human
Can you provide a the Python code you requested given the following:
I am working on the file "MachineLearning/Backpropagation.ipynb".
The first task is:
Example for Backprop of a simple Neural Networks
$$ \sigma(x) = \frac{1}{1 + exp(-x)} $$
$$ \frac{d \sigma(x)}{dx}  = \sigma(x) * (1 - \sigma(x)) $$
Can you write Python code for it?
assistant
#Here is the Python code you requested.

def sigmoid(x):
    return 1.0/(1.0 + np.exp(-x))

def sigmoid_prime(x):
    return sigmoid(x)*(1.0-sigmoid(x))

def tanh(x):
    return np.tanh(x)

def tanh_prime(x):
    return 1.0 - x**2

class NeuralNetwork(object):
    
    # fix the seed
    np.random.seed(1)
    
    def __init__(self, layers, learning_rate, epochs):
        self.activation = sigmoid
        self.activation_prime = sigmoid_prime
        self.weights = []
        # input layers -> hidden layers
        for i in range(1, len(layers) - 1):
            # + 1 due to bias
            r = 2 * np.random.random((layers[i-1] + 1, layers[i] + 1)) -1
            self.weights.append(r)
        # hidden layers -> output layer
        r = 2 * np.random.random((layers[i] + 1, layers[i+1])) - 1
        self.weights.append(r)
        self.learning_rate = learning_rate
        self.epochs = epochs
        
    def train(self, X, y):
        # Add bias to X
        ones = np.atleast_2d(np.ones(X.shape[0]))
        X = np.concatenate((ones.T, X), axis=1)
        
        for epoch in range(self.epochs):
            # forward propagation
            i = np.random.randint(X.shape[0])
            a = [X[i]] # mini-batch

            for l in range(len(self.weights)):
                z = np.dot(a[l], self.weights[l])
                activation = self.activation(z)
                a.append(activation) # (row, a_hidden_layer, a_output_layer)
                
            # how much did we miss??
            error = y[i] - a[-1]
            deltas = [error * self.activation_prime(a[-1])]
            
            for l in range(len(a) - 2, 0, -1):
                deltas.append(deltas[-1].dot(self.weights[l].T) * self.activation_prime(a[l]))
            
            # [level3(output)->level2(hidden)]  => [level2(hidden)->level3(output)]
            deltas.reverse()            
            
            # backpropagation => update weights
            for i in range(len(self.weights)):
                layer = np.atleast_2d(a[i])
                delta =...