John J. Hopfield and Geoffrey E. Hinton received the Nobel Prize in physics on Oct. 8, 2024, for their research on machine learning algorithms and neural networks that help computers learn. Their work has been fundamental in developing neural network theories that underpin generative artificial intelligence.
A neural network is a computational model consisting of layers of interconnected neurons. Like the neurons in your brain, these neurons process and send along a piece of information. Each neural layer receives a piece of data, processes it and passes the result to the next layer. By the end of the sequence, the network has processed and refined the data into something more useful.
While it might seem surprising that Hopfield and Hinton received the physics prize for their contributions to neural networks, used in computer science, their work is deeply rooted in the principles of physics, particularly a subfield called statistical mechanics.
As a computational materials scientist, I was excited to see this area of research recognized with the prize. Hopfield and Hinton’s work has allowed my colleagues and me to study a process called generative learning for materials sciences, a method that is behind many popular technologies like ChatGPT.
What is statistical mechanics?
Statistical mechanics is a branch of physics that uses statistical methods to explain the behavior of systems made up of a large number of particles.
Instead of focusing on individual particles, researchers using statistical mechanics look at the collective behavior of many particles. Seeing how they all act together helps researchers understand the system’s large-scale macroscopic properties like temperature, pressure and magnetization.
For example, physicist Ernst Ising developed a statistical mechanics model for magnetism in the 1920s. Ising imagined magnetism as the collective behavior of atomic spins interacting with their neighbors.
In Ising’s model, there are higher and lower energy states for the system, and the material is more likely to exist in the lowest energy state.
One key idea in statistical mechanics is the Boltzmann distribution, which quantifies how likely a given state is. This distribution describes the probability of a system being in a particular state – like solid, liquid or gas – based on its energy and temperature.
Ising exactly predicted the phase transition of a magnet using the Boltzmann distribution. He figured out the temperature at which the material changed from being magnetic to nonmagnetic.
Phase changes happen at predictable temperatures. Ice melts to water at a specific temperature because the Boltzmann distribution predicts that when it gets warm, the water molecules are more likely to take on a disordered – or liquid – state.
