The Loop

Instructions

• You can use the function sigmoid() . It is built-in (imported) in the notebook.
• You can use the function np.tanh() . It is part of the numpy library.
• Values needed in the backpropagation are stored in ” cache “. The cache will be given as an input to the backpropagation function.

def forward_propagation(X, parameters):
    """
    Argument:
    X -- input data of size (n_x, m)
    parameters -- python dictionary containing your parameters (output of initial
    Returns:
    A2 -- The sigmoid output of the second activation
    cache -- a dictionary containing "Z1", "A1", "Z2" and "A2"
    """

    return A2, cache

Assert Variable

assert(A2.shape == (1, X.shape[1]))

Formula

\[J = (-1/m) sum_{i=0}^m (y^i log(a^{[2](i)}) + (1 - y^i) log(1 - a^{[2](i)})\]

Instructions

There are many ways to implement the cross-entropy loss, have a look at the example

logprobs = np.multiply(np.log(A2), Y)
cost = - np.sum(logprobs)

Note:- You can use either np.multiply() and then np.sum() or directly np.dot())

def compute_cost(A2, Y, parameters):
    """
    Computes the cross-entropy cost given in equation (13)
    Arguments:
    A2 -- The sigmoid output of the second activation, of shape (1, number of exam
    Y -- "true" labels vector of shape (1, number of examples)
    parameters -- python dictionary containing your parameters W1, b1, W2 and b2
    Returns:
    cost -- cross-entropy cost given equation (13)
    """

    return cost

m and cost Variable

m = Y.shape[1]

cost = np.squeeze(cost)

Expected Output

• cost 0.693058761..

Using the cache computed during forward propagation, you can now implement backward propagation.

Using the cache computed during Forward Propogation, we need to implement Backward Propogation.

def backward_propagation(parameters, cache, X, Y):

     """
     Implement the backward propagation using the instructions above.
     Arguments:
     parameters -- python dictionary containing our parameters
     cache -- a dictionary containing "Z1", "A1", "Z2" and "A2".
     X -- input data of shape (2, number of examples)
     Y -- "true" labels vector of shape (1, number of examples)
     Returns:
     grads -- python dictionary containing your gradients with respect to different
     """

     return grads

Expected Output

This should throw up the values for dW1, db1, dW2, db2