as we'll see, really reduce things down to what are the simplest possible components, and be that the fundamental particles of matter or whatever. But often the really interesting stuff is not those particles themselves, it's the interactions between particles. And simple behaviour at the particle level, when you bring all of them together, as in a neural net, can give rise to just incredibly fascinating, and important, and functional behaviour. We had Hopfield networks, and then we had a sort of extension of those, or a slightly different take, which is Boltzmann machines, and these are essentially generative models. So a generative model is similar in a sense to the ones we see now, where you generate pictures, and you generate text, but we were generating essentially new samples of very simple images, or very simple bits of data. So, board game, can I stand up Sean? Right, okay, we've got that, so I know how to reassemble it. Here's where lots of the links between physics and computer science come across. We're going to describe something called the Ising model. I've spoken with some people whose first language is German, but actually it should be pronounced Ising, or easing, closer to easing probably. So if I lapse into the Ising model term, I apologise, but really it should be Ising model. Ising model was originally developed to explain magnetism, to get some insights into just why magnets become magnets. Why are some materials magnets, some materials not. Magnetism in a nutshell is all about a characteristic of electrons that we're not going to get into, you're just going to have to take it for granted. There are lots of 60 symbols videos about magnetism that you can go and look at, and other sources as well, where electrons have a spin. And we're just going to say for the purposes of this, that that electron can be, that spin can be spin up or spin down. So we've got these wonderful counters or game board pieces, which are different colours. Of course, by doing that we've taken an incredibly complicated system with gazillions upon gazillions of electrons and gazillions upon gazillions of atoms, and we've forced it down into a really simple model. We're going to represent the solid, the atomic lattice, so here is an example of an atomic lattice. So we're going to reduce this, which is three-dimensional, we're going to make it even simpler, we're going to reduce it down to two dimensions, a grid. Even though we're reducing this down and losing layers and layers of complexity, we're getting down to what are the brass tacks here, what drives this behaviour. So really simple, this can be either spin up or spin down, and we're going to put it on the board. There's one there. We'll start with four, let's put in the middle of the board. So these represent our spins. So first of all, I'll reiterate, this is really simple, really, really dumb. It's got one of two values, it's binary. That by itself is boring as hell, but it's when you bring in the interactions with the other spins that the really interesting stuff happens. The question, of course, is how does what Hopfield got the Nobel Prize for relate to an because how does magnetism connect to neural nets? That doesn't seem entirely obvious. So what Hopfield did was to develop arguably the simplest possible version of a neural net, and he was interested in, well, one of the fundamental things of this thing between our ears or an artificial neural net is that it has a memory, and it's not like the traditional memory in computer science whereby you have pointers and you have little boxes and this, it's in here, you've got a certain memory location, there's a number. This is what's called associative memory. So there's a pattern. Can the system remember that pattern or indeed even better from corrupted data, can it pull out, well, actually the pattern that should be here is this. That smiley face is, we set up our system, so that's what we want. That's our memory. That's the thing we want to remember. That's our low energy state, and we weight the connections or the interactions between the neurons, these things. We weight those, so that's our lowest energy state. And then what we do is if we feed in something like this, which is a distorted, corrupted pattern, and we tune those weights and tune those interactions in terms of does this reduce the energy, then we keep it. If it pushes the energy up, then we reject it. What we will evolve towards is the original pattern, because we've set that as our lowest energy state. One of the natural questions, how many patterns you can encode in the original Hopfield model? And a very important result in that field was to calculate the capacity. How many patterns can you put in a model of a certain size? And the tools to solve that problem were those invented by Giorgio Parisi, who received the Nobel Prize for Spain glasses in 2021. So there is a direct connection to that field, which no one doubts is within physics. And those tools were the ones to use to solve the Hopfield problem. Since then, Geoffrey Hinton has done a huge amount more for AI. So since then, he was pushing artificial neural networks quite a lot. So a Boltzmann machine actually is quite unwieldy, and you can restructure it into something called a restricted Boltzmann machine, which starts to look a little bit like an artificial neural network. So adding some layers, and suddenly you can sort of see this kind of trajectory of things improving. And one of the things that Geoffrey Hinton did was he was one of the people that popularized the use of backpropagation to train neural networks. And it's hard to express. I mean, actually, the text of the Nobel Prize said Boltzmann machines and other AI, essentially. So I think it's covered. But backpropagation is essentially the way that you correct a neural network when it makes a mistake to get slightly better next time. And that algorithm is unbelievably prevalent, to the point of, you know, it's ludicrous how important that algorithm is. Every network that we train, pretty much, trains using backpropagation. It doesn't matter if it's reinforcement learning, deep learning, some giant large language model, you're still ultimately using some kind of backpropagation to adjust that model to get better next time. The other important thing about this, for those whining about, oh, this isn't a physics Nobel Prize, look at the title of the paper, which is incredibly heavily cited right across the board, Neural Networks and Physical Systems. He spells it out even in the title, he's making that link between physical systems and physics and neural networks. And this underpinned, obviously, there are limitations, but that idea of representing a neural net as this sort of binary system with interactions, Hinton built on that, others built on that, and you build, you build, you build, and then there's an explosion. And that's why artificial neural nets are absolutely everywhere. I think it would be unrealistic to assume that we would be having anywhere near the number of groundbreaking breakthroughs in any other discipline if it wasn't underpinned by computer science at some point in the process. Not least because we write all our papers and disseminate all our publications using computers. So this idea that we don't need computer science, it's a bit soft as a science, I don't think that's really accurate. I think that the biggest work now is happening in interdisciplinary domains. I mean, the Chemistry Nobel Prize has gone to essentially the developers of AlphaFold, which is essentially an application of deep learning to chemistry. So we're past the time where you can sit doing just one subject and just another subject. It's good to know about lots of different things. And I think that the best work we're doing as a species is across disciplines. And it's much more fun as well, having real impact elsewhere. There is a lot of research ongoing at the interface between physics, in particular statistical physics, which is my area, and machine learning. Translating ideas and concepts from one field to the other. And this is extremely rich. And it's been ongoing since the time of Hopfield and it's ever increasing. Thanks for watching. If you'd like to see some previous videos we've made about physics Nobel Prizes in years gone by, there'll be a link in the description. I'll also have a link to our Chemistry Nobel Prize videos, including this year's, which was also awarded for some AI-type research. And if you liked this video, you're probably going to like our channel Computerphile. Do you watch those videos? There'll be a link to Computerphile as well.