simple_neural_network.py

import numpy as np


# sigmoid function
def nonlin(x):
    return 1 / (1 + np.exp(-x))


# sigmoid derivative
def noniln_deriv(x):
    return x * (1 - x)


# input
X = np.array([[0, 0, 1],
              [0, 1, 1],
              [1, 0, 1],
              [1, 1, 1]])


# output - X1,: ^ X2,:
Y = np.array([[0],
              [1],
              [1],
              [0]])


np.random.seed(0)


# synapses initialization
syn0 = 2 * np.random.random((3, 4)) # input -> hidden layer weights matrix
syn1 = 2 * np.random.random((4, 1)) # hidden layer -> output weights matrix


# training
for j in range(80000):

    # forward
    l0 = X # input layer
    l1 = nonlin(np.dot(l0, syn0)) # hidden layer
    l2 = nonlin(np.dot(l1, syn1)) # output layer

    # Back propagation of errors using chain rule
    l2_error = Y - l2

    if (j % 10000) == 0:
        print(f'Error: {str(np.mean(np.abs(l2_error)))}')

    l2_delta = l2_error * noniln_deriv(l2)

    l1_error = l2_delta.dot(syn1.T)

    l1_delta = l1_error * noniln_deriv(l1)

    # unpdate weights
    syn1 += l1.T.dot(l2_delta)
    syn0 += l0.T.dot(l1_delta)


print('Output after training:')
print(l2)