Implementation of Artificial Neural Network for NOR Logic Gate with 2-bit Binary Input - GeeksforGeeks

28 Jul, 2021
Artificial Neural Network (ANN) is a computational model based on the biological neural networks of animal brains. ANN is modeled with three types of layers: an input layer, hidden layers (one or more), and an output layer. Each layer comprises nodes (like biological neurons) are called Artificial Neurons. All nodes are connected with weighted edges (like synapses in biological brains) between two layers. Initially, with the forward propagation function, the output is predicted. Then through backpropagation, the weight and bias to the nodes are updated to minimizing the error in prediction to attain the convergence of cost function in determining the final output.
NOR logical function truth table for 2-bit binary variables, i.e, the input vector  and the corresponding output  –
Approach:Step1: Import the required Python librariesStep2: Define Activation Function : Sigmoid FunctionStep3: Initialize neural network parameters (weights, bias)and define model hyperparameters (number of iterations, learning rate)Step4: Forward PropagationStep5: Backward PropagationStep6: Update weight and bias parametersStep7: Train the learning modelStep8: Plot Loss value vs EpochStep9: Test the model performance
Python Implementation:
# import Python Librariesimport numpy as npfrom matplotlib import pyplot as plt  # Sigmoid Functiondef sigmoid(z):    return 1 / (1 + np.exp(-z))  # Initialization of the neural network parameters# Initialized all the weights in the range of between 0 and 1# Bias values are initialized to 0def initializeParameters(inputFeatures, neuronsInHiddenLayers, outputFeatures):    W1 = np.random.randn(neuronsInHiddenLayers, inputFeatures)    W2 = np.random.randn(outputFeatures, neuronsInHiddenLayers)    b1 = np.zeros((neuronsInHiddenLayers, 1))    b2 = np.zeros((outputFeatures, 1))          parameters = {"W1" : W1, "b1": b1,                  "W2" : W2, "b2": b2}    return parameters  # Forward Propagationdef forwardPropagation(X, Y, parameters):    m = X.shape[1]    W1 = parameters["W1"]    W2 = parameters["W2"]    b1 = parameters["b1"]    b2 = parameters["b2"]      Z1 = np.dot(W1, X) + b1    A1 = sigmoid(Z1)    Z2 = np.dot(W2, A1) + b2    A2 = sigmoid(Z2)      cache = (Z1, A1, W1, b1, Z2, A2, W2, b2)    logprobs = np.multiply(np.log(A2), Y) + np.multiply(np.log(1 - A2), (1 - Y))    cost = -np.sum(logprobs) / m    return cost, cache, A2  # Backward Propagationdef backwardPropagation(X, Y, cache):    m = X.shape[1]    (Z1, A1, W1, b1, Z2, A2, W2, b2) = cache          dZ2 = A2 - Y    dW2 = np.dot(dZ2, A1.T) / m    db2 = np.sum(dZ2, axis = 1, keepdims = True)          dA1 = np.dot(W2.T, dZ2)    dZ1 = np.multiply(dA1, A1 * (1- A1))    dW1 = np.dot(dZ1, X.T) / m    db1 = np.sum(dZ1, axis = 1, keepdims = True) / m          gradients = {"dZ2": dZ2, "dW2": dW2, "db2": db2,                 "dZ1": dZ1, "dW1": dW1, "db1": db1}    return gradients  # Updating the weights based on the negative gradientsdef updateParameters(parameters, gradients, learningRate):    parameters["W1"] = parameters["W1"] - learningRate * gradients["dW1"]    parameters["W2"] = parameters["W2"] - learningRate * gradients["dW2"]    parameters["b1"] = parameters["b1"] - learningRate * gradients["db1"]    parameters["b2"] = parameters["b2"] - learningRate * gradients["db2"]    return parameters  # Model to learn the NOR truth table X = np.array([[0, 0, 1, 1], [0, 1, 0, 1]]) # NOR inputY = np.array([[1, 0, 0, 0]]) # NOR output  # Define model parametersneuronsInHiddenLayers = 2 # number of hidden layer neurons (2)inputFeatures = X.shape[0] # number of input features (2)outputFeatures = Y.shape[0] # number of output features (1)parameters = initializeParameters(inputFeatures, neuronsInHiddenLayers, outputFeatures)epoch = 100000learningRate = 0.01losses = np.zeros((epoch, 1))  for i in range(epoch):    losses[i, 0], cache, A2 = forwardPropagation(X, Y, parameters)    gradients = backwardPropagation(X, Y, cache)    parameters = updateParameters(parameters, gradients, learningRate)  # Evaluating the performanceplt.figure()plt.plot(losses)plt.xlabel("EPOCHS")plt.ylabel("Loss value")plt.show()  # TestingX = np.array([[1, 1, 0, 0], [0, 1, 0, 1]]) # NOR inputcost, _, A2 = forwardPropagation(X, Y, parameters)prediction = (A2 > 0.5) * 1.0# print(A2)print(prediction)


[[ 0.  0.  1.  0.]]

Here, the model predicted output for each of the test inputs are exactly matched with the NOR logic gate conventional output () according to the truth table and the cost function is also continuously converging.Hence, it signifies that the Artificial Neural Network for the NOR logic gate is correctly implemented.
Neural Network
Machine Learning
Python
Machine Learning
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