Fundamental Physics behind Artificial Intelligence

Artificial intelligence (AI) has rapidly spread across society, powering chatbots, image generators, black-hole image reconstruction, and protein structure prediction.

On October 8th, 2024,

John Hopfield and Geoffrey Hinton received the Nobel Prize in Physics for foundational contributions to AI.

This raises an intriguing question: Why a physics Nobel Prize for AI?

Because,

Artificial Intelligence is the thermodynamic limit of information-processing systems seeking minimum-energy representations of data.

Physics didn’t “inspire” AI. Physics is AI when we push the math to infinity.

Let us begin in a place that does not look like intelligence at all: a block of iron.

Inside it, tiny magnetic spins wobble under the nudges of temperature and the persuasion of neighbouring atoms. And when enough spins align, a magnetic field is produced.

This humble story is where our journey truly begins.

The Ising Model (1920)

In 1920, Ernst Ising, working under the stern guidance of Wilhelm Lenz, sought to understand why iron sometimes develops a permanent magnetic field and sometimes doesn’t.

The Ising model told him:

local interactions create global order.

In the Ising model each site 𝑖 carries a spin s_i ∈{+1,−1}. The system’s macroscopic behaviour is encoded in an energy (Hamiltonian)

H(s) = -\sum_{i<j} J_{ij} s_i s_j - \sum_i h_i s_i

At temperature ( T ), configurations are sampled according to the Boltzmann distribution

P(s) \propto e^{-H(s)/T}

so, the probability of a configuration is determined by its energy. Low-energy configurations are exponentially preferred.

The Hopfield Network (1982)

Hopfield took this exact architecture and repackaged it as memory.

Replace spins by neurons $( \sigma_i \in \{\pm 1\} )$ , choose couplings by a Hebbian rule

J_{ij} = \frac{1}{N} \sum_{\mu} \xi_i^{\mu} \, \xi_j^{\mu}

where $( \xi^{\mu} )$ are stored patterns.
The dynamics of asynchronous updates causes the network to fall into attractors that reproduce those patterns.

The same energy function governs both magnetization and associative recall. Capacity emerges: the network reliably stores a finite fraction of patterns (on the order of 0.1N with naive Hebbian weights) before attractors collide and memory breaks into spurious states.

He realized that the brain’s ability to recall a patter, like a face from childhood is simply the dynamics of a field relaxing toward a minimum of energy.

And so the Hopfield network was born:

a machine that remembers by relaxing into stable patterns, just as a magnet relaxes into aligned domains.

A physical model of matter became a cognitive model of memory.

Then the Gaussian Arrives

Scaling the size, increasing 𝑁, the law of large numbers, central limit intuitions, and mean-field approximations begin to apply. Randomly chosen couplings or random initializations produce distributions over outputs; as 𝑁→∞, many microscopic irregularities wash out and macroscopic fields become smooth. In neural networks, this is the observation that infinitely wide networks converge, under reasonable random initialization, to Gaussian processes (GPs): the pre-activations at each layer are sums of many independent terms and therefore tend to Gaussian statistics

Fast forward to 1995: Radford Neal proves that infinitely wide neural networks converge into Gaussian processes, the same mathematical structures that appear in free quantum fields.

It was the first crack in the wall separating physics and cognition.

By 2020, researchers at the Institute for Artificial Intelligence and Fundamental Interactions (IAIFI) made the connection explicit:

Neural networks are quantum fields.

A neural network with inputs x produces an output 𝑓(𝑥).

Changing network weights is distorting the field over space.

Just as a quantum field fluctuates and finds equilibrium under the influence of interactions, so does a neural network’s parameter distribution evolve under the pushes and pulls of training.

Culmination

Artificial intelligence is the statistical mechanics of function approximation, and quantum field theory is the physics of infinite-dimensional probability distributions. They are the same mathematics wearing different costumes.

All the stories from the iron block of 1920, the Hopfield network of 1982, the infinite-width neural networks of the 1990s, and the quantum fields of modern physics were concentric rings around the same, quiet center:

The universe organizes complexity through the same mathematical principles, whether it is organizing electrons, particles, or ideas.

The Ising model showed how simple interactions give rise to collective order.
The Hopfield network showed how those same interactions can store memories.
The Gaussian processes showed how chaos converges into smooth, universal structure when systems become large.
Quantum fields used identical mathematics to describe the behaviour of matter itself.
Modern AI revealed that learning machines navigate energy landscapes indistinguishable from those of physical systems.

The magnet organizes itself through local alignment. The neural network organizes itself through local alignment. The quantum field organizes itself through fluctuations constrained by structure.

So magnetism, memory, and matter are not separate categories, they are different dialects of the same language: the language of interacting units seeking stability.

Thus, physics explains AI not metaphorically but literally. And AI models reflect physical laws not coincidentally but fundamentally.