Physics

From Spin Glasses to AI: The Hopfield Model, Explained

Kari Jaaskelainen

13 Jan 2026 — 1 min read

Ever wondered how a simple physics idea can power memory in neural networks? This paper revisits the classic Hopfield model—born from spin-glass physics—and shows why it’s a perfect bridge from undergraduate physics to modern AI.

Clear tour: A friendly intro using familiar physics tools (energy, dynamics, stability).
How it "remembers": Patterns become valleys in an energy landscape; the system rolls back to them—even with noise.
Beyond memory: Links to near-optimal solutions of tough puzzles and optimization problems.
Hands-on: Free simulation code and classroom-ready problems that mirror real research.

Why it matters: students learn core statistical mechanics, linear algebra, and dynamical systems while building intuition for AI—no deep-learning toolkit required.

Read the open-access preprint: https://arxiv.org/abs/2601.07635

Paper: https://arxiv.org/abs/2601.07635v1

Register: https://www.AiFeta.com

Physics AI NeuralNetworks Education Hopfield SpinGlass Optimization ArXiv

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