from numpy import exp, array, random, dot

​

class NeuronLayer():

    def __init__(self, number_of_neurons, number_of_inputs_per_neuron):

        self.synaptic_weights = 2 * random.random((number_of_inputs_per_neuron, number_of_neurons)) - 1

​

class NeuralNetwork():

    def __init__(self, layer1, layer2):

        self.layer1 = layer1

        self.layer2 = layer2

​

    # The Sigmoid function, which describes an S shaped curve.

    # We pass the weighted sum of the inputs through this function to

    # normalise them between 0 and 1.

    def __sigmoid(self, x):

        return 1 / (1 + exp(-x))

​

    # The derivative of the Sigmoid function.

    # This is the gradient of the Sigmoid curve.

    # It indicates how confident we are about the existing weight.

    def __sigmoid_derivative(self, x):

        return x * (1 - x)

​

    # We train the neural network through a process of trial and error.

    # Adjusting the synaptic weights each time.

    def train(self, training_set_inputs, training_set_outputs, number_of_training_iterations):

        for iteration in range(number_of_training_iterations):

            # Pass the training set through our neural network

            output_from_layer_1, output_from_layer_2 = self.think(training_set_inputs)

​

            # Calculate the error for layer 2 (The difference between the desired output

            # and the predicted output).

            layer2_error = training_set_outputs - output_from_layer_2

            layer2_delta = layer2_error * self.__sigmoid_derivative(output_from_layer_2)

​

            # Calculate the error for layer 1 (By looking at the weights in layer 1,

            # we can determine by how much layer 1 contributed to the error in layer 2).

            layer1_error = layer2_delta.dot(self.layer2.synaptic_weights.T)

            layer1_delta = layer1_error * self.__sigmoid_derivative(output_from_layer_1)

​

            # Calculate how much to adjust the weights by

            layer1_adjustment = training_set_inputs.T.dot(layer1_delta)

            layer2_adjustment = output_from_layer_1.T.dot(layer2_delta)

​

            # Adjust the weights.

            self.layer1.synaptic_weights += layer1_adjustment

            self.layer2.synaptic_weights += layer2_adjustment

​

    # The neural network thinks.

    def think(self, inputs):

        output_from_layer1 = self.__sigmoid(dot(inputs, self.layer1.synaptic_weights))

        output_from_layer2 = self.__sigmoid(dot(output_from_layer1, self.layer2.synaptic_weights))

        return output_from_layer1, output_from_layer2

​

    # The neural network prints its weights

    def print_weights(self):

        print ("    Layer 1 (4 neurons, each with 3 inputs): ")

        print (self.layer1.synaptic_weights)

        print ("    Layer 2 (1 neuron, with 4 inputs):")

        print (self.layer2.synaptic_weights)

​

if __name__ == "__main__":

​

    #Seed the random number generator

    random.seed(1)

​

    # Create layer 1 (4 neurons, each with 3 inputs)

    layer1 = NeuronLayer(4, 3)

​

    # Create layer 2 (a single neuron with 4 inputs)

    layer2 = NeuronLayer(1, 4)

​

    # Combine the layers to create a neural network

    neural_network = NeuralNetwork(layer1, layer2)

​

    print ("Stage 1) Random starting synaptic weights: ")

    neural_network.print_weights()

​

    # The training set. We have 7 examples, each consisting of 3 input values

    # and 1 output value.

    training_set_inputs = array([[0, 0, 1], [0, 1, 1], [1, 0, 1], [0, 1, 0], [1, 0, 0], [1, 1, 1], [0, 0, 0]])

    training_set_outputs = array([[0, 1, 1, 1, 1, 0, 0]]).T

​

    # Train the neural network using the training set.

    # Do it 60,000 times and make small adjustments each time.

    neural_network.train(training_set_inputs, training_set_outputs, 60000)

​

    print ("Stage 2) New synaptic weights after training: ")

    neural_network.print_weights()

​

    # Test the neural network with a new situation.

    print ("Stage 3) Considering a new situation [1, 1, 0] -> ?: ")

    hidden_state, output = neural_network.think(array([1, 1, 0]))

    print (output)