Neural networks — the physics behind artificial intelligence

What are you seeing in the simulation?

The dots are the network's nodes (neurons), and the lines are the connections between them (couplings). At low coupling $J$ the node states look random — that is noise, although in this simulation it is fully deterministic. As you increase $J$ successive nodes "lock" into a state consistent with the stored pattern, and the whole network converges to an ordered shape — the visual counterpart of a system settling into a low-energy state.

Physics of magnetism → the Hopfield network (1982)

John Hopfield used the physics describing how the magnetic moments of atoms arrange themselves in solids — the so-called spin model, known from the physics of magnetism — to build a neural network able to store and reproduce patterns (the Hopfield network). Each neuron, like a spin in a magnet, takes one of two states, and the network "searches" for the configuration of lowest energy, which corresponds to the stored pattern:

where $s_i \in \{-1,+1\}$ is the state of a node (neuron), and $w_{ij}$ is the coupling strength between nodes $i$ and $j$ (set by the Hebbian rule, based on the stored patterns). Such a network is used, among others, in image analysis.

Statistical physics → the Boltzmann machine (Hinton, 1983–1985)

Geoffrey Hinton went a step further and used the tools of statistical physics (which describes systems made of an enormous number of particles at a given temperature) to create the Boltzmann machine — a network that learns on its own to recognize characteristic features in a data set. This found use, among others, in image classification and generation.

A surprising Nobel — in physics, for the foundations of artificial intelligence

In 2024 Hopfield and Hinton received the Nobel Prize in PHYSICS (not in computer science!) "for foundational discoveries and inventions that enable machine learning with artificial neural networks". It is a surprising union of fields: their work from the 1980s, rooted in the physics of magnetism and statistical physics, laid the foundations for the machine-learning revolution that only truly began around 2010.

Why this matters for your exam:

It is a good example of how the same mathematical tools — statistical physics, the energy of a system, the drive toward an equilibrium state — describe both purely physical systems (spins in a magnet) and complex systems seemingly far from physics, such as neural networks. If a problem brings up a spin model or asks about the equilibrium state (energy minimum) of a system of many interacting elements — this is exactly the same conceptual apparatus.

Remember: Hopfield (1982) used the spin model from the physics of magnetism to build a network that stores patterns; Hinton (1983–1985) used statistical physics to create the Boltzmann machine that recognizes patterns in data. For this work both received the 2024 Nobel Prize — in physics, not in computer science.