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from numpy import exp, array, random, dotclass NeuralNetwork():
 # generate the weights
 def __init__(self):
 # Seed the random number generator, so it generates the same numbers # every time the program runs.random.seed(1)
 # We model a single neuron, with 3 input connections and 1 output connection. # We assign random weights to a 3 x 1 matrix, with values in the range -1 to 1 # and mean 0.self.synaptic_weights = 2 * random.random((3, 1)) - 1# 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.
 #sigmoid function
 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 (a single neuron).output = self.think(training_set_inputs)
 # Calculate the error (The difference between the desired output # and the predicted output).error = training_set_outputs - output
 # Multiply the error by the input and again by the gradient of the Sigmoid curve. # This means less confident weights are adjusted more. # This means inputs, which are zero, do not cause changes to the weights.adjustment = dot(training_set_inputs.T, error * self.__sigmoid_derivative(output))
 # Adjust the weights.self.synaptic_weights += adjustment
 # The neural network thinks.def think(self, inputs):
 # Pass inputs through our neural network (our single neuron).return self.__sigmoid(dot(inputs, self.synaptic_weights))if __name__ == "__main__":
 #Intialise a single neuron neural network.neural_network = NeuralNetwork()
 print ("Random starting synaptic weights:")
 print (neural_network.synaptic_weights)
 # The training set. We have 4 examples, each consisting of 3 input values # and 1 output value.training_set_inputs = array([[0, 0, 1], [1, 1, 1], [1, 0, 1], [0, 1, 1]])
 training_set_outputs = array([[0, 1, 1, 0]]).T
 # Train the neural network using a training set. # Do it 10,000 times and make small adjustments each time.neural_network.train(training_set_inputs, training_set_outputs, 10000)
 print ("New synaptic weights after training:")
 print (neural_network.synaptic_weights)
 # Test the neural network with a new situation.print ("Considering new situation [1, 0, 0] ->?:")
 print (neural_network.think(array([1, 0, 0])))
first : generate the weights
second: sigmoid function -> x_ij * weights -> values(-1,1)
error = y_ij - output
# the gradient decent
weights = weights + (x_ij).T * error*dependecy 
1.A neural Network is an algorithm that learns to identify patterns in data
2.Backpropagation is a technique to train a Neural Net by updating weights via gradient descent
3.deep learning = many layers neural net + big data + big compute
a simple single layer Feedforward neural network



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