This is a research library to study the emergent properties of undirected neural networks, including Hopfield networks and Boltzmann machines.

Contributors: Sonia Joseph, Andreanne Lemay (andreanne-lemay)

To read more about Hopfield networks, see the primer I wrote here.

Set up your local environment and install package.

python3 -m venv env
pip3 install -e .

See /tests for sample use cases.

Hopfield networks are fascinating one-shot data-denoisers. We train the network to "remember" the top row of fashion MNIST images using Hebbian learning. The network does not store the actual image, but encodes information of the image in its weights.

Then, we add noise to the image, randomly setting 30% of the pixels to the opposite value. When we feed each random image into the pre-trained Hopfield network, we get the original image back (bottom row)!

Original
Noisy
Reconstructed

from emergence.hopfield import Hopfield
from emergence.preprocess.preprocess_image import * 

# Preprocess data
fashion_mnist = keras.datasets.fashion_mnist
(train_images, train_labels), (test_images, test_labels) = fashion_mnist.load_data()
row, col = train_images[0].shape
data = train_images[5:9]
data = [normalize_binarize(i) for i in data]
data = [i.flatten() for i in data]

# Train network
hn = Hopfield()
hn.train(data)

# Get noisy data
noise_data = [noise_image(i, .3) for i in data]

# Run network on noisy data
data_hat = [hn.run(i, 1) for i in noise_data]

Run above file

python -m emergence.tests.hopfield_fmnist

See /tests for more examples.

Hopfield Networks - A Primer

Neural networks and physical systems with emergent collective computational abilities