The Hopfield network

John Hopfield was a condensed-matter physicist who had spent a decade on the physics of biological molecules before turning to the brain. His April 1982 paper in PNAS treats a network of McCulloch–Pitts neurons the way a physicist treats a magnet. If the connections are symmetric, the network has an energy, and every update of a neuron lowers it. Start the network anywhere and it rolls downhill into a stable state. Choose the weights by Hebb's rule from a set of patterns, and those patterns become the valleys: show the network a corrupted version of one and it settles into the clean original.

It was a content-addressable memory built from physics, and it did two things for the field. It brought physicists, with their tools for analysing systems of many simple interacting parts, into neural networks in numbers. And it made the networks respectable again after Perceptrons, by giving them an exact theory rather than an empirical rule.

The Boltzmann machine of 1985 added noise and hidden units to Hopfield's design and could learn. The 2024 Nobel Prize in Physics, shared by Hopfield and Geoffrey Hinton, cites the 1982 paper as the foundation of machine learning with artificial neural networks.