Hopfield network (Amari-Hopfield network) implemented with Python. Two update rules are implemented: Asynchronous & Synchronous.

• Python >= 3.5
• numpy
• matplotlib
• skimage
• tqdm
• keras (to load MNIST dataset)

Run train.py or train_mnist.py.

The following is the result of using Synchronous update.

Start to data preprocessing...
Start to train weights...
100%|██████████| 4/4 [00:06<00:00,  1.67s/it]
Start to predict...
100%|██████████| 4/4 [00:02<00:00,  1.80it/s]
Show prediction results...

Show network weights matrix...

The following is the result of using Asynchronous update.

Start to data preprocessing...
Start to train weights...
100%|██████████| 3/3 [00:00<00:00, 274.99it/s]
Start to predict...
100%|██████████| 3/3 [00:00<00:00, 32.52it/s]
Show prediction results...

Show network weights matrix...

• Amari, "Neural theory of association and concept-formation", SI. Biol. Cybernetics (1977) 26: 175. https://doi.org/10.1007/BF00365229
• J. J. Hopfield, "Neural networks and physical systems with emergent collective computational abilities", Proceedings of the National Academy of Sciences of the USA, vol. 79 no. 8 pp. 2554–2558, April 1982.