I'm trying to implement a Hopfield Network in python using the NumPy library. The network has 2500 nodes (50 height x 50 width). The network learns 10 patterns from images of size 50x50 stored in "patterns" folder. The images are of numbers 0 to 9. The images are converted to 2d Array, flattened to 1d (2500x1) and learned.

The 10 images it's supposed to learn

After learning the patterns, it is given a number of an image (from which I have removed a few pixels from) to match the stored patterns with. But the issue I'm facing is that it does not converge to one of the stored patterns but rather outputs something sort of random.

enter image description here

Even if I try to input it exact pattern from one of the ones it has learnt it still doesn't converge to that pattern.

enter image description here

Here's the code of my try at implementing Hopfield networks.

import numpy as np
import matplotlib.pyplot as plt
from matplotlib import image
from os import listdir
import random
from os.path import isfile, join

# Hopefiel Network parameters
input_width = 50
input_height = 50
number_of_nodes = input_width * input_height
learning_rate = 1

# initialise node/input array to -1, and weights array to 0
input = np.zeros((number_of_nodes))
input[True] = -1
weights = np.zeros((number_of_nodes,number_of_nodes))

# Main Hopefield Functions
# Randomly fire nodes until the overall output doesn't change
# match the pattern stored in the Hopefield Net.
def calculate_output(input, weights):
    changed = True
    while changed:
        indices = list(range(len(input)))
        new_input = np.zeros((number_of_nodes))
        clamped_input = input.clip(min=0) # eliminate nodes with negative value, doesn't work either way
        for i in indices:
            sum = np.dot(weights[i], clamped_input)
            new_input[i] = 1 if sum >= 0 else -1
            changed = not np.allclose(input[i], new_input[i], atol=1e-3)
        input = np.array(new_input)
    return np.array(input)
# activation(W x I) = Output
# match the pattern stored in the Hopefield Net.
def calculate_output_2(input, weights):
    output = np.dot(weights,input)
    # apply threshhold
    output[output >= 0] = 1 # green in image
    output[output < 0] = -1 # purple in image
    return output

# Store the patterns in the Hopfield Network
def learn(input, weights):
    I = np.identity(number_of_nodes) # diagnol will always be 1 if input is only 1/-1
    updates = learning_rate * np.outer(input,input) - I
    updates = updates/number_of_nodes
    weights[:] = weights + updates

# Misc. Functions
# plot an array and show on the screen
def show_array(arr):
    data = arr.reshape((-1, input_width))
    plt.imshow(data) # plotting by columns
# learn the patterns (images) placed in "patterns" folder (images of numbers 0-9)
def learn_numbers():
    for f in listdir("patterns/"):
        file = join("patterns/", f)
        if isfile(file):
            im = image.imread(file)
            grey = im[:,:,0] # convert to 2d array from 3channel rgb image
            grey = np.where(grey==1,-1,1) # convert white pixel to -1 and otherwise (black) to 1
            learn(grey.flatten(), weights) # convert 2d image to 1d array (2500) and store in weights

# read a test image and match the nearest pattern
def calculate_img_output(weights, image_address):
    # show the image being tested
    im = image.imread(image_address)
    grey = im[:,:,0] # convert to 2d array from 3channel rgb image
    grey = np.where(grey==1,-1,1) # convert white pixel to -1 and otherwise (black) to 1
    plt.imshow(grey) # plotting by columns
    # retrieve the pattern using random firing
    output = calculate_output(grey.flatten(), weights)
    # show the pattern
    # retrieve the pattern
    output = calculate_output_2(grey.flatten(), weights)
    # show the pattern
# Testing code

# learn the patterns of image of number 0-9
# Try to match the partial pattern
calculate_img_output(weights, "partial/p.png")

Any help on why the Network is behaving this way and what can be done to fix this is greatly appreciated.


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