Hopfield Network

hopfield.py

import matplotlib.pyplot as plt
import numpy as np

# Set random seed for reproducibility
np.random.seed(1000)

nb_patterns = 4
pattern_width = 4
pattern_height = 4
max_iterations = 10

# Initialize the patterns
X = np.zeros((nb_patterns, pattern_width * pattern_height))

X[0] = [-1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1]
X[1] = [-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1]
X[2] = [-1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1]
X[3] = [1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1]

# Show the patterns
fig, ax = plt.subplots(1, nb_patterns, figsize=(10, 5))

for i in range(nb_patterns):
    ax[i].matshow(X[i].reshape((pattern_height, pattern_width)), cmap='gray')
    ax[i].set_xticks([])
    ax[i].set_yticks([])
    
plt.show()

# Train the network
W = np.zeros((pattern_width * pattern_height, pattern_width * pattern_height))

for i in range(pattern_width * pattern_height):
    for j in range(pattern_width * pattern_height):
        if i == j or W[i, j] != 0.0:
            continue
            
        w = 0.0
        
        for n in range(nb_patterns):
            w += X[n, i] * X[n, j]
            
        W[i, j] = w / X.shape[0]
        W[j, i] = W[i, j]
        
# Create a corrupted test pattern
x_test = np.array([1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1])

# Recover the original patterns
A = x_test.copy()

for _ in range(max_iterations):
    for i in range(pattern_width * pattern_height):
        A[i] = 1.0 if np.dot(W[i], A) > 0 else -1.0

# Show corrupted and recovered patterns
fig, ax = plt.subplots(1, 2, figsize=(10, 5))

ax[0].matshow(x_test.reshape(pattern_height, pattern_width), cmap='gray')
ax[0].set_title('Corrupted pattern')
ax[0].set_xticks([])
ax[0].set_yticks([])

ax[1].matshow(A.reshape(pattern_height, pattern_width), cmap='gray')
ax[1].set_title('Recovered pattern')
ax[1].set_xticks([])
ax[1].set_yticks([])

plt.show()