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🧲 Hopfield Networks: Associative Memory as Energy Minimization

Explore how Hopfield networks store patterns as stable low-energy states of a recurrent network, recalling complete memories from partial or noisy cues through Hebbian-learned weights and energy-descending updates.

Machine Learning & Neural Networks3DModerate60 FPS

The simulation shows a grid of binary neurons whose pairwise weights are set by Hebbian learning from a handful of stored patterns, visualizing the network's energy landscape and watching a noisy or partial cue update neuron by neuron, monotonically descending in energy until it locks onto the nearest stored memory.

🔬 What It Demonstrates

🎮 How to Use

Choose which patterns to memorize, then corrupt or partially erase a cue pattern and press play to watch asynchronous updates flip neurons one at a time; track the energy value as it descends step by step, and try adding more patterns to see when recall starts failing near the ~0.14N capacity limit.

💡 Did You Know?

John Hopfield's 1982 paper on these networks helped launch the modern resurgence of neural network research, and in 2024 he was awarded the Nobel Prize in Physics for this foundational work connecting statistical physics to associative memory and machine learning.

⚙ Under the hood

Watch a noisy pattern converge back to a clean stored memory as asynchronous neuron updates monotonically decrease the network's energy.

hopfield networkassociative memoryenergy minimizationhebbian learningmachine-learningrecurrent network

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install