nn.py

"""
Jeraldy Deus | deusjeraldy@gmail.com
Implementing an Artificial Neural Network in numpy
BSD License
"""
import numpy as np

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

Y = np.array([
    [0],
    [1],
    [1],
    [0]
])

m = X.shape[0]
num_nodes = 400

W1 = np.random.randn(num_nodes,X.shape[1])
b1 = np.zeros((num_nodes,1))

W2 = np.random.randn(1,num_nodes)
b2 = np.zeros((1,X.shape[0]))

X = X.T
Y = Y.T

costs = []

for i in range(4000):
    # Foward Prop
    # LAYER 1
    Z1 = np.dot(W1,X) + b1
    A1 = 1/(1+np.exp(-Z1))
    # LAYER 2
    Z2 = np.dot(W2,A1) + b2
    A2 = 1/(1+np.exp(-Z2))
    
    # Back Prop
    dZ2 = A2 - Y
    dW2 = (1/m)*np.dot(dZ2,A1.T)
    db2 = (1/m)*np.sum(dZ2,axis=1,keepdims=True)
    
    dZ1 = np.multiply(np.dot(W2.T, dZ2), 1 - np.power(A1, 2))
    dW1 = (1/m)*np.dot(dZ1,X.T)
    db1 = (1/m)*np.sum(dZ1,axis=1,keepdims=True)
    
    # Gradient Descent
    W2 = W2 - 0.01*dW2
    b2 = b2 - 0.01*db2
    
    W1 = W1 - 0.01*dW1
    b1 = b1 - 0.01*db1
    
    # Loss
    L = (-1/m)*np.sum(Y*np.log(A2) + (1-Y)*np.log(1-A2))
    L = np.squeeze(L)
    if i%500 == 0:
        print("=======================================")
        print("Loss = ",L)
        print("Predictions == ",A2)