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Week 2 Quiz – Neural Network Basics

Week 2 Quiz – Neural Network Basics

Week 2 Quiz – Neural Network Basics

  1. What does a neuron compute?

    •  A neuron computes an activation function followed by a linear function (z = Wx + b)

    •  A neuron computes a linear function (z = Wx + b) followed by an activation function

    •  A neuron computes a function g that scales the input x linearly (Wx + b)

    •  A neuron computes the mean of all features before applying the output to an activation function

    Note: we generally say that the output of a neuron is a = g(Wx + b) where g is the activation function (sigmoid, tanh, ReLU, …).

  2. Which of these is the “Logistic Loss”?

    Note: this is the logistic loss you’ve seen in lecture!

  3. Suppose img is a (32,32,3) array, representing a 32×32 image with 3 color channels red, green and blue. How do you reshape this into a column vector?

    • x = img.reshape((32 * 32 * 3, 1))
  4. Consider the two following random arrays “a” and “b”:

    a = np.random.randn(2, 3) # a.shape = (2, 3)
    b = np.random.randn(2, 1) # b.shape = (2, 1)
    c = a + b
    

    What will be the shape of “c”?

    b (column vector) is copied 3 times so that it can be summed to each column of a. Therefore, c.shape = (2, 3).

  5. Consider the two following random arrays “a” and “b”:

    a = np.random.randn(4, 3) # a.shape = (4, 3)
    b = np.random.randn(3, 2) # b.shape = (3, 2)
    c = a * b
    

    What will be the shape of “c”?

    “*” operator indicates element-wise multiplication. Element-wise multiplication requires same dimension between two matrices. It’s going to be an error.

  6. Suppose you have n_x input features per example. Recall that X=[x^(1), x^(2)…x^(m)]. What is the dimension of X?

    (n_x, m)

  7. Recall that np.dot(a,b) performs a matrix multiplication on a and b, whereas a*b performs an element-wise multiplication.

    Consider the two following random arrays “a” and “b”:

    a = np.random.randn(12288, 150) # a.shape = (12288, 150)
    b = np.random.randn(150, 45) # b.shape = (150, 45)
    c = np.dot(a, b)
    

    What is the shape of c?

    c.shape = (12288, 45), this is a simple matrix multiplication example.

  8. Consider the following code snippet:

    # a.shape = (3,4)
    # b.shape = (4,1)
    for i in range(3):
      for j in range(4):
        c[i][j] = a[i][j] + b[j]
    

    How do you vectorize this?

    c = a + b.T

  9. Consider the following code:

    a = np.random.randn(3, 3)
    b = np.random.randn(3, 1)
    c = a * b
    

    What will be c?

    This will invoke broadcasting, so b is copied three times to become (3,3), and ∗ is an element-wise product so c.shape = (3, 3).

  10. Consider the following computation graph.

    J = u + v - w
      = a * b + a * c - (b + c)
      = a * (b + c) - (b + c)
      = (a - 1) * (b + c)
    

    Answer: (a - 1) * (b + c)

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